Columbia Economics Review: Fall 2015

Columbia Economics Review

in gold we trust trending in art run the risk no brain, no gain if you pay it, they will run it that 70’s shock

Vol. VI No. I Fall 2015

Frontiers of Economics Pushing the boundaries of economic thought

Fall 2015

2

COLUMBIA ECONOMICS REVIEW PUBLICATION INFORMATION Columbia Economics Review (CER) aims to promote discourse and research at the intersection of economics, business, politics, and society by publishing a rigorous selection of student essays, opinions, and research papers. CER also holds the Columbia Economics Forum, a speaker series established to promote dialogue and encourage deeper insights into economic issues.

2015-2016 E D I T O R I A L B O A R D EDITOR-IN-CHIEF

Eitan Neugut

JOURNAL SENIOR EDITORS

PUBLISHER MANAGING EDITOR

Carol Shou

Nancy Xu

DESIGN DIRECTOR

Mira Dayal

Francis Afriyie Michael Greenberg Larry Xiao LAYOUT EDITORS

Benjamin Titlebaum Minzi Keem

PUBLISHING EDITORS

Sungmin An Jakob Brounstein James McCarthy Manuel Perez Shambhavi Tiwari Sharleen Yu Mitchell Zhang

CONTRIBUTING ARTISTS

Daniela Brunner Mira Dayal Kevin Jiang Anna Kaplan (cover) Maham Karatela Desislava Petkova

ONLINE CONTRIBUTORS

EXECUTIVE EDITOR

Max Rosenberg

WEB DIRECTOR

Evangeline Heath

WEB EDITOR

Kevin Jiang

Guillermo Carranza Jordan Arnold Lee Catalina Piccato Jack Ruiz Amar Zaidi

ILLUSTRATORS

Adil Mughal Emily Callison Mira Dayal Noa Herman

OPERATIONS OPERATIONS MEMBERS EXECUTIVE DIRECTOR

Raymond de Oliveira Alan Lin

Pranav Mohan Balan Ayda Basaran Zoey Chopra Bryan Li Boya Wang Jing Qu

SENIOR TEAM OPERATIONS MEMBERS

Daniel Morgan Chris Sabatis

A special thanks to the Columbia University Economics Department and to the 2014-2015 CER Editorial Board for their help in the publication of this issue.

Columbia Economics Review would like to thank its donors for their generous support of the publication.

We welcome your comments. To send a letter to the editor, please email: econreview@columbia.edu We reserve the right to edit and condense all letters.

Licensed under Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License

Columbia Economics | Program for Economic Research

Printed with generous support from the Columbia University Program for Economic Research Columbia Economics Review

Fall 2015

TABLE OF CONTENTS

Political Economics 6

In Gold We Trust

Gold, Trust, and Political Attitudes: Evidence from Ghana

Art and Economics 13

Trending in Art

Location Models in the Art Market: Artists as Firms Visualized on a Product Space

Econometric Analysis 21

Run the Risk

Value-at-Risk: the Effect of Autoregression in a Quantile Process

Developmental Economics 26

No Brain, No Gain

Migration, Development, and the “Brain Drain”: Dynamic Effects Between Migration and Growth Measures

Sports Economics 36

If You Pay it, They Will Run

Human Capital in Major League Baseball: The Relationship between Major League Baseball Players’ Performance and Salary

Macroeconomics 42

That 70’s Shock

The Persistence of Memory: How Demographic & Monetary Shocks Affect Macroeconomic Expectations

For a complete list of papers cited by our authors and a full version of all editorials, please visit our website at columbiaeconreview.com

Opinions expressed herein do not necessarily reflect the views of Columbia University or Columbia Economics Review, its staff, sponsors, or affiliates.

Columbia Economics Review

3

4

Fall 2015

COLUMBIA ECONOMICS REVIEW

Call for Submissions Columbia Economics Review is interested in your article proposals, senior theses, seminar papers, editorials, art and photography.

GUIDELINES CER is currently accepting pitches for its upcoming issue. You are encouraged to submit your article proposals, academic scholarship, senior seminar papers, editorials, art and photography broadly relating to the field of economics.

You may submit multiple pitches.

Your pitch or complete article should include the following information: 1. Name, school, year, and contact information (email and phone number) 2. If you are submitting a pitch, please state your argument clearly and expand upon it in one brief paragraph. List sources and professors/industry professionals you intend to contact to support your argument. Note that a full source list is not required.

3. If you are submitting a completed paper, please make sure the file is accessible through MS Word.

Pitches will be accepted throughout the Spring and are due by February 15th, 2016. Send all pitches to econreview@ columbia.edu with the subject “CER Pitch- Last Name, First Name.� If you have any questions regarding this process, please do not hesitate to e-mail us at econreview@columbia.edu. We look forward to reading your submissions!

Columbia Economics Review

Fall 2015

A LETTER FROM THE EDITORS Dear Readers, With the mass popularization of economic methods and statistical analysis through media like Nate Silver’s Five-Thirty-Eight blog and Steven Levitt’s Freakonomics, there has never been a better time for economists to stretch the bounds of their analytical techniques and methods. As economists continue to explore the application of economics to the humanities, social sciences, and natural sciences, non-economists have used the same analytical methods to explore the arts, pop culture, sports, and technology. In an era of big data and information systems, the call for economic frameworks and rigorous statistical answers has permeated into every sector of work and play.

The next generation of economists will not simply be discussing classical economic topics, like GDP growth and financial markets, but will be forced to broaden their outlook on what issues economics can explain and mediate. While this can be liberating for budding economists, it also disrupts the classical definitions of economics as a field concerned with finance, incentives, and human rationality. Now, scholars from disparate disciplines come together to explore the economic links that influence of decision-making and incentives outside the realm of traditional economics. It is with this mindset, that Daniel Kahneman, a psychologist with little formal economics training, could pioneer a new subfield of economics: behavioral economics.

When reading through our submissions, we were excited to receive articles that engage economics within the context of other disciplines. While we had never thought about the strategic decision-making that influences how artists create their new masterpieces (p.

13), these insights provided a framework for learning not only about the particulars of the art world, but also the ways that incentives structures affect artists on a conscious and subconscious level. Similarly, as the field of labor economics remains one of the most well-studied subfields in economics, we were pleasantly surprised to read about the pay structures for baseball player from the standpoint of economists rather than sports specialists (p. 36) Besides this radical expansion in the reach of economics, the technological advances in the internet, communications, and travel have created a globe network rooted in social interaction, international trade, and technological connectivity. It is no longer sufficient to understand what is going on down the block, but imperative to explore how ideas at home can be applied elsewhere and vice versa.

Recent discussions of the “brain drain,” (p. 26) the phenomenon that the most educated individuals in developing countries are rapidly moving to and settling in richer countries, has emphasized the fluidity of global labor markets. Even a retrospective examination of market and inflation expectations from the 1970s (p. 42) take on a new flavor when contemporary discussions of foreign exchange and international trade factor into how private business and governments make investment decisions.

Similarly, in the international hunt for natural resources, like gold and oil, regional politics affect the worldwide markets and expectations for these resources. A seemingly political question of parliamentary trust among Ghanaian communities reopens the concerns of the resource curse in a regional dialogue with international implications (p. 6). While political economy is far from a new field of economics, the introduction of ecological and environmental factors continue to push economics in the direction of natural sciences.

The diverse subject matter and bounds of our articles showcase this year’s theme of “Frontiers of Economics.” As our authors continue to tread in interesting and distinct disciplines, we applaud the mix of descriptive industry insight and quantitative economy analysis in forming and defending their claims. While we continue to have classic econometric papers that examine the efficacy of established models of autoregression (p.21), we also hope that the more qualitative links constructed between economics and these other fields will inspire others to explore non-conventional areas of applied economic theory and methods.

Our purpose is not only to educate our readership on a wide array of economic topics, but also to engage our readers in a discussion of how economics research can be applicable to new aspects of both academic and contemporary life. Our hope is that this issue challenges our economics enthusiasts and inspires those with a less technical economic background. We look forward to exploring these new frontiers in the pages to follow and keeping up the conversation with you through our online platform. It has been a pleasure.

Until next issue, Carol Shou CC’17 | Managing Editor Eitan Neugut CC’17 | Editor-in-Chief Nancy Xu CC’18 | Publisher

Columbia Economics Review

5

Fall 2015

6

In Gold We Trust Gold, Trust, and Political Attitudes: Evidence from Ghana Roxanne Rahnama University of California, Berkeley

Roxanne Rahnama’s top-down analysis of Ghanaian households’ political behavior formation resonates with Acemoglu-esque undertones as she provides a unique methodology in concretely linking households’ proximity to gold mines with largely abstract, incommensurable socio-political values such as political engagement and trust levels. A great deal of economic literature deals with policy and political conflict through generally macro-focused, overly quantitative procedures, so we were particularly excited to explore the author’s remarkably attached approach in dealing with trends in human behaviors and attitudes. In tying in data from the Afrobarometer, a value-based research group similar to the World Value Survey, and geocoded mining data, the author argues that Ghanaian household political values are closely linked to their spatial proximity to gold mines, while hinting at potential causal mechanisms and deeper implications. Although this article, beyond its OLS econometric regressions, is one of our less quantitative pieces, it demonstrates uniqueness in economically bridging qualitative and quantitative attributes, and we hope that it inspires further effort to understand the effects of institutions on the formation of human values. -J.A.B.

Introduction Africa is endowed with the largest reserve of mineral resources in the world and, in 2012, received 15 percent of global exploration and mining investment (KPMG, 2013). The export-oriented mining sector in Africa continues to burgeon, with gold as the main mineral resource.

Whereas the body of empirical literature on both the relationship between conflict and natural resources and the welfare effects of mining continues to grow, research on the psychological and social effects of mineral resources on political attitudes has been left unexplored. This paper is a detailed country case study on the multinational gold mining sector in Ghana; it seeks to shed light on the linkages between mining, trust and political engagement in local mining communities.

In doing so, this study contributes to the existing literature on trust and local col-

lective action.

This paper combines geocoded data on 16 industrial gold mines from IntierraRMG and political attitudes data from Afrobarometer (Rounds 1-4) to conduct an individual-level difference-in-differences analysis, using a spatial econometric methodology developed by Tolonen (2014). The key political engagement outcome variables include discussion of politics, attendance at community meetings, and the likelihood to raise issues. Additionally, the main trust outcome variables are trust in parliament and trust in local assembly. Using a linear probability model, with year and district fixed-effects, I find that living within a 20 kilometer radius from an active mine has a significant positive effect on individuals’ propensity to discuss politics and a significant negative effect on individuals’ likelihood to trust the Ghanaian parliament.

Columbia Economics Review

Literature Review While many countries in Africa house an abundance of natural resources, the wealth of the natural landscape most often lies paradoxically in the backdrop of extreme human deprivation, poverty, and often, conflict (Collier and Hoeffler, 2005). As the mining sector continues to expand rapidly throughout resource-rich African nations (World Bank, 2011) and decentralized natural resource management policies take hold (Ribot, 2003), there is a greater need to further investigate its uncertain and heterogeneous effects on economic growth and human development (Gajigo et al, 2012). Using geographically-dispersed gold mining in Ghana as a micro-study, this paper draws from existing literature on resources, conflict, political attitudes, growth, and the role of community expectations to explore the new question: What effect

Fall 2015 does the expansion of mining activities have on political engagement and trust?

Resources, Conflict, and Political Engagement There has been a growth of interest in the last decade in empirical research on the link between conflict and natural resources, including oil (Lei and Michaels, 2011; Dube and Vargas, 2013), diamonds (Humphreys, 2005), and other major minerals (Aragon and Rud, 2015; De Luca et al, 2013; Berman et al, 2014). Diverse case studies provide welldocumented evidence of the “resource curse,” in which low levels of income and heavy reliance on primary commodities can enable susceptibility to economic shocks, which is further linked to rebellion and civil war (Collier and Hoeffler, 2005; Miguel et al, 2004). For example, Berman et al (2014) find that “mining not only increases the scope for localized protests and riots, but it also systematically fuels larger-scale battles.”

mining not only increases the scope for localized protests and riots, but it also systemically fuels larger-scale battles Similarly, numerous researchers have also begun to increasingly examine the empirical relationship between legacies of conflict and political engagement in different African countries. While Adhvaryu et al (2013) find negligible effects of early-life war exposure on later-life political activism throughout Africa, Bellows and Miguel (2009) and Blattman (2009) find that war victimization results in a greater likelihood of political engagement and participation in local collective action in Sierra Leone and Uganda, respectively. Congruently, in a social anthropological study on mining and democratization in Tanzania, Fisher et al (2013) detail the pivotal political significance of small-scale artisanal gold mining and collective action in the

context of the present growth of mineral extraction in the overall continent.

Shared experiences provide miners with both a collective identity and a communal identity that impacts a sense of purpose and cohesion, which they are likely to draw on when they confront problems necessitating negotiation or prompting retaliatory action vis-à-vis external non-mining institutions. The collective identity of miners imparts confidence and strength, vital for struggles against predatory states and exploitative markets. Miners are likely to demand their rights as a collective (Fisher et al, 2013).

A key contribution of this paper is the attempt to empirically understand the psychological and social linkages between mineral resources and political engagement, adding to the growing research on determinants of political mobilization (Bellows and Miguel, 2009).

These linkages are important to investigate in the context of the current United Nations Post-2015 Development Agenda, which prioritizes inclusivity and environmental and resource issues. Considering the anecdotal evidence that African governments have generally failed to establish democratic decentralization of natural resources (Ribot, 2003; Poteete, 2013) and that resource rich states often rely on systems of undemocratic patronage politics (Collier and Hoeffler, 2005; Gajigo et al, 2012), there is a need to question the ways in which this evidence manifests itself in the relationship between resources and political activism.

Trust, Expectation, and Economic Development This paper further adds to the growing literature of cases studies on trust as a key element of economic development (Algan and Cahuc, 2010; Rohner et al, 2013). In anthropological studies on gold mining in Ghana, researchers have found that inflated community expectations of government and businesses often coincide with disillusionment and lack of trust and confidence (Garvin et al, 2009; Hilson et al, 2005) Community members reported that issues of royalties fueled their high expectations – royalties are paid by the companies directly to central government and little of these royalties ‘trickle down’ to the affected communities. Both community members and company representatives reported being disappointed and disillusioned by the actions and behaviors of the other party. Interestingly, community members and company interviewees also Columbia Economics Review

7 implicated the central and district governments as carrying some responsibility for negative impact (Garvin et al, 2009) Since the launch of the Structural Adjustment Program, the Ghanaian government has tended to favor the awarding of land concessions to large-scale mining and mineral exploration companies…

Between 1990 and 1998, the company [Teberebie Goldfields] uprooted some 30,000 farmers from 14 mining villages to accommodate its mining operations – the people now blame the government of Ghana and contend that the government does nothing to protect people like them from large companies who want their land (Hilson et al, 2005).

shared experiences provide miners with both a collective identity and a communal identity that impacts a sense of purpose Lowe (2014) finds evidence similar to the anecdotes reported above in an empirical study on the impact of railway privatization in Sub-Saharan Africa, in which private operators tended to disappoint governments’ high initial expectations and views toward government worsened upon privatization. In a parallel way, such findings relate to a set of results in the seminal Nunn and Wantchekon (2011) study on trust and the slave trade in Africa. Nunn and Wantchekon discuss how the history of chiefs selling their own people into slavery may have provoked the legacy of modern-day mistrust in political figures, in particular local figures. A question in the 1999 Afrobarometer survey for Ghana, which asks, “The government should retain ownership of its factories, businesses and firms (A- agree, B-disagree). Is it better for the government to sell its businesses to private companies and individuals?” provides basic support for some of the findings described in the papers above: over 2/3 agreed that the government should retain ownership (Afrobarometer, 1999).

The negative legacy of trust, percep-

Fall 2015

8 tions of freedom, and civilian attitudes toward government actors resulting from violence and human suppression (Garcia-Ponce et al, 2013) have important implications for economic growth and development. Numerous studies have explored different aspects of the relationship between trust, “social capital,” growth, and market participation (Cassar et al, 2013; Algan and Cahuc, 2010; Algan and Cahuc, 2009; Rohner et al, 2013; Giuliano and Spilimbergo, 2009), finding strong links between higher trust and positive development outcomes. These findings are in line with the theory of growth in the neoclassical Solow model, in which trustworthy institutions with lower levels of corruptions can be considered an integral factor in the technology that drives long-run growth (Miguel, Economics 174, 2013).

In addition to examining the relationship between mining and political engagement, I aim to develop an empirical understanding of a small aspect of the complex inter-linkages between community expectations and trust, as it pertains to gold mining in Ghana. An analysis of these seemingly diverse, yet intricately connected relationships, is valuable for the creation of environmental and social policies that promote not only economic development, but also ultimately, freedom and democracy.

trustworthy institutions with lower levels of corruptions can be considered an integral factor in the technology that drives longrun growth Gold Mining in Ghana Ghana, which is the second largest producer of gold in Africa, has undergone a rapid expansion of annual production in the last 20 years, in which there has been a 700 percent increase in annual gold production since 1985, as shown in Figure 1. The mineral sector overall has

experienced an average annual growth rate of 12 percent between 1990 and 2009 (Gajigo et al, 2012). Mineral exports account for 44 percent of the country’s total exports (IMF, 2011) and gold, in particular, makes up 95 percent of mineral revenues (Ayee et al, 2011). In 2010, approximately 20,000 Ghanaian nationals were directly employed in large-scale mining, 6000 in providing services to the mineral sector, and 500,000 in small-scale artisanal mining (Bermudez-Lugo, 2010).

ghana has predominantly prioritized awarding land concessions to large-scale mining companies Despite recent growth, Ghana experienced deteriorating performance in the gold sector in the 1980s, likely due to stagnant gold prices and insolvent stateowned mining companies. This weak performance resulted in a number of structural adjustment policies, which set forth diverse reforms in the existing mining codes, in order to create a more attractive private investment environment in the mineral sector, including lowering the range of royalty rates from 3-12% to 3-6% and further reducing the corporate income tax to 25 percent (Gajigo et al, 2012). While the massive growth in the gold sector points at positive effects of these reforms, there is nonetheless evidence of significant challenges in the sector. For example, an Extractive Industries Transparency Initiative (EITI) study found that all companies operating in Ghana paid only the minimum royalty of 3% (out of a range of 3-6%) and Stürmer (2010) describes the problem of mis-invoicing in Ghana, in which mining companies report lower-than-market gold prices to the government, resulting in lower royalties and income tax revenues to the government. Furthermore, since the launch of the SAP, the government of Ghana has predominantly prioritized awarding land concessions to large-scale mining companies, making it ever more

Columbia Economics Review

difficult for small-scale artisanal miners to legally obtain productive land (Hilson et al, 2005). The competing interests of the large-scale and small-scale gold mining sector, which employs far more Ghanaians, can sometimes lead to conflict (Hilson and Yakovleva, 2007).

The recent substantial expansion of the gold mining sector in Ghana presents an opportunity to explore the potential political and trust-related consequences of mining that are discussed in this paper.

While this analysis pertains to large-scale mining, there is an understanding that there may be a geographical correlation between small and large-scale mining operations (Chuhan-Pole et al, 2015). If data on small-scale mines becomes available in the future, the separated effects of small and large-scale mining would be an interesting research endeavor.

Figure 1: World Price of Gold and Ghana’s Annual Gold Production (ChuhanPole et al, 2015)

Econometric Analysis Data The econometric analysis in this paper involves a combination of mining and political attitudes data with a spatial analysis methodology developed by Tolonen (2014). The main source of political attitudes data derives from a dataset called Afrobarometer, detailed under section 3.1.1. The geo-coded mining dataset that is linked to the individual-level geo-coded Afrobarometer data is called IntierraRMG, further described under section 3.1.2 and shown in Figure 2. Latitude and longitude points for both datasets allow me to match individuals in Afrobarometer surveys to mines, by calculating different distance ranges from geo-coded mine locations to surveyed individuals.

The main analysis uses concentric circles with a cut-off of 20 km radii, under the assumption that the economic effects become negligible beyond this distance. .

To assess any potential spatial heterogeneity, I also use varying cut-off distances (30, 40, and 50 km).

Fall 2015 Figure 2: Gold Mines and Afrobarometer Households

a. Gold minds and 20 km buffer zones

9 There are 16 industrial gold mines for this micro-study on Ghana, which have been tracked from 1990 to 2012. Table 1 shows active mining companies in Ghana, in addition to opening and closing years, and the country from which the mining company originates.

Table 1: Gold Mines in Ghana

b. Gold mines, Afrobarometer Clusters and 100 km buffer zones

Afrobarometer Data My data largely derives from the first four rounds (1999, 2002, 2005 and 2008) of Afrobarometer surveys for Ghana, for which there are geocoded identifiers. Afrobarometer is an independent, cross-national research project that tracks trends in public attitudes in comparative surveys over years and 35 African countries. Samples are randomly selected in such a way to provide a representative cross-section of all citizens of voting age in a given country and are “stratified by key social characteristics in the population, such as sub-national area (region/province) and residential locality (urban/rural)” (Afrobarometer, 2014). The total Ghana dataset includes 5552 observations (49.34% male, 50.66% female), age 18110 from 10 regions. The geo-coordinates for observations in survey rounds 1-4 in Ghana are of varying precision: for round 1, the geocodes represent the centroid of the district, while for rounds 2-4, the coordinates represent the centroid of the subdistrict, town or even village (Lowe, 2014; Garcia-Ponce et al, 2013).

The validity of this dataset is supported by numerous papers, which have utilized Afrobarometer data to explore a diverse range of questions, from measuring voting patterns (Barkan et al, 2006) to political participation (Adhvaryu et al, 2013), knowledge (Mattes and Bratton, 2007), views toward government (Lowe, 2014) and trust (Nunn and Wantchekon, 2011; Rohner et al, 2013).

Figure 3: Gold Mines and Afrobarometer Household Clusters in Ghana

Main Variables The main dependent, independent and control variables, drawn from Afrobarometer and the Raw Materials Data are further explained in the following sections.

Dependent Variables

Figure 3a shows the gold mines that are considered in the study, each marked by circular areas with a 20 km diameter. These buffer zones signify the baseline treatment areas in the difference-in-difference analysis. Figure 3b shows 100 km buffer zones and includes Afrobarometer household clusters.

Mining Data The Raw Materials Data (RMS) comes from IntierraRMG (InterraRMD, 2012) and contains information on the location of large-scale mining companies around the world, usually operated by multinationals or the national government, since 1980. The dataset further contains information on whether mines are active or not and annual production volumes for different minerals (Berman et al, 2014). Satellite imagery from Mine-Atlas was used to locate geo-coordinates for mines, in order to verify mine boundaries and centroids (Chuhan-Pole et al, 2015).

Columbia Economics Review

Drawing from a number of empirical (Bellows and Miguel, 2009; Adhvaryu et al, 2013; Mattes et al, 2007) and anecdotal (Ribot, 2003; Fisher et al, 2013) studies on political engagement and local collective action, I consider the following set of questions from Afrobarometer rounds 1-4 to construct binary variables at the individual level: Discussion of politics: “When you get together with your friends or family, would you say you discuss political matters?”

The variable takes the value of one if the respondent answers either “Occasionally/ Sometimes” or “Frequently/Often” and zero otherwise.

Attendance at community meetings: “Here is a list of actions that people sometimes take as citizens. For each of these, please tell me whether you, personally, have done any of these things during the past year – attended a community meeting?” The variable takes the value of one if the respondent answers either “Yes, once or twice/Only once,” “Yes, several times/ Sometimes” or “Yes, often/Often,” and zero otherwise.

Raising issues: “Here is a list of actions that people sometimes take as citizens.

For each of these, please tell me whether you, personally, have done any of these things during the past year – got together with others to raise an issue?” The variable takes the value of one if the respondent answers either “Yes, once or twice/Only

Fall 2015

10 once,” “Yes, several times/Sometimes” or “Yes, often/Often,” and zero otherwise Trust Drawing from a variety of empirical (Nunn and Wantchekon, 2011; Mattes and Bratton, 2007; Garcia-Ponce et al, 2013; Cassar et al, 2013; Algan and Cahuc, 2010; Rohner et al, 2013; Giuliano and Spilimbergo, 2009) and anecdotal (Garvin et al, 2009; Hilson et al, 2005; Fisher et al, 2013) papers in the growing literature on trust and expectations, I consider the following set of questions from Afrobarometer rounds 1-4 to construct binary variables at the individual level: Trust in parliament: “How much do you trust each of the following, or haven’t you heard enough about them to say: The Parliament?” The variable takes the value of one if the respondent answers either “Somewhat” or “A lot” and zero otherwise.

Trust in local assembly: “How much do you trust each of the following, or haven’t you heard enough about them to say: Your assemblymen/women?” The variable takes the value of one if the respondent answers either “Somewhat” or “A lot” and zero otherwise.

Independent Variables I use the Afrobarometer dataset to construct an indicator variable for whether the respondent lives within a 20 kilometers radius from an active mine. Similarly, I utilize the RMD mining data to create an indicator variable that is equal to 1 if a mine is active at the time of the Afrobarometer survey and an interaction term between the indicator for actives mines and the indicator for whether a respondent lives close to an active mine (Berman et al, 2014; Chuhan-Pole et al, 2015; Tolonen, 2014).

Main Control Variables I control for living in an urban or rural area, education, age, and gender (Nunn et al, 2011; Lowe, 2014; Chuhan-Pole et al, 2015) in the varying regressions. The inclusion of district-fixed effects will allow me to partial out time-invariant characteristics that affect political attitudes and the activity of mines, such as institutional or cultural factors.

The different Afrobarometer survey rounds and time-varying mineral production data allows me to adopt a temporal and spatial difference-in-

differences analysis developed by Tolonen (2014). Combining the variables described in sections 3.2.1-3.2.3, I estimate the following individual level difference-in-differences analysis: Yikt= β0+ β1∙activet+ β2∙nearmine+ β3∙active*nearmine+ αg+ γt+ φXi’+ εikt The dependent variable Yikt measures the specified political engagement or trust outcome of an individual i in cluster k (confined to include respondents within 20 km from an active mine) for year t. This is regressed onto the independent variables: an indicator for whether a mine is active during the time of the Afrobarometer survey (activet), an indicator for whether the Afrobarometer survey respondent lives within a 20 kilometer radius from an active mine (nearmine) and an interaction between the latter two indicator variables (active*nearmine).

District fixed effects, year fixed effects, and varying control variables are included in the regressions. All standard errors in these analyses are clustered at the district level. The distance chosen for this analysis derive from spatial studies on Columbia Economics Review

mining, which used distances ranging from 20 – 100 km (Aragon and Rud, 2013b; Kotsadam and Tolonen, 2013; Tolonen, 2014).

This difference-in-difference methodology is shown geographically in Figures 3a and 3b, where the small circles with a 20 km buffer zone constitute the treatment group and the survey respondents outside the 20 km buffers make up the control group. The parallel trend assumption for a difference-in-difference analysis, which requires treatment communities (<= 20 km from a mine) and control communities (>20 km from a mine ) to be on a similar trajectory before the opening of a mine, is discussed under results.

Results In this section, I present the results of the individual-level difference-in-difference analyses, including district and year fixed effects, for the three political engagement and two trust outcome variables. In this econometric methodology, it is important for the sample to be balanced and for the treatment and control

Fall 2015 groups to follow similar trajectories, in order to satisfy the parallel trend assumption.

Table 2 shows the Afrobarometer survey summary statistics for individuals who live far from a non-active mine, far from an active mine, close to a non-active mine and close to an active mine. Columns 1 and 3, which comprise the pre-treatment groups are generally balanced across most outcome variables. There is a statistically significant difference between the pretreatment groups for the discussion of politics and trust in parliament outcome variables based upon t-tests on the combined years of data. However, separate ttests for 1999, 2002, 2005, and 2008 reveal insignificant differences between pre-treatment groups for 1999, 2002 and 2008. The statistically significant difference between the pre-treatment groups is driven by the data for 2005, a year in which the president was inaugurated, 29 new ministers were sworn into parliament, and the government announced a 50 percent increase in fuel prices (GhanaWeb, 2005). However, the year variation is controlled for by year fixed-effects in all regression analyses. The overall results across the four pre and post-

treatment groups are very balanced, in satisfaction of the parallel trend assumption.

Political Engagement Using the difference-in-difference method described earlier and the linear probability regression model, I estimated results for the Discussion of Politics, Attendance at Community Meetings, and Raising Issues political engagement binary outcome variables.

The results in Table 3 show that individuals who live within 20 km from an active mine are more likely to discuss political matters when they get together with friends or family. Controlling for age, gender, urban or rural residence, education, and including year and district-level fixed effects, Afrobarometer survey respondents are 36.8% more likely to discuss politics. However, as shown in Table 4 and 5, there are no significant effects of living in active mining communities on individualsâ&#x20AC;&#x2122; propensity to attend local community meetings or likelihood to get together with others to raise an issue. Even though these estimates are positive and indicate a gen-

Columbia Economics Review

11 erally higher proclivity for political activity, in congruence with the opening of a mine, they are statistically insignificant.

While there is no data available on migration or survey-respondent mobility for any of the rounds of the Ghana Afrobarometer surveys, there is a considerable possibility that migration played a mechanistic role in the shift in political attitudes among residents living near an active mine. Although the mining sector in Ghana has been studied thoroughly, other factors such as migration and community dynamics have received less attention. While data on both large and small-scale mining activities is limited, Nyame et al (2009) nonetheless outlines labor, commercial and institutional migration patterns, both internal and cross-border, that have potential linkages with the growth phase of mine development in Ghana. Prior research by scholars on the effect of transnational mining on migration has also uncovered increasing rates of migration to mineral production sites in Africa and across Latin America (Bury, 2008) and the impact of this mineral-driven migration on regional economies, labor force structures, and political

Fall 2015

12

networks (Long and Roberts, 1978; Becker, 1983). For example, Bury (2008) found that the establishment of an LSM company in the Peruvian Andes could have catalyzed inward migration to the gold mining sites. In a recent study on migration and political attitudes in Central and Eastern Europe, Careja and Emmenegger (2012) also find that migration experiences broaden the range of political attitudes. If reliable migration data and ASM mining data in Ghana become available in the future, the impact of these specific aspects of mining production on political engagement and trust would be an edifying research endeavor.

Trust The effects of living in an active mining community on individuals’ trust in the Ghanaian parliament and in their local assemblymen or women are examined in this section. Data on trust in the president is unavailable for Afrobarometer Round As evident in the results in Table 6, the individuals who live within 20 km from an active mine are less likely to have trust in the parliament. Including year and district fixed effects, and controlling for age, gender, urban or rural residence, and education, I find that respondents residing near active mines are one third less likely to trust the Ghanaian parliament.

In contrast to the findings in Table 6, none of the negative effects of living near an active mine on an individual’s probability of losing trust in the local assembly are statistically significant. These results

presented in Tables 6 and 7 may lend support to the idea that inflated community expectations of high-level government officials, especially with regards to the issues of royalty payments, correlate with lower trust, confidence and disenchantment toward these government officials (Garvin et al, 2009). In a study on the empirical relationship between employees’ trust in their employers and experiences with a breach in psychological contracts, Robinson (1996) finds that when expectations are unmet, there is a decline in trust among employees and a negative effect on subsequent contributions to the firm. Analogously, if government officials of Ghana are perceived as the employers and miners are the employees, unmet expectations with regards to the benefits of mining on local communities can drive the negative trust results in the different regressions. The reductions in trust among individuals living near an active mine and ensuing negative effects on growth and market participation (Cassar et al, 2013; Algan and Cahuc, 2010; Algan and Cahuc, 2009; Rohner et al, 2013) can plausibly offset the positive impacts of mining activities. If individual-level data on expectations becomes available, it would be a very interesting mechanism to investigate, especially with regards to its policy implications.

Conclusion Ghana has been experiencing enormous expansion in its export-oriented mineral sector in the last 20 years, particularly in

Columbia Economics Review

gold. Whereas the mineral sector is the largest recipient of foreign direct investment and contributes appreciably to Ghana’s economic growth, historical experiences of the purported natural resource curse throughout Africa nonetheless call to question the social and psychological effects of these expanded mining activities. I use geo-coded gold mining data and four rounds of Afrobarometer political attitude surveys combined with an individual-level, geo-spatial differencein-differences method to analyze the relationships between mining, trust in government, and political engagement

by Ghanaian citizens. In applying these strategies, I find that living within 20 kilometers from an active mine gives rise to a higher likelihood to discuss politics, attend community meetings and raise issues, and a lower propensity to trust the Ghanaian parliament and local assembly. The results for the discussion of politics and trust in parliament outcome variables are statistically significant.

Although empirical information on migration and expectations is currently unavailable in the Afrobarometer database, these factors seem to anecdotally explain the phenomenon of increased political engagement and diminishing trust. In light of the post-2015 Development Agenda and its intensified focus on environmental, resource and community inclusion issues, further research on the migration and expectation aspects of the story can help provide for future policy recommendations for affected populations. n

Fall 2015

13

Trending in Art Location Models in the Art Market: Artists as Firms Visualized on a Product Space Ricardo R. Rodriguez Columbia University

While we might never find an appropriate way to mathematically describe the sublime beauty of a painting or the mystical feeling that a sculpture produces, the art world is still a field where economics research is not only possible but also crucial. The following paper discusses some of the existing approaches to understanding the art market by describing artists as firms and using the existing models of Industrial Organization. The author is particularly interested in showing the relations that exist between the participating actors of the market –in this case, well-known artists- and how they determine their strategies of product design and differentiation. A location model is then introduced to visualize and conceptualize such relations. With this groundwork built, the author proceeds to answer other questions regarding influential artists. Why are some artists more successful in redefining their styles than others? Who are the most influential modern artists? And who among them will influence art in the future the most?

While these are tough questions that are not necessarily answered in this paper, by setting a framework to address them, Rodriguez’s work might be a first step towards a better comprehension of artistic production and the markets that surround it. – M.F.P.

We know firms have many decisions to make: from entry and exit, to vertical relationships, price setting, research and development, advertisement, and product design, among others. Industrial Organization has provided the framework and produced the theory that attempts to model these decisions and understand the behavior of firms and markets. While the art market certainly has its idiosyncrasies, it is not unlike other markets in that many of the intuitions from Industrial Organization can be extended and adapted to explain the behavior of the players in the world of art. Whether they are galleries, dealers, collectors, auction houses, or artists, each of these players and their actions can be studied from the lens of Industrial Organization. Moreover, many of the models in this field can become even richer when we introduce the particularities of the art market.

This paper will focus on analyzing artists as the central “firms” of the art market, producing what is by definition the essential “product” of the market itself, and will attempt to extend one major topic of Industrial Organization to the behavior of these artists: that of product design and differentiation. In short, the paper asks: how do artists choose their “product”—be that any number of characteristics that define the artist as a firm and that define her work? There will be both an analysis of previous economic work on the product design choice of artists, and a discussion on the possibility of applying a location model of product differentiation to study this artistic choice. The focus will be on the visual arts and in particular on painting, though of course most of the theories and models may be applicable to other mediums as well.

Columbia Economics Review

An Economic Look at Artistic Production To consider artistic production, most economists have focused on labor supply—what drives an artist to enter the art market and supply hours of artistic labor.

They have focused on the effect of nonarts wages (the wages artists may find in careers and part-time jobs that will complement their earnings), arts wages, creativity, earnings outlooks compared to other careers, nonmonetary rewards, etc. Yet, comparatively scant attention has been paid to what drives their choice of what to produce in the time they have allocated to artistic production—if they have decided to enter the market at all.

William Bryant and David Throsby look at a creative optimization decision, in which an artist chooses the amount of “creative effort” to invest in a particular

Fall 2015

14 work. This choice is conditioned on the artist’s expectation of the reaction to the work in two main domains: the “market” and the “world of ideas”, or “artworld”.

They assume the market only cares about the economic value of the product, while the artworld is only concerned with its cultural value. The artist, naturally, is assumed to care about both. Like in earlier work by Throsby (1994), this model is realistic in that it constrains artists to sustain a level of consumption. Thus, while perhaps in an ideal world only creativity and artistic inspiration would play into product design choice, an artist must keep the customer in mind and produce what she thinks will sell. Financial considerations have a role to play in her choice in that she needs to produce for the market as well as the artworld.

an artist chooses the amount of “creative effort” to invest in a particular work Other models have artists working part-time in both the artistic world and non-artistic world [Throsby (1994)]. Others further complement the non-arts earnings with earnings not directly related to an artist’s labor activities in a given period; instead, the artist also earns income from royalties from past work [Casacuberta and Gandelman, (2006)]. Artists of course must earn these non-arts market earnings to financially support their activities in the world of art, a realm where they gain utility rather than disutility from work, which is what typical models of labor supply assume in other, more “traditional” labor markets [Steiner and Schneider (2012)].

As Richard Caves writes, “The artist’s preferences over how to execute creative work complicate the contracting process, particularly the definition and allocation of decision rights.” [Caves (2006)]. In a world where an artist may hypothetically live entirely off grants, subsidies, or advances that are guaranteed independent of the outcome of her work (as long as a work is actually produced, guaranteeing renewal of contract), then she has complete discretion over product design, and

economic valuations have no effect on her choice of creative effort, once again in the context of Bryant and Throsby. Parties to contracts in the art world then have to consider the effect on the creative efforts of an artist of the type of earnings structures and conditions they create.

This may also apply where the earnings potential has been facilitated already, when an artist has a contract with a dealer to display her work, though there is no guaranteed cash inflow that is tied to that relationship. The creative preference may thus increase slightly, as financial concerns become a less important parameter to the artist who has thus succeeded in securing a contract that removes or eases some of the earnings uncertainty.

In short, an extremely important factor to consider when modeling an artistic product design choice is what actually motivates an artist to enter the art market, and what kind of factors play into her utility function. In particular, attention has to be paid to the weighting of both financial and nonmonetary rewards, and how these rewards are determined by the artist’s choice of product [Frey (1997)].

Some further considerations for creative optimization decision include complicating the utility function of the artist by no longer assuming that the market and the artworld have separate and independent valuations of the painting. In real life we know this obviously not to be true, as paintings with varying degrees of commercial inclination may be regarded very differently by the artworld: depending on the mastery with which the commercial component of the work is executed (e.g.

Warhol), it may be possible that highly commercialized works can have high cultural value. Describing then a more general valuation that allows each of these two components to be functions of the same variables (and perhaps even of each other) might provide further insights into whether or not an artist ever does choose to not be “fully” creative when creating an art piece.

While there are many possible ways to build upon and adjust a model like Bryant and Throsby’s, perhaps the main difficulty with many of the present models that attempt to explain product design and differentiation in the art market is that they seem to overlook the social aspects of the market itself and the interpersonal relationships between artists.

Bryant and Throsby simply mention that in their model, the artist is a member of a non-empty set of artists. Yet, they fail to delve into the way the artists in this set

Columbia Economics Review

influence the products other artists are producing. In effect, most models ignore the role of competition and of influence in this art market structure, and the role they play in product design.

models ignore the role of competition and of influence in this art market structure, and the role they play in product design.

Social Contexts of Artistic Production D.K. Simonton talks about a “social psychology of creativity” which “demands that the creative individual be placed within a network of interpersonal relationships and group influences.”

While he defines these relationships with the aim of measuring achieved eminence, these relationships certainly play an integral part in the decision-making process behind designing an artistic product. By definition, product differentiation requires another product to differentiate from, and in a creative field such as the arts, the importance of relationships and associations between artists is paramount in determining product design. Particularly because we usually divide and visualize art history by movements and schools of artists that we have identified either ex-post or during the times of their careers as having similar traits, styles, or aims in their art, the use of sociological methods to evaluate product differentiation and design might be useful in the art market.

The sociologist Katherine Giuffre “conceptualizes artists’ careers as transitions through positions within a constantly shifting web of relationships that are without a priori hierarchical demarcations.” Like Simonton, she uses this framework to analyze the career paths of artists and the critical attention some may receive based on the relationships they’ve had in that network. This perspective on artists as a network of interpersonal relationships defined by influence and competition inspires the possibility of applying a location model to study: how these

Fall 2015

artists choose the art pieces they produce, define their personal brand and style in the universe of artists, and influence those around them that share that same universe.

The Artistic Product Space: A Location Model For the development of a location model and an artistic product space, we can think about individual artists as locations on a one-dimensional, two-dimensional, or three-dimensional space defined by a set of artistic characteristics that determine an artist’s style. The artists represent their own horizontally differentiated products; this hedonic approach to a location model

will thus have artists competing and influencing each other in the product space to define their work, producing a general “Picasso product” or “Rembrandt product”, etc. Like Singer describes, each piece or artist in the product space is a bundle of Lancastrian characteristics of ‘decorativeness” and ‘intellectual appeal’ [Singer (1981)].

Yet, a first challenge is identifying what drives an artist to choose her location in the first place. For firms, it is simple to state that they compete in the product space to maximize profits. But for artists, commercial and financial considerations are likely not the primary consideration behind product design. Other than financial considerations, we can think of an artColumbia Economics Review

15 ist as being motivated by the search for success and recognition, general love of their craft and the nonmonetary rewards they obtain from pursuing their passion, etc. Inspired by Bryant and Throsby’s own creative optimization decision, perhaps a utility function could be devised that defines artistic profits as a function of different monetary and nonmonetary rewards. These might include the expected earnings associated with a particular product or style (so the product characteristic on that axis of the product space might be an artist’s commercial orientation and the commercial quality of her work), the probability of success and eminence given the observed success of artists close to or located on that position of the product space, etc. As Singer detailed, “The artist’s decision depends not only on his human capital endowments but also on his attitudes towards risk. He has to balance high potential rewards, attainable with relatively low probability, against low potential rewards, attainable with high probability.”

Further dimensions can be added to the product space by thinking of how much of the overall space each artist occupies in terms of the size of her point (measured by how diverse her style is, or how eminent she is), and by imbuing each artist with a measure of how closely related she is to other artists in the space. We can indeed define this as an artist’s “mass”, or influence in product design. While this applies to other markets and industries as well (many firms might look to others for ideas), this is perhaps most true for the art market, where artists are deliberately grouped together into movements based on the similarities of their styles.

Of course, there’s an initial caveat: defining an artistic product can be limiting and reductive. How can we indeed reduce a decades-long Picasso career into a single point on a product space? This product space is therefore abstract, and theoretical. If we think of art as limitless and boundless, constraining to a physically defined space may be inappropriate.

What’s important then is to see a location model in the art market as a framework for studying artistic influence, art movements and their development over time, and, of course, how an artist may choose her own location based on the careers of other artists she observes in the space (the art market) and her own expectations of the career she desires to have.

Another feature of a location model that lends itself to interesting considerations on artistic production is that of minimal versus maximal product differentiation.

16 Sensitive to how models are specified, the optimal strategy for some markets can be either the former or the latter. We can then ask and investigate: which is more likely to apply to the art market?

We can consider artists as being motivated by both choosing a completely new, unoccupied space in the product space far from other artists as something truly new and innovative, or choosing a wellestablished, crowded location as a way to benefit from association with the artists already located there. There are clearly benefits to being both part of a defined cluster of artists on the product space and not being part of one. In fact, under some definitions, innovation might happen not only by picking a new, unoccupied location on the product space, but also by picking an occupied space where an artist is pulled to the most by the influence of those already in that space and what they’ve already done. Artistic movements indeed don’t just exist to label and classify art, but oftentimes as formal ways of characterizing the common (yet uncoordinated) efforts of a group of artists that produce a new style or approach. The sociologists Balazs Vedres, David Stark, and Andrew Hargadon define this recombinative approach as the key to innovation in most industries: brokering connections between seemingly disparate concepts to produce something new [Hargadon (2003); Stark and Vedres (2010)]. As Fabien Accominotti writes: “Artistic innovations are thus seen as sometimes relying on a body of more or less innovative previous work, the swift or slow assimilation of which can only marginally speed up or delay the blossoming of other artists’ subsequent innovations.” [Accominotti (2009)] He expands that concept by including intragenerational innovation—not just intergenerational. Artists thus look to the artists that are present at the same time as they are in the product space, not just those from previous generations.

This concept of interplay of artists both across and within generations is at the center of Giuffre’s “Sandpiles of Success”. She writes: “Present-day status is based on a position within a web of ties and also has embedded within it the history of past positions... Career ladders in the art world are not so much ladders as they are sandpiles. The movement of actors within the field changes the shape of the field.” [Giuffre (1999)] We can thus view artists as forming into dynamic clusters based on proximity to each other on the product space. These clusters can

Fall 2015 grow, shrink, move together around the space, separate, etc. based on the influence and the cohesion of the artists in the cluster, and the artists in the product space itself. We can further think about the Zeitgeist as the cluster of artists that dominates the space, be it by the number of artists in a cluster, space occupied in the product space, total influence held on the product design of other artists, etc.

By creating the product space in different time periods, we can track and visualize the development of art movements and careers of individual artists, as a network of artistic connections and associations, and identification with product-defining characteristics. We can see how movements or Zeitgeists have been born, died, and evolved, linking a continuum of artistic careers over history to trace the development of artistic styles over time.

we can see how movements or zeitgeists have been born, died, and evolved, linking a continuum of artistic careers over history

Constructing the Product Space Because we use an approach that emphasizes interpersonal relationships, the methodology for constructing the product space will require identifying the artists in the desired time period, and observing a measure of their relationships with each other. For the purposes of this paper, in order to define the product space, Google ngrams were used to find the correlation between the mention of artists’ names in books with the mention of other artists and with the movement with which they are most usually associated. Google ngram reports and plots the yearly percentage of all the words in a database of more than 5 million digitized books that correspond to a particular search query (e.g. the word “art” was

Columbia Economics Review

0.0169% of all words in the digitized books in the English language database for the year 2008; meaning that for every 1,000,000 words in the books in that sample in that year, “art” was on average 169 of them). This “culturomic” approach has particular advantages and disadvantages, which will be covered later in the paper.

The assumption behind the use of ngrams is that the more influential an artist, the more he will be mentioned in books when other artists are mentioned as well. Even more importantly, the assumption is that an artist will be mentioned more in books in a given year, when artists that are similar to him in style are mentioned as well that year.

Thus, if in a given year the mention of “Claude Monet” in English language books is higher than the previous year, we would expect the mention of “Édouard Manet” to be higher as well. That high or low correlation will be defined as the degree to which these two artists are stylistically related and associated together. A product space would then be constructed by plotting the correlations among artists with each other.

Ideally, more sophisticated techniques could be used that better controlled for some of the issues with this approach that will be addressed later in the paper. In particular, it can be a strong assumption that high correlation implies a stylistic similarity between the products of two artists, especially when the data used only reveals the frequency of mentions independent of each other, and not the information on how artists may be linked, why some artists may be mentioned more often in given years, etc. Instead, one could directly look at art textbooks or exhibitions that directly compare, mention, or place artists and their products together in the same context. For the purpose of this paper, however, the correlation between mentions in Google ngrams will be assumed to be a valid proxy for stylistic and product similarity.

Artist Correlations and Artistic Movements Once the frequencies/ mentions of artists are obtained, a correlation matrix is calculated that will show the correlation between each artist on the product space.

For the application shown in this paper, 74 artists were used ranging mainly from Impressionism to Pop Art, though some Renaissance and Baroque painters were

Fall 2015 included. Data was obtained for mentions in books starting in 1870 and ending in 2008.

The average correlation of each artist with every other artist was calculated, and a measure called mass for every artist i was devised that was simply:

or the inverse of 1 minus the average correlation of an artist with all other artists.

The average correlation, of course, will depend precisely on the artists included in the product space, and can be defined to be as limited or broad as possible: we can calculate an artist’s average correlation with all artists in a product space, with artists contemporaneous to his career, with artists in his same country or region of origin, medium, etc.

Finally, artists’ correlations with the different artists on each axis are plotted to define the product space. For the purpose of this paper, the size of each marker on the plot was designed to reflect the average percent of mentions in each year for every artist. This measure is thus independent of other artists’ mentions and implies that more popular artists that are mentioned more often in books will have a larger presence on the product space. The filling of each marker is in turn a reflection of each artist’s mass: the deeper the red, the more correlated each artist is with the other artists in the product space. The more blue, the less correlated. If possible of course, the axes on the product space would be more representative of product characteristics. While we can identify styles with the artists on the axes, this is not entirely synonymous with a specific product characteristic, like level of abstraction, or commercial inclination, etc. However, in order to actually create a product space beyond the abstract and theoretical, the axes were defined to be the correlation with the specific artist on the axis.

Because the plot is defined by the correlation of all artists with those on the axes, and the “mass” of each artist is itself defined by the average correlation with every other artist in the product space, we can visualize how Guffrie’s “sandpiles” are put in practice: every new artist in the space changes the mass for everyone. The artists in the product space inherently define it, and no artist can be located on the space without a relation to another artist.

Because of this relationship, we can de-

fine then the artist’s “mass” as his gravitational pull and his influence in product design. Of special importance is the distinction that this is not necessarily correlated with influence in terms of achieved eminence, reputation, or renown. Instead, artists with a high “mass”—because we assumed from the start that correlations imply stylistic connections—are those artists that are overall more closely related to the styles and products of the other artists in the product space. Thus, we presume that someone with a very high mass is one who has had a major influence in how artists design their products.

Thus, it makes sense that really popular artists who are monumental figures in the pantheon of art history—such as Raphael, Michelangelo, Rembrandt—have a low “mass” if they are uncorrelated with the type of work that the other artists in the product space are producing. Especially because these big names are far separated from us in terms of time, it is unlikely that many artists are painting in the same styles as Michelangelo or Rembrandt were. On the other hand, artists are likely to appear more closely related and produce works more stylistically comparable to someone like the 20th century abstract painter Wassily Kandinsky, who occupies position no. 3 in the list of artists with the highest mass in the product space of 74 artists constructed in this paper. He follows only Edgar Degas and, unsurprisingly, Pablo Picasso. These three artists are joined by the likes of Piet Mondrian, Édouard Manet, and Henri Matisse in the top 10 most influential artists in product design of the 74 included in this paper. Table 1 presents the top 10 most influential artists in this product space, and 10 least influential artists, which, as ventured above, are particularly influential figures in the history of art, but have all died hundreds of years ago and are thus unlikely to be directly influencing modernday painters in terms of product design.

Table 1: Rankings of Product Design Influence

17

Note that for Da Vinci, Rembrandt, van Eyck, and Botticelli, their mass below 1 implies their average correlation with the other artists in the product space was actually negative, implying that a higher interest in the other artists in the space (as measured by the mention in books) was correlated with a decrease in interest in these other artists. Once again, the assumption is that this reveals information on the stylistic connection between these artists and their products.

Now, giving the artists in the “least influential” column the benefit of the doubt, perhaps our bias toward including more recent artists in the product space is affecting these results, and had more early artists been included (specially more in the period after the Renaissance and before Impressionism), their average correlations would have been higher, and the ones for the “most influential” artists been lower.

Once again, this reiterates the sensitivity of this approach to the actual artists included in the product space, since by definition these average correlations and the resulting visualization of the product space depend on the artists included.

From the 74 artists included, 26 died more than 100 years ago (of which 13 died more than 300 years ago), 44 died within the last 100 years, and 4 (Wayne Thiebaud, Jasper Johns, Bridget Riley, and Frank Stella) are actually still alive.

Observations and Implications As is evident then, this approach may have serious implications both in terms of how a new artist chooses her location in this universe of artists (with consideration as to the success she may gain by choosing the same location as Picasso and his cluster of artists versus choosing the one for Andy Warhol, for example, or an entirely unoccupied location), and a very strong implication for how we measure the influence of artists on other artists when it comes to product design. In particular, eminence in art history does not necessarily translate

Columbia Economics Review

18 to eminence and influence in art production. Two potential hypotheses arise to describe the observed phenomena.

The first is the intuition that perhaps longer-lived artists (like Joan Miró, or Pablo Picasso) will have higher mass on the assumption that because they lived longer, they perhaps had the chance to explore different styles of art, and had contact with many more artists, thus creating in the minds of art history the kinds of stylistic and historical associations that will produce very high correlations with the other artists in the product space, and thus, a higher mass.

For this particular product space of 74 artists (which requires us assuming that we actually could have Picasso, Rembrandt, Michelangelo, etc. all together in one product space), this potential hypothesis does not seem supported at first glance. Looking at a plot of lifespan on mass (Figure 2), we cannot observe much of a significant relationship. Note that the large green marker corresponds to Pierre-Auguste Renoir:

Running a simple OLS regression of mass and of average both on a constant, lifespan, and separation (defined as years since the death of the artist) yields the following results:

The regression thus seems to find a small, but positive and significant effect of an artist’s lifespan (assuming it correlates closely with length of career) on her mass. Therefore, the intuition that someone with a long artistic career like Pablo Picasso would have a higher mass based on that expected association with many more artists would appear to be correct.

However, this may very well just be an effect of our transformation of average

Fall 2015 correlation into the measure mass= 1/(1 average), as the second regression offers up a significant, small but negative relationship between an artist’s lifespan and his average correlation with all other artists. Given that the function 1/(1-x) is not linear and will overweight values of x (in this case, average) closer to 1 (mass approaches infinity as average approaches 1), it’s likely that the effect between lifespan and an artist’s influence is actually slightly negative, as in the second regression.

The longer since one’s death, the less of an impact one’s ideas have on the thinkers and creators of tomorrow The second hypothesis is related to the years since an artist’s death, and seems to provide an explanation for why some of the biggest names in art are considered here as the least influential in terms of product design. That is, the longer since an artist has died, the less of an impact he will have on present and future artists’ styles and product design decisions. As discussed above, and with all due deference to the role of major artists in history, an artist like Michelangelo is only important in shaping today’s product design indirectly, in the sense that he greatly shaped the future development of art hundreds of years ago. But, just as in time series we usually assume that for j large enough, the covariance with a lag j is usually 0, this is true for the influence of artists on future art. The longer since one’s death, the less of an impact one’s ideas have on the thinkers and creators of tomorrow. Three hundred or four hundred years from now, it will be possible and very likely that Pablo Picasso will have a much smaller impact on the arts of that time, instead being supplanted by a future artist as the most influential in product design. The regression in Table 2 seem to confirm this hypothesis: the more separation in time

Columbia Economics Review

from an artist, the less of a mass she has, and therefore the less influential she is in determining today’s product design. Figure 3 displays this relationship. Note that the two outliers in top-right corner of the plot are Pieter Bruegel and Hieronymus Bosch, whose styles seem rather similar and, in the eyes of a modern viewer, potentially familiar to the works we might expect from more contemporary artists (explaining, perhaps, their high mass).

Another point of interest is the correlation of artists with general art move-

ments. In particular, if we apply the same concept of mass to these movements, then we can rank art movements themselves in terms of their influence on product design. Using this approach, it appears German Expressionism is the most influential art movement in terms of product design in this paper’s product space, followed by Surrealism and Abstract Expressionism. Figures 5 and 6 finally present a sample product space, with Pablo Picasso and Vincent Van Gogh as the defining artists for Figure 5, and Picasso, Van Gogh, and Claude Monet for Figure 6:

Fall 2015

Critiquing and Evaluating the Model A question that must be considered is: does the approach actually work? Succinctly, the correlation between movements and their corresponding artists tends to be very high. For example, the artist with the highest correlation with the Pop Art movement is Tom Wesselmann (ρ = 0.9833), while for Cubism it’s Georges Braque (ρ = 0.9526), and with Abstract Expressionism we have Jackson Pollock (ρ = 0.9903). Of course, no method is perfect; for Surrealism we do not observe Salvador Dalí as the artist with the highest correlation with the movement, nor do we observe other major artists as being correlated highly with Impressionism when we would expect them to be (Claude Monet is only the 16th highest correlated artist with the term Impressionism, behind unexpected artists like El Greco, or Juan Gris).

Nevertheless, we do observe some high correlations between artists that we know are closely related in style and movement.

A particularly salient example is that of Jasper Johns, Robert Rauschenberg, and Roy Lichtenstein, where the correlation between Johns and Rauschenberg is 0.9933, and between Johns and Lichtenstein is 0.9792. Their ngram in Figure 7 (which is plotted as well with Frank Stella, Mark Rothko, and Barnett Newman) demonstrates how closely together the mentions of artists of related styles can vary.

The use of ngram carries with it certain issues and considerations, which ideally would be corrected by the use of more sophisticated approaches to measure the correlation between artists. Firstly, one must decide on the specific phrase to use for each artist. This becomes particularly important for names like “Pierre-Auguste Renoir”, who some authors may have simply called “Pierre Auguste Renoir”, or even “Auguste Renoir”. The same applies for artists typically known solely by their first or last names, such as Raphael, Titian, or Michelangelo. If only the phrase “Raphael” is searched, it is likely that the results would include many other instances of the word “Raphael” that are not at all related to the artist. Using the full name “Raphael Sanzio da Urbino” or “Raphael Urbino” is also problematic, since in that case we’d be underestimating his mentions in books, since he is so infrequently referred to by his full name. This same issue also applies to names with alternative spellings, such as “Alphonse Mucha” versus “Alfons Mucha”, though luckily, Google allows for the grouping together of alternative spellings by simply searching for the phrase “Alfons Mucha + Alphonse Mucha”. Another useful function is searching for caseinsensitive phrases, so that a mention of “CLAUDE MONET” in a book would be counted as a mention of the artist just as much as a mention of “Claude Monet”, or “claude monet”. This becomes particularly important for names like “Jan Van Eyck” versus “Jan van Eyck”.

In short, using this approach relies very much on the specifications of the search, and more generally on the accuracy of the search engine itself. If Google allowed for approximate matches, we’d then need to rely on the machine being accurate enough to not over or underestimate the actual number of mentions an artist is getting.

Another issue to consider with Google ngram is the sample of books to use. At the moment, one can only carry out a search on one language at a time. For artists that

19 are perhaps more regional and would thus appear much more in languages other than English (the language used for searching here), then that artist would be underrepresented by not including all these other languages as well.

we do observe some high correlations between artists that we know are closely related in style and movement

A third important issue is when to begin counting the mentions of artists. For example, are the frequencies of the mentions of artists’ names in books measured starting in 1800? Or 1900? After all, for many artists, their mention in books is 0 in 1890, when Monet was being mentioned already. That may of course bias the correlations but only because the artists just weren’t even alive by that time. In a way, this is acceptable, since it seems like just a natural way to separate out members of art movements by lowering the correlations of artists who were born or became famous much later than the artists of earlier movements. So indeed, artists who were around for long before other artists will have lower correlation with those much younger artists, which was discussed above. However, if an artist revives an old style, then perhaps this might be an issue. Then, the correlation would be lower than it should be, since the assumption for this model is that the correlation will be able to capture the degree of similarity in styles between artists.

Limitations in Defining Artists and Movements Moreover, another issue is whether lesser-known artists will even show up in the product space. The approach relies on artists being mentioned in books, so then “smaller” artists (who are the large bulk of the market) might not show up as often, and when they do, it may reveal more about an artist’s capacity to be interesting

Columbia Economics Review

Fall 2015

20 enough to be mentioned in a book than being related to another artist stylistically.

Final considerations are the possible critique that this approach will only reinforce the art movements that have been defined already. Artists will thus be close to other artists in the product space precisely because they’ve already been historically associated to the artists they’re close to. However, the approach is not particularly aimed at redefining art movements, but at empirically showing how they may appear on a product space, since the assumption is that art movements have been historically defined precisely because of the stylistic similarity of the artists included in them.

if the art market is in a boom, popular artists get mentioned much more all together than less popular artists do Lastly, what about systematic movements in the art market? In particular, if popular artists are highly correlated with the state of the art market, while less popular artists are less correlated with it (meaning, if the art market is in a boom, popular artists get mentioned much more all together than less popular artists do), then we may have another issue measuring the correlation of artists. Moreover, perhaps most of the correlation between artists can simply be explained as correlation with the state of the art market overall, meaning in that case that an artist’s increased mention in books is not due to the increased mention of artists similar to her because they’re stylistically related to her, but because all artists are being increasingly talked about with the better state of the art market. Being able to better break down then what explains the changes in the frequency of an artist’s mention between systematic movements and the mention of other artists might be useful. A regression could be thought up where we regress the men-

tion of an artist’s name in each year on a measure of the state of the art market, such as the total revenues in art auctions in that year, or less directly, GDP and GDP growth in that year (which we then assume would be correlated with the art market), and then of course on the other artists in the product space. Because the OLS coefficient on a variable is defined as the covariance between the regressor and the regressand over the variance of the regressor (controlling of course for the effect of other variables), our approach is not that far off from this idea. The issue is in controlling for things like the systematic movements or a constant term.

Not particularly touched upon in this paper is how to define the clusters of artists once they’ve been plotted on the product space. A more methodical approach might take some benchmark level of correlation to define the clusters, or a certain measure of variance below a correlation of 1. This might potentially lead to overlaps in clusters, of course, and then the question is whether or not overlaps are possible, since if one artist belongs to two clusters at a time, then those two clusters may as well just become one large cluster all the artists belong to.

the approach may be useful as a framework for thinking about product design and differentiation in the art market Clearly, this is not a perfect method, and more sophisticated approaches would ideally be developed to tackle the issues mentioned above. Yet, the approach may be useful as a framework for thinking about product design and differentiation in the art market, and as an opportunity to test other hypotheses on creativity, achieved eminence, artistic production, and the relationships among artists. For example, we could regress an artist’s achieved eminence on the correlation with other artists (meaning, how much of being successful can we attribute to being a unique artist versus being part of a very crowded portion of the product

Columbia Economics Review

space?). We could also think about how this correlation with other artists affects an artist’s career earnings, and thus draw some potential conclusions on the issue of maximal versus minimal product differentiation in the art market.

Conclusion While economists have looked at topics like the amount of creativity an artist may choose to use on the production of a given painting, and the relationship between the economic and the cultural considerations of an artist with regard to her work, little has been written about how artists may choose to design their style and their brand, the definition of “innovation” in the art market and how it takes place, and the relationships between artists and their products. My attempt was to visualize a product space of artists and their styles as a framework that would facilitate thinking about each of these issues.

there are those concepts that may be wholly beyond models.

At the end of the day, while there are aspects of the art market that may be much better explained by the art historians who have studied the lives and the historical contexts of these artists, there is certainly an opportunity for each of the fields of Economics (particularly Industrial Organization), Art History, and Sociology to incorporate some of their respective methods to begin answering some of the big questions regarding art.

And then, there are those concepts that may be wholly beyond models. How can we model inspiration, quality, the underlying motivations behind the messages artists want to convey, the contribution of personal, political, and social crises to artistic creativity, and generally the immeasurable, indefinable, transcendent aspects of art?

If art boils down simply to how different people see the world around them, in that sense, perhaps simple frameworks may be as far as we may go. But perhaps, for the time being, they’re just the first steps. n

Fall 2015

21

Run The Risk Value-at-Risk: The Effect of Autoregression in a Quantile Process Khizar Qureshi Massachusetts Institute of Technology Developed after the stock market crash of 1987, Value at Risk (VaR) utilizes statistical techniques to systematically measure and quantify financial risk. Supporters of it hail its greatest benefit in imposing a structured methodology for thinking critically about risk. Detractors on the other end object to its role in encouraging the kind of excessive risk taking that contributed to the financial crisis of 20072008. By looking at a number of the existing VaR models, Qureshi weighs in on this debate, speaking to some of its shortcomings and suggesting methods for increasing its accuracy. While there is yet no consensus on the debate, VaR’s usefulness to risk experts is clear nonetheless. -F.A.

Introduction The necessity for a diverse set of risk management tools was exhibited clearly in several recent financial disasters. Traditional models of risk management frequently rely on trivial probabilistic tools and often fail to relax key assumptions for the underlying statistics. An effective tool for risk management should be a withstanding measure of uncertainty that is robust to a large set of situations, suitable for its users, adaptive to complex situations, and compatible for various sample sizes. Risk management is not simply a tool to establish the upper bound on a loss, but also a preventative measure that should lead to the development of an informed decisionmaking process.

Perhaps the most well known tool for risk management amongst finance practitioners is Value at Risk (VaR). Conceptually, VaR measures the supremum of a portfolio’s loss with a particular level of confidence. Consider a portfolio of unitary value with an annual standard deviation of 15%. The 95% daily VaR is simply the product of the daily standard deviation and the total value, or 1 × 2.35 × 0.15 = 0.3525. We say with 95% confidence that on a given day, the maximum loss im-

plied by VaR is 0.3525 for the one dollar portfolio.

A more rigorous definition of VaR is a particular quantile of future portfolio values, conditional on current information. In particular, we say that P (yt < −V aRt |Ωt-1 ) = α, where yt is a return corresponding to time t , Ω is the set of available information on an approximate basis, and α is the confidence level or probability. The immediate considerations for a legitimate, functional model include a closedform representation, a set of well defined intermediary parameters, and a test to validate the proposed model. In advance of our model proposition(s), we will review and evaluate existing models for VaR. The remainder of the paper is organized as follows. Section II will introduce and evaluate existing models for Value at Risk, all of which will guide us in constructing CAViaR. Section III will cover the notion of Conditional Autoregression, the understanding of which is critical to realistic noni.i.d processes. Section IV will incorporate various methods of testing quantile regression, which will enable us to compare the set of well known models with ours. Section V will focus on the empirical test of CAViaR on IBM, GM, and

Columbia Economics Review

SPX time series data. We will conclude with section VI. Existing Models VaR has developed into a quintessential tool for portfolio management that enables funds to estimate and efficiently allocate the cost of risk. Moreover, a growing number of regulatory committees now require institutions to monitor and report VaR frequently. Such a measure helps prevent excessively levered positions and transparency of the “worstcase scenario.” While the importance of VaR is agreed upon nearly globally, the methods of estimating it vary across both markets and firms. For ease and convenience of terminology, we will refer to all institutions and funds concerned with monitoring VaR as “holders.”

One component that often varies between different VaR models is the method by which the distribution of portfolio returns is estimated. The beginning of this paper introduced a rudimentary example in which returns were assumed to be independently and identically distributed, or i.i.d. As we will see, however, returns almost never follow a martingale process, but rather, are Markov. The calculation of

Fall 2015

22 returns falls within two categories: 1. Factor Models: Here, a universe of assets is studied for its factors, all of which are correlated.

Thus, the time variation in the risk of the portfolio is derived from the volatility of the correlations. A well known example is the FamaFrench fourfactor model.

The approach, however, assumes that negative returns follow the same distribution as nonnegative returns. Perhaps an even more alarming assumption by such models is the homoscedasticity between returns per unit risk.

2. Portfolio Models: Here, VaR is instantaneously constructed using statistical inference of past portfolios. Quantiles are then forecasted via several approaches, including Generalized Autoregressive Conditional Heteroscedasticity (GARCH), exponential smoothing, etc., most of which incorrectly assume normality. Moreover, these models assume that after a certain amount of time, a particular historical return has probability zero of recurring.

Needless of an empirical demonstration, we can deduce that portfolio models will underestimate VaR after time T, and factor models will fail to account for autoregression. Interestingly enough, the last decade has sparked the introduction of extreme quantile estimation, and the notion of asymptotic tail distributions.

Many of these models, however, are only representative of especially low (< 1%) quantiles, and do not relax the weak i.i.d. assumption.

We will study the asymptotic distribution and account for autocorrelation under various regimes

Conditional Autoregressive Value-at-Risk We now address many of the concerns expressed above with CAViaR. In particular, we will study the asymptotic distri-

bution and account for autocorrelation under various regimes. Suppose that there exists an observable vector of returns, .

We denote θ as the probability associated with the Valueat Risk.

Letting xt be a vector of time t observable variables (i.e. returns), and β be a vector of unknown parameters, a Conditional Autoregressive VaR model may take the following form:

Interpretation: The quantile of portfolio returns at a time t is a function of not only the past period returns, but also the past period quantile of returns. That is, . The lag operator in the third term, l, links the set of available information at t − j to the quantile of returns at t. The autoregressive function, , creates a smooth path between t i m e oriented quantiles. The first term, , is simply a constant. The example provided at the beginning of the paper, which does not account for autoregression, would simply remain a constant: .

Now that we have developed an understanding of the basic form for a CAViaR model, we will explore a few examples.

Adaptive Model: In general, an adaptive model follows the form

Symmetric Absolute Value The SAV model takes the form The SAV is an autoregressive model in which a change in returns, regardless of its direction, results in a change in VaR. What is particularly useful about this model is its ability to generalize volatility in portfolio value. However, it is because of this very feature that SAV should not be used as a primary tool for measurement. Consider a series of large deviations in portfolio value, alternating upwards and downwards. While the longrun change in value is zero, the VaR implied by SAV would be unrealistically high. Similarly, a series of small deviations would imply an unrealistically low VaR.

Columbia Economics Review

Asymmetric Slope The AS model takes the form The AS model is intended to capture the asymmetric leverage effect. Namely, it was designed to detect the tendency for volatility following a negative return to be greater than that of a positive return of equal magnitude. The model relies on magnitude of error, rather than squared error, as in GARCH Indirect GARCH(1,1) The Indirect GARCH model takes the form

While the GARCH model is estimated by maximum likelihood, Indirect GARCH is estimated via quantile regression.

Autoregressive Parameters and Regression Quantiles

How are the underlying parameters actually measured?

Thus far, we have understood the general form of a Conditional Autoregressive Value at Risk model, and have also seen several possible forms. The main difference between any pair of CAViaR models is their organization and treatment of βi , the regressive parameter. In the case of SAV, we were interested in a β that reflected magnitude of change in portfolio returns, while in AS, we were only interested in the extreme ends of a series of returns. The question now is: how are the underlying parameters actually measured? Koenker and Basset (1978) introduced the notion of a sample quantile to a linear regression. Consider a sample of observations y1 , . . . , yT generated by the linear model

where xt is a length p vector of regressors (i.e. returns), and is the θ quantile of θt conditional on xt .

Consider the linear representation of an adaptive process: .

Fall 2015 The θ regression quantile is βˆ to satisfy the objective

Qualitatively, we adjust beta until VaR is no longer exceeded, or “hit” by a certain amount. Such a condition is satisfied when the observed indicator variables are 0. To account for the set of available information, we use the following equation: Theorem 1 (Consistency). For generalized model (8), in probability, where

solves

Proof left as exercise for reader Theorem 2 (Asymptotic Normality). In testing for asymptotic normality, for statistic T,

Proof left as exercise for reader Testing Quantile Models While the expanded models available now account for both the autocorrelation of returns and the large deviations, they must be tested. Given a new observation, the model remains valid if P [yt < ft (β0 )] = θ. If such a condition holds for the entirety of the time series, then it is proven valid.

As shown by Christoffersen (1998), such a method is equivalent to testing for the independence of indicator variables for the same condition. In other words, While this provides for a natural test of forecasting models, it does not fully assess the validity of quantiles. To test conditional quantile models, we introduce a representative indicator variable that changes with the quantile itself. Define a sequence

23

of independent random variables {zt} such that

Expressing positive or negative autocorrelated returns in terms of zt indeed accounts for the probability of exceeding a quantile. However, whilst the unconditional probabilities are uncorrelated, the conditional probabilities for a hit still depend on one another. Because these tests evaluate the lower bound of the VaR in the weakest sense, we work towards defining a dynamic quantile. Let

H itt (β0 ) assumes a value of (1 − θ) for underestimations of VaR, and −θ otherwise. Notice that the expected value is zero, and that there should be no autocorrelation in the values between successive hits.

For our first test, we determine whether the test statistic, T − 2 X 0 ( )H it( ) is significantly different from z e r o where Xt ( ), t = 1, . . . , T may depend on and is qmeasurable information (i.e. returns). Suppose we wish to test the significance of an entire set of data along several β simultaneously. Then, let

Here, H is a diagonal matrix with binary indicators conditioned on available information, running both insample and outofsample. We will define and prove the conditions of each.

Theorem 3 (InSample Dynamic Quantile Test). If the assumptions made (see appendix) are valid, the following holds Proof. Proof left as exercise for reader Essentially, the DQ test above tests whether or not the test statistic follows a normal distribution in the sense of an identity matrix, and whether the set of all dynamic quantiles insample follow a chisquared distribution. We now shift our focus to a test statistic for dynamic quantiles outofsample.

Theorem 4 (OutofSample Dynamic Quantile Test). Let TR denote the number of insample observations and NR denote the number of outofsample observations.

Then Columbia Economics Review

Proof. Proof left as exercise for reader Use of the dynamic quantile tests allows for an estimation of the independence in “hits”. The ideal quantile test would be one in which all hits (yt < V aRt ) are independent. Regulators would be able to choose between different measures of VaR when evaluating a portfolio.

Empirical Results The historical series of portfolio returns were studied for four different regimes of CAViaR. A total of 2,553 daily prices from WDRS/CRSP for General Motors (GM), International Business Machines (IBM), and the SP 500 (SPX) were retrieved. Daily returns were computed as 100 times the difference of the log of the prices. Two sets of ranges were used: one from April 7, 1986 to April 7, 1999, and the other from April 7, 1999 to June 1, 2009. From the total set of daily prices, 2,253 were used insample, and the last 300 were used outofsample.

Both 1% and 5% dayend VaR were estimated for each of the four regimes.

The optimization was completed using MATLAB R2015 and Gurobi Optimizer under a QuasiNewton Method. The loops for recursive quantile functions (i.e. SAV) were coded in C. Optimization Methodology Using a random number generator, n vectors were generated, each with uniform distribution in [0, 1]. The regression quantile function was computed, and from the n vectors, m n vectors with the lowest regression quantile criteria were selected as initial values for optimization. For each of the four regimes, we first used the simplex algorithm. Following the approximation, we applied a robust quasiNewton method to determine new optimal parameters to feed into the simplex algorithm.

This process was repeated until convergence, and tolerance for the regression quantile was set to 10−10 .

Simplex Algorithm The algorithm operates on linear programs in standard form to determine a feasible region. The first step of the algorithm (Phase 1) involves the identification of an extrema as a guess. Either a basic feasible solution is found, or the feasible region is said to be empty. In the second step of the algorithm (Phase 2), the basic feasible solution from Phase 1 is used as a guess, and either an optimal basic feasible solution is

24

found, or an infinite edge.

Quasi-Newton Method

Fall 2015

ing regimes: (a) Symmetric Absolute Value; (b) Asymmetric Slope; (c) Indirect GARCH; (d) Adaptive.

QN methods are used to locate roots, local maxima, or local minima if the Hessian is unavailable at each step. Rather, the Hessian is updated through analyzing gradient vectors. In general, a second order approximation is used to find a function minimum. Such a taylor series is

toregressive models capture nonsystemic risk. While the market crash in 1987 affected all betapositive assets, we also see less severe increases in VaR during 1999.

With high probability, this is due to an idiosyncratic event–a total inventory recall by GM. Such a recall likely created uncertainty in expected cash flows, thus increasing the periodic volatility of the stock. The persistent volatility was exponentially weighted in the adaptive regime, resulting in a significant increase towards the end of the period of study.

for a gradient ∆f and a Hessian approximate B, the gradient of the approximation is Interpretation with root CAViaR Results We now review Conditional Autoregressive ValueatRisk, methodology introduced by (Engle, Man ganelli, 2001). First we review results from 19861999. Then we extend to 19992009. To test the significance of autoregression, we study values of βt−1 , as well as pvalues, for three regimes. Finally, we compare results of conditional VaR to unconditional VaR., the traditional risk measurement tool.

Figure 1: The figure below shows 5% CAViaR plots for GM under the follow-

As previously discussed, the arrival of information creates uncertainty, and increases VaR. While this is true in both the conditional and unconditional cases, it is emphasized in the former. It is wellknown that the period between 1986 and 1999 was volatile, and was affected by events such as LTCM and Global crises in Russia and Asia. If VaR truly increases with the arrival of information, then it is sensible to observe the peak in 1987, where all positive beta assets faced an increase in systemic risk with the market crash. The adaptive regime adjusts for changes in VaR, so the momentary increase in 1987 was given less weight.

It is also interesting to note that the auColumbia Economics Review

Figure 3: The figure above shows the News Impact curve for 1% VaR estimates of the SP500. For V aRt−1 = −1.645, the curves show how VaRt changes with lagging portfolio returns (x). The AS curve suggests that negative returns may have a much stronger effect on the actual VaR estimate than do positive returns.

Fall 2015

Table 1: The table above shows the regressive parameter β2, for each asset under each of the three CAViaR regimes. With the exception of IBM by a slight margin, all three assets suggest significant autoregressive VaR at the 95% level for (a) Asymmetric Slope and (b) Symmetric Absolute Value, and (c) Indirect GARCH.

Figure 4: The figure above shows the 95 % VaR for Exxon Mobil calculated through unconditional quantile regression.

Figure 5: The figure above shows the 99 % VaR for Exxon Mobil calculated through unconditional quantile regression. The VaR for quantile p = 99 is higher than the VaR for quantile p = 95 both in mean and in distribution. This is because the maximum loss must be determined with more certainty.

Broader Interpretation The arrival of news results in an expansion of information available. If the market is truly efficient, asset prices will reflect the expectations of those exposed to this information (Fama, 1997). However, expectations are not always dynamic, and

integration of information may not be continuous. Consequently, volatility, a form of uncertainty, will be autoregressive on a particular day while depending on the volatility of previous days. It becomes necessary to use autoregression when calculating the expected loss within a p−quantile.

We demonstrate several adaptive models, including Symmetric Absolute Value, Asymmetric Slope, and Indirect GARCH (1,1). We recognize that while all of these models satisfy the requirements of autoregression, they differ in their treatment of βt , the autoregressive parameter. When evaluating Value at Risk, conditional on information, we must carefully choose the model, and understand its underlying assumptions.

It is well known that for a monotonically increasing cumulative distribution function, an increase in p will cover a larger portion of the distribution of risk. An immediate consequence of this is that the 99% VaR exceeds the 95%. We reconfirm that notion. We show that conditioning on the arrival of information may increase or decrease VaR, depending on the change in expectation. We contrast conditional against unconditional VaR, and autoregressive against independent VaR. In both contrasts, the former is a more proper treatment.

Conclusion We have demonstrated the autoregressive properties of VaR conditioned on information available. Existing methods for calculating VaR fail to relax several assumptions including (i) the i.i.d. behavior of returns and (ii) the large deviations at the tail of the return distribution. CAViaR addresses both issues, and suggests that there is significant autocorrelation for the data used used (GM, IBM, SPX 19992009).

Regressive parameters (βi ) were estimated through minimizing the regression quantile loss function, and the models were tested via dynamic quantiles.

The worst performing method was the adaptive method, which failed to detect poor returns in 1999. The best performing method was Asymmetric Slope, which captured the larger effect of negative returns vs. positive returns on VaR. Symmetric Absolute Value (SAV), which does not segregate positive and negative returns, illustrated general portfolio movement. Indirect GARCH, which does not distinguish tails of distributions, overemphasized movement in 1999, 2001, and 2009. These very same results are reflected in the 1% SPX News curves, which study the effect of newsdriven returns on the SP 500.

Columbia Economics Review

25 Standard, nonconditional quantile regressions were studied for XOM, a largecap stock similar to GM. Without autoregressive properties, 95 % VaR was underestimated relative to the CAViaR case. Such a result motivates the use of multiple risk measurement tools, each carrying different treatment of (βi ) and distinct underlying assumptions.

The most typical use of VaR involves determining the expected loss with 95% certainty. While useful as bare approximations, a more proper analysis of risk should be carried across various quantiles and multiple distributions. Moreover, the loss function for a given day should be clustered within time frames. We have reconfirmed that volatility is autoregressive and conditional on the arrival of information. Treating value at risk independently will almost surely underestimate maximum losses during periods of high volatility and overestimate during periods of low volatility. The use of multiple tools may be beneficial to financial institutions, the individuals they represent, and the wellbeing of market participants as a whole.

volatility, a form of uncertainty, will be autoregressive on a partcular day while depending on the volatility of previous days Extensions Future applications include: smaller time frames, different sets of stocks, an extension to the multivariable case, and quantile sensitivity. It is also worth investigating the implied volatility of outofthemoney options calculated under the conditional and nonconditional regime. We expect the skew to carry more weight in the conditional regime to account for disasterous risks.

There also exists potential to improve the methodology used within the paper.

Namely, cost regularization of autoregressive parameters, and local inference of Hessian matrices to employ interior point methods for optimization n

26

Fall 2015

No Brain, No Gain Migration, Development, and the “Brain Drain”: Dynamic Effects Between Migration and Growth Measures Andrew Barnett Princeton University

The journey followed by large numbers of migrants, frequently featured in modern media and discussed in fierce policy debates, is certainly reshaping the world’s cultural and economic landscape. Just as migrants’ presence has a significant impact on the countries to which they travel, both their absence from their native lands and continuing interactions with their home countries bear great influence on developing economies throughout the world. The migration of skilled individuals from developing to developed countries leaves a dearth of human capital, referred to as a “brain drain,” in their home countries. In this paper, the author explores the effect of the “brain drain” on economic growth in small developing countries. Using three different methods involving panel vector autoregressions, the author found no statistically significant effects of the outflow of skilled migrants on these countries’ GDP growth per capita. This result raises valuable questions in development economics: additional research is needed to identify which effects of the “brain drain” may be offsetting each other — and to what magnitude they do so — to produce no significant change in GDP growth per capita. – M.R.

Homo sapiens, originating in Africa, has managed to inhabit nearly every corner of the world through its impressive migratory skills — first out of Africa, then to Europe and Asia, and finally the Americas and Oceania. Indeed, human migratory patterns have profoundly shaped history — for how the heterogeneous migratory patterns of European settlers over 200 years ago have shaped the development and institutions of countries even to this day. By no means has this process stopped — there were over 190 million migrants in 2005, representing 2.9% of the world population at that time. This is an increase from 75 million migrants in 1960, and the increase has slightly outpaced population growth (Docquier and Rapoport, 2012). However, what is most notable about these figures is their distribution — the number of migrants from “developing” to “developed countries”

(i.e. the US, Canada, New Zealand, Australia, Japan, and countries in the EU-15) and the share of migrants with tertiary education have both risen fourfold over the period from 1960 to 2005. Although part of this change in migration demographics can be accounted for by changes in population dynamics, part is due to a “brain drain”; that is, the migration of skilled professionals with university training from developing to developed countries has risen quite rapidly. Indeed, the rate of high skill migration (the percentage of educated workers in a country migrating) is 12.8% in Sub-Saharan Africa and over 40% in the Caribbean and Pacific Islands, while it is less than 1% in the US and Canada.

Such a disparity in migration rates creates headaches for the governments of these small and developing countries, who worry if their expenditures on edu-

Columbia Economics Review

cation are being “wasted” on individuals who will soon migrate to more developed countries. These countries often publicly decry the migration of their most skilled individuals, while those in developed countries often take the opposite perspective and try to encourage the immigration of more highly skilled individuals. This tension between the interests of the developing and developed world creates a situation of international intrigue, made more compelling to us as economists by the fact that barriers to migration and labor mobility are key drivers of the large disparity in average incomes across countries.

Although the practical implications alone make understanding the effects of brain drains a compelling area of research, the analysis of brain drains raises some questions that are at the heart of development economics. For example, while some argue that brain drains may have

Fall 2015 negative developmental effects on the sending countries, other scholars argue that they could be viewed positively for the welfare gains reaped by individuals of those countries. Indeed, it is apparent that the individual migrants are better off by revealed preference, as the choice to migrate is generally voluntary. The important implication of this fact is that skilled migration is then Pareto efficient if the sending (developing) country is neutral or better off after a brain drain (under the uncontroversial assumption that the receiving country is better off ).

determining the effects of brain drains is fundamentally, at least in the long run, a question about growth However, the trillion dollar question still remains: are developing countries better or worse off after a brain drain? Do the positive externalities of a brain drain (e.g. remittances, currency stabilization, increased expected returns to education, network effects) have any noticeable impact, and if so, do they outweigh the negative externalities (namely loss of human capital useful for adopting and using technology and supporting institutions)? If we take “better off” to mean higher GDP/capita, and if we realize that increasing GDP/capita over time is the same as increasing the growth rate of GDP/capita, it now is apparent that determining the effects of brain drains is fundamentally, at least in the long run, a question about growth. We know from Hall and Jones (1999) that total factor productivity (TFP) and human capital are in that order the two most significant reasons for differences in productivity per worker across countries, but the net effect of a brain drain and all that it encompasses have ambiguous effects on TFP and human capital. Some articles show empirically and theoretically that skilled migration contributes to TFP growth by facilitating the diffusion of ideas from developed countries back to developing

countries. Marchiori, Shen, and Docquier (2013) take a more technical view of the effects of brain drains. Their theoretical model leads them to state that while the overall effect of a brain drain depends on many factors, “the certain losers of brain drain are those countries that have already experienced large outflows of their highly skilled,” a likely reference to the African, Caribbean, and Pacific Island nations with large migration rate for their skilled workers.

Indeed, as it stands, the net effect of skilled migration on the growth of countries, developing countries in particular, is not completely understood. The economic literature has reached a consensus about neither the magnitude nor the direction of these effects. With that in mind, this paper addresses the following question: what are the dynamics between brain drain’s effects (measured as skilled migration and remittances) and growth (measured as income and human capital growth)? Understanding that brain drain effects are likely to be highest where the rate of skilled migration is highest, I will focus my analysis for the time being on the effects of a brain drain on small developing countries, with the assumption being that if the effects are not significant in those countries, they are unlikely to be significant anywhere. This also serves to simplify the analysis. To answer this question, I look at growth rates in human capital and GDP/capita, as well as the number of skilled migrants and the value of their remittances sent home. In order to deal with the obvious endogeneity issues (e.g. a recession causes people to leave, but people leaving might hurt GDP growth), I follow in the footsteps of Budvytyte and Kasnauskiene (2013) and perform a vector autoregression and then look at the impulse response functions in response to shocks in the number of migrants or the value of remittances.

In addition, since I am dealing with longitudinal data for multiples countries, I run a panel vector autoregression in order to handle state-dependent effects on growth. I use data collected from the UN and World Bank on remittances and GDP, from Barro on human capital, and from the IAB for bilateral migration matrices broken down by education level.

Literature Review This paper deals with the topics of brain drain, the migration of educated/skilled workers from developing to developed countries. There is not yet a consensus regarding the effects of the brain drain Columbia Economics Review

27 on growth for developing countries, but “Eight Questions about Brain Drain by Gibson and McKenzie (2011) provides a solid introduction and states what we do know about brain drain. Relevant to this discussion, skilled migration levels are increasing worldwide, but the overall brain drain rate is more or less constant after adjusting for increases in education over the years. However, the brain drain is increasing from developed countries to developed countries. We also know that brain drain rates are increasing with factors relating to political instability, and that migration rates are generally the highest among the most educated, as they are the best equipped to navigate the bureaucracy (Gibson and McKenzie, 2010).

the overall brain drain rate is more or less constant after adjusting for increases in education over the years More tenuously, there is also some evidence of possible brain gains - that the mere possibility of migrating to a country with higher wages increases the expected return to education, which may in certain circumstances increase the overall human capital of the original country. Related to the brain drain, there is also evidence of positive network effects leading to faster technology adoption and TFP growth. Positives for the brain drain are potentially higher remittances sent home by the migrants, potential brain gain effects, positive network effects (for trade, investment, and research), and potentially serving as a check on the home government (by preventing it from paying artificially low salaries, examples). Negatives include most notably the loss of human capital, loss of skills needed for long run development, and the lack of intellectual influence on home institutions.

First, I note that a Solow growth model augmented to account for human capital matches our observation much better and that differences across countries in human capital and TFP explain al-

28

Fall 2015 mists have tried to capture the possible dynamic effects of migration on growth or related measures. For example, Lodigiani (2008) looks at panel data for migration and TFP data with entity and time varying effects. From this data, Lodigiani concludes that while time has a minimal effect, skilled migration from developing countries can speed the diffusion of technology from the developed to the developing. However, she does not consider remittances in her analysis. This is appropriate for her analysis of technology diffusion, but limits the applicability of her results to income growth for a country.

when the probability of migration is not too high, the loss of human capital to migration is outweighed by an increase in the expected return to education most the entire difference across countries in terms of TFP. It then stands to reason that factors determining human capital and TFP significantly impact growth. It is apparent how the brain drain might affect these two variables (e.g., skilled migration reduces the current human capital stock now but may increase it later via brain gain effects, while remittances may boost TFP by allowing for investment in and adoption of better technology), but issues arise when trying to determine the net impact of these forces.

From a theoretical perspective, Mountford (1994) establishes the plausibility of a beneficial brain drain using a simplified Galor and Tsiddon model. That is, he finds that when the probability of migration is not too high, the loss of human capital to migration is outweighed by an increase in the expected return to education, which leads to an overall increase in human capital and growth. However, this model ignores remittances and does

not consider the effect that a negative shock to GDP might spur the skilled to migrate to greener pastures. Still, Beine, Rapoport, and Docquier (2001) later show that the idea of beneficial brain drain is more than a theoretical possibility using an instrumental variable to recursively estimate a system of three equations (migration, human capital, and growth).

In particular, they show with statistical significance that a beneficial brain drain can exist in certain situations. However, as they explicitly point out, their model does not examine potential dynamic effects between growth and migration variables, as that would require panel data and a harmonized time series on human capital levels. Fortunately, with Barro and Lees (forthcoming) release of a cross-country time series on human capital levels, it is now possible to do such an analysis and examine the dynamic effects of growth variables and migration related variables.

Since Beine et alâ&#x20AC;&#x2122;s paper, other econo-

Columbia Economics Review

A complimentary result from Tabata, Suzuki, and Nakanishi (2010) comes to a similarly positive conclusion, using a vector autoregression for remittances and several financial and economic indicators (e.g. trade deficit, unemployment), to conclude that remittances have a positive effect on Asian economies. While their analysis does not include skilled migration and is not a paper on the brain drain per se, in conjunction with Lodigiani (2008), these results suggest that skilled migration and remittances have positive effects, at least in some circumstances. However, one cannot make any serious conclusions until the likely significant dynamic effects of remittances and skilled migration are accounted for in the context of growth, as it is likely that an increase in skilled migration may lead to an increase in remittances (Bollard, McKenzie, Morten, and Rapoport, 2011).

A paper that comes close to determining the dynamic effects of skilled migra-

Fall 2015 tion and remittances on measure of growth (e.g. human capital growth, GDP/capita growth) is a recent paper entitled Brain Drain in Globalization by Marchiori, Shen, and Docquier (2013). They construct a sophisticated dynamic general equilibrium model that takes into account factors such as geography and financial restrictions to examine the effects of a brain drain on growth. In order to estimate these dynamic effects, they estimate the parameter value for variables in their model, and then project the relative changes to their forecasts given a shock to a parameter. While a very interesting exercise, I note that the dynamics they observe are highly dependent on their numerous structural assumptions that they use to construct their comprehensive model.

As we have seen, the current literature regarding the effects of brain drain on growth either makes structural form assumptions that may not hold, does not address dynamic effects or endogeneity concerns, or addresses a related but more specific effect of the brain drain. Notably absent is a comprehensive analysis on the dynamic effects of the brain drain on growth measures. Therefore, as I simply want to determine the dynamic effects of the skilled migration and remittances on growth, I will eschew the structural assumptions and use a reduced form vector autoregression to calculate the effects. This provide a more comprehensive dynamic analysis with reduced endogeneity and structural form concerns.

Data Variable Selection The first task in determining a model that measures the effect of a brain drain on growth in a small developing country entails determining what variables belong in the regression. Following in the footsteps of Lodigiani (2008) and Beine, Docquier, and Rapoport (2001), variables that I will include in the regression are human capital growth (∆h), GDP/capita growth (∆GDP P C ), remittances as a percentage of GDP (rem), and the share of skilled migrants (net) relative to the entire population (θi,t ), and transformation of them.

That is, if the goal is to look at the effects of skilled migration on measures of growth, I must include those variables. I pick the share of skilled migrants (net) relative to the whole population in order to account for the varying sizes of different countries.

Beine et al (2012) made a similar choice of representing remittances as a percentage of GDP . However, unlike Lodigiani, I do not

include time dummies in the regression, as her own evidence suggests that time varying effects have a minimal impact, if any, on growth (2008). I do include a population measure in the form of population growth, but contrary to Beine et al (2001), I do not include possible interaction effects with country size. I do this because I have already limited my analysis to smaller countries and have adjusted for effects to be relative to size (i.e. choosing remittances as a share of GDP and skilled migration rates, not levels). Moreover, since I am doing a time series analysis, I prefer to look at growth measures (essentially a normalized first difference) instead of levels because doing so absolves some of the problems inherent in analyzing highly persistent time series like GDP per capita. However, for completeness, I will also be measuring the variables in levels.

i simply want to determine the dynamic effects of the skilled migration and remittances on growth Data Sources Having identified which variables will be used in the analysis of the impact of skilled migration and remittances, have on growth, the task becomes finding data for the variables. For human capital, I will use Barro and Lee’s excellent dataset from 1950-2010 on educational outcomes for 146 countries, recorded in 5 year increments.

To measure human capital growth (∆hi ) for a country, I look at the logged difference between the share of individuals over 25 years of age who have complete tertiary education, which approximates the growth rate over a period (as can be seen by a simple Taylor series expansion). This approach closely follows Beine et al (2001), except with a better dataset for human capital.

In order to measure the growth GDP/ capita (∆GDP P C ), I use a time series for population and another for GDP (in current US dollars). I then use both of these to construct a GDP per capita time series, which can then be logged and differenced

Columbia Economics Review

29 to get the growth in GDP/capita for individual countries period to period. For the population time series, I use United Nations Populations Division World Population Prospects 2012 revision (UN Department of Economic and Social Affairs, 2013), which is a time series for the populations (in thousands) of 268 current and present nations from 1950 to 2012. Similarly, I use data from the United Nations Statistics Division to get a time series of GDP in current US dollars from 1970 to 2011 of 218 current and former countries (United Nations Statistics Division 2012).

For data on migration across countries, I use the IAB brain-drain data set, which is a panel data time series from 1980 to 2010, broken down into 5 year increments.

The dataset breaks down the immigration population of 20 developed economies by education level and sending country. This makes it easy to calculate θi,t — simply sum the number of educated migrants in the OECD countries at time t for a particular source country, and subtract the number of educated migrants from that source country at time t − 1 to get the number of people from the source country who have migrated in the interim. This becomes the share of workers who are skilled and migrants after division by the population of the source country at time t. That is,

where educated.migrantsi,t is the number of educated individuals who migrate from country i at time t, educated. immigrantsji,tis the stock of educated immigrants in country j from country i at time t, and populationi,t is the population of country i at time t. Ideally, θt would be sampled every year, but since there’s no comprehensive annual data set on migration, I am constrained to look at 5 year increments.

Finally, I will measure remittances using an annual time series for remittances from 1970 to 2012 from the World Bank (World Bank Data and Research, 2013). This dataset contains remittance data on the country level for 213 countries, measured in million of current US dollars. However, care will have to be taken in analyzing this dataset, as the countries for which I will be analyzing have the least remittance data and shortest time series.

Country Selection Although I have previously stated that I will conduct my analysis on small developing countries, I will now formally

Fall 2015

30 clarify this criterion. According to the World Bank, low-income countries have GDPs per capita of less than $1,035, while lower-middle-income countries have incomes from $1,035 to $4,085 (2014). Similarly, Docquier defines small countries as countries with less than 2.5 million people and lower-middle sized countries as countries with between 2.5 and 10 million people (2006). Given the issues with the data available - many countries lack data for at least one of the variables of interest at least once between 1980 and 2010 â&#x20AC;&#x201D; there are actually no countries that are both small and developing by those definitions that also have data for all periods. At the same time, if we extend the definition of small developing countries to include lower-middle income, lowermiddle sized countries, we actually pick up several more countries, all of which are arguably small developing countries in more casual definitions of the terms (e.g. Togo, Benin, and Nicaragua, among others). Increasing the threshold of lower-middle-income to $5,000, I now have 13 countries to run my analysis on, a small sample but sufficient for my analysis. The list of these countries along with their GDP per capita and population can be seen below in Table A, and a more comprehensive list of these countries with summary statistics for 2010 can be found in the appendix as Table 1.

Table A: GDP per Capita and Population for 13 Small Developing Countries Country Albania Benin El Salvador Fiji Haiti Honduras Jordan Lesotho Nicaragua Papua New Guinea Paraguay Swaziland Togo Units

GDP/ Capita 3,730 741 3,460 3,686 608 2,026 4,270 1,003 1,138

Population

1,415 2,840 3,281 526 $ (2010)

6,858,945 6,459,721 1,193,148 6,306,014

3,150,143 9,509,798 6,218,195 860,559 9,896,400 7,621,204 6,454,554 2,008,921 5,822,209

Other Concerns While I have done my best to find the highest quality data available, there are still several reasons to be concerned about use of this data in empirical analysis. For

example, I am only using countries for which the time series are complete from 1980 to 2010 for all variables. This is often not random, and often excludes countries that experienced times of turmoil (such as Burkina Faso during the late 1990s), which may skew the results, and rule out less stable countries. There is not much that can be done to get around this problem, so the analysis will proceed as usual.

macroeconomic data is notoriously hard to estimate precisely and credible sources can disagree in their estimates of key macroeconomic figures At the same time, there is also the issue of measurement error â&#x20AC;&#x201D; macroeconomic data is notoriously hard to estimate precisely, and credible sources can disagree in their estimates of key macroeconomic figures. While this could cause attenuation bias in the analysis, this is likely mitigated by the use of quality datasets from the UN and World Bank. What is more problematic, however, is the possibility of a systematic bias to data, which can happen if estimates are based on or influences by government reports on the matter. There is not much to be done about the latter problem of bias in the reported data, but if there is classical measurement error, there are models that can control for that problem, and those models will be used in this paper.

Methodology Model Design Looking at the arrangement of the variables and the data to be used, several potential criticisms appear almost immediately, such as the significant endogeneity issues between the variables (does GDP fall because people migrate, or do people migrate because GDP fell?) and likely country specific effects, per-

Columbia Economics Review

haps owing to differing policies across the countries. With the full panel only running from 1980 to 2010 and the large number of variables present once lags taken into account, the issues of biasedness and over fitting also loom large over my results. However, I note that while I have panel data, by restricting the countries to be analyzed to small, developing countries, it is reasonable to assume that the regressors have similar behavior for each country. In order to deal with these issues, I use a panel vector autoregression to analyze the effect of the brain drain on growth, taking inspiration from Georgiadis (2012). He states that in the case of panel data with endogenous variables, one can address the issue of endogeneity by using a panel VAR framework, and then pooling the cross-sectional data of the countries to gain degrees of freedom.

This approach is particularly helpful when dealing with a vector autoregression on a relatively short time series, as the number of coefficients to be estimated rises geometrically with the number of regressors, quickly exhausting the available degrees of freedom.

Assumptions of fixed effects of heteroskedasticity make the model more flexible and capture at least some of the deeper difference across the countries Furthermore, by restricting my data set to small, developing countries, I reduce several structural differences between the countries that may lead to heterogeneous behavior and bias the coefficients.

Encouragingly, Gavin and Teodorou (2004) come to a similar conclusion when they show that despite idiosyncrasies across countries, the common model of the economy imposed by a panel VAR on separate countries successfully captures common macroeconomic dynamics and reduces forecasting error. Indeed, a panel

Fall 2015 VAR is an excellent tool for uncovering common macroeconomic dynamics that might otherwise be obscured by country specific idiosyncrasies.

Having settled on a panel VAR approach, it becomes necessary to specify the assumptions of the model in greater detail. While it is possible to specify the model so that all regressors and errors are time and country specific, the more common model is to assume homogenous time and country effects for the regressors with fixed effects and heteroskedasticity in the error. By restricting the analysis to small developing countries, it is reasonable to assume that the homogenous regressor holds, while the assumptions of fixed effects of heteroskedasticity make the model more flexible and capture at least some of the deeper difference across the countries. This is similar to the model used in “Estimating Vector Autoregressions with Panel Data, and my analysis henceforth will use the techniques and address the pitfalls described within the paper (Holtz-Eakin et al, 1988). Not only does this paper comprehensively cover many of the issues inherent to panel VAR analysis (such as shallow time series with large panels, measurement error, heterogeneity across units, hy- pothesis testing, among others), it also is the basis for the main empirical tool for analyzing panel VARs, the pvar package for STATA by Love (2006). Their model is for a panel VAR with fixed effects and heteroskedasticity, and is therefore highly applicable to the problem at hand. The only difference between their model and mine is that they only assume homogeneity for coefficients across countries but not across time. They do, however, provide a test for the hypothesis indicating that coefficients are stable across time (i.e. time stationary).

Note that while the panel VAR approach successfully addresses many of the limitations inherent in analyzing the effect of the brain on growth with the given data, it also limits the interpretation of the results. That is, in the words of Stock and Watson (2001) In data description and forecasting, VARs have proven to be powerful and reliable tools that are now, rightly, in everyday use. Structural inference and policy analysis are, however, inherently more difficult because they require differentiating between correlation and causation; this is the identification problem, in the jargon of econometrics.

Still, estimating the parameters governing the interrelationships between

31

growth and skilled migration can be done accurately and theoretically without bias.

With this in mind, I focus my efforts elucidating the connection between the brain drain and growth as a necessary first step to understanding their relationship more fully.

Model Estimation The general model for a panel vector autoregression is Yi,t = A(L)Yi,t + i,t

(2)

where A(L) is a matrix of coefficients on lags of the endogenous variables and Yi,t is a vector of endogenous variables, such that for the model in levels Yi,t=[GDPPCi,t,hi,t,θi,t,remi,t,popi,t] and the error term i,t

(3)

it

= fi + µt + νit

(4)

where fi is a vector of country-specific fixed effects, µt is a vector of time specific effects, and νit is a time and country specific effect, as in the model used by Nickell (1981). By assumption, µt = 0; that is, there are no time specific effects, which is made on the basis of previous work has suggested the lack of time specific effects in the brain drain context. I additionally assume E[A(L)Yi,t ∙ νit ] = 0 and e[νit ] = 0, i.e. νit is a classic noise term. However, given that broad, country-specific macroeconomic variables like GDP per capita growth and the education level of a country are likely relevant to other unobserved but important variables (such as country stability), we have that E[A(L)Yit ∙ i,t ] = E[A(L)Yi,t (fi + νit )] = E[A(L)Yi,t (fi)] = 0 (5) and so estimates of (2) will produce biased results in general. This is the general fixed effects model for panel data, which is usually dealt with by time demeaning the variable such that _ _ _ Yi,t−Yi =A(L)(Yi,−Yi) + (i,t− i ) (6) _ where Zi is the average of variable Zit for country i across all time periods.

However, as Nickell shows, this too will produce biased results in the autoregressive case, and hence the vector autoregressive case, because the lagged dependent variables are correlated with i (1981).

Columbia Economics Review

The approach suggested by “Estimating Vector Autoregressions” (Holtz-Eakin et al, 1988) and used in “Evidence from a Panel VAR” (Love, 2006) deals with this problem in particular. It also and estimates the coefficients of the model using the untransformed variables as instruments for the helmert-transformed (forward mean-differenced) variables.

This will remove the bias and fixed effects faced in the original specification of the model, but requires that there exist enough instrumental variables to identify the system of equations, which occurs when T ≥ L + 4, where L is the number of lags in the model (Holtz-Eakin, 1988). The assembled brain drain dataset in this paper has 7 time periods, occurring every 5 years from 1980 to 2010, and so the maximum number of lags my model can have is 4. However, the above model is complicated by the possibility of measurement error, which is almost certainly a problem with data like remittances for developing countries, even if the data comes from the World Bank. If we assume that the measurement errors are independent of observations and time, then we have classical measurement error, which in general can be dealt with by proper instrumentation of the variables, and applied in this paper.

Since our set of instrumental variables is smaller than the set of instrumental variables in the case with no measurement error, the model is only feasible when T ≥ 2L + 2, which in this case where T = 7.

This indicates means that the number of lags cannot exceed 2 when there is measurement error (Holtz-Eakin et al, 1988).

Having manipulated the model to take account of fixed effects and measurement error, the full model with heteroskedastic errors can be estimated. Following Heatz-Eakin et al (1988), in order to estimate the model, we rewrite the fully identified model for each of the variables in the panel vector autoregression as Y=WB+ ε (7) Define Y = [YL+3 > , ..., Y T> ]> , B= [BL+3>, ..., BT> ]> , = [ L+3 >, ..., T > ]> , W= diag[W L+3 >, ..., WT > ], ( diag denoting a block diagonal matrix here), where Yt = [y1t , ..., ynt ]> is the vector of observations from each country of one of the variables for time period t, Xt = [x1t , ..., xnt ] is the vector of the rest of the observations for time period t, e1 is the vector of ones, Wt = [e, Yt−1, ..., Yt−L−1, Xt−1, ..., Xt−L−1] is the matrix of regressors for the time period t, ε t =[ ε 1t , ..., ε 1t ] is the vector of errors at time period t, Bt = [a, c1 , ..., cm+1 , d1, ..., dm+1 ]0 is the

Fall 2015

32

vector of coefficients for the equations, as done by Holtz-Eakin et al (1988). Notably, I differ from the general model they presented by constraining the effects of the regressors to be the same for all time periods. Using the matrix Z of instrumental variables, written as Z = diag[ZL+3 , ..., ZT ] with Zt = [e1, Yt−2 , ..., Y1, Xt−2, ..., X1] being the matrix of valid instruments available at time t, the estimated coefficient matrix B^ for variable Y is calculated by using GLS with a consistent estimate Ω˜ of the covariance matrix (8) which both corrects for heteroskedasticity and measurement error, and is efficient in the class of IV estimators (Holtz-Eakin, 1988).

Model Selection When performing time series analysis with any sort of autoregression, it is necessary to properly select the number of lags in the model. While it is unlikely that a model with quinquennial data such as this one will have a lag greater than 1, it is possible that a higher order lag might be necessary to fully capture the dynamics of the model, which could operate over a very long time frame (e.g. the percent educated of a population having greater predictive power of GDP in 10 years compared to 5). With this in mind, I test for the correct number of lags using AIC as opposed to BIC. This is because, as BIC is “likely to be inconsistent in panel data models that include cross section specific parameters,” such as a fixed effects model. Meanwhile, , whereas minimizing the AIC is an asymptotically consistent, albeit not efficient, way to select the number of lags (Greenaway-McGrevy, 2013).

Upon determining the correct number of lags, I proceed to determine the validity of the model. As per Stock and Watson (2001), I will look at Granger causality to assess the predictive power one time series has for another time series as a measure of statistical significance, in lieu of reporting R2, which is hard to interpret given the dynamics of a VAR. That is, according to Stock and Watson (2001), ”Granger-causality statistics examine whether lagged values of one variable helps to predict another variable. For example, if the unemployment rate does not help predict inflation, then the coefficients on the lags of

unemployment will all be zero in the reduced form inflation equation.” In other words, the Granger causality statistics will help determine if my results are statistically significant. Mathematically speaking, a time series X Granger causes a time series Y if E[yt |yt−1, ..., xt−1, ...] = E[yt |yt−1, ...]

In the panel VAR framework, the null hypothesis of Granger non-causality is tested using a likelihood ratio test of the sum of square residuals for the restricted and unrestricted models, and is nested within the null hypothesis of time-stationary coefficients, which is tested use Wald statistics (Holtz-Eakin et al., 1988).

In particular, I will look to see if the time series for the skilled migration and remittances Granger cause the time series for GDP/capita growth.

i will look to see if the time series for the skilled migration and remittances granger cause the time series for gdp/ capita growth

Model Interpretation In looking at the impact of a brain drain on growth, it is useful to look at the impulse response functions for a surprise shock in the share of skilled migration on growth over a horizon of the next several years. Although I cannot attach a causal interpretation to it, especially in a reduced form VAR where the error terms are likely correlated, it is still informational for the policy maker as an indicator of the impact of a brain drain on growth. This is a similar approach to what Tabata et al (2010) used to analyze the effect remittances have on the growth

Columbia Economics Review

on Asian trade imbalances, although my focus is more growth and migration oriented as opposed to their remittance and finance focused study. For example, given a forecast error today in variable i, ui , the impulse response function gives the change in the forecasted value at time t + h, i.e.

(9) By looking at the impulse response function for each of my variables for several values of h, one can get a sense of the size and duration of the impact of the change in skilled migration or remittances on growth for future time periods.

Moreover, the impulse response function better captures the dynamics of the variables and is easier to interpret than the coefficients on the variables, and hence impulse response function graphs are an apt way of interpreting results.

Results and Discussion As stated before, the goal of this paper is to determine the effect of the brain drain, i.e. skilled migration, on growth for small, developing countries. This consists of two parts: seeing if skilled migration has any effect on GDP per capita growth once other key variables have been accounted for, and if so, in what direction. I showed in the methodology that the first part of this question can be answered with Granger causality statistics, and the second part can be answered by looking at impulse response functions for the VAR. While the model is constrained by shallow time series and a relatively narrow panel, the panel is still fully balanced and the panel vector autoregression is estimable. This allows me to compare my results with Beine et al (2001), who found little impact of migration on growth using a similar system of equations model analysis of brain drain an growth. I, however, differentiate between skilled and unskilled migrants due to the data presented by Barro and Lee (forthcoming). Moreover, my results will help evaluate the validity of theories regarding the brain drain and growth does the brain drain not affect growth, as suggested by some models, does it harm growth as is thought by some scholars and in popular culture as well, or can the brain drain help growth, as suggested by

Fall 2015 some recent theoretical models? To do this, I consider three models: a baseline panel VAR in levels with trends in GDP per capita and population accounted for, a model in growth rates to address heterogeneity and stationarity concerns, and finally, individual VARs between GDP per capita growth and skilled migration for each country.

This consists of two parts: seeing if skilled migration has any effect on GDP, and if so, in what direction

capita, which can be seen in the impulse response function b Graph A

As can be seen, while this suggests that skilled migration hurts GDP per capita for those who remain in the country, the effect is tiny and more or less economically insignificant - it would be unreasonable to prevent a skilled individual from migrating solely because the average worker would earn 30 cents less on average in the future. This effect isn’t masked by the effect of remittances either, which also has a similarly neutral, albeit slightly negative, effect on GDP per capita, as seen in graph b.

Graph B

Baseline Panel VAR Results The baseline panel vector autoregression that I consider looks at the variables in levels with GDP per capita and population trends. We try to reduce stationarity concerns, as we expect both GDP per capita and population to rise. If possible, the variables are modeled as a percentage (such as remittances / GDP) so that the panel VAR picks up the relative relationships between variables and is more robust to the differences in size of the countries. This also allows the estimation of the model using the full panel, improving estimates. Running the panel VAR on the set of detrended variables Y = [G, P, h, rem, θ], with all the variables as originally described but using human capital (percent of adults age 25 or older with tertiary education) instead of human capital growth. Given that the AIC selected 1 lag for the model (as expected since the data is quinquennial), the analysis here on our focuses on the model with 1 lag. The result of interest here is the effect of θ, the skilled migrant share of the population, on GDP per

The delayed negative effect of remittances as a share of GDP on GDP per capita is somewhat surprising - we might think that more into an economy helps (ceteris paribus). However, it’s also possible that more remittances induce people to work less, hurting the economy. At the same time, the effect is insignificant for the first several time periods after the shock, and even later effects pale in magnitude to the effect that a shock in other regressors have on GDP per capita (see Appendix B - interestingly enough, skilled migration and remittances seem to appear to have a minimal effect on each other as well). Moreover, the nested hypothesis of granger non-causality of

Columbia Economics Review

33

remittances’ share of GDP and skilled migration rates is very much not rejected. Thus, after first very strongly rejecting the null hypothesis of time stationary regressors, we can conclude that there is both economic and statistical evidence that proves the insignificance of remittances on GDP per capita.

it’s also possible that more remittances induce people to work less, hurting the economy

This result, or lack thereof, agrees with Beine et al’s empirical result (2001) that the skilled migration does not really affect growth. Additionally, these results suggest that the avenues through which skilled migration could affect the economy - increased returns to education, increased diffusion of technology, opportunity cost of lost human capital - balance out somehow. If this is true, then the implication for policy makers should be that they can stop worrying so much about the loss of their educated and skilled to other countries, because in the end everyone else is not worse off, and the migrants are surely better off by revealed preference. At the very least, policy makers in developing countries shouldn’t make their policies on skilled migration tougher, because the only one worse off is the potential migrant.

However, that preceding analysis was made on the assumption that the detrended panel VAR model was correct, and we have every reason to believe that may not be. A straight- forward criticism is that even though the model was estimated after removal of time trends, the model is still in levels and not relative metrics. Therefore, the model will weight effects from countries with larger populations and higher GDP per capita, which can be large relatively speaking even if only small on an absolute level.

Moreover, the linearity inherent in this

34 can lead to a violation in the model assumption of homogenous cross-country effects when using level effects - if a country’s GDP is growing a 4% annually for all countries, the dollar amount by which GDP per capita increase by is twice as high for a country with a GDP per capita of $2, 000 compared a country with a GDP per capita of $1, 000. This bias alone could lead to misleading results and obfuscation of the true relationships, but as Clarke et al mentions (2012), the use of instrumentation to eliminate in Holtz-Eakin et al’s (1988) model can lead to “poor efficiency and significant bias,” where the latter problem is more or less unavoidable when dealing with fixed effects in panel autoregressions.

The former problem is magnified due to the (lack of ) size of this dataset. These issues suggest that the detrended model is not in general correct, and another model should be used instead. Still, the result of the apparently zero effect skilled migration has on GDP per capita is a solid baseline that is consistent with previous results of others.

First Difference Panel VAR Results Some, but not all, of the issues inherent in the detrended model in levels above are because of distortions in the parameter estimates derived from varying GDP and population levels. These issues can theoretically be absolved by a transformation of the variables. Specifically, I use GDP per capita growth, population growth, and human capital growth instead of their counterparts, as in the original model. Importantly, since growth rates are inherently differences, this model avoids the stationarity concerns found in the model in levels. However, differencing also reduces the number of time observation available by 1, which is of particular concern with such a shallow time series. In particular, tests of lag length are now irrelevant for this model because the original parameters (of primary concern because they are needed to estimate the impulse response functions and interpret results) are only estimable when the lag length is 1 when T = 6, and so I only consider the model with one lag here. There is a discrepancy between the levels and differences model is because for the levels model with lag length L = 2, T = 7 > 2L + 2 = 6. However, when the model is in differences, T = 6 2L + 2 = 6, which is a requirement for estimat-

Fall 2015 ing the original parameters of the model (this requirement arises out of need for instruments to eliminate measurement error and fixed effects from the model, the latter of which is still problematic even in a first difference model) (HoltzEakin et al, 1988). On the other hand, since the data is quinquennial, it is unlikely that the lag length is greater than 1 anyway, so I proceed without being too concerned that the model is using the incorrect lag length.

Graph C

Graph D

Graph C shows that a positive effect on GDP per capita growth for a shock in skilled migration, in contrast to and without nearly as much delay as the levels model. Also in contrast to the model in levels is the effect of remittances, which now boosts GDP per capita growth as opposed to lowering GDP per capita.

The positive externality on growth seen from skilled migration could be the result of “diaspora externalities,” such as increased technology diffusion. This diffusion generally outweighs the loss of human capital for countries far from the technology frontier (such as small developing countries like here). Likewise, Docquier and Rapoport suggest that

Columbia Economics Review

positive trade externalities induced by migration outweigh the negative externality of capital loss, so that we would see the initial positive shock of skilled migration on GDP and then persistence then on out, as trade would be persistently higher in their framework. They would also argue for the positive effect (or at least non-negative) of remittances on growth due to potentially positive effects it has on capital formation.

the positive externality on growth seen from skilled migration could be the result of “diaspora externalities,” such as increased technology diffusion If this actually is the case and skilled migration does increase GDP per capita growth, then surely policy makers in smaller developing countries need to reevaluate policies restricting skilled migration, as it does not help the country nor the migrant, and both would be better served without the restriction due to the positive externalities of the migration. However, that is a big “if,” and there is still much reason to disbelieve the results. Most obviously, the Granger causality statistic for the null hypothesis that skilled migration and remittances growth do not affect growth implies a pvalue of essentially 1 (see Appendix C).

This means that the model fails to reject the null hypothesis of Granger non-causality, and so we gain minimal to no predictive power by including the share of skilled migrants and remittances growth in the panel VAR. While the observed non-causality may be due to having too small of a data set to notice any difference, there are more subtle but still serious econometric issues as well. Notably, while the test of the Wald statistic leads to the conclusion that the coefficients are homogenous across time and country (as

Fall 2015 originally assumed), the p-value is rather extreme at 97.9% (see Appendix C). In fact, all of the calculated statics for both panel VARs have extreme p-values in one way or another. While this is in no way conclusive, it would not be surprising to find out that the observation of extreme p-values is somehow linked to the observed bias that instrumentation often introduces into panel VARs in practice.

policy makers in smaller developing countries need to reevaluate policies restricting skilled migration, as it does not help the country nor the migrant, and both would be better Country Specific VAR Results One way to avoid the problems introduced by fixed effects, instrumentation, and homogeneity cross-country effects assumptions from the panel VAR is to estimate the model for each country. However, this also has two disadvantages: (1) we can no longer determine the dynamic effect of the brain drain common across countries, and (2), we can no longer estimate the full model due to degrees of freedom issues and hence invites more omitted variable bias criticisms. The issue named in (2) was in fact a large reason why a panel VAR with cross- country homogeneity assumptions was made, as it allowed the pooling of observations and the estimation of a larger system. Limited to 7 time periods, I am limited to estimating the model with only two endogenous variables: skilled migration and GDP per capita (as opposed to the model in differences, which was too small to allow for statistical inference). Estimates of these systems for each country with associated impulse response functions and granger causality statistics of skilled mi-

gration on GDP per capita can be found in Appendix D, where the impulse response functions again show a negative effect of a shock to skilled migration on GDP per capita. However, only 3 of these models have a p-value less than 10.0% and only 2 reject the null of Granger noncausality at the 5% level (which may be an overly optimistic due to multiple testing problems imposed by testing Granger non-causality for each country). Furthermore, seeing that the test statistic for Albania is 2.6 ∙ 1026 , it is likely that the only former Soviet bloc nation in the dataset is an anomaly,which may be because of an extremely tumultuous 1990s that saw the end of communism and mass emigrations of Albanians to other countries. This created a relationship between skilled migration and GDP over the period not present in other countries. Still, there is a noticeable negative relation between skilled migration and GDP per capita for most of the countries, which would appear to confirm the hypotheses of the “second generation” of brain drain scholarship which emphasized the negative externalities of the brain drain. In particular, this would be the case if the cost of losing human capital that skilled migration represents outweighs the potential benefits of increased technological diffusion. At the same time, this analysis has not accounted for other key variables like remittances due to sample size restrictions, and so omitted variables bias may be driving these results to an obscured conclusion.

Conclusions Each of the three different models I considered led to different conclusions, with the only consistency in the results being that all of the models do not pass tests of significance. At the same time, the most econometrically justified model I consider — the panel VAR in differences — finds the effect of brain drain on growth to be positive but insignificant (at least for this set of countries), while the panel VAR in levels and the country specific VARs in levels found slight but insignificant negative effects of skilled migration on growth. Taking all of these results together, the conclusion that seems most reasonable to draw is that the brain drain does not affect GDP per capita growth in a statistically noticeable way, which is harmonious with both the first genera-

Columbia Economics Review

35 tion of scholars on the brain drain back in the 1960s as well as the more recent conclusions of Beine et al (2001). However, since this model is atheoretic and not based on “micro foundation,” the reasons why there appears to be no net effect is unclear — does technology diffusion offset human capital loss, or are they both minimally affected? These results do not provide insight to those questions.

there is a noticeable negative relation between skilled migration and GDP per capita for most of the countries, scholarship Throughout the paper, I have spoken about implications for policy given the results from a welfare maximization standpoint. However, it is important to stress that even if the results previously presented were statistically significant in one way or another, the conclusions to be drawn from them must be made with care. Since I am using an unrestricted panel VAR to estimate the effect of the brain drain on growth (via impulse response functions), I cannot give any particular causal interpretation to the effects thus estimated. Indeed, while this paper does attempt to describe the “what” of the brain drain’s effect on growth, it does so without asking “why.” Hence, while the results presented here can be used to inform policy, policy should not be made on these results alone.

While it is my hope that this paper bridges some of the gaps in the existing brain drain literature (i.e. the dynamic effects of the brain drain), as well as being of some use to policy makers (even if the results are inconclusive), there is still much more that can be done. Notably, this analysis would benefit greatly from a wider panel and longer time series, as better estimates could be found and more hypotheses tested. n

36

Fall 2015

If You Pay It, They Will Run Human Capital in Major League Baseball: The Relationship Between Major League Baseball Players’ Performance and Salary Jonathan Hoffer, Yilin Guo, & Michael Nan Bai New York University Following the spirit of player valuation, this paper injects an interesting discussion into the world of sabermetrics and sports economics. One need not be a baseball fan to appreciate the breadth of data used to build the author’s model or the statistically significant effects of home runs and nationality on increasing salary. Yet, even with such a comprehensive model, it was necessary to cast a critical light on the author’s decision to focus only on position players by assuming that hitting performance is less dependent on team performance. As an avid baseball fan who plays fantasy baseball, I link batter’s statistics to the strength of his team’s lineup. Take the example of the San Francisco Giants’ Buster Posey, who used to bat before the slugging Pablo Sandoval.

In past years, the opposing pitcher would not pitch around Posey because he might walk and allow Sandoval to bat in multiple runs through a homer. This season, the Giants lack a formidable cleanup hitter, which means that Posey’s statistics are likely to decrease given the lower risk of a home run if he is walked by a pitcher. Upon careful consideration, we believed that the merits of the econometrics sustain a thorough investigation of hitters’ performance and personal traits in relation to salary levels. Home runs may be a key indicator of player value, but it is this paper’s theoretical and empirical analyses that hit it out of the park. -D.L.

Major League Baseball (MLB) players are among the highest paid workers in the American economy. In the year of 201314, the minimum annual player salary in Major League Baseball was $500,000, about ten times that of the average American salary. The average annual salary exceeded $2 million, an even greater multiple. What makes a Major League Baseball player so valuable? What determines the salaries of Major League Baseball players?

In this paper we will address the above questions by developing an Ordinary Least Squares (OLS) regression model containing variables linked theoretically to how a player’s salary is determined.

The most important economic theory we used in building our model was the human capital theory. In the standard approach of labor economics, human capital is viewed as corresponding to a stock of knowledge or characteristics that can improve a worker’s productivity. According

to Gary S. Becker (Becker, 1964), human capital is directly useful in the production process and thus will be valued in the market because it increases firms’ profits. Social psychologist Howard Gardener (Gardener, 1983) agreed with Becker on this point and he further suggests that human capital is multi-dimensional, and there are many types of intelligence and skills.

This theory led us to think that an increase in the human capital of a baseball player may lead to an increase in the productivity of the team and consequently leads to an increase in firm’s profits and the player’s wage. Hence the human capital of a player, as reflected by certain performance statistics and characteristics, may be vital determinants for the player’s value.

In our model, we will focus solely on hitters because they are less dependent on team performance than pitchers, and

Columbia Economics Review

the performance criteria for pitchers and non-pitcher players also differ radically.

We chose to look at MLB player data for the periods of 1985-87 and 2011-13. By using the relatively short three consecutive year periods, as similar to many other studies, we are allowed to obtain more observations without worrying much about some complex and unobserved effects that might be brought by a lengthy time span.

Furthermore, choosing periods before and after the 1990’s steroid period, during which players illegally used performance-enhancing drugs, allows us to detect changes potentially caused by the steroid period, and by contrasting the two periods, we may be able to see if there are changes in the game of MLB over time in general. Also, MLB teams grew from 26 to 30 between the periods, and there was an MLBPA strike from 1994-5, in which players won better bargaining powers and

Fall 2015 thereafter received substantially higher salaries.

Our focus will lie mainly with performance variables; in particular, we believe that power and run production will add more to the valuation of player capital than other performance variables such as contact, patience, and ability to get on base. We expect all performance variables to have positive correlations with salary, except our variable for batting inefficiency. Also, experience is expected to be positively correlated, but to have a turning point after a certain number of years; nationality is ambiguous and could have positive or negative effects depending on talent and scarcity, or conversely discrimination.

Over the two periods, we expect some variation in player valuation due to factors such as the steroid era, MLBPA strike, and globalization of the game. Our empirical results support our main hypothesis of run production and power as the greatest contributor to human capital, and our secondary hypothesis of structural break also has strong evidence.

we believe that power and run production will add more to player capital than contact, patience, and ability to get on base

Theoretical Model Our model aims to explore the relationship between various MLB player performance and characteristic variables and salary. Based on the human capital theory, we believe that a player’s salary is associated with the built-in skill set of the player, measured by his performance and certain characteristics. Since a player’s performance may improve a team’s results, revenue, and popularity, the market for baseball players may be viewed in a similar fashion to that of the market for

labor; thus, salary is a logical assumption of player worth as determined by the market. The dependent variable in our model will be a player’s salary in a given year. Performance and specific characteristics of the player will be the independent variables. The first two independent variables we chose are associated with characteristics of the player, and the rest of the independent variables will be measurements of performance.

As mentioned in the introduction, we are focusing on hitters in MLB to get a more independent estimation.

our model aims to explore the relationship between various mlb player performance and characteristic variables and salary We think that a player’s experience is an important factor affecting the salary, as more experience in MLB usually means higher human capital. According to Krautmann (1999), older players are typically paid up to their marginal revenue product, whereas younger players are paid well below their marginal revenue product. Therefore, a player with more past experience in MLB is usually compensated better than a less experienced player.

We also believe that there will be diminishing marginal effects of the experience factor, as professional baseball players usually reach their career peak during their mid-30’s. This should decrease the salary. Hence, we expect the experience variable to increase human capital until a certain point and then negatively impact it. Another variable associated with players’ characteristics is a player’s nationality. We believe that a player’s country of origin might be a significant factor.

There are two channels through which nationality can affect human capital. On one hand, teams may value specific skillsets, talents, and characteristics overseas more if they could not find them in the U.S. In this case, players born outside of the U.S. in the MLB may have higher huColumbia Economics Review

37 man capital because of such attributes.

On the other hand, foreign players may be valued less due to discrimination, as suggested by Audet (2009) in relation to Japanese players in MLB. Hence, we take a player’s nationality as a control variable in our theoretical model.

we believe that a player’s country of origin might be a significant factor The remaining four independent variables in our theoretical model are related to the performance of players. As a measurement of human capital, we believe that certain performance metrics should be relied upon to gauge the capability and skills of a player. Since hitters are the key players in the offense of a team, our variables related to performance also emphasize the offensive ability of a player.

The first independent variable we measure is power, which is also our main variable of interest.

As the score in baseball comes from hitting and running bases, a hitter with higher power usually contributes more to a team’s offense, and thus, is more highly valued. Also, power can reflect the level of training, diligence of work, as well as the talent a player has. All these factors accumulate a player’s human capital.

Another important factor is the player’s ability to make contact and get on base.

As we are focusing on hitters, hitting efficiency is as important as a skill.

A hitter with better efficiency and the ability to get on base usually means a higher possibility to score. Therefore, the demand for such players is much higher due to their valuable human capital. Besides power and efficiency, an excellent baseball player must have patience to wait for opportunities to get on base. Such a characteristic can be part of the natural personality, or acquired by training and past experience. Therefore, we think patience also enhances human capital and the player’s value in the market. A baseball player with great human capital that is highly demanded in the market usually has a balanced characteristic. A player with over-aggressive batting, poor hitting ability, and difficulty to make contact is

Fall 2015

38 considered inefficient in the offense, as there is a higher possibility of not putting the ball in play. This inefficiency is due to a lack of training and poor self-control, which drags down the offensive performance, and therefore, may reduce the player’s human capital. The linear equation of our theoretical model is:

The coefficients of power, hitting ability, patience, and experience are expected to be positive, while batting inefficiency is expected to have a negative coefficient.

The player’s nationality will be a control variable, and the sign of its coefficient remains uncertain.

since hitters are the key players in the offense of a team, our variables related to performance also emphasize the offensive ability of a player.

Our model differs from those of Lackritz (1990), Bollinger and Hotchkiss (2003), and Hakes and Sauer (2006), as they use only one offensive concept, the ability to reach base, whereas we split our offensive measures into individual concepts. We thus share more similarities with Kahn (1993), who uses more detailed offensive indicators. For the structural form of our model, we will use a semi-logarithm (log) model, a technique used in many papers we have reviewed, such as Kahn (1993) and Scully (1974). A few reasons led us to this transformation.

Firstly, salary data in baseball tends to be highly skewed, and thus using the natural log may help to account for the skewness. Our results also revealed heteroskedasticity (explained later) and using the natural log may correct for this source of error as well. Finally, this transformation

allows us to view the effects on salary of the independent variables in percentage terms, which may give an easier interpretation. Also, to capture the diminishing marginal effect of the experience factor, we squared age to estimate any penalties caused by a drop in performance.

to indicate the disturbances. Our model is:

Empirical Model and Data Our empirical model measures the value (human capital) of MLB players by using players’ salary (the dependent variable) as a function of performance and personal characteristics. Our model will be run through three separate regressions. One regression is for the period 1985-87, another for the period 2011-13, and the last one is a pooled regression of the two periods. We do this in order to see if there are any changes over time (structural breaks) in the determination of baseball human capital, and we employ a Chow Test at the end of our regressions to test for the significance of these breaks.

Salary is adjusted into 2013 U.S. dollars for the years 1985, 1986, 1987, 2011, and 2012. We used the inflation calculator from the U.S. Bureau of Labor Statistics’ website. The respective multipliers for this transformation for each year is as follows: 1985-2.1650, 1986-2.1255, 19872.0507, 2011-1.0356, 2012-1.0146.

Furthermore, we used only those players listed on active rosters during the regular season whose salaries were listed; we also excluded any players in a season whose number of games played was below 50 (the regular season contains 162 games), which we deemed was not enough data for significance in our models.

The model includes several performance variables such as walks, home runs, strikeouts, and hits (specifically singles), and personal variables such as whether the player was born in the U.S. and age. Therefore, in our model the natural log of salary (in 2013 U.S. dollars) is a function of age, nationality, walks, hits, home runs, and strikeouts. We measure power by home runs, hitting ability and contact by hits (singles), patience and ability to reach base by walks, and batting inefficiency by strikeouts. We measure experience, leadership, and maturity by age (in years) at the time of the season in question, and nationality by place of birth. The data series corresponds to the variables as follows: REALSALARY is for salary, AGE for age, AGE2 for age^2, DFOREIGN for nationality, BB for walks, H for hits (singles), HR for home runs, and SO for strikeouts; the epsilon is used Columbia Economics Review

the model includes several performance variables such as walks, home runs, strikeouts, and hits (specifically singles), and personal variables

A home run is when a ball is hit outside of the field of play within the foul boundary lines. A home run displays power and contributes to run-production, as a home run drives in all players on base including the batter. A walk is when a batter takes four pitches as a ball, and indicates both ability to get on base and patience by not swinging at poor pitches.

A hit is when a batter hits a ball into the field and reaches first base (not caused by fielding error). Hits show a player’s ability to make contact and get on base, as well as overall batting ability. A strikeout occurs when a batter takes three strikes either swinging or missing; a player with many strikeouts may be over-aggressive, or may overall be someone who struggles to make contact, making this a serious drag on performance. Age is a proxy for experience, maturity, and possibly leadership credibility. Finally, nationality is a binary variable indicating whether a player was born in the U.S., which may affect a player’s wages via discrimination or popular appeal.

Our original model had some important differences from the above model. We began by using OPS (on-base plus slugging percentage) as a total offensive production and efficiency measure based on its popular use in other papers, such as Alm,

Fall 2015

Kaempfer and Sennoga’s (2012) work on the effects of state and local income taxes on salary. But, we observed a large drop in the R-Squared of our regressions with OPS as compared with the above model, a difference of about 9-13% depending on which period was estimated.

The reason behind this disparity may lie in the fact that OPS obscures individual offensive indicators by bundling up many offensive statistics into one crude statistic. While this may be a decent average indicator across the whole league, it may be less important when looking at an individual’s characteristics and salary.

Brown and Jepsen (2009) in their analysis of the impact of team revenues on salaries use on-base percentage and slugging percentage as two separate variables. Thus, we split OPS up into walks, hits, home runs, and strikeouts, which greatly improved our fit, and gave us better insight into which specific parts of offensive production are valued most highly.

Furthermore, we originally included errors and stolen bases in our model in order to capture an individual’s fielding ability and speed. These variables were surprisingly insignificant in the 1985-87 period regression, which may be due to the fact that there are only a few great base stealers, and only a few fielders

with abnormally high errors. Weight was also dropped due to insignificance in the 1985-87 period regression.

Finally, we originally had a dummy variable taking the value of one if the player was a catcher and zero otherwise.

Catcher is considered to be an important position, but it too was insignificant in the 1985-87 period regression, possibly because there are normally only two catchers on each team.

Testing these four variables jointly using an F-Test still led to insignificance.

We thus dropped these variables from the 1985-87 period and used the above empirical model, and then proceeded forward with the same model in the 2011-13 period and the pooled regression.

All of our data is measured in a single season for each player, and since we have two periods with three years spanning each, we have six seasons of data for these measures (1985,86,87; 2011,12,13). The data is collected at the end of each regular season, which typically ends at the end of September or beginning of October.

Home runs, hits, walks, and strikeouts are measured in integer units. Age is measured in years. Nationality (DFOREIGN) is a dummy variable. Finally, as mentioned above, salary is measured in the natural logarithm of 2013 U.S. dollars.

Columbia Economics Review

39

All of our data was collected from Sean Lahman’s baseball database. This database contains team and individual player data from 1871-2013. Once obtained, we separate those players’ statistics from the three other sheets and thus have two combined sheets for players in the periods 1985-87 and 2011-13 with all of the necessary data for our regressions. Finally, in order to conduct the Chow test, we create a third sheet by simply combining the two periods into one sheet. The numbers of observations our data series in each period and the pooled regression are: (19851987)-830, (2011-13)-1038, (pooled)-1868.

Summary statistics and correlation matrices for 1985-87 and 2011-13 are on the next page (Real Salary in non-log units is added just to give the reader a sense of how much real salaries changed between the two periods; but only the natural log of this is used in our regressions).

Estimation and Results We used OLS to estimate our empirical model. Our model was run through three separate regressions (as mentioned above). It is: LN(REALSALARY) = β1 + β2AGE + β3AGE2 + β4DFOREIGN + β5BB + β6H + β7HR + β8SO + ε

Fall 2015

40 Summary Statistics 1985-87 RealSalary LNREALSALARY AGE AGE2 DFOREIGN BB H HR SO Summary Statistics 2011-13 RealSalary LNREALSALARY AGE AGE2 DFOREIGN BB H HR SO

Observations Mean Std. Dev. Min Max 830 1111745 887361.8 127530 4612100 830 13.57104 0.8996955 11.75611 15.34419 830 30.40241 4.334004 22 45 830 943.0675 274.8114 484 2025 830 0.1277108 0.3339688 0 1 830 39.14578 23.34716 2 136 830 100.2301 50.12396 6 240 830 11.46024 9.654976 0 49 830 58.96747 32.94866 4 186 Observations Mean Std. Dev. Min Max 1038 4406006 5404029 428738.4 33100000 1038 14.52912 1.286194 12.9686 17.31623 1038 29.71965 4.032345 20 45 1038 899.5019 248.6477 400 2025 1038 0.2870906 0.4526223 0 1 1038 35.54624 20.99472 2 135 1038 99.65896 46.61243 7 216 1038 11.65125 9.346731 0 53 1038 77.41137 37.72206 10 222

Since our interest is in testing whether power is the most valuable performance indicator in player salaries, we will test whether home runs has a greater slope coefficient than walks and hits (the test is individually for these two variables, not together). Strikeouts are not necessary as they are negative indicators, and should logically never be of positive value in determination of salary. The other variables, age, age^2, and nationality are personal characteristics, rather than performance characteristics, so we will not measure them against performance characteristics. Our null hypothesis is that home runs are just as valuable as walks and just as valuable as hits, and our alternative hypothesis is that they are more valuable (these hypotheses are applied to each regression individually for the two periods): Ho: β7HR= β6H, β7HR=β5BB Ha: β7HR> β6H, β7HR> β5BB This is a Wald Test, which is computed using the estimated coefficients and the variances and covariances of the estimates from the unconstrained model.

This is calculated as:

where s^2 is the variance, and sb7HRb6H the covariance. This gives a test statistic with an F distribution with (1, n-k) degrees of freedom, where n is the number of observations, and k the number of parameters, including the constant. If the difference from home runs and the other two variables is positive (one-sided test) and statistically significant from zero at the 5% level of significance, then we will reject the null hypothesis. All of our results for testing in this paper will be examined at the 5% level of significance, as this is typically the standard in statistical analysis. Furthermore, all of the effects of the coefficients will be estimated precisely using the formula:

Correlation Matrix 1985-87 LNREALSALARY~Y AGE AGE2 BB LNREALSALARY 1 AGE 0.4482 1 AGE2 0.4252 0.9968 1 BB 0.4352 -0.0468 -0.047 H 0.412 -0.2081 -0.207 HR 0.3443 -0.087 -0.0827 SO 0.1944 -0.2255 -0.2184 Correlation Matrix 2011-13 LNREALSALARY~Y AGE AGE2 BB LNREALSALARY~Y 1 AGE 0.5056 1 AGE2 0.4844 0.9963 1 BB 0.3448 -0.0898 -0.0962 H 0.3526 -0.1493 -0.1512 HR 0.356 -0.0876 -0.0932 SO 0.1829 -0.2294 -0.2331

For our model, all of the assumptions of the Classical Linear Model hold except for heteroskedasticity. As shown in the correlation matrices, the independent variables do not appear to be too highly correlated such as to exhibit multicollinearity. Our model is linear in the parameters with only two exceptions: Salary is log-transformed and age is squared.

There does not appear to be any endogeneity in our model, as theoretically there is nothing to suggest that our independent variables are correlated with the disturbances.

our null hypothesis is that home runs are just as valuable as walks, and just as valuable as hits, and our alternative hypothesis is that they are more valuable

We conducted White’s Test for heteroskedasticity in Stata (which is a large sample Lagrange Multiplier Test) in order to verify if Assumption 4 of the Classical Linear Model holds for our model.

Columbia Economics Review

H

1 0.6882 0.583 0.5755

HR

1 0.6164 0.6336 H

1 0.685 0.6676 0.6822

SO

1 0.7112 HR

1 0.6433 0.616

1 SO

1 0.7177

The null hypothesis for this test is that the variance of the disturbances is constant (homoskedasticity) across all observations. The alternative hypothesis is that the variance is not constant (heteroskedasticity) across all observations.

The test statistic is nR^2 which is obtained in a regression of the squared disturbances on a constant and all unique variables contained in the model, and all the squares and cross products of those variables. This statistic is asymptotically distributed with a Chi-Squared distribution with P-1 degrees of freedom, where P is the number of unique variables in the auxiliary equation, including the constant. For 1985-87 we obtained a statistic of 77.71, for 2011-13 a value of 95.48, and for the pooled regression a result of 74.70.

All of these had 33 degrees of freedom.

These values are all significant below the 1% level, and thus we reject the null hypothesis of homoscedasticity, proving the existence of heteroskedasticity in our data.

What this implies is that the OLS estimators will be inefficient (their variance will be larger than other unbiased estimators). The estimators of the standard errors of the coefficients will not be consistent, making our resulting standard errors a poor measure in our analysis. This is not surprising as other papers we read found the same problem in their models; also, data on expenditures and income tend to exhibit this problem. They used White’s standard errors (which are consistent under very general conditions) in order to correct for this. We apply the same solution, and thus use robust standard errors, in order to correct for the inefficiency.

Furthermore, with such a large sample size, it should be appropriate to proceed with this treatment in our analysis. Plots of the heteroskedasticity for 1985-87 and 2011-2013 are shown on the next page, as are the results for all of our regressions.

1

Fall 2015

Regressions: Dependent Variable: LNREALSALARY AGE

AGE2

DFOREIGN

BB

H

HR

SO

_cons

Descriptive Statistics R^2 Adj. R^2 SSE F Statistic Prob>F Observations White Test Chi-Squared Statistic White Test P>Chi-Squared Test βHR>βH [F Statistic] Prob>F Test βHR>βBB [F Statistic] Prob>F Chow Test [F Statistic] Prob>F

1985-87 Coefficients (Robust Standard Errors) t-statistic P-value 0.8314439 (0.0696181) 11.94 0.000 -0.0114238 (0.0010997) -10.39 0.000 0.1525288 (0.0608247) 2.51 0.012 0.0070104 (0.0012661) 5.54 0.000 0.0067584 (0.0006206) 10.89 0.000 0.0143426 (0.0033451) 4.29 0.000 -0.0032505 (0.001004) -3.24 0.001 -1.877468 (1.085524) -1.73 0.084 Values (DF) 0.5735 0.5699 286.166 208.70 (7, 822) 0.000 830 77.71 (33) 0.000 4.70 (1, 822) 0.0305 3.95 (1, 822) 0.0473

2011-2013 Coefficients (Robust Standard Errors) t-statistic P-value 0.9605584 (0.0768842) 12.49 0.000 -0.0127646 (0.0012389) -10.30 0.000 0.3016872 (0.0612883) 4.92 0.000 0.0077289 (0.0021166) 3.65 0.000 0.0069126 (0.0008389) 8.24 0.000 0.0270672 (0.0044274) 6.11 0.000 -0.0023383 (0.0012247) -1.91 0.057 -3.721114 (1.177884) -3.16 0.002 Values (DF) 0.5287 0.5255 808.58 257.58 (7, 1030) 0.000 1038 95.48 (33) 0.000 18.19 (1, 1030) 0.000 13.73 (1, 1030) 0.000

41

Pooled Coefficients (Robust Standard Errors) t-statistic P-value 1.047164 (0.0595411) 17.59 0.000 -0.0144483 (0.0009443) -15.30 0.000 0.524663 (0.0524455) 10.00 0.000 0.0013517 (0.0014062) 0.960 0.337 0.0060314 (0.0006508) 9.27 0.000 0.0111462 (0.0035157) 3.17 0.002 0.0056958 (0.0008987) 6.34 0.000 -5.349144 (0.9256928) -5.78 0.000 Values (DF) 0.4497 0.4477 1546.18 255.55 (7, 1860) 0.000 1868 74.7 (33) 0.000 95.46 (8. 1852) 0.000

Variance-Covariance Matrix 1985-87 Variable AGE AGE2 BB H HR SO _cons Variance-Covariance Matrix 2011-13 Variable AGE AGE2 BB H HR SO _cons

AGE AGE2 BB H HR SO _cons 0.00465477 -7.323E-05 1.16E-06 -1.277E-05 1.77E-07 1.60E-06 2.29E-07 5.33E-09 -4.37E-07 3.85E-07 -2.90E-06 2.65E-09 -4.48E-07 -3.31E-07 0.00001123 5.40E-06 -6.91E-08 -1.76E-07 -1.02E-07 -1.92E-06 1.01E-06 -0.0723322 0.00113162 0.0002188 -2.601E-05 0.00012833 -0.00012 1.133384 AGE AGE2 BB H HR SO _cons 0.00629801 -0.0001011 1.63E-06 -1.164E-05 1.54E-07 4.40E-06 3.31E-06 -5.53E-08 -6.30E-07 6.68E-07 -4.468E-05 6.84E-07 -1.76E-06 -1.11E-06 0.00001972 7.34E-06 -8.96E-08 -9.06E-07 -1.03E-07 -2.17E-06 1.39E-06 -0.0961056 0.00153139 0.00020682 -7.288E-05 0.00081778 -0.0001749 1.4812519

Columbia Economics Review

Fall 2015

42 The independent variables (excluding the constant) in each regression are jointly significant with F statistics of (in order): 208.7, 257.58, and 255.55, all with corresponding p-values of 0.000, below the 1% level of significance. Thus, we reject the null hypothesis at the 1% level that the variables in our models are jointly insignificant. Also, the R^2’s are as follows (also in order): .5735, .5287, and .4497. The last one is significantly lower, but this is from the pooled regression, in which we may expect a loss of fit when combining two different periods over 20 years apart from each other. The R^2’s indicate that for 1985-87, 57.35%, and for 2011-13, 52.87%, respectively, of the variation in the dependent variable can be explained by variation in the independent variables (i.e. our model).

holding other variables constant, on average, the salary of an international player is approximately 16.48% more per year than of a u.s. player

The results for our two regressions of the two periods confirmed our original expectations. The estimated coefficient for DFOREIGN is 0.1525288 in the 198587 period, meaning that holding other variables constant, on average the salary of an international player is approximately 100[exp(0.1525288)-1]=16.48% more per year than that of a U.S. player.

This coefficient almost doubled in the period 2011-13, revealing that holding other variables constant, on average an international player is paid approximately 35.21% more per year than a U.S. player. The coefficient on age is large in both periods. Including the diminishing effects of age^2, the effect is [bAGE-2bAGE2 AGE]ΔAGE, giving the turning point (bAGE/2bAGE2), which means that for the earlier period the positive effect of age diminishes at around 36.5 years, and in the later period at around 37.5 years. This

diminishing effect occurring at a relatively older age may be attributed to the arbitration and free agency processes.

Only after two or three seasons can players arbitrate for higher salaries, but they are still bound to negotiate with one team (similar to monopsony); after six seasons they can enter the market for free agency.

Therefore, age is a huge factor as older players gain more bargaining power, and eventually can enter the market, bidding up their value substantially.

for the performance variables, all the variables except strikeouts had positive effects, as expected

For the performance variables, all of the variables except strikeouts had positive effects, as expected. For home runs, the coefficients indicate that a player hitting one more home run in the 1985-87 period, on average and holding everything else constant, increased his salary by 1.44%, while a player in the 2011-13 period increased his salary on average and holding everything else constant by 2.74%.

This was by far the highest value-added performance variable affecting salary.

For 1985-87, one more hit, on average, led to a 0.68% increase in salary, and for 1 more walk a 0.704% increase. For 201113, 1 more hit, on average, led to a 0.69% increase in salary, and for 1 more walk a 0.78% increase. Testing our null hypothesis that the coefficient of HR is equal to BB in 1985-87, we obtained an F(1, 822) statistic of 3.95 with a p-value of .0473, which means we reject the null hypothesis at the 5% level. For the same period except against H, we obtain an F(1, 822) statistic of 4.70 with a p-value of .0305, leading to the same rejection. Therefore, we reject the null hypothesis that walks and hits (individually) are equal to home runs in their coefficient values. There is evidence that home runs had a greater effect on salary in the period 1985-87. We came to the exact same conclusions for 2011-2013, except that our results were

Columbia Economics Review

statistically significant at the 1% level; p-values for both F(1, 1030) statistics [for test against hits: 18.19; against walks: 13.73] were 0.000. Thus, in the later period, there is also evidence that home runs had a greater effect than walks and hits (individually) on salary, and at an even higher level of significance.

After conducting our two separate regressions for the two periods, we conducted a Chow Test for structural break in order to see if there was any difference in the value of the coefficients. Essentially, this was to analyze any difference over time in how players were valued in baseball. The null hypothesis for this test is that the vector of parameter coefficients, β, is constant over time, or equally that β1985-87 = β2011-13. The alternative is that it is not constant, or β1985-87 β2011-13. The test statistic is calculated as: {[SSEpooled( S S E 1985-87+ S S E 2011-13) ] / ( k ) } / { ( S S E 198587+SSE2011-13)/(n-2k)}, where k is the number of parameters, including the constant, and n is the number of observations. We thus calculated: {[1546.18(808.5797+286.166)]/[8]}/ [(808.5797+286.166)/(1868-16)] = 95.46239.

homeruns had a greater effect than walk and hits (individually) on salary

This statistic has an F distribution with (k, n-2k) degrees of freedom [or (8, 1852)].

This result gives us a p-value well below the 1% level of significance, meaning we have enough evidence to reject the null hypothesis at the 1% level. There is evidence of structural break across these two time periods. It should be noted that the constant for 1985-87 was much larger at -1.877, while in 2011-2013 it was -3.721; but the slopes are larger in the latter period (some greatly so). This means the intercept (or base) is lower for the later period, but the greater slopes indicate a much higher rate of increase in salary. If analyzed with the summary statistics, in which real salary increased drastically, it appears that players on average were rewarded much more for their performance, and for each individual

Fall 2015 performance and personal characteristic variable in the 2011-13 period. The average real salary (in 2013 U.S. dollars; for players in our sample with more than 50 games) for the later period was almost $4.5 million, while in the earlier period it was just about $1.1 million (see summary statistics).

Specifically, the slope of HR almost doubled in value across the two time periods. Home runs seems to have dramatically increased in its importance to a player’s human capital. This may be due to the steroid era and the dominance of power hitting in the game that emerged in the mid-1990’s. Yet, in the summary statistics, the average of home runs was roughly the same in both periods at around 11-12 home runs. Thus, it may specifically be that after the player strike in 1995, and the accompanying rise in average real salaries, power hitters were able to bid up their value in the market, and thus it may even be that power hitters were being underpaid relative to their true value before the strike.

power hitters were able to bid up their value in the market, and thus it may even that power hitters were being underpaid relative to their true value A few other changes are worth mentioning. A player’s turning point for age also increased in value in the later period by one year. It could be that experience has become more valued, especially the idea of a leader or “captain,” such as Derek Jeter. It may also be that players have better ways and resources in order to keep themselves healthy over longer periods of time. Hits did not change drastically, and walks and strikeouts changed only moderately. Foreigners, on the other hand, seem to have been valued much more highly in the later period. The intercept coefficient on the dummy variable for foreigners more than doubled.

Demand could be the reason for this as

the globalization of the game has made access to foreign players easier. The total number of foreigners (including those who played less than 50 games in a season) increased from 39 in 1985 to 137 in 2013. This is a large increase and indicates the growing demand for foreign talent.

Conclusion The results we obtained support our initial hypothesis about the importance of power and run production in the determination of player capital valuation.

Home runs was the performance variable which had the largest positive effect on salary in both periods tested. Its effect was statistically significantly greater than that of walks and that of hits at the 5% level. Also, in the later period home runs’ effect increased much more substantially than those of the other two variables and therefore increased its dominance over the other two variables in terms of salary determination. Thus, a power hitter can expect to see a premium in valuation over contact or patient hitters. The results also show that players were paid much more in the later period on average, providing evidence that after the strike players were being valued more fairly. This higher valuation appears to be greatest in terms of power and run production and thus power hitters probably were undervalued in the earlier period, and therefore the later period resulted in a much higher coefficient for home runs. This coincides somewhat with Scully’s (1974) finding of the bargaining power effects of superstars on salaries, as power hitters are usually considered star players, and thus after the MLBPA strike, power hitters gained even greater bargaining power than before.

players were paid much more in teh later period on average, providing evidence that after the strike, players were valued more fairly

Columbia Economics Review

43 It is also interesting to observe the characteristic variables’ results. Foreigners fetched a premium, and this most likely has to do with demand, as even though far more foreign players played in the later period, this increase in supply did not stop the coefficient on foreigners in the later period from doubling. Apparently the talents of those foreign players sought out by MLB teams are in high demand, and thus like Audet (2009) there are not any discernible discriminatory effects. Age was somewhat surprising in that the turning point tended toward the higher end of the 30’s range. This is a bit higher than what might be suggested by Hoaglin’s and Velleman’s (1995) results (yet they do measure experience directly rather than age). Baseball is not as physically demanding as football or hockey, but even so there is most likely a “veteran” effect of leadership and experience, thus stability and less risk, that allows for higher pay on average until a fairly late age.

age was somewhat surprising in that the turning point tended towards the higher end of the 30’s range

With these results and analysis, it may be interesting for later studies to focus on separating older players from younger players or foreigners from Americans. Research of globalization of the game and supply and demand models for foreign players may be valuable. Also, more studies on power hitters themselves might give more detail and explanation as to what makes a player a power hitter. Maybe other measures of power should be looked at or developed in order to gauge the full effects of power in the game. As we found, power has only become more important over time, and the demand for greater power hitters may be changing the game of baseball itself. In terms of value and capital, according to our findings, it is safe to say players with power fetch a high premium. n

Fall 2015

44

That 70’s Shock The Persistence of Memory: How Demographic & Monetary Shocks Affect Macroeconomic Expectations Rui Yu Columbia University “Since monetary policy works via the expectations of future instrument rate settings rather than the current instrument rate, and since expectations of future inflation and output matter for the private sector’s current pricing and production decisions, monetary policy is to a large extent the management of expectations.” – Lars Svensson (2004) The last seven years of unconventional monetary policy has transformed Lars Svensson’s characterization of monetary policy as “the management of expectations” into one of the core tenets of modern central banking. After having spent some time working on the interactions between inflation targeting regimes and central banking credibility, I was excited to read about Yu’s take on an area of monetary policy that I had previously taken for granted – inflation expectations. In particular, the formation and the heterogeneous nature of inflation expectations. Yu takes Malmendier and Nagel’s (2013) “Learning from Experience” model and successfully applies it to inflation expectations data from the Michigan Survey of Consumers.

One of the most interesting results to come out of this paper is the net interaction between two observations – firstly, that older generations are less responsive to new information, hence appearing to be more strongly anchored to a long run expectations trend; and secondly, that because the older generation in the sample experienced the Great Inflation of the 1970s, their inflationary outlook is less stable. Finally, it would be interesting to see this study expanded in two ways – by taking into account how inflation expectations affect realized future inflation (not just how past inflation affects inflation expectations) and by expanding the dataset to include other OECD economies with rich inflation expectations data. – HYTY. Malthus (1794) argued that population is critical for economic outcomes.

But little is still known about the role of demographics, or traits of populations, on macroeconomic phenomena. Inflation and inflation expectations are examples of such critical macroeconomic variables (Friedman 1968, Woodford 2003). Recent research links personal experiences to macroeconomic expectations, producing expectations that differ across demographic groups. A natural but unexplored question is whether demographics, de ned hereafter as the population age distribution, affect inflation expectations.

Do demographic shocks affect aggregate inflation expectations? In a similar vein, does demographic aging in the U.S. explain better anchoring of inflation expectations during the Great Moderation?

I replicate a learning-from-experience model (Malmendier and Nagel 2013) using survey reported inflation expectations from the Michigan Surveys of Consumers.

Using the model, I answer these questions by simulating the effect of demographic shocks and aging on aggregate inflation expectations. In addition, I exploit the historical component of learning-fromexperience. What is the legacy of high inflation in the 1970s on current expectations? Does downweighting past histories explain stable inflation expectations? I run counterfactual simulations to directly address these questions.

A growing literature has sought to explain the moderation of macroeconomic volatility in the U.S., with little convergence (Stock and Watson 2003, Campbell and Hercowitz 2005, Ramey and

Columbia Economics Review

Vine 2006, Arias, Hansen, and Ohanian 2007). One feature of the so-called Great Moderation is the unprecedented stability, or well-anchoredness, of inflation expectations. Inflation expectations are well-anchored if long-run expectations are in-variant to short-run fluctuations in inflation. The roots of this phenomenon are still unclear due to three obstacles to research. First, hypotheses need to match the specific timing of better anchored expectations - i.e., why now rather than at another time? Second, a model of expectations formation that is compatible with and can test the hypothesis might not exist. Third, data on inflation expectations are sparse, and even when available it is unclear how to evaluate the anchoredness of expectations.

Fall 2015

Figure 1: Perceived Autocorrelation and Surveyee Age: Solid line is perceived autocorrelation of inflation predicted by learning-from-experience AR(1) model. Dashed line is average age of respondents to the Michigan Surveys. Note that Malmendier and Nagel (2013) only use respondents who were aged 25 to 74 at the time of their survey interview. Both series above are constructed from respondents aged 25 to 74.

Jaimovich and Siu (2009) find, by exploiting variation across the G7 nations, that demographic makeup of the workforce strongly explains business cycle volatility. They extend their results and find that demographic aging in the U.S. explains a substantial portion of the Great Moderation. Could demographic change also affect inflation expectations?

Figure 1 plots (1) perceived autocorrelation of inflation, a measure of anchoredness of expectations, and (2) the average age of surveyees in the Michigan Surveys of Consumers. Better anchoring of expectations seems to coincide with aging of the survey-ees. Jaimovich and Siu’s hypothesis is appealing, because the timing of aging matches up well with the start of the Great Moderation.

Malmendier and Nagel (2013) build a learning-from-experience model that predicts individual inflation expectations based on lifetime inflation history. The model proposes that generations with higher inflation experiences form higher inflation expectations and older populations tend to be less responsive to new experiences, relative to the young. The model directly relates micro-level demographic variation to aggregate inflation expectations. Alternatively, learningfrom-experience also posits that history affects inflation expectations. Thus, learning-from-experience model can test two breeds of hypotheses, demographics versus history, to explain the trend of aggregate inflation expectations. Counterfactual simulations on the model can then isolate the incremental contribution

of demographics or history on aggregate expectations.

I estimate the model using micro-level survey responses about inflation expectations from the Michigan Surveys of Consumers. The survey data is a rotating panel covering 1966-2013, and it captures a sufficient amount of demographic information for analysis. Learning-fromexperience exploits the variation in inflation expectations across cohorts and time in these surveys for estimation, setting it apart from models limited to aggregate time-series. In addition, the AR(1) structure of learning-from-experience produces an intuitive measurement of the anchoredness of both individual and aggregate inflation expectations.

Therefore my analysis overcomes the three obstacles to studying the roots of the moderation in inflation expectations.

I re-estimate a learning-from-experience model using survey responses from the Michigan Surveys of Consumers and obtain almost identical estimates to Malmendier and Nagel’s. I study the effect of demographic shocks on inflation expectations by running simulations, but and that demographic shocks have little effect on expectations. In counterfactual simulations with no population aging, I find that demographic change does not explain better anchoring of inflation expectations. On the other hand, high inflation in the 1970s had long-lasting effects on aggregate expectations. It is the downweighting of past inflation history, in turn, that explains a substantial amount of the better anchoring of inflation expectations.

Literature Review Macroeconomic expectations, particularly inflation expectations, play a critical role in macroeconomics and policy.

The perception of inflation by firms and agents affects prices, influencing actual inflation as embodied in the Phillips Curve (Romer 2012). Inflation expectations may affect the financial decisions of individuals, as expected inflation affects perceived interest rates and in turn influences financial decisions such as whether or not to buy a house. Inflation expectations thus affect individual and macroeconomic outcomes (Woodford 2003).

Naturally, inflation expectations figure prominently to central banks seeking to maintain price and output stability (Bernanke 2007).

But inflation expectations stubbornly differ across demographic groups, generations, and time. Empirical evidence Columbia Economics Review

45 from surveys on expectations documents persistent heterogeneity, which does not sit well with conventional models with agents having the same expectations.

Bryan and Venkatu (2001) document heterogeneity in inflation expectations along gender. De Bruine et al. (2010) expand the analysis and and persistently higher inflation expectations by individuals who are female, poorer, single, and less educated. Piazzesi, Salomo, and Schneider (2013) find significant divergence in inflation expectations between young and old households in the 1970s and show that the heterogeneity accounts for differences in financial decision making. Studies on heterogeneous expectations link differences to demographic and individual traits.

However, little agreement exists on how agents form inflation expectations and why expectations differ. Carroll (2003) suggests that macroeconomic news diffuse through the economy slowly through an epidemiological model.

Thus, professional forecasters update their expectations rapidly while others do not, leading to disagreement about inflation expectations. Mankiw and Reis (2002) propose a sticky information” model where agents rationally choose to update information intermittently. The model accounts for observed heterogeneity in inflation expectations (Mankiw, Reis, and Wolfers 2006).

professional forecasters update their expectations while others do not, leading to disagreement about inflation expectations Malmendier and Nagel (2013) propose a learning from experience model where a weighted average of lifetime inflation experiences predict inflation expectations. The weights have two features.

First, individuals weigh recent and past experiences differently. Experiences dur-

46

ing formative years or teachings by parents may shape adult decision, a process represented by higher weights on past experiences. On the other hand, it may be possible that memory fades over time, so recent experiences hold more weight.

The model allows the data to speak; data shapes the behavior of memory. Second, older individuals weigh recent experiences lower than younger individuals. Using survey reported inflation expectations from 57 years of the Michigan Surveys of Consumers, differences in lifetime inflation experiences strongly predict inflation expectations. However, their model does not disentangle cohort effects from cohort-specific inflation experiences. One advantage of learning from experience is that it bridges observed heterogeneity and demographic factors by hypothesizing a channel through which demographics affect expectations.

Learning from experience follows a small but growing literature incorporating personal experiences to economic decision making. The psychology literature separates information from experiences and information from summaries, arguing that personal experiences, particularly recent ones, have a greater effect than information extracted from summaries (Hertwig et al. 2004). Choi et. al (2009) find that individuals earning

Fall 2015

high returns on his/her 401(k) are associated with higher 401(k) saving rates.

Greenwood and Nagel (2009) show that younger mutual fund managers tend to invest more in tech stocks relative to older managers, suggesting that experience shapes risk aversion. Studies find that corporate leaders who experienced the Great Depression tend to shy away from external financing or leverage (Malmendier and Tate 2005, Graham and Narasimhan 2004). Most closely related is Malmendier and Nagel (2011) who find that individuals surveyed by the Survey of Consumer Finances who experienced low stock market returns in their lifetimes report higher risk aversion, are less likely to own stocks, and are more pessimistic about future stock returns.

Learning from experience draws on adaptive learning models popular in macroeconomics. Adaptive learning posits that individualsâ&#x20AC;&#x2122; expectations can be approximated by a simple forecasting rule that uses available historical data (Bray 1982, Sargent 1993). Malmendier and Nagel posit that individuals recursively estimate inflation using an AR(1) model and data from lifetime inflation history. Each recursion includes the most recent inflation experience, but a gain parameter controls and weights the relative impact of new information on the AR(1) Columbia Economics Review

model. A simple adjustment to the gain parameter, detailed later in this paper, yields a recursive formulation of the ordinary least squares (Evans and Honkapohja 2001). Their specification is close to Honkapohja and Mitra (2003) where memory of past data gets downweighted over time. The advantage of learning from experience that depend on individual history is it yields heterogeneous inflation expectations that do not necessarily converge, matching observations about inflation expectations.

I focus on an unexplored demographic component of the learning-from-experience model. Since experiences are weighted according to age, their model suggests a link between demographics and inflation expectations. This perspective taps into a thin but timely vein of research on demographics and macroeconomic performance. Jaimovich and Siu (2009) use demographic trends and business cycle volatility from the G7 nations and find that the age composition of the workforce strongly accounts for business cycle volatility. They also find that onefifth to one-third of recent moderation in the U.S. business cycle can be explained by demographic factors. Interestingly, they suggest that greater numbers of old people increase volatility, cutting slightly against Malmendier and Nagelâ&#x20AC;&#x2122;s model where older individuals tend to stabilize macroeconomic expectations. Shimer (1998) attributes what were declining unemployment rates in the U.S. to demographic aging, based on the observation that unemployment is highest among the young. Given the aging population in the U.S., exploring the effect of demographic changes on inflation expectations opens a new path through which demographics may exert real macroeconomic effects.

In particular, I explore one facet of the widely reported macroeconomic stability before the financial crisis in the U.S., known as the Great Moderation (Stock and Watson 2003). One feature of the Great Moderation are well-anchored inflation expectations after decades of volatile expectations (Davis 2012). A common refrain among central banks is that sophisticated monetary policy has improved central bank credibility, leading to inflation expectations invariant to short-run inflation surprises. However, Learning-from-Experience suggests that older individuals have a lower gain parameter, or they react less to recent inflation surprises. Is it possible that well-anchored inflation expectations are due to demographic aging?

Fall 2015 Learning from Experience Learning-from-experience posits that individuals’ lifetime inflation experiences predict inflation expectations. Formally, the model is a recursive formulation of weighted least squares that estimates an AR(1) model to predict inflation. A simple intuition for learning-from-experience is that when an individual experiences inflation, she adds that new experience to a personal dataset of past, lifetime, inflation rates. That personal dataset is weighted, so that past and recent inflation experiences differ in importance. The individual then fits a line to the personal dataset, and uses the line to forecast expected inflation in the next period. For estimation, time period is a quarter Formally, Malmendier and Nagel (2013) propose that an individual born at time s forecasts inflation for time t + 1 as if with an AR(1) model:

Set

and

Where θ is a parameter that determines the shape and weights of past experiences, γt,s is a gain parameter that decreases with age, reflecting how older individuals already possess a large set of experiences and thus practices less updating to recent experiences. Crucially, setting γt,s = 1 whenever t − s ≥ θ implies that inflation experiences before and around birth are ignored. Evans and Honkapohja (2001) show that setting γt,s = 1/t results in a recursive formulation of ordinary least squares. In the same vein, Malmendier and Nagel’s specifications for the gain parameter results in a recursive formulation of weighted least squares. The authors begin recursion “at some point in the distant past” and argue that initial conditions get downweighted fast enough so that they are irrelevant. I make a slight adjustment during estimation, due to the singularity of the Rt;s matrix.

.

The coefficents are estimated recursively:

where t is time and s is birth year of individual and

measures the degree and direction of the inflation surprise at period t. γt,s controls how much an individual updates the forecast given an inflation surprise at time t. A low γt,s implies nearly unchanged expectations while a high γt,s implies expectations sensitive to inflation surprises.

Key to this model is that individuals ignore experiences before birth in their forecast. Since each cohort has a unique set of lifetime inflation experiences, this allows bt,s to vary across time and cohort, producing heterogeneous inflation expectations in one period. Malmendier and Nagel show that this heterogeneity in expectations is due to either (1) differences in individuals’ perceived long-run, mean inflation, or (2) from perceived persistence , or autocorrelation, of deviation of inflation from this mean.

Malmendier and Nagel specify:

Figure 2: Implied Weights on Past Data: Implied weights on past experiences based on parameter values. This figure is a replication of Figure 2 in Malmendier and Nagel (2013) Rather than assuming whether recent or past experiences hold more weight, the model allows the data to shape the behavior of memory. Consider Figure 2, which plots the implied weights on inflation experiences for a 50-year old individual.

For θ= 1, individuals weigh all historical data since birth equally. θ< 1 implies experiences in the distant past receive more weight while θ> 1 means recent experiences hold more weight.

The psychology literature (Hertwig et al. 2004) posits that individuals use information from personal experiences and or from summary information, which includes news or historical information.

The authors allow such summary information to influence expectations by adding a common factor ft into the learningfrom-experience model:

Columbia Economics Review

47 Expected inflation is a weighted average of learning from experience and a common factor to the time period. The β represents the contribution of lifetime experiences to inflation expectations. The common factor captures any effect that is common to a time period by varies across time. Included in the factors are, for example, the opinions of professional forecasters or available historical information. For estimation, time fixed effects replace the common factor:

The authors also add disturbances εt;s which are assumed to be uncorrelated with τt+1|t,s. The disturbances are allowed to be correlated within a cohort across time or between cohorts in one time period. The authors estimate β and θ .

the survey primarily asks interviewees about expectations of their own and broader economic conditions Data Following Malmendier and Nagel, I estimate the learning-from-experience model by using 46 years of cross sectional data from the Michigan Surveys of Consumers and the Survey of Consumer Attitudes and Behavior. The Michigan Surveys of Consumers is a monthly survey of consumer expectations in operation since 1978. Each month, the survey center telephones and interviews approximately 500 adults in the contiguous United States. Interviewees are selected by random telephone sampling aided by a proprietary sampling mechanism that approximates a representative sample of households. An independent subset of interviewees, approximately 40 percent, are reinterviewed six months later, resulting in a rotating panel design.

The survey primarily asks interviewees about expectations of their own and broader economic conditions. In addition,

48 a few questions ask about current personal economic conditions and demographic information of interviewees including age, race, assets, income, and education.

The sum of weighted re-sponses to five core questions, normalized to a base, is the Index of Consumer Sentiment widely reported in the media. The survey responses from 1978 are available from the Thomson Reuters/University of Michigan Survey Research Center.

Of interest are responses to the question: By about what percent do you expect prices to go (up/down) on average during the next 12 months? Respondents give a percent estimate of future inflation.

While the official survey began in 1978, an earlier version of the survey that asks about inflation expectations began in 1954 as the Survey of Consumer Attitudes and Behavior (SCAB). These surveys are available from the Inter-University Consortium on Social and Political Research (ICSRP). However, the earliest versions of this survey from 1954-1965 only elicit categorical responses about whether prices were expected to rise or fall, but do not have continuous estimates. Malmendier and Nagel calculate continuous responses from categorical responses for these early surveys, an exercise omitted in my analysis. Therefore, I only use survey responses from 1966-2013 that give continuous responses.

I use historical data on the quarterly Consumer Price Index (CPI) from Shiller (2005). Data extend from 1872-2013.

Detailed procedure for data collection and preparation is in Appendix A. Following Malmendier and Nagel, I subset the data to those that who were 24 to 75 years old at the time of the survey. In addition, for each survey period and cohort, I calculate the mean weighted inflation expectation. If there are more than one survey in a period, I take the mean inflation expectations of all surveys in a quarter for each cohort.

Figure 3: Inflation Expectations by Age Group: Four-quarter moving average

Fall 2015 representation of mean inflation expectations by age group, depicted as deviations from the cross-sectional mean expectation. Data from the Michigan Surveys of Consumers.

Using the Michigan Surveys, Figure 3 plots four quarter moving averages of inflation expectations of different age groups, shown as deviations from the mean. The figure depicts three hallmark observations of inflation expectations.

One, inflation expectations are heterogeneous, with almost 0.3 deviations in expectations between individuals under 40 and over 60 in the late 1970s. Two, the inflation shock of the 1970s affected young people’s expectations immediately, while old people’s expectations reacted slowly.

A similar observation occurs in the nearde ationary episode in the 2000s. This supports a feature of the weights in the learning from experience model, where older people discount information from recent experiences. Finally, young people began with above average expectations that trended down until they became below average in the 2010s, and vice-versa for old respondents. This supports learning from experience; young individuals in the 2010s lived through relatively stable inflation history while old people today experienced high and volatile inflation in the 1970s.

Figure 4: Demographic Change among Interviewees 1960-2010: Age distribution of respondents to the Michigan Surveys by decade. Note that Malmendier and Nagel (2013) only use respondents who were aged 25 to 74 at the time of their survey interview. However, above figure is constructed using all respondents to the survey, to capture the full dynamic of demographic aging. The survey does not interview individuals under 18.

Figure 4 plots the evolution of the age distribution of respondents to the Michigan Surveys. Note that the survey only interviews those over 18, skewing the distribution, particularly in the 1960s. In addition, while Malmendier and Nagel’s estimation only includes respondents

Columbia Economics Review

who were 25 to 74 years old, I include all in Figure 4 to capture the full age distribution over time. The trend is striking and clear. It charts the post-war demographic evolution in the U.S. The plot in the 1960s excludes the then recent post-war baby boom, since most of the baby boomers were likely under 18 and ineligibile for the survey. But in all later decades the baby boomers are represented by a visible bump, which ages over time. Later, in the 2010s the plot appears left-skewed.

Simple cross-sections confirm well-documented facts about demographic aging in the U.S.

Figure 5: Annual CPI Inflation Rates: Four-quarter moving average of annual CPI inflation rates.

Figure 5 plots log differenced annualized inflation rates by quarter, from 1873 to 2013. I took, as do Malmendier and Nagel, four quarter moving average of inflation to smooth fluctuations. Of note is modern inflation history after World War II. After decades of low inflation, the oil shocks in the 1970s began a period of persistent and unstable high inflation. Only starting in the mid 1980s does inflation subside, beginning the so-called Great Moderation of low and stable inflation rates. During the Great Recession, there was a possibility of deflation and the figure captures both rapid disinflation as well as increasingly unstable inflation.

Estimation Results I estimate the learning from experience model using non linear least squares.

Note that the Michigan Surveys of Consumers solicit expectations about inflation one year later, while the inflation series and the learning-from-experience forecast uses quarterly data. Therefore the authors employ multi-period forecasts by iterating on the AR(1) model at time t and producing forecasts for t + 1, t + 2, t + 3, and t + 4. The final learningfrom-experience forecast is the mean of the four forecasts.

Table 1 reports results of the estimation,

Fall 2015 withholding the time fixed effects.

Table 1: Estimates from AR(1) Learning-from-Experience Model: The estimates are from a non-linear regression of one-year survey-reported inflation expectations on learning-from-experience forecasts. Malmendier and Nagel (2013) withhold significance levels of estimates, an approach adopted in my analysis. Malmendier and Nagel calculate standard errors that are clustered twoway by time and cohort. Due to the computational cost of calculating two-way standard errors for non-linear parameters (Cameron et al. 2009), I only include unrobust standard errors.

It is worth emphasizing that Malmendier and Nagel do not indicate the significance levels of their estimates, so I also omit them from my table. Column (1) reports Malmendier and Nagel’s results.

Their estimate for θ, 3.144 (cl. s.e. 0.257), suggests that recent experiences receive higher weight than past experiences, and the weights decrease slightly faster than linearly over time. Surprisingly, when Malmendier and Nagel (2011) fit a similar model to experienced stock returns and stock market participation in a separate dataset, they receive almost identical sequence of weights on past data.

The sensitivity parameter β, 0.675 (cl. s.e.

0.079), suggests that for every 1% point difference in learning-from-experience forecasts between two individuals, their inflation expectations differ, on average, by 0.672% points.

There may be serial correlation in the error terms within a cohort across time or correlation in the errors within a cohort in a time period. Malmendier and Nagel use standard errors that are robust to two-way clustering, with clusters by cohort and quarter. But calculating twoway clustered standard errors for a nonlinear model is computationally costly (Cameron et al. 2009) relative to my analysis, which does not ultimately depend on these standard errors. My errors are non-linear least square estimators, but are not clustered. This does not affect my actual parameter estimates for θ or β, but the standard errors will potentially be biased downward. Care needs to be taken when interpreting the significance of my

estimates. Although this is one drawback to the replication, it is immaterial to the interpretation of simulated counterfactuals considered later.

Malmendier and Nagel do not report the significance of their estimates. Although they mention that the estimate of β is significant, they do not indicate at what level. Since our is a non-linear least squares estimator, I assume that β is asymptotically normally distributed.

The authors’ estimate of β is significant at the 1% level under this assumption. The gain parameter θ is also a non-linear least squares estimator, but Malmendier and Nagel never assess its significance.

My replication results are nearly identical to those of Malmendier and Nagel.

Column (2) of Table 1 reports my estimates. My θ, 3.070 (s.e. 0.263) and β, 0.630 (s.e. 0.057), are close to the authors’ original estimates in column (1), with my estimate of β falling in a 95% confidence interval around Malmendier and Nagel’s estimate.

My estimate for θ confirms that experiences decline in importance over time.

The sensitivity parameter β, 0.632, suggests that for every 1% point difference in learning-from-experience forecasts between two individuals, their inflation expectations differ, on average, by 0.632% points. The replication results show that 52.9% of the variation in inflation expectations can be explained by learningfrom-experience. While my replicated model has explanatory power, it does not fit the data as well as Malmendier and Nagel’s estimates. I cannot compare the standard errors, as Malmendier and Nagel use two-way clustered errors while my standard errors are non-linear least square estimates. Given that the disturbances can be correlated within a cohort and across time, my standard errors may be underestimating the error.

While Malmendier and Nagel use inflation expectations data from 1965 to 2009, I re-estimate the model using the most recent Michigan Surveys data on inflation expectations, which range from 1965q2 to 2013q1. They are reported in column (3) of Table 1. The estimate of θ using recent data is slightly higher than in column (2), but the unrobust standard errors are identical. The sensitivity β falls slightly but is more precise relative to (2).

Malmendier and Nagel consider possible omitted variable bias in their model.

They focus on the possibility that their results are driven by different inflation rates in age-specific consumption baskets. That is, lifetime inflation experiences may be correlated with recent age-specific inflaColumbia Economics Review

49 tion rates. The authors re-run estimation controlling for differences between the overall CPI inflation rate and a CPI constructed from a common consumption basket for the elderly obtained from the Bureau of Labor Statistics. They find that their new results are not statistically different from original estimates, suggesting that their results are robust to age-specific inflation rates.

The authors in addition explore the common factor captured by the time fixed effects. They first consider the possibility that the time fixed effects capture the opinions of professional forecasters by replacing the time fixed effects with professional forecasts from the Survey of Professional Forecasters (SPF). They obtain similar estimates for β and θ, suggesting that SPF forecasts align closely with the common factors captured by time fixed effects. Another possibility they consider is that the common factor is a result of socializing with others about inflation expectations. Malmendier and Nagel rerun the model but replacing the mean learning-from-experience forecast across all age groups instead of the time fixed effects. They obtain almost identical estimates as with learning-from-experience, suggesting that the time fixed effect is absorbing the effect of socializing on inflation expectations.

The analysis depends on estimating personal inflation experiences based on birth date and headline inflation rates.

But a prominent literature has suggested that headline inflation masks considerable heterogeneity in actual, individually experienced inflation (Hobijn et al 2009).

Therefore approximating individual experiences with macroeconomic history is imprecise. Maderia and Zafar (2012) exploit demographic information available in the Michigan Surveys, such as gender, ethnicity, and education levels, to construct group-specific inflation rates. They estimate a similar learning-from-experience model using these group-specific inflation rates to more precisely predict individual-level inflation experiences.

They find that such an adjustment has little extra explanatory power, suggesting that headline inflation rates sufficiently capture inflation experiences. Their result follows other work that confirms different individual inflation experiences do not explain observed heterogeneity in infla-tion expectations (McGranahan and Paulson 2006).

However, this class of models does not have complete identification. While Malmendier and Nagel show that learningfrom-experience strongly explains infla-

Fall 2015

50 tion heterogeneity, there is unconvincing analysis on whether the memory of high inflation experiences is causing individuals to give higher inflation expectations.

They claim that time fixed effects in the model “rule out that omitted macroeconomic variables or any other unobserved effects common to all individuals bias the estimation results.” They do not disentangle other effects that may bias their estimates. Formally, their assumption that the εt;s is uncorrelated with the learningfrom-experience forecast is problematic.

For example, there may be cohort-level effects. Since lifetime inflation experiences are determined by birth, any cohort-level effect will be correlated with the learning-from-experience forecast. It is fairly possible that this cohort effect, which can capture generational attitudes toward economic decisions, can affect how individuals form expectations. A cohort effect, by definition, varies across individuals in one time period. Therefore the time fixed effects Malmendier and Nagel place do not cleanly identify the model

since lifetime inflation experiences are determined by birth, any cohortlevel effect will be correlated with the learning-fromexperience forecast

It is worth noting that, since I make predictions using the learning-from-experience model, I do not depend entirely on the robustness of Malmendier and Nagel’s identification.

Simulation In this section I run simulations on the learning-from-experience model. The following counterfactuals will assess the relative importance of demographics and history in aggregate inflation expectations. Particular attention is given to how well the model explains stable inflation

expectations during the Great Moderation.

It is possible that individuals consult others when forming expectations. Since a demogaphic shock may remove people who could have influenced others’ beliefs, simulating predictions based on the model described by equation (6) will be inaccurate. I estimate Malmendier and Nagel’s learning-from-experience model with social learning. It is based on the assumption that as individuals share opinions, their opinion tends toward to the average opinion (DeGroot 1974). Denote τt+1|t,s=b’t,sxt the learning-from-experience fore-cast at time t for individual of cohort s. Let therefore be the average learning-from-experience forecast across all individuals in a time t. Learning-fromexperience with social learning is therefore:

Column (4) of Table 1 reports estimates.

The gain parameter is higher than the one reported in column (3), which is a pattern Malmendier and Nagel also find. They compare estimates, but do not perform inference to verify that the variation is insignificant.

I examine five aggregate properties of inflation expectations in simulation: (1) the inflation expectation, (2) inflation expectations with social learning, (3) the perceived autocorrelation, or mean-reversion, (4) the perceived mean, (5) disagreement about inflation expectations, and (6) disagreement about inflation expectations with social learning. Variables (1) to (4) are simply the weighted mean across all surveyees at time t.

The perceived autocorrelation (3), φ, is the tendency for expectations to return to the perceived long-run mean. Thus, it is one measure of the anchoredness of inflation expectations. For positive values, a low φ denotes well-anchored expectations while a high φ represents unanchored expectations. It is difficult to interpret a negative φ. I treat a more negative phi to mean unanchored expectations, because in that case expectations can change dramatically from short-run fluctuations. The aggregate perceived autocorrelation is simply the mean perceived autocorrelation across individuals at time t.

A note on language. For clarity, I will refer to the baseline, unsimulated time series produced by learning-from-experience as the “actual series.” The actual

Columbia Economics Review

series are time series predictions by the learning-from-experience model using (1) actual U.S. inflation history and (2) actual distribution of the sur-veyees.

Demographic Shock What is the effect of demographic shocks on aggregate inflation expectations? If there are two individuals, the rest born in year s and the second in s + j, only the first individual experiences events between s and s + j. Learningfrom-experience implies that they may form different inflation expectations since their experiences differ. It is possible, then, that a demographic shock that removes either individual could change aggregate inflation expectations.

I define several demographic groups: those younger than 16, 16 to 30, 31 to 45, 46 to 60, and 61 to 74 year olds. The demographic shock permanently removes one cohort. For example consider a shock that removes all 40 year olds at time t. After the shock, there are no longer 40 year olds at time t. At time t + 1, there are no 41 year olds in the sample, but there are 40 year olds at t + 1 since those aged 39 at t have aged one year. Since Malmendier and Nagel excluded respondents older than 74, my demographic set excludes them also. I do include groups of people younger than 25, even though they are not in the authors’ analysis. They enter the population after some time. For example, although a 1 year old does not respond to the survey, the 1 year old does enter the surveyee pool decades later.

I set the shock at 1988 for the simulation considered here. This is because it is approximately the beginning of Alan Greenspan’s tenure at the Federal Reserve, thus signaling a change in the monetary policy regime. The timing may be informative, because some have attributed low inflation and stable expectations in the past two-and-a-half decades to prudent monetary policy (Davis 2012).

The goal of setting demographic shocks at 1988 is to explore an alternative explanation for the path of inflation expectations during the Great Moderation.

Figures 6 to 11 show the effect of removing each cohort on aggregate prop-erties of inflation expectations. Each figure corresponds to the variables of interest described early in this section. Overall, these demographic shocks did not substantially affect the variables studied, or the effect dies out by 2013.

Fall 2015 ing by 0.32% points. In contrast, removing those between 30-45 reduced inflation expectations by 0.6% points by 2013.

However, none of these changes is relatively substantial.

Figure 6: Change in Aggregate Inflation Expectations Due to Demographic Shock at 1988: Change is shown as the difference between aggregate inflation expectations with demographic shock and actual expectations, both predicted by learning-from-experience. The shock occurs at 1988. To remove high-frequency variation, differences are shown as fourquarter moving averages. The aggregate inflation expectation is simply the average predicted expectation from learningfrom-experience. Individual titles correspond to age group removed at shock.

Figure 7: Change in Aggregate Inflation Expectations with Social Learning Due to Demographic Shock at 1988: Change is shown as difference between aggregate inflation expectations with demographic shock and actual expectations, both predicted by learning- from-experience with social learning. The shock occurs at 1988.

To remove high-frequency variation, differences are shown as four-quarter moving averages. The aggregate inflation expectation is simply the average predicted expectation from learning-from-experience with social learning. Individual titles correspond to age group removed at shock.

According to Figure 6 and 7, aggregate expectations stayed nearly un-changed.

At most, removing the <16 years old cohort increased inflation ex-pectations by 0.01% points by 2013. With social learning, the change in expec-tations is of a slightly greater magnitude than with learning-from-experience predictions. By 2013, removing <16 year olds increased inflation expectations with social learn-

Figure 8: Change in Aggregate Perceived Autocorrelation of Inflation Due to Demographic Shock at 1988: Change is shown as difference between aggregate perceived autocorrelation of inflation due to demographic shock and actual perceived autocorrelation, both predicted by learning-from-experience. The shock occurs at 1988. To remove high- frequency variation, differences are shown as fourquarter moving averages. The aggregate perceived autocorrelation of inflation is simply the average perceived autocorrelation at t from learning-from-experience.

Titles correspond to age group removed at shock.

Similarly, Figure 8 shows that removing the cohort younger than 16 increases the perceived autocorrelation of inflation by 0.04% points while remov-ing those aged 31 to 45 decreases it by 0.05% points. This loosely suggests that the young comprise the component with the best anchored expectations and those aged 31-45 is the component with the worst anchored inflation ex-pectations. Since better anchoring of inflation expectations is a welcome but puzzling recent phenomenon (Davis 2012), these demographic shocks suggest that better anchoring is associated with different demographic groups.

Figure 9: Change in Perceived Mean Inflation Due to Demographic Shock at 1988: Change is shown as difference between aggregate perceived mean of Columbia Economics Review

51 inflation from demographic shock and actual perceived mean, both predicted by learning-from-experience. The shock occurs at 1988. To remove high-frequency variation, differences are shown as fourquarter moving averages. The perceived mean of inflation is simply the average perceived mean at t from learning-fromexperience. Individual titles correspond to age group removed at shock.

Figure 10: Change in Disagreement about Inflation Expectations due to Demo- graphic Shock: Change is shown as difference between disagreement in inflation expecta- tions due to demographic shock and actual disagreement, both predicted by learning-from-experience. The shock occurs at 1988. To remove high-frequency variation, differences are shown as four-quarter moving averages. The perceived mean of inflation is the average perceived mean at t from learning-fromexperience. Individual titles correspond to age group removed at shock.

Figure 11: Change in Disagreement About Inflation Expectations Due to Demographic Shock with Social Learning: Change is shown as difference between disagreement in inflation expectations due to demographic shock and actual disagreement, both predicted by learning-from-experience with social learning. The shock occurs at 1988. To remove high-frequency variation, differences are shown as four-quarter moving averages.

The perceived mean of inflation is simply the average perceived mean at t from learning-from- experience. Individual titles correspond to age group removed at shock.

Fall 2015

52 Demographic Aging Learning-from-experience posits that older individuals, already with more experiences, are less impressionable to new inflation surprises. Formally, the gain parameter,γt,s,declines with age. Given the coincidence of demographic aging in the U.S. captured by Figure 1 and better anchored inflation expectations, a natural question is to ask whether there exists a link between the two. That is, does demographic aging explain (1) lower and stable inflation expectations and (2) better anchored inflation expectations according to learning-from-experience?

The relevant counterfactual for comparison is if the U.S. did not experience demographic aging. I take the population distribution at 1985 and fix it for every time period after 1985. Individuals still age in this counterfactual, but the population as a whole, or the average age, has stopped aging. 1985 is what some consider as the start of the Great Moderation (Stock and Watson 2003). Jaimovich and Siu (2009), in their counterfactual analysis of demographic change and the Great Moderation, set the age distribution of the population fixed after 1985 for this reason.

Figure 12: Change in Aggregate Properties of Inflation Expectations with NonAging Demographic Distribution After 1985: Change is shown as difference between simulated series and actual series.

Inflation expectations are average inflation expectations at time t predicted by learning-from-experience.

Expectation with social learning is average inflation expectations at t predicted by learningfrom-experience with social learning.

Perceived autocorrelation is mean perceived autocorrelation of inflation in AR(1). Disagreement in inflation expectations is the standard deviation of expectations predicted by learning- from-experience. Disagreement with social learning is the standard deviation of expectations predicted by learning-from-experience with social learning. To remove high-fre-

quency variation, differences are shown as four-quarter moving averages.

Figure 12 illustrates the change in the six variables of inflation expectations with the demographic freeze” at 1985.

Aggregate inflation expectations predicted by learning from experience and with social learning barely changes; by 2013 aggregate expectations and expectations with social learning in the simulation are 0.06% points and 0.08% points lower, respectively. Against this counterfactual, aging population since 1985 is associated with higher inflation expectations, at most up to 0.15 percentage points by 2010. While the absolute change is modest, it is evidence against the role of demographic aging in lowering inflation expectations.

Figure 13: Comparison of Perceived Autocorrelation: Both series are the means at time t of perceived autocorrelation of inflation predicted by learning-from-experience model. The solid line is actual perceived autocorrelation while the dotted line is perceived autocorrelation with non-aging demographic distribution at 1985.

Surprisingly, perceived autocorrelation fell. Figure 13 compares the time series of perceived correlation under actual demographics and under the demographic freeze.” In 2013 for example, a one-percentage point increase in inflation in the past quarter is associated with a 0.13 per-centage point increase in inflation expectations, compared to 0.05 percentage point increase in a world without population aging. In the counterfactual world where there is no demographic aging after 1985, inflation expectations became more anchored, being nearly perfectly anchored for a few years in the 2000s.

According to learning-from-experience, demographic aging since 1985 does not explain better anchored inflation expectations; in fact, demographic aging seems to exert the opposite effect. The result is unusual, since it was hypothesized that an aging population is less impressionable to new inflation experiences.

Columbia Economics Review

Legacy of 1970s Learning-from-experience accepts a demographic distribution and an inflation history to predict aggregate inflation expectations. The prior simulations investigated the role of demographic shocks and shifts on inflation expectations, but found they have a minor impact on inflation expectations. I investigate the effect of history on predictions by learningfrom-experience.

What is the effect of experiencing above-average inflation in the 1970s on inflation expectations today? Since the learning-from-experience model places some weight on past events, events in the 1970s should have a measurable effect on expectations in the future.

The relevant counterfactual is the time series of inflation expectations and its properties if the 1970s actually had average inflation rates. For simulation, I propose a hypothetical situation where between 1965 and 1985 the average inflation rate in this country equals that of the U.S. from 1985-2013. Essentially, in the counterfactual, the U.S. did not have historically above-average inflation experiences. The experience of, for example, West Germany is roughly analogous to this counterfactual. I produce a counterfactual inflation history for this country, tnew where πtnew:

The effect of this rescaling is that the mean inflation in this new series from 1965 to 1985 is the same as that from 1985 to 2013. The constructed and actual inflation series are shown in Figure 14.

Figure 14: Actual Versus Generated Inflation Rates: Solid line is actual annualized CPI inflation rates. Dashed line is alternative, annualized CPI inflation rates rescaled from 1965 to 1985. The alternative inflation series was created by rescaling inflation in 1965-1985 so that average inflation in that period equals the aver-

Fall 2015 age inflation from 1985-2013.

I can now use the learning-from-experience model to generate aggregate inflation expectations for this migrant group.

Comparing expectations for this migrant group to that of the general population (excluding the group) shows us the effect of above-average inflation in the 1970s on current inflation expectations.

Figure 15: Change in Aggregate Properties of Inflation Expectations with Alternate Inflation Series: The alternative inflation series is produced by rescaling inflation from 1965-1985 so that the average in that period is the same as average inflation after 1985. Change is shown as difference between simulated series and actual series. Inflation expectations are average inflation expectations at time t predicted by learning-from-experience.

Expectation with social learning is average inflation expectations at t predicted by learning-from-experience with social learning. Perceived autocorrelation is mean perceived autocorrelation of inflation in AR(1). Disagreement in inflation expectations is the standard deviation of expectations predicted by learningfrom-experience. Disagreement with social learning is the standard deviation of expectations predicted by learningfrom-experience with social learning. To remove high-frequency variation, differences are shown as four-quarter moving averages.

Figure 15 shows the difference between aggregate expectations in this new counterfactual inflation history and expectations with historical inflation. Unsurpringly, inflation expectations before 1985 are substantially lower, because actual inflation in those years is scaled lower. More interesting is the time series of expectations after 1985, when inflation returns to normal, so there is no difference in inflation between the counterfactual and actual series. Aggregate inflation expectations with learning-from-experience and with social learning show that migrant inflation expectations remain lower than that of the general popula-

tion, up to 1% points lower a decade later in 1995. But both expectations converge, and by 2013, counterfactual expectations are 0.07% points lower than the general population.

There is evidence the 1970s unanchored inflation expectations, even decades later. Under the counterfactual inflation series, perceived autocorrelation steadily falls through the 1970s. It is not, however, obvious that autocorrelation should fall by rescaling inflation lower. Even after 1985, when inflation returns to normal rates, autocorrelation continues to fall relative to actual perceived autocorrelation. In the mid 2000s perceived autocorrelation is lower by 0.3% points. These counterfactual inflation expectations are better anchored for every year except for 2006Q1 to 2008Q2, when the autocorrelation is negative. By 2013 in this counterfactual, a one percentage point increase in inflation decreases inflation expectations by -0.02 percentage points. This is compared to the perceived autocorrelation with actual inflation history, where a one percentage point increase in inflation in 2013 leads to a 0.13 percentage point increase in inflation expectations.

Disagreement in inflation expectations decreases for almost every year in the counterfactual. By 2013, the standard deviation in inflation expectations is -0.04% points lower.

disagreement in inflation expectations decreases for almost every year in the counterfactual Downweighting My estimate of suggests that past inflation experiences decline in importance over time. The precise reason for this is undetermined. It could be that past experiences are forgotten and thus carry little weight in expectations. Alternatively, it can reflect the possibility of parametric drift, where past data no longer has predictive content today. One question is to ask what the consequence of downweighting is on current inflation expectations.

Columbia Economics Review

53 The relevant counterfactuals are a time series of inflation expectations where past data does not get downweighted.

I alter learning-from-experience by setting the gain parameter,Îłt,s=1/t which is a recursive formulation for ordinary least squares (Evans and Honkapohja 2005).

Figure 16: Change in Aggregate Properties of Inflation Expectations without Downweighting Past Experiences: Change is shown as difference between simulated series and actual series. Inflation expectations are average inflation expectations at time t predicted by learningfrom-experience. Expectation with social learning is average inflation expectations at t predicted by learning-from-experience with social learning. Perceived autocorrelation is average at time t of perceived autocorrelation of inflation in AR(1). Disagreement in inflation expectations is the standard deviation of expectations predicted by learning-from-experience. Disagreement with social learning is the standard deviation of expectations predicted by learning-from-experience with social learning. To remove high- frequency variation, differences are shown as four-quarter moving averages.

Figure 16 plots the difference in inflation expectations between predictions where past data does not get downweighted the actual series. Both aggregate mean inflation expectations as well as expectations with social learning predict that expectations would be below actual expectations from 1966Q2 to 1997Q3. Expectations without downweighting past experiences are higher, albeit with fluctuations, than the actual series after 1997Q3. There is nearly no difference - about 0.04 percentage points - by 2013 between the two series.

But removing downweighting increases the perceived autocorrelation of inflation expectations. While without downweighting the autocorrelation of expectations fluctuate around actual autocorrelation before 1986Q2, after that the simulated autocorrelation trends higher.

By 2013, a one percentage point increase

Fall 2015

54 in inflation raises inflation expectations by 0.44 percentage points, substantially higher than 0.13 percentage points for a one percent increase predicted with downweighting of past data. In the counterfactual world where individuals do not downweigh past data, inflation expectations are substantially less anchored.

The result suggests that downweighing past data has explanatory power for the recent anchoring of inflation expectations. I follow the method employed in Jaimovich and Siu (2009) for a simple accounting exercise to approximate the magnitude of this effect. I compare the counterfactual autocorrelation and actual correlation predicted by learning-fromexperience. From 1985, had individuals not downweighted past experiences, perceived autocorrelation would have fallen 0.202 percentage points by 2013. This is in comparison to 0.529 percentage points observed with downweighting. Therefore the downweight-ing of inflation experiences explains (0.529-0.202)/0.529 or 61.8 percent of the improved anchoring in inflation expectations since 1985.

the result suggests that downweighing past data has explanatory power for the recent anchoring of inflation expectations Discussion I estimate a learning-from-experience model in which individuals use their lifetime inflation experiences to form inflation exflectations. Using survey-reported inflation expectations from 1966 to 2013, I confirm key findings by Malmendier and Nagel (2013). First, the learning-from-experience model explains 52.3% of the heterogeneity in inflation expectations. Second, my estimate of the gain parameter implies that individuals downweigh past experiences when forming inflation expectations. In fact, when Malmendier and Nagel (2011) estimate a similar learningfrom-experience model to explain stock market participation using experienced

stock market returns, they receive almost identical sequence of weights on past experiences (Malmendier and Nagel 2013).

Third, a 1% point difference in learningfrom-experience forecast is associated with a 0.829% point difference in overall inflation expectations on average. In the model, this implies that differences in inflation experiences, even when holding summary information costant, is correlate with inflation expectations.

Using the replicated model, I study the response of aggregate variables to demographic shocks. Setting the shock at 1988, the beginning of a new monetary policy regime that also coincided with stabilizing inflation in the U.S., demographic shocks might shed life on the path of inflation expectations during the Great Moderation.

Unexpectedly, aggregate expectations, with or without social learning, changed little from any of the demographic shocks.

It is surprising, because the U.S. experienced high inflation in the 1970s that fell in the mid-1980s, which by the learningfrom-experience model should show up as generational differences in inflation expectations. It is possible that after decades of low inflation post-1988, past data gets sufficiently downweighted. In this case, generational differences in experience narrows over time, and expectations converge so that demographic shocks exert little change on aggregate expectations.

The Great Moderation coincided with the aging of the baby-boomers in the U.S. Jaimovich and Siu (2009) show that this demographic shift strongly explains the reduction in business cycle volatility in the U.S. Since learning-from-experience posits that older individuals are less impressionable to new information, there is a possibility that demographic aging can explain better anchoring of inflation expectations. Surprisingly, a simulation that freezesâ&#x20AC;? the age distribution after 1985 produced lower inflation expectations and better anchoring. This implies that population aging since 1985 had actually raised and unanchored, though minimally, inflation expectations. According to the model, inflation expectations fell and became better anchored in the U.S. despite, not because of, demographic aging.

This surprising result is probably due to the specific history of inflation in the U.S. While older individuals in the model are less responsive to new information, people still use lifetime inflation history to forecast inflation. Stopping population aging is essentially reducing the proportion of old people. Therefore, reducing the ranks of older people at 1985 reduces the number of people who experienced high

Columbia Economics Review

inflation in the 1970s. If it is true that the 1970s had raised and unanchored inflation expectations, then it is reasonable for expectations to stabilize when we remove the old cohort who experienced the 1970s.

I also create an alternative inflation history where the U.S. did not experience high inflation in the 1970s. Using the model, I predicted aggregate inflation expectations using this alternate series. As expected, reducing in-ation produced lower inflation expectations between 1965-1985.

After 1985, expectations remain lower than actual expectations, and even a decade later in 1995 counterfactual inflation expectation is 1% point lower than the baseline. There is a slow convergence back to actual inflation expectations, such that by 2013 inflation expectations using alternative inflation history is nearly identical to the actual expectation. This implies that high inflation in the 1970s raised inflation expectations decades afterward, with the effect slowly fading out by 2013.

Not only did the 1970s unanchor inflation expectations, but its effect surprisingly increased with time. Whereas high inflation seemed to have raised perceived autocorrelation by 0.1% points in the early 1980s, by 2000s inflation in the 1970s raised autocorrelation by 0.3% points.

This result that the effect of history increases, rather than diminishes, over time is puzzling and diffcult to reconcile with the model. However, it must be true that given enough time, actual and simulated perceived autocorrelations must converge. This is because at some point everyone who experienced the years before 1985 must die, and the 1970s will become irrelevant to aggregate inflation expectations.

Another result of this simulation is that disagreement in inflation expectations decreases by rescaling inflation in the 1970s.

What this implies is that a modest portion of recent disagreement in inflation expectations can be explained by those who experienced high inflation in the 1970s. This is a sensible finding, since it attributes disagreement to specific episodes of inflation his-tory. People who experienced the 1970s tend to have higher expectations than those that did not, leading to disagreement.

The signal simulation examined the effect of downweighting past experiences on aggregate inflation expectations. Downweighting past data does not seem to exert a clear effect on aggregate expectations, perceived mean inflation, or disagreement. It does, however, have the effect of anchoring inflation expectations substantially. The results imply that

Fall 2015 beginning in the mid 1980s, the downweighting of past inflation experiences better anchored inflation expectations. A simple accounting exercise confirms that roughly three- fifths of the better anchoring of inflation expectations since 1985 can be explained by downweighting past experiences.

This result may be counterintuitive, because downweighting past experiences necessarily implies putting more importance to recent data. Why does downweighting improve anchoring if downweighting must make an individual more sensitive to recent events? One possible explanation is that recent inflation itself has become less persistent, a feature observed in Figure 17, so expectations have become more stable. Downweighting induces higher sensitivity to this less persistent recent inflation. In turn, this translates into lower perceived autocorrelation.

The inevitable challenge of inflation expectations is simultaneity bias. Learningfrom-experience posits that actual inflation predicts inflation expectations. But inflation expectations clearly affects actual inflation, as expectations may drive price-setting decisions (Romer 2003). This requires a system of two equations that are determined simultaneously. Estimating one equation without the other, say regressing inflation expectations on inflation, potentially leaves errors that are correlated with a regressor, namely inflation. This biases estimates.

Figure 17: Comparison of Perceived and Actual Autocorrelations: The dotted line is actual autocorrelation of inflation, as estimated using an AR(1) model fit to inflation rates with a 10-year rolling window. The solid line is perceived autocorrelation as predicted by learning-fromexperience.

Consider Figure 17. It compares the perceived autocorrelation from learningfrom-experience to a 10-year rolling win-

dow estimate of the autocorrelation of actual, not expected, inflation rates. Just as perceived autocorrelation has fallen, so has actual autocorrelation of inflation.

While actual autocorrelation began declining in the early 1990s while perceived autocorrelation only start declining in the 2000s, the two series roughly move together. Since my analysis requires regressing inflation expectations on inflation, simultaneity potentially poses a serious problem for interpreting coeffecients on the AR(1) model.

high inflation in the 1970s raised inflation expectations decades afterward, with the effects slowly fading out by 2013 But the setup of the learning-fromexperience model may sidestep the simultaneity bias. The model posits that at time t, an individual forecasts inflation at t + 1 and her forecast uses available lifetime inflation rates until the end of period t - 1. In other words at t the individual uses data up to and including πt, which she just experienced in its entirety, to form πet+1. The simultaneity problem arises if πet+1 affects πt. But this is improbable, as beliefs cannot change events that have already happened. πet may affect πt., but πt. cannot affect πet in learning-fromexperience, because timing of the model dictates that te is formed before t even happens, thus averting simultaneity bias.

It remains, however, that inflation expectation affects inflation. My analyses only consider the effect of inflation on inflation expectations, and not the opposite effect described for example by the Phillips Curve (Romer 2002). In fact, changes in perceived autocorrelation of inflation are likely to influence autocorrelation of inflation (Milani 2007). This can affect the accuracy of simulations. For example, a demographic shock can change inflation expectations, but later expectations may affect actual future inflation rates. In

Columbia Economics Review

55 turn, the change in actual future inflation causes future inflation expectations to change as well. Running counterfactual simulations on learning-from-experience alone does not account for the response of inflation to inflation expectations. Ultimately, the value of the simulations considered here is the implications of the learning-from-experience model on demographics and history.

Conclusion My analysis shows that the learningfrom-experience model does not predict substantial changes in aggregate inflation expectations due to demographic shocks.

Demographic aging since 1985 also does not explain better anchoring of inflation expectations. Rather, history matters; high inflation in the 1970s raised and unanchored inflation expectations for decades afterward. I estimate that threefifths of the better anchoring in inflation expectations can be accounted for by the downweighting of personal experiences.

A more realistic simulation than the ones considered here would account for the effect of inflation expectations on inflation. Such a modest, but more realistic, addition would help verify the conclusions found here. In addition, future interest in learning-from-experience ought to disentangle the effect of history and demographics. Changing demographics necessarily changes experienced inflation. It is unclear from the simulations which effect, history or demographics, is driving the often surprising results.

The central appeal of learning-fromexperience models is that experience is ubiquitous. Everyone experiences it. It is intuitively appealing that most people are swayed by personal experience in economic decisions, an effect learningfrom-experience quanties. Moreover, an advantage of learning-from-experience is it links micro-level behavior to aggregate outcomes. Models based on experience potentially can explain other macroeconomic phenomena besides inflation expectations.

But why does personal experience matter? Learning-from-experience documents how personal experience predict expectations, and that there is evidence experience explains the differences in subjective expectations. Their model does not, however, explain why individuals weigh personal experience more than information gleaned from summaries. n

CER Journal & Content Online at

columbiaeconreview.com Read, share, and discuss Keep up to date with web-exclusive content

Columbia Economics | Program for Economic Research Printed with generous support from the Columbia University Program for Economic Research