Aenorm 79

The winning paper of the Econometric Game:

Forecasting Spanish GDP in a Rich Data Environment And:

Avoiding Simplification Strategies by Introducing Multi-Objectiveness in Real World Problems.

What is the Appropriate Size of the Banking System?

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vol. 21 jul ‘13

Colofon Editorial Board Marc van Houdt Bas Koolstra Design United Creations © 2009 Lay-out Marc van Houdt Bas Koolstra Cover design United Creations

Farewell UvA by: Jan F. Kiviet

Circulation 1750 A free subscription can be obtained at www.aenorm.eu.

Advertisers DNB Flow Traders Mercer NIBC TNO Towers Watson Information about advertising can be obtained from Marc van Houdt via info@vsae.nl Insertion of an article does not mean that the opinion of the board of the VSAE, or the redactional staff is verbalized.

Nothing from this magazine can be duplicated without permission of VSAE. No rights can be taken from the content of this magazine.

ISSN 1568-2188 Editorial Board adress VSAE Roetersstraat 11, E2.02 1018 WB Amsterdam tel. 020-5254134

Reaching the age of 65 years this summer, Dutch law declares me a pensioner! Whereas until recently my marginal product was still appraised at 10K Euros gross per month (with some exaggeration), soon my domestic market value will suddenly drop to nil. Isn’t that curious? Such ruthless age discrimination should be unlawful. In the US and Canada employees cannot be sacked simply because of their age. Retirement decisions are made by the individual concerned. They are fully based on personal circumstances, such as health, ambition, work ethic and morale, and on the individually collected financial provisions to survive as a senior citizen. Employers may use particular sticks and carrots to influence the outcome of that decision, but tenure means tenure, as long as the employee fulfils her or his duties. As a result, overseas, many professors happily work on until well into their seventies, enjoying double income, namely their salary and their pension. Dutch mentality may qualify this as greedy, but it is not. A (state) pension is not charity. It is the repayment of mandatory life-time personal savings and contributions, under deduction of the lavish salaries earned by investors and actuaries and any miscalculations that they made. These days many young professionals object to mandatory pensions, believing they can manage their savings better and cheaper themselves. I sympathize with them.

I always liked life as an academic very much, both the teaching part and the challenges of doing research, and even the administration involved. So, why passively await being sent home at 65? Two years back I entered a new very stimulating work environment at a young university in Singapore. After 45 years at UvA, first as a student, then as a lecturer etc. time was really ripe for a change. What about pensions and age discrimination in Singapore?

As far as I understand it their system works as follows. To get tenure at a Singaporean university is not easy these days. And when you get it, you lose it at the age of 60. So, during one’s career one should make financial provisions for life after 60. Participating in a pension scheme is not popular and it is not mandatory. So, my Singaporean colleagues actively invest themselves, many of them in private housing. So, as they reach 60, they may own a few houses. The rent provides a steady monthly income. Moreover, this “private pension” – unlike our Dutch (state) pensions – will later be inherited by their children.

However, those able and keen to continue their academic career after 60 are offered a short-term contract, which is renewable, in exceptional cases even until 80+. I’m thrilled by the continuation of the appreciation and flattering compensation of my marginal product in this fascinating part of the world, during the six months per year that my wife and I choose to live and work there, as long as health, ambitions and good fortune will permit.

That is why I will not obey the Dutch tradition to give a valedictory lecture, in which one reflects on the end of one’s career. I’m still in the forward looking phase, not ready yet to say farewell to econometrics and academia. However, I’m keen to exploit the podium offered by this preface to thank all faculty, staff and students with whom I had the pleasure to work over so many decades at the University of Amsterdam. I hope to keep seeing many of you during the years to come, and to continue collaborating with some of you. Farewell UvA.

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BSc - Recommended for readers of Bachelor-level MSc - Recommended for readers of Master-level PhD - Recommended for readers of PhD-level

Equity Risk under Solvency II

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by: Timo van der Veen and Hans Heintz

by: Dewi Werkhoven and Dirk Schoenmaker After the global financial crisis, the size of the banking sector has become a hotly debated topic, as the government rescued several banks. To measure the size of the banking system a country’s banking assets divided by the country’s gross domestic product (GDP) is commonly applied as a yardstick. We argue that this yardstick is too simplistic, as it does not take into account differences in financial needs. In particular, countries differ with regard to the number and size of multinational enterprises. In a cross-country empirical study, we find a strong relationship between the presence of large banks and the presence of multinationals.

Report: Econometric Game 2013

vol. 21 00 June m. y. ‘ 13

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All regulations induce both intended and unintended effects. The aim of Solvency II is clear, but certain consequences of the regulation may lead to an undesirable situation.

This article illustrates that regulations imposed by Solvency II may not lower the risk for policyholders as much as intended. This is particularly true with respect to the treatment of equity risk. The analysis of CEIOPS to measure equity risk neglects a variety of factors that are important for analyzing portfolio risk in the long-term. This article argues that the duration of liabilities plays an important role in insurance companies’ risk profile, and that the requirements for equity risk should explicitly incorporate this. Literature shows that as the investment horizon increases, stocks become less risky while providing relatively high returns. This implies that capital requirements on equity must be decreasing with the duration of liabilities of a life insurance company.

Target rate of return as an alternative to the funding ratio

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by: Mara Laboyrie A special report on the Econometric Game 2013 that took place in April in Amsterdam.

Econometric Game 2013: Forecasting Spanish GDP in a Rich Data Environment

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by: Guillermo Carlomagno, Andres Garca-Suaza, Salvatore Lobello, Michelle Sanchez and Pedro Sant’Anna Recently, there is some evidence that the effectiveness of fiscal policies are not independent of the economic situations. Hence, being able to provide real GDP growth forecasts using all the available information is crucially important for economic authorities. In this paper, using a dataset of 70 different variables for the period 1970-2012 at quarterly frequency, we employ dynamic factors models and LASSO regression techniques to provide different forecasts for the Spanish quarterly GDP growth in 2013. We conclude that these techniques provide superior predictive ability than a simple AR(4) model. Nonetheless, we find superiority of combined forecasts over single-model based predictions. With our preferred model, we forecast for Spanish 2013 yearly GDP growth to be 0.08%.

Data Sharpening in Practice: An Application to Nonlinear Granger Causality

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by: Marcin Wolski and Cees Diks Since the introduction of Granger causality over four decades ago (Granger, 1969), the body of literature on (mainly linear) Granger causality has grown substantially, becoming a standard methodology not only among economists and econometricians, but also finding followers in physics or even biology.

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by: Agnes Joseph and Arno van Mullekom The funding ratio is often seen as the key indicator of financial health of pension funds. In the period 2008 till 2010 the funding ratios of Dutch pension funds dropped spectacularly, raising questions on the adequacy of current regulation and the overall sustainability of the second pillar pension contracts in the Netherlands. All elements of contracts and regulation are currently under reconsideration, but the funding ratio seems to remain the key indicator in every discussion. Nonetheless we think the funding ratio as leading indicator for regulation should also be reconsidered. As an alternative for the funding ratio we mention the target rate of return.

Avoiding Simplification Strategies by Introducing Multi-objectiveness in Real World Problems

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by: Charlotte Rietveld, Gijs Hendrix, Frank Berkers, Nadine Croes and Selmar Smit In business analysis, models are sometimes oversimplified. We pragmatically approach many problems with a single financial objective and include monetary values for nonmonetary variables. We enforce constraints which may not be as strict in reality. Based on a case in distributed energy production, we illustrate how we can avoid simplification by modeling multiple objectives, solving it with an NSGA-II algorithm with a novel comparison operator. Advantages include a strengthened focus on the trade-off relation between financial and non-monetary objectives. We conclude that this approach is very applicable in a business analysis setting.

Puzzle

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Facultive

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What is the Appropriate Size of the Banking System? by: Dirk Schoenmaker and Dewi Werkhoven After the global financial crisis, the size of the banking sector has become a hotly debated topic, as the government rescued several banks. To measure the size of the banking system a country’s banking assets divided by the country’s gross domestic product (GDP) is commonly applied as a yardstick. We argue that this yardstick is too simplistic, as it does not take into account differences in financial needs. In particular, countries differ with regard to the number and size of multinational enterprises. In a cross-country empirical study, we find a strong relationship between the presence of large banks and the presence of multinationals.

Introduction After the global financial crisis (2007-2009), the size of the banking system has become a hotly debated topic as a substantial number of banks needed to be rescued by the government and received state aid in the form of guarantees, provision of equity, transfer of bad assets or a (partial) nationalisation. The average direct fiscal costs of government bailouts over the period 1970-2011 are about 7 percent of Gross Domestic Product (GDP). The size of the financial sector is an important driver of fiscal costs.

This raises the question whether the banking system has become too large and some banks are ‘too-big-to-fail’.

However, being a large international bank is not necessarily troublesome as this allows for ‘risk diversification’. A good example is Spain where small Spanish banks (the so-called cajas) are currently more exposed to the real estate bubble than the large international banks, like Banco Santander and Banco Bilbao Vizcaya Argentaria. In order to assess whether a country’s banking system is too big, a country’s banking assets divided by the country’s GDP is commonly applied as a general yardstick to measure the size of the banking system. But is the banking assets to GDP ratio an appropriate yardstick? It is important to use the right yardstick, because it might otherwise lead to misguided policy decisions. This article questions the use of GDP and will look at the size of the banking system from an economic perspective. We look beyond the banking system itself and investigate a country’s financial needs.

In particular, we examine the relationship between the number and size of multinationals and banks in a country.

banking system. The first view argues that the size of the banking sector should be related to the capacity of the country. This means that, for the government to be able to rescue troubled banks, the size of the sector should not be too large compared to the size of the country. This view uses the ratio of a country’s value of banking assets to GDP, as a general yardstick to measure the size of a country’s banking sector (Levine, 2005).

Dirk Schoenmaker Dirk Schoenmaker is Dean of the Duisenberg school of finance. He is an expert in the areas of central banking, financial supervision and stability, and European financial integration.

Before his appointment at the Duisenberg school in 2009, he served at the Ministry of Finance and the Ministry of Economic Affairs in the Netherlands. Dirk Schoenmaker was a member of the European Banking Committee as well as the Financial Services Committee of the European Union.

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Begin je carrière bij DNB. Ontdek de mogelijkheden op werkenbijdnb.nl

Dewi Werkhoven Dewi Werkhoven is an alumnus of Duisenberg school of finance. He studied at the University of Amsterdam (Business Studies – Strategy & Organisation) prior coming to DSF. At DSF he was enrolled in the MSc Finance, Corporate Finance & Banking track 2011-2012.

Views on size banking sector There is common agreement that the ultimate purpose of the financial sector should be to serve the real economy.

However, there is disagreement about what would be an appropriate yardstick for the size of the financial sector.

There are two main views regarding the size of the

Als je het goed doet, kom je in de krant. Als je het niet goed doet ook.

The second view, which is based on the follow-the-client principle, states that the banking sector should support its clients (Grosse and Goldberg, 1991). According to

Bij DNB werk je in het zenuwcentrum van onze economie.

Iedere beslissing die we nemen, wordt dan ook kritisch besproken door alle Europese kranten. Door de dynamiek van de financiële wereld is geen dag hetzelfde. Steeds weer krijg je te maken met een ander complex vraagstuk en moet je de actualiteit zien voor te blijven. Daarmee lever je een belangrijke bijdrage aan financiële stabiliteit en zorg je voor vertrouwen.

Kun jij die druk aan en zie je het als een uitdaging om onze economie vooruit te helpen? Denk dan eens aan een carrière bij DNB. Kijk voor meer informatie en de mogelijkheden op werkenbijdnb.nl.

Werken aan vertrouwen.

Econometrics

this view, the size of the banking sector should be in line with the financial needs of households and firms. In this article, we focus on the financial needs of an important subset of firms, the multinationals, as multinationals typically prefer to use a main bank of their home country with which they have a good strategic relationship. This means that home banks should follow their clients abroad to service their business needs fully. With regard to this view a possible yardstick is to compare the size of the private sector (in particular the multinationals) to the size of the banking sector.

There are different explanations why multinational enterprises might prefer to use a main bank of their home country. First, Poelhekke (2011) argues that an important benefit of large international banks is their role in facilitating investment in foreign markets. In particular, firms wishing to expand abroad through foreign direct investment may find the services offered by large international banks essential to overcome the market frictions and information asymmetries associated with foreign investment.

Second, scale and scope economies can create sources of competitive advantage in the banking sector. An example of revenue-based economies of scale is corporate banking, for which a large equity base and an international presence are sources of competitive advantage in servicing large international corporate clients. Therefore, countries with relative large multinationals - such as the Netherlands and Switzerland - may also have larger banks because small banks have difficulties catering for multinationals (Dermine and Schoenmaker, 2010).

Finally, (corporate) governance issues might explain why multinationals have a preference for their home bank.

The fact that multinationals and banks are from the same social and political network and judicial environment reduces uncertainty and subsequently risk exposure when multinationals are expanding abroad. For example, Akbel and Schnitzer (2011) identify how the choice of multinationals between centralised or decentralised borrowing is affected by the legal environment –that is creditor rights and bankruptcy costs- of the countries in which a multinational’s subsidiaries operate. They reveal that in countries with weak as well as strong creditor rights, partially centralised borrowing structures are optimal. Moreover, they show that if the bankruptcy costs are higher, the attractiveness of centralised borrowing increases.

these banks serve. We empirically test the following hypothesis: countries that have larger multinational enterprises in terms of consolidated assets also have larger banks.

The focus of the empirical study is on the EU-15 (Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Luxembourg, the Netherlands, Portugal, Spain, Sweden, and the United Kingdom) and Switzerland. To compare the consolidated size of a country’s banks and multinationals, we need to find proxies for large banks and multinationals. For banks, we use the consolidated assets of the four largest banks, because smaller banks have difficulties catering for multinationals. These large banks also account for a large part of a country’s consolidated banking assets.

For multinationals, we use the consolidated assets of multinationals of that country in the world top 100 of non-financial transnational companies (UNCTAD, 2011).

Out of the world’s top 100 largest multinationals, 61 are European enterprises and 60 are located in the countries covered by this study. Thus, the top 100 is dominated by European multinationals.

To make a comparison at the country level the consolidated assets of banks are measured as the aggregate of the consolidated assets of the four largest banks in each country (see Table 1). An exceptional case are countries that have less than four banks ranked in the top-500 of The Banker (2011); these are Belgium, Finland and Luxembourg. Table 1 shows that the United Kingdom, France and Germany have the largest amount of consolidated banking assets in absolute values; € 6.8 trillion, € 6.0 trillion and € 3.6 trillion respectively.

However, if the consolidated assets of a country’s banks are expressed as a ratio to GDP, we see that both the Netherlands and Switzerland have relatively very large banks of 4.2 and 4.9 times the country’s GDP (see Table 1).

Follow the client: multinational enterprises In this section, we investigate which factors explain why some countries have a banking system with larger banks. In line with the follow-the-client principle, it may be that these countries have larger banks due to the fact that they have more and larger global multinationals that

Table 1: Consolidated Banking Assets at Country Level 1

1. This table depicts the consolidated assets of the top four banks per country. Source: Worldscope / Banks (Thomson Reuters), International Financial Statistics (IMF)

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Next, Table 2 shows the consolidated assets of multinationals at the country-level as the aggregate of the consolidated assets of the country’s multinationals that are ranked in the top-100 of non-financial transnational companies. Schoenmaker and Werkhoven (2012) provide a detailed overview of the 60 multinationals that are included in this study. The five largest multinationals -as measured by their consolidated assets in 2011- are Royal Dutch Shell plc (€ 263 billion), Volkswagen Group (€ 247 billion), Électricité de France S.A. (€ 229 billion), BP plc (€ 225 billion) and GDF Suez (€ 212 billion).

As some multinationals have a dual country nationality –for example, Royal Dutch Shell in the Netherlands and the United Kingdom- we include the assets of these

of large banks by 0.5%. In Schoenmaker and Werkhoven (2012), we provide a detailed elaboration of the measurement of the variables, the statistical setup of this study and the regression results.

In sum, our empirical study indicates that the size of a country’s multinationals is related to the size of a country’s large banks. Expressing the size of a country’s financial sector to GDP may thus be an incomplete measure as countries a) differ in their financial needs and b) differ in the number and size of multinationals. We therefore suggest to compare the assets of the banking system in a country to the country’s GDP and to compare the size of large banks to the size of a country’s multinationals. The following yardsticks to measure the size of the financial sector would thus emerge: a.

Banking assets in a country / GDP b.

Consolidated assets of large banks - consolidated assets of multinationals

Table 2: Consolidated Assets Multinationals at Country Level 2

multinationals for 50% in the totals of both countries.

Note that some countries (Austria, Greece, Ireland and Portugal) do not have multinationals in the top 100.

Figure 1 pictures for each EU-15 country and Switzerland the consolidated assets of banks and multinational enterprises for 2011. The graph illustrates that countries that have larger banks also have larger multinational enterprises. Moreover, the size of the ball indicates the number of multinationals, suggesting that countries with larger banks also have more multinationals. Figure 1 thus suggests that there is a relationship between the size of a country’s multinationals and the size of a country’s banks.

This relationship has also been tested statistically. The results suggest that an increase of 1% in the country’s consolidated assets of multinationals may lead to an increase of 0.2% in the consolidated assets of its large banks. Moreover, the results indicate that a 1% increase of the country’s GDP increases the consolidated assets

Figure 1: Consolidated Assets Banks vs Multinationals (2011) 3

Conclusions As a yardstick to measure the size of the banking system, a country’s banking assets are usually divided by the country’s gross domestic product (GDP). But is this an appropriate way to compare the size of the financial sector between countries and to assess whether a country’s financial sector is too large? This study shows that comparing countries’ banking sectors only by using the country’s GDP does not take into account that (1)

2. The table reports the consolidated assets and sales of multinationals at the country level. Source: Worldscope / Industrials (Thomson Reuters), International Financial Statistics (IMF), World Development Indicators (World Bank) 3. The figure shows the consolidated assets of the country’s multinationals and compares this with the consolidated assets of the top four banks for each country (in case less banks’ of a country are listed in The Banker’s top 500, the consolidated value is based on less than four banks). The size of the ball indicates the number of the country’s multinationals in the world’s top 100. Source: Worldscope – Banks and Industrials (Thomson Reuters), International Financial Statistics (IMF), The world’s top 100 non-financial transnational companies (UNCTAD, 2011), Banks’ Annual Report 2011.

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NOTHING BEATS WINNING

countries have distinctive financial needs, as indicated by credit to financial institutions, the government, nonfinancial corporations and households, and (2) countries with more and larger multinational enterprises also have larger banks.

Thus GDP may be an incomplete measure as -besides GDP- other factors are important in explaining the size of a country’s banks. We therefore argue that an additional yardstick for firm-specific financial needs, which compares the size of large banks to the size of a country’s multinationals, may be useful. Countries with one or more large multinationals may thus find it beneficial to have large banks to serve these multinationals. So, the size of banks should also be judged from a wider industry policy perspective.

References Akbel, Basak and Monika Schnitzer (2011). Creditor Rights and Debt Allocation within Multinationals, Journal of Banking & Finance. 35: 1367-1379.

Dermine, Jean and Dirk Schoenmaker (2010). In Banking, Is Small Beautiful?, Financial Markets, Institutions & Instruments. 19: 1-19.

Grosse, Robert and Lawrence G. Goldberg (1991).

Foreign Bank Activity in the United States: An Analysis by Country of Origin, Journal of Banking & Finance. 15: 1093-1112.

Do you thrive on outsmarting your competition?

Levine, Ross (2005). Finance and Growth: Theory and Evidence, in Aghion, Philippe and Steven N. Durlauf (eds.), Handbook of Economic Growth. North Holland: Academic Press Elsevier: 865-934.

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Poelhekke, Steven (2011). Home Bank Intermediation of Foreign Direct Investment, CESifo Working Paper No. 3490.

Schoenmaker, Dirk and Dewi Werkhoven (2012). What is the Appropriate Size of the Banking System?, Duisenberg School of Finance Policy Paper No. 28.

The Banker (2011). The Top 1000 World Banks Ranking: 181-215.

For more information call Dainahara Polonia at 020 7996799.

UNCTAD (2011). World Investment Report 2011: Non-Equity Model of International Production and Development. Annex Table 29: The world’s top 100 non-financial TNCs, ranked by foreign assets, 2010.

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Report: Econometric Game 2013 by: Mara Laboyrie

Introduction

The second day

This year the study association for Actuarial Science, Econometrics and Operation Research and Management (VSAE) of the University of Amsterdam organised the fourteenth edition of the Econometric Game. On the 9th, 10th and 11th of April 2013, the most talented econometricians from all over the world came to Amsterdam to compete against each other in a challenging and socially relevant case.

With the support of the Faculty of Economics and Business of the University of Amsterdam, the college fund of the University of Amsterdam, the Royal Economic Society and our sponsor PwC for the Econometric Game congress, we managed to organise a successful fourteenth edition. Thanks to the hard work of the committee and board of the VSAE for over a year we organized a succesful event. Again there was an oversubscription of universities and this year we welcomed five universities that participated for the first time: The University of Southern California, Nanyang Technological University from Singapore, Perm State University from Russia, Seoul National University from South Korea and the University of Mannheim. We also found two successful professors of the University of Bonn, Jörg Breitung and Matei Demetrescu who created a new and challenging case.

Wednesday the 10th of April the participants started working on the first case. After the case makers gave a short introduction about the case, the teams had until 6 p.m. to hand in their paper. After a long day of hard work and some stressful moments at the end of the day, the committee guided all the participants to the restaurant.

While the participants were enjoying a well-deserved diner, the hard work for the six jury members began.

Around 11 p.m. the jury members joined the participants in the Heeren van Aemstel, near Rembrandtsquare. They announced the top 10 universities that would proceed to the finals. The selected universities were: Seoul National University, Trinity College Dublin, Nanyang Technological University, University of Bristol, University of Essex, University Carlos III Madrid, University of Copenhagen, Warsaw School of Economics, Tilburg University and in particular we were really proud of our own team, the University of Amsterdam, mainly because they didn’t make it to the finals in the last couple of years. With this amazing list of universities most of the finalists immediately returned to their hotel. For the non-finalists, and also some of the finalists, the nightlife of Amsterdam was a complete different challenge than the one they had faced the days before.

The first day After months of preparation, in the morning of the 9th of April, the committee was ready to start the week.

They were all looking forward to meet the contestants, case makers and members of the jury. In the Mozes & Aäronkerk, located at Waterlooplein, the chairman of the committee officially opened the Econometric Game 2013. Thereafter Alexander Rinnooy Kan gave his opinion about the future of econometricians, and the case makers Jörg Breitung and Matei Demetrescu gave an introduction about the case. This year’s topic was ‘The effects of fiscal policy on economic growth’. Dean Han van Dissel of the University of Amsterdam closed the opening ceremony with his welcoming word.

After lunch the participants were guided to the University of Amsterdam where they would be working on the cases for the next three days. They had until 5 p.m. to do research about the subject. After they joined diner, the participants went back to the hotel to prepare themselves for the next day.

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Meanwhile a group of non-finalists got a guided tour from some of our committee members. Despite of the rain, they enjoyed their walk through the beautiful city centre of Amsterdam. In the afternoon, at 2 p.m. the Econometric Game Congress sponsored by PwC took place again in the Mozes & Aaronkerk. PwC opened the congress with speaker Jacques de Swart. Thereafter professor Siem Jan Koopman, one of the judges, and Matei Demetrescu gave a presentation about this year’s topic. At 5 pm the finalists joined the congress to present their solutions to the case.

After the congress the whole group moved to Marie at Marie Heinekenplein where they had dinner and waited for the judges with their results. Around 11 p.m. the redeeming word came and the case makers Jörg Breitung and Matei Demetrescu named the University Carlos III Madrid winner of the Econometric Game edition 2013.

The winners of last year’s edition, the University of Copenhagen, became second and Warsaw School of Economics ended third. After some final words of the case makers and chairman the Econometric Game 2013 was officially ended. The committee and board of VSAE can be proud of this amazing event and it is now up to the next year’s chairman, Kees Ouboter, to organize another successful and great event in 2014.

The final day Early in the morning on thursday the 11th of April, while the non-finalists tried to get some more sleep, the finalists were already on their way to the University. At 9 a.m. the case makers handed out the final case and after a short introduction the finalists began. They had until 4 p.m. to work on a new paper and to prepare a presentation.

Mara Laboyrie Mara Laboyrie is 21 years old and is currently finishing her BSc Econometrics and Operational Research at the University of Amsterdam. After she will finish her BSc she wants to travel around the world and continue with her MSc, probably at the University of Amsterdam. The last two years she was member of the Econometric Game, committee organised by the VSAE. In April 2013 she was chairman of the committee.

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Econometric Game 2013: Forecasting Spanish GDP in a Rich Data Environment by: Guillermo Carlomagno, Andres Garca-Suaza, Salvatore Lobello, Michelle Sanchez and Pedro Sant’Anna Recently, there is some evidence that the effectiveness of fiscal policies is not independent of the economic situations.

Hence, being able to provide real GDP growth forecasts using all the available information is crucially important for economic authorities. In this paper, using a dataset of 70 different variables for the period 1970-2012 at quarterly frequency, we employ dynamic factors models and LASSO regression techniques to provide different forecasts for the Spanish quarterly GDP growth in 2013. We conclude that these techniques have a better predictive ability than a simple AR(4) model. Nonetheless, we find superiority of combined forecasts over single-model based predictions.

With our preferred model, we forecast Spanish 2013 yearly GDP growth to be 0.08%.

Introduction Forecasting the real GDP growth rate is crucially important for economic authorities in order to take efficient policy decisions. This is in general a very challenging task. It becomes even more relevant in times of crisis, when governments tend to make key interventions to correct the adverse situation of the economy.

Nowadays countries in Southern Europe, such as Spain, are experiencing the biggest fiscal imbalances in recent economic history. The current situation seems to call for fiscal stabilization policies, which have to be properly assessed by also taking into account the growth perspective of the countries. Forcing a fiscal adjustment during a crisis might generate vicious circles difficult to escape from. Hence, selecting the inappropriate mechanism can have severe economic and social costs that may last for long periods.

The choice of most appealing fiscal policy is not independent of the economic situation. As we have seen during the first day of the Econometric Game 2013, there is indeed some empirical evidence in the literature on nonlinearities in the way fiscal policy affects the economy, that is, the fiscal multipliers change depending if the

Team Carlos III Madrid University The winning team of the Econometric Game 2013 consisted of the following participants: Pedro Sant’Anna, who is interested in econometric theory and policy evaluation; Guillermo Carlomagno, who is interested in dynamic econometric models, time series and economic forecasting; Salvatore Lo Bello, who is interested in macroeconomic theory and labour markets; Michelle Sánchez, whose interests are in the field of industrial organization and labour economics; and Andrés GarcíaSuaza, whose interest lies in microeconometrics and labour economics.

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economy is in a boom or in a burst period. Therefore, to this extent it is of crucial importance to be able to forecast GDP growth properly.

In order to forecast GDP growth, economists traditionally use classical time series models such as ARMA, ARMAX and VAR models, where in ARMAX and VAR models one can take advantage of additional information through economic variables apart from the GDP. Nonetheless, economists and practitioners tend to use small scale models, in order to avoid in-sample overfitting. This way, an underlying primitive of these models is that the economist knows which variables have strong predictability effect on GDP growth, which might not be too realistic in a time where we have access to hundreds of different macroeconomic and financial variables.

Given the advance of Econometrics and Statistics techniques, recent approaches implemented to forecast key macroeconomic variables take advantage of today’s rich data bases. The possibility of extracting value from the additional information available can significantly improve the forecasting. Because of the nature of these datasets, classical techniques, such as ARMA, ARMAX or VAR, are not feasible for estimation and forecasting, as the

Econometrics

number of regressors (therefore of parameters) is usually bigger than the number of observations. Nonetheless, different techniques have been proposed in the literature to deal with the dimensionality problem, e.g. Dynamic Factor Models, LASSO Models, Factor Augmented VAR, among others.

Our goal in this paper is to forecast the real GDP growth rate for Spain in 2013 by using a rich dataset from the OECD Economic Outlook. In order to do so, we use different models such as a classical ARMA, Dynamic Factor Models, LASSO Models and Factor Augmented VAR. Being agnostic about which model is the “true” one, we also consider a forecasting combination of all the methods. In order to assess the performance of the methods, we perform several forecasting evaluations.

In general, the forecast combination provides the most accurate forecasting in terms of Mean Square Predicted Errors. In line with this model, we predict that Spanish real GDP will grow by 0.08% in 2013.

The rest of the paper is organized as follows. In the next section we perform a detailed data description.

Section 3 presents the models and the estimation results.

In section 4 we perform forecast comparison and evaluation, section 5 concludes.

Data Description We use a rich dataset for Spain coming from the OECD Economic Outlook. It includes all relevant macroeconomic variables for the period 1970-2012 at quarterly frequency. The information includes time series of GDP, prices, expenditures, current accounts, exports, imports, exchange rates, prices, deflators, employment and interest rates. We have a total of 70 variables. Several variables are repeated at different price levels, or both in value and volume. Whenever possible, we decide to keep the variables at 2005 prices in USD and in volume rather than in value. We also add the appropriate deflators. As our target is to forecast the volume of GDP, the strategy that we use does not generate any information loss and at the same time it prevents us from overfitting the model with redundant variables. After deleting the observations with missing values, we are left with a balanced panel spanning the period 1977-2012, with 143 observations.

We work with a total of 45 variables.

Plotting all the series, we can observe that almost all of them are clearly trending over time, while many present a dynamic evolution which could be consistent with a white noise process. Before using these variables in our forecasting model, we therefore need to test for stationarity. For every time serie we run the Augmented Dickey Fuller (ADF) test, the null hypothesis is that the process has a unit root. Given that the data is quarterly we use 4 lags to take into account the likely high correlation between the variables within the same year. The result of ADF tests suggests that we cannot reject the null hypothesis for any of the variables. This is an expected result when dealing with macroeconomic variables

and we can easily tackle this difficulty. We compute growth rates of all the series rather than log-differences (as we have several negative values), solving the nonstationarity in this way. Price levels and deflators are the only problematic variables, as the plot of their growth rate makes us still doubtful about their non-stationarity.

We follow the common practice of taking growth rates again, in order to make sure to have stationary series.

The presence of large outliers in the time series might distort the inference of our analysis. In order to control for this potential threat, we decide to replace the extreme values (over the 97.5 and before the 2.5 percentile) of each time series by the mean of the neighboring values (linear interpolation). To this extent, we simply follow the strategy of Beck, Marcelino and Banerjee (2011).

Methodology In order to exploit the data rich environment, we use different approaches. In particular, we use diffusion Indexes via estimation of a dynamic factor models a-la Stock and Watson (2002) and LASSO model initially proposed by Tibshirani (1996). We prefer to use different models in order to have some room for making comparisons. In this section we provide a brief introduction to Dynamic Factor Models and Lasso.

Dynamic Factor Models Dynamic factor models (DFMs) were initially proposed

by Geweke (1977) as the time-series extension of factor models previously designed for cross-sectional data. The starting point of DFMs is that the dynamics of a high dimensional (n) time-series vector (Xt) are driven by few (q) common factors fit and an idiosyncratic n-vector of disturbances et. The use of DFMs in economics became widespread after Geweke (1977) and Sims and Sargent (1977) who allowed both the factors and the idiosyncratic errors to be serially correlated. The factors (ft) are usually assumed to follow a VAR process whereas the idiosyncratic disturbances (et) are assumed to follow univariate autoregressive processes. Thus, DFMs can be written as: (1) (2) where the lag polynomials i(L) are the dynamic factor loadings of each series in Xt. Assume initially that both equations (1) and (2) are stationary. The idiosyncratic error et is assumed to be uncorrelated with factors’ innovations at all leads and lags (E(et, ETA t-k) = 0 : k).

In the exact dynamic factor model it is also assumed that idiosyncratic disturbances are mutually uncorrelated at all leads and lags, that is, E(eitejs = 0) s if i j .

As noted by Stock and Watson (2011), when the factors are known and the errors (et and t) are Gaussian, an individual variable can be efficiently forecasted

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regressing it on the lagged factors and lags of the variable itself, so that we do not need to include all the variables in the regression. Thus, in words of Stock and Watson (2006) DFMs allow to turn dimensionality from a curse into a blessing. However, not only the factors are unknown but also we do not know how many of them are driving the data. In order to select the number of factors, Bai and Ng (2008) highlight three possible information criteria for determining the number of factors, which are asymptotically consistent.

Lasso Regression Method Another solution to deal with the dimensionality problem in forecasting is to use the Least Absolute Shrinkage and Selection Operator (Lasso), proposed by Tibshirani (1996). The Lasso method is a regularized version of the least squares, which adds the constraint that the L1-norm of the parameter vector, ||β|| is no greater than a given threshold. As it is well known, one can write the constrained problem as an unconstrained one using the Lagrange form of the problem. Hence, the Lasso estimator can be seen as the solution of the least-squares problem with the penalty ||β|| added, where is a given constant. More formally, the Lasso estimate is the solution to

where 0 . If is equal to 0, we have the OLS problem, and as gets bigger, more parameters are shrunk to 0, and hence more regressors are excluded from the model. Knight and Fu (2000) studied the asymptotic properties of Lasso-type estimators. They showed that under appropriate conditions, the Lasso estimators are consistent for estimating the regression coefficients. Moreover, it has been demonstrated in Tibshirani (1996) that the Lasso is more stable and accurate than traditional variable selection methods such as best subset selection.

Results and Forecasts Evaluation ARMA Model We consider the ARMA model as a benchmark. Based on information criteria (AIC and BIC) and Box-Pierce test, we selected a AR(4) model. The model was estimated for the period 1977.3 - 2002.4, and use to forecast the period 2003.1 - 2012.4.

DFM Results We estimate the space spanned by the factors using the principal components approach. For estimating the factors we used the usual normalization criteria, described in Bai and Ng (2008). We select 1, 4 or 5 factors depending on the information criteria used. We consider these three

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possibilities for the forecasting exercise. In the three cases we consider the following model for producing one step ahead forecast of GDP’s growth rate where (L) and (L) are polynomials in the lag operator.

Lasso Results Given the above mentioned advantages of the Lasso methodology, we also use it to forecast the GDP growth.

We consider 8 lags of both the GDP and the other macroeconomic variables as covariates, summing to 360 regressors, more than 2 times the number of observations available. We normalize all the variables to have mean 0 and variance 1, and hence, we do not consider an intercept in the model.

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combination often outperforms estimated optimal forecast combinations - see e.g. Stock and Watson (2004).

For comparing the models we consider one-step ahead forecast errors for the period 2003.1-2012.4. Note that in this exercise we are producing true out of sample forecast given that models are estimated using data up to 2002.4.

In order to be able to statistically compare the models via Mean Squared Predicted Error, we considered the Diebold-Mariano test.

Table 1 shows the sign of the difference between the mean squared errors across the different models. The asterisk makes reference to the statistical significance.

For reading the table, (+) means that the model in the row has a higher mean squared error than the one in the corresponding column. From Table 1 we conclude that the model with one factor and the Lasso model with 4 variables are the best options when comparing to the other models, but we cannot reject that the Factor 1 and Lasso 4 have the same forecasting power. Additionally, the combination of forecasts seems to be the best option overall.

2013 Forecasts Table 1: Diebold-Mariano forecast comparison test Note: * ; ** and *** denote statistically different from 0 at 10, 5 or 1% level.

A crucial step to enjoy the nice properties of the Lasso estimator is to optimize the tuning parameter .

We follow two approaches: first, we set it to the value 0.5, arbitrarily. Alternatively, we use cross-validation and it sets to 0.1, approximately.

It is important to notice that, regardless of the two choices of the tuning parameter, we only select first lag variables. With the ad-hoc value of , we select only two variables (in first lag): total employment (National Accounts basis) and private final consumption expenditure (volume). As expected, once we reduce the threshold, the optimal number of variables decreases: on the top of the aforementioned variables, export market for goods and services (volume, USD, 2005 prices) and inflation (GDP deflator with market prices). All the estimates have the expected signs: higher employment, inflation, exports and consumption lead to higher GDP. An interesting feature is that the Lasso constrains the lags of GDP to zero. Nonetheless, we expect that this variable would improve the forecast accuracy of the model, and hence we introduce the extra restriction that the first lag of GDP must be different from zero.

We now consider the forecasts of GDP growth produced by our models. The four periods ahead forecast with the Lasso model presents an additional difficulty since we need to forecast the “explanatory” variables. In order to do this without losing the rich information contained in the dataset, we do it in a Factor Augmented VAR (see Bernanke, Boivin and Eliasz, 2005).

In Table 2 we present the forecasts of Spanish GDP growth for all 2013 quarters, using the best three models.

All the values are in percentage points. On overall, all models present different forecasts. The Factor model forecasts an overall contraction of 0.24 %, the Lasso an expansion of 0.88 % and the linear combination an expansion of 0.08 %. The forecasts of both Factor and Lasso model are statistically significant. Nonetheless, since the Forecast combination has been shown to have superior predictability than the others two, we believe that the Spanish GDP will present growth very close to zero in 2013.

Conclusions Forecasting the real GDP growth rate becomes even more important in times of crisis, when governments need to choose public interventions with much more care to restore the macroeconomic equilibrium. For instance, economies in Southern Europe are currently experiencing a historical peak in debt to GDP ratios. Hence, public measures have to be properly implemented by taking the growth perspective of the countries into account.

In this report we have analyzed some of the possible models to forecast GDP growth for Spain. We provide some theoretical background on the different specifications and provide our own forecasts for 2013.

Our forecast results for the GDP growth rate in 2013 are very close to zero. This means that Spain is still not recovering from the crisis. Even in the absence of growth, one should find it comforting that the models don’t forecast any further recession. Regarding the fiscal crisis, this result supports the arguments for a smoother adjustment that can also be found in the IMFs country report for Spain of July 2012.

From a methodological point of view, we find that using the high dimensional models is important. This allows a more efficient use of all the information contained in the large dataset and this is reflected in significantly more accurate forecasts.

Forecast Evaluation In this subsection we discuss the forecasting power of the aforementioned models. Moreover, we consider a combination of all forecasts, since different studies find superiority of combined forecasts over single-model based predictions. Moreover, we consider the simple case of equal weights, since equal weighted forecast

Table 2: Point estimates for forecast of GDP growth. All models.

Note: * , ** and *** denote statistically different from 0 at 10, 5 or 1% level.

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References Bai, J., and S. Ng (2008): “Large Dimensional Factor Analysis,” Foundations and Trends in Econometrics, 3(2).

Beck, G., K. Hubrich, and M. Marcellino (2011): “On the importance of sectoral and regional shocks for pricesetting,” CEPR Discussion Papers 8357.

Bernanke, B. S., J. Boivin, and P. Eliasz (2005): “Measuring the Effects of Monetary Policy: A Factor-Augmented Vector Autoregressive (FAVAR) Approach,” The Quarterly Journal of Economics, 120(1), 387-422.

Geweke, J. (1977): “The Dynamic Factor Analysis of Economic Time Series Models,” in Latent Variable in Socioeconomic Models, ed. by D. J. Aigner, and A. S. Goldberger, pp. 365-387. North-Holland, Amsterdam.

Knight, K., and W. Fu (2000): “Asymptotics for lassotype estimators,” Annals of Statistics, 28(5).

Marcellino, M., J. H. Stock, and M. W. Watson (2006): “A comparison of direct and iterated multistep AR methods for forecasting macroeconomic time series,” Journal of Econometrics, 135(1-2), 499-526.

Stock, J. H., and M. W. Watson (2002): “Macroeconomic Forecasting Using Diffusion Indexes,” Journal of Business and Economic Statistics, 20(2).

Tibshirani, R. (1996): “Regression Shrinkage and Selection via the Lasso,” Journal of the Royal Statistical Society. Series B (Methodological), 58(1).

Watson, M. W., and J. H. Stock (2004): “Combination forecasts of output growth in a seven-country data set,” Journal of Forecasting, 23(6), 405-430.

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Data Sharpening in Practice: An Application to Nonlinear Granger Causality by: Marcin Wolski and Cees Diks

Introduction Since the introduction of Granger causality over four decades ago (Granger, 1969), the body of literature on (mainly linear) Granger causality has grown substantially, becoming a standard methodology not only among economists and econometricians, but also finding followers in physics or even biology.

To put it formally, imagine a strictly stationary bivariate process {Xt,Yt}, t Z. We say that {Xt} is a Granger cause of {Yt} if past and current values of X contain additional information on future values of Y that is not contained in past and current Y-values alone. If we denote the information contained in past observations {Xs} and {Ys}, s ≤ t, by FX,t and FY,t , respectively, and let ‘~’ denote equivalence in distribution, the property might be stated in the following definition.

Definition 1. For a strictly stationary bivariate time series process{Xt,Yt }, t N, Xt is a Granger cause of Yt if, for some k ≥ 1 Here it is worth pointing out the difference between the bivariate and multivariate setting. Throughout this paper, we will refer to a multivariate setting by a situation where vectors {Xt} and {Yt} are allowed to be multidimensional, i.e. {Xt} ={X1,t,X2,t,…,Xm,t} and {Yt }={Y1,t,Y2,t,…,Ym,t}, m > 1. Similarly, by a bivariate setting we will refer to a situation where both vectors are univariate (m = 1).

The most commonly used nonparametric test for the above hypothesis testing (Def.1) is that proposed by Hiemstra and Jones (1994). Its main advantage lies in a very clear and intuitive reasoning together with a strong asymptotic theory, derived even for a multivariate setting.

Nevertheless, the test can severely over-reject if the null is satisfied (Diks and Panchenko, 2005). Therefore, Diks and Panchenko (2006) (hereafter DP) proposed a new test statistic, which corrects for this shortcoming but, as it turns out, because of the relatively large kernel estimator bias compared to the variance the DP test can no longer be shown to be asymptotically standard normally distributed in the multivariate setting.

To illustrate this phenomenon, let us first consider the standard, i.e. bivariate, the DP test in a case when k = 1.

Let us further denote {Xt} = X,{Yt} = Y and {Yt+1} = Z. The null hypothesis might be then simplified to and the test statistic becomes

with (.) being the ordinary kernel density estimator ( f o r an example see the next section) with bandwidth being given by εn ~ n-β. For clarity, let W = (X,Y,Z).

Following the methodology developed in DP, the test statistics has a corresponding U-statistics representation, with a mean squared error being dependent on the true variance (Var[r0 (Wi)]), the bandwidth, kernel estimator bias (here α) and the dimensionality of the multivariate

Marcin Wolski Marcin is a second year PhD student, pursuing the European Doctorate in Economics - Erasmus Mundus, at the University of Amsterdam and Bielefeld University. His core topics comprise nonlinear dynamics and econometrics with applications to the macro models. Currently, he explores his interests in collaboration with the International Monetary Fund.

Cees Diks Cees Diks is professor of Data-analysis and Economic Statistics at the University of Amsterdam. He is an expert on non-linear time series analysis, a new field at the border between non-linear dynamical systems and statistical data-analysis. Within his research in the Center for Nonlinear Dynamics in Economics and Finance (CeNDEF) he focuses on detecting and modelling nonlinearities, which often arise in systems with boundedly rational economic agents.

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vector at hand (γ = dX + dY + dZ and δ = dX + 2dY + dZ), i.e.

Assuming ordinary kernel density estimator (with the bias of order 2), it is clear that for the simplest bivariate case, there is a range for parameter, i.e. β (1⁄4,1⁄3), where the mean squared error is dominated by the true variance in the limit. This eventually guarantees that the test statistic is asymptotically normally distributed, i.e. and the properties of the test might be derived analytically.

However, if we increase the system dimensionality by 1, without changing the kernel specification, in order to guarantee asymptotic normality β parameter would have to be between 1⁄(2α) and 1⁄(dx + dy + dz+1), which clearly gives an empty set for the possible β-values.

The solution to the above mentioned problem is the bias reduction in the kernel density estimator. Given that it is lower (so that α-values are larger) there would be enough space for β to endow the test statistics with asymptotic normality.

In this study we apply the Data Sharpening methodology, as it seems to bring extraordinary advantages over the standard bias reduction methods.

Firstly, it is simple and straightforward to implement.

Secondly, it does not affect the derivation of the test properties, i.e. it reduces the bias without having any other impact on the test characteristics, which is clearly very practical in such a complex environment.

Data Sharpening Data Sharpening (DS), as formally introduced by Choi and Hall in 1999, comprises a class of methods, which by a slight perturbation of the original dataset, improves the performance of relatively conventional statistical procedures without any severe consequences.

The applications of DS include, inter alia, estimating a regression function subject to qualitative constraints, increasing the robustness of statistical procedures or reducing the variability of the bootstrap methods.

However, the most widely cited practical adaptation of the DS method is bias reduction in ordinary kernel density estimators. To put it formally, let f denote the unknown distribution of some random variable x. Given a sample of observations (X1,X2,…,Xn), we may estimate the density by the ordinary kernel estimator

where K(.) is a smooth, bounded and symmetric probability density function and h is a bandwidth.

Assuming the standard Gaussian kernel, the bias of the estimator is of order h2 with variance of order . As argued by Choi and Hall (1999), by applying a perturbation (or sharpening) function, Ψ, to the original dataset we may reduce the bias of the estimator, without

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affecting its variance. Imagine a sharpened form of the kernel density estimator

of the sharpening. In general it concentrates the points around high-density regions and makes it more dispersed where their density is low. In small samples it is difficult to determine the ‘true’ high and low density regions which biases the procedure. However, the more observations, the more likely it is that DS works well, which might be clearly observed in Figure 2 – correcting for the nominal size of the test, the power of the test is higher for longer time series.

with the following sharpening function

where hs = 1⁄√(2h) . Choi and Hall (1999) prove that the bias of the sharpened estimator is of order h4 (hence much smaller than the original order h2 with variance’s order unchanged.

Although the range and the scope of DS methods seem to be unlimited, in practice the number of applications remains surprisingly low. For instance, the Web of Science returns only 39 papers which link directly to the original paper of Choi and Hall (1999). One of the reasons for that is fierce competition from the other bias reduction methods, including, for example, higher order kernel estimators, or relatively larger computing power required for more sophisticated problems. Nevertheless, due to its simplicity and straightforward application, we find DS a powerful tool which turned out to solve the majority of difficulties we were facing with the nonparametric Granger causality test in a multivariate setting.

Conclusions

Figure 1. Size-size and power-size plot of the test performance. The length of time series is given in brackets.

Source: own calculations.

Data Sharpening in Practice Let us turn back to the original problem of the bias reduction in the nonlinear Granger causality, described in the introduction. Imagine now that instead of using the ordinary kernel estimator, we replace it by its sharpened form. The expected value of the estimator becomes

In this study we show a practical application of the DS methodology in the nonparametric Granger causality testing. The problems with the asymptotic behavior of the test statistics, which arise as a consequence of the kernel estimator bias in a multivariate setting, might be effectively narrowed bringing back the desired properties.

The numerical results suggest that DS performs rather well in the large samples. Smaller samples might be suffering from the under-rejection bias when the null is satisfied. Nevertheless, practical applications of the Granger causality testing suggest that the size of the samples is much higher than 1000, narrowing the influence of the above-mentioned bias.

Because of the increasing popularity of the nonlinear methods, the DS might quickly find a broader range of applications as it seems that it serves as an ideal solution to possible issues with the nonparametric models.

References Choi, E., and P. Hall. Data Sharpening as a Prelude to Density Estimation. Biometrika 86.4 (1999): 941-47.

Figure 2. Size-corrected power plot of the test performance.

Source: own calculations.

This guarantees that the bias α is of order 4 and, using the same reasoning as before, we may find that for β (1⁄8,1⁄4) the test statistics is asymptotically normally distributed. In principal, it is possible to reduce the kernel estimator bias to arbitrary low levels by applying more sophisticated sharpening functions; see Choi and Hall (1999).

Numerical results In order to evaluate our methodology, we assess the test performance in a situation when the null is satisfied and when it is violated. We simulate 1000 multivariate time series where Granger causality is present (the null is violated) and where it is not. The results are presented in Figures 1 and 2.

We observe that the test performs well in case of the presence of Granger causality. For a time series of length 500 we observe a very high rejection rate, as expected. When the time series are relatively short (100 observations), the test performs worse. If there is no Granger causality between the time series, the test underrejects. However, the longer the time series the closer we are to the 45 degree line, which is the expected shape when the null is satisfied. In fact, the test might be viewed as conservative, in a sense that under-rejection under the null is better than over-rejection.

In practice, Granger causality is assessed on the time series of length much larger than 1000, which increases the power of the test. Nevertheless, it seems that the number of observations plays an important role when DS bias reduction is applied. The straightforward explanation for this phenomenon lies in the functional

Diks, Cees, and Valentyn Panchenko. A New Statistical and Practical Guidelines for Nonparametric Granger Causality Testing. Journal of Economic Dynamics and Control 30 (2006): 1647-669.

Diks, Cees, and Valentyn Panchenko. A Note on the Hiemstra-Jones Test for Granger Non-causality.

Studies in Nonlinear Dynamics & Econometrics 9.4 (2005).

Granger, C. W. J. Investigating Causal Relations by Econometric Models and Cross-spectral Methods.

Econometrica 37.3 (1969): 424-38.

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Equity Risk under Solvency II by: Hans Heintz & Timo van der Veen All regulations induce both intended and unintended effects. The aim of Solvency II is clear, but certain consequences of the regulation may lead to an undesirable situation. This article illustrates that regulations imposed by Solvency II may not lower the risk for policyholders as much as intended. This is particularly true with respect to the treatment of equity risk. The analysis of CEIOPS to measure equity risk neglects a variety of factors that are important for analyzing portfolio risk in the long-term. This article argues that the duration of liabilities plays an important role in insurance companies’ risk profile, and that the requirements for equity risk should explicitly incorporate this. Literature shows that as the investment horizon increases, stocks become less risky while providing relatively high returns. This implies that capital requirements on equity must be decreasing with the duration of liabilities of a life insurance company.

Introduction The main objective of Solvency II is policyholder protection by ensuring financial soundness of insurance companies. The insolvency risk of an insurance company must be reduced to at most 0.5 percent for the coming year, leading to the requirement of holding a minimum amount of capital. Investments in risky assets require higher amounts of capital than less risky investments.

As the (1 year) volatility of stocks is higher than the volatility on bonds, Solvency II considers equity to be riskier than bonds.

Solvency II defines risk as the probability that assets will be insufficient to cover liabilities during the following year. This definition, however, does not take the duration of the liabilities into account. This can be problematic for life insurance companies with long term liabilities. Solvency II requires them to use a mark to market valuation of assets and liabilities. Mark to market valuation introduces swings in their solvency ratios as equity prices are volatile. But there is no reason to liquidate investments in the short term if liabilities lay in the far future. It therefore seems more reasonable to require a life insurance company to meet its (future) liabilities with a probability of 99.5 percent. This seems like a nuance in formulation, but it is not. The difference will become clear at the end of this article.

In his book ‘Stock for the Long Run’ Jeremy Siegel argues that in the long run stocks bear less risk than bonds, while they have a higher return. If true, Solvency II does not only introduce adverse side effects, it also misses its goal to decrease the risk for insurance companies.

Solvency II might bring the insolvency risk for insurance companies to 0.5 percent for the year ahead, but this could lead to a suboptimal asset allocation if a longer time span is taken into consideration.

Multiple institutions saw their capital evaporate during the financial crises of 2008. Regulators responded by increasing the capital requirements. Low supply of capital, combined with a high demand, makes capital expensive as a mean for funding. However, if capital is expensive and the capital requirements for equities

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are high, equity becomes unaffordable for insurance companies. Accordingly, by implementing high capital requirements for equity, Solvency II stimulates insurance companies to reduce their investments in equity. The change of asset allocation increases several risks in the economy. The problem is that this increase in risk is not measurable, but surely affects the policyholders.

Capital Requirements of Solvency II The high capital requirements do not only make equity unaffordable, they also incentivize insurance companies to change their product mix. Products with a defined benefit scheme become too expensive under the new

Hans Heintz After graduating in business econometrics in 1995, Hans joined ING Barings to work within the Trading Risk department. In 2000, Hans became account manager large corporate relations at Deutsche Bank Corporate Finance. In 2006 Hans moved back to ING, where he helped to establish a new model validation department. In 2008 Hans, together with three other partners, founded RiskQuest, an Amsterdam based consultancy firm specialized in mathematical models for financial solutions.

Timo van der Veen In August 2012 Timo graduated with a bachelors degree in econometrics and operational research at the University of Amsterdam.

In September 2012 Timo started the master financial econometrics at the UvA. In the same month he joined RiskQuest to acquire empirical competence in Risk management and to write his thesis.

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regulations. The market-consistent approach of Solvency II values assets at current market prices. The liabilities of defined benefit products are fixed for sometimes more than 30 years, while the assets covering these liabilities bear the risk of a sharp decline in prices every day. It therefore seems attractive to transfer this risk to the policyholder. Defined benefit products become rarer and defined contribution products may be the new norm.

Danielsson et al. (2012) state that “market-consistent valuation induces excessive volatility in solvency ratios for insurers with matched long-term liabilities. Solvency II should introduce measures recognizing the possibility of temporary adjustments in required solvency ratios, to facilitate carrying matched long-term promises.”

Solvency II does introduce a symmetric adjustment mechanism1, which should cover the risk arising from changes in the level of equity prices. If the equity index (MSCI World developed index) is smaller than a weighted average level of this index, the equity capital charge will be lower than the standard capital charge.2 But according to Danielsson et al. (2012) “The proposed countercyclical premium adjustment defines a valuation concept with no economic foundations, and is thus easily manipulated. It even fails to be countercyclical, as it adjusts reserve requirements only in distress.” Although the adjustment mechanism indeed discourages fire sales of equities during an equity crash and thus pro-cyclical effects on the equity market during the first few months of a crisis, it does not prevent pro-cyclical effects if the crisis has a longer time span.

The shift from equities to bonds will affect the economy. As insurance companies (used to) hold a notable share of Dutch stocks3, the portfolio shift to bonds may depress the stock market prices. This shall consequently diminish people’s wealth, which decreases consumption; moreover it decreases the investments of companies, since they will be less inclined to issue new shares and invest the revenues in capital4. There exists a variety of literature that endorses this relationship5.

Please note in this context that insurance companies are highly appreciated shareholders as their long horizon makes them stable partners. Since Dutch insurers invest in Dutch companies, losing them as a shareholder is a clear loss.

CEIOPS’s Model The Dutch central bank (DNB) does not deny that Solvency II gives the incentive to invest in short-term bonds. When asked6 whether this incentive would not be detrimental for the economy, DNB responded: “that might be, but we need solid insurance companies”. The assumption behind this statement is that a larger amount of short term bonds makes an insurance company more solid. We are, however, not convinced that this assumption holds in the long run.

The analysis of risk chosen by CEIOPS determines the cost for holding equity. It is therefore important to assess this model. There are some complications in the measurement of risk. Besides the fact that all quantitative analyses rely on the implicit assumption that information from the past resembles information about the future, the form of the model on which the test are based will influence the outcome. It is therefore crucial to have good arguments that justify the specification of the model.

This specification, again, is an unavoidable assumption in every quantitative model. For that very reason it is important to substantiate the specification of the model not only with economic theory, but also with common sense. The lack of the latter in econometric models is more often considered the reason for the financial crisis.

Within CEIOPS there were three proposals for the equity charge for global equities, each proposal based on the usual Value at Risk (VaR) of different analyses.

The choice for the basis7 level of capital requirement of 45% was grounded on the first proposal, supported by the majority of member states. The analysis for this proposal used the frequency distribution of the MSCI World Developed Markets Price Equity Index annual returns from 1973 to 2009. In this analysis CEIOPS has chosen to “take a rolling one-year window in order to make use of the greatest possible quantity of relevant data.” Although the possibility of distortion resulting from autocorrelation is mentioned, the model does not correct for it. This is quite strange, as it is known that if data contains autocorrelation and the model does not adjust for it, inference on the outcomes is unreliable.

Another invalid assumption underlying this model is that the variance of equity is constant over time. Also note that the time interval is 1 year, so that it is assumed that the risk of equity is equal to the 1 year risk, irrespective of the investment horizon.

1. The symmetric adjustment mechanism tries to reduce pro-cyclical effects during an equity crash, by reducing the capital requirements during such a crash.

2. If the index is higher than the weighted average level, the equity charge will be higher than the standard capital charge.

Moreover If the index is higher than the weighted average level, the equity charge will be higher than the standard capital.

3. Their total portfolio is worth about 300 billion Euros 4. Tobin’s q 5. See for example: Poterba, J. (2000), and Davis, M., and M.G. Palumbo. (2001).

6. In “het Financieele dagblad Monday 10 December 2012” 7. Basis in the sense that there is no adjustment from the symmetric adjustment mechanism

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Optimal Asset Allocation Consider a stylized example: suppose that each year a certain asset either has a return of 20 percent with a probability of 95 percent or a return of -50 percent with a probability of 5 percent. If an insurance company has liabilities for the next year, the capital requirement must certainly be 50 percent. But if the insurance company has a liability to meet 30 years from now, the capital requirement of 50 percent is not adequate. Using the binomial distribution one can calculate the probability that more than 5 crashes occur in 30 years. This probability is less than 0.58 percent and even if 5 of these crashes occur the annualized return is 3.7 percent (i.e. the monetary value of assets has grown with 200 percent in 30 years).

Of course the return of an asset is not distributed as mentioned, but this example does show some important characteristics in the measure of risk that are left out in the analysis of Solvency II. Jeremy Siegel (2006) argues that in the long run stocks bear less risk than bonds, while they have a higher return. Bonds are risky in real terms, because they give a negative return if the inflation turns out to be higher than the interest rate of the bond. Currently, Dutch Government Bonds already have negative real yields, i.e. capital invested in bonds will erode if the inflation keeps at the current low level of 1.7%.

Siegel uses historical data from the US to display (see figure 5) the best and worse after-inflation returns for stocks, bonds and bills from 1802 to 2006 over holding periods ranging from 1 to 30 years. Stock returns are measured by dividends plus capital gains or losses available on a broad capitalization-weighted index of U.S small and large stocks.

Diebold (2012) argues that time-varying volatility can play a crucial role in portfolio management: “The amount of shares in an optimal portfolio depends on variances and covariances of the assets in the portfolio.

In particular, if an investor wants to minimize portfolio return volatility subject to achieving target return ‘µp’, she must minimize w’∑w subject to w’µ = µp, where ‘w’ is the vector of portfolio shares, µ is the conditional mean vector of returns and ‘∑’ is the conditional covariance matrix of returns. If ∑ is time-varying, then so too are optimal portfolio shares”. So if the volatility changes due to an adjustment in measuring the volatility with respect to time, the optimal allocation changes as well.9

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contribution plans rather than defined benefit. In fact, investment risk is shifted to the policy holders.

The combination of mark-to-market accounting and measuring portfolio risk as short term volatility is, in our humble opinion, not appropriate. Literature shows that at a longer horizon equity prices are less volatile and that the equity returns exceed those of other asset classes. Hence, we argue that Solvency II should take the investment horizon into account as well. This horizon is largely based on the duration of liabilities.

References Campbell, J. and VICEIRA, M., 2002, Appendix to ‘Strategic Asset Allocation: Portfolio Choice for Long-Term Investors’. Oxford University Press, USA. Davis, M., and M.G. Palumbo, 2001, A Primer on the Economics and Time Series Econometrics of Wealth Effects, Federal Reserve Board Finance and Economics Discussion Series No. 09.

Diebold, F.X. 2012, 100+ Years of Financial Risk Measurement and Management.

Figure 2: Although the annualized standard error is high for short time periods such as a year, if the holding period is 25 years the standard deviation is cut by half.

Campbell and Viceira (2002) find that the volatility of equity decreases as the horizon increases (see figure 1).

Hence the risk for equity measured in annualized standard deviations is decreasing in the holding period. On basis of these conclusions we think it is more appropriate to use an alternative conduct in the measurement of capital requirements. One in which the basis capital requirement is decreasing in the average liability duration of the insurance company.

Jon Danielsson, Roger Laeven, Enrico Perotti, Mario Wüthrich, Rym Ayadi, Antoon Pelsser, 2012, Countercyclical regulation in Solvency II: Merits and flaws: http://www.voxeu.org/ar-ticle/countercyclicalregulation-solvency-ii-merits-and-flaws.

Poterba J., 2000, Stock Market Wealth and Consumption, Journal of Economic Perspectives, 14(2), pp. 99-119.

Siegel, J., 2006, Stocks in the long run. Mc Graw Hill.

Conclusion

Figure 1: This figure shows the best and worse afterinflation returns for stocks and bonds from 1802 to 2006.

Solvency II intends to protect policyholders. However, mark-to-market accounting and the application of the Solvency II capital requirements may have counterproductive effects by stimulating life insurers to opt for less volatile investments, irrespective of their liability structure or duration. This may lead to an excess demand for fixed income instruments, as currently observed in recent Dutch Government Bond issues. In real terms, yields are negative and expose the investor to inflation risk. As a consequence, life insurers will make less strong guarantees and hence opt for defined

8. 0.33 percent 9. This part of the paper of Diebold, however, was written to argue that if the volatility changes from time to time, you should adjust the portfolio dynamically.

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Target rate of return as an alternative for the funding ratio by: Agnes Joseph and Arno van Mullekom The funding ratio is often seen as the key indicator of financial health of pension funds. In the period 2008 till 2010 the funding ratios of Dutch pension funds dropped spectacularly, raising questions on the adequacy of current regulation and the overall sustainability of the second pillar pension contracts in the Netherlands. All elements of contracts and regulation are currently under reconsideration, but the funding ratio seems to remain the key indicator in every discussion. Nonetheless we think the funding ratio as leading indicator for regulation should also be reconsidered. As an alternative for the funding ratio we mention the target rate of return.

Introduction Due to low interest rates and rising life expectancies the market value of the liabilities of the Dutch pension funds increased spectacularly in the last few years. This increase in the value of the liabilities resulted in a drop of the funding ratios, which is the key indicator of financial health of a pension fund in the current supervisory regime in the Netherlands. Once the funding ratio is below the (minimum) required level, pension funds need to draw up a recovery plan. The recovery plan shows how the funding ratio is expected to recover above the required level within the maximum recovery period, by means of for example cuts on conditional indexation, additional contributions and expected excess investment returns.

If, at the end of the recovery period, the funding ratio is still not above the required level, a pension fund has no other options but to cut also the unconditional (nominal) benefits and to de-risk the investment portfolio as to lower the required funding ratio. The result is that future nominal benefits are well protected, but the chances to compensate for future inflation are reduced to a minimum, leaving all purchasing power risk to the participants.

There now is a strong debate on the sustainability of current second pillar pension contracts and also on the current supervisory regime. One of the disadvantages of the current supervisory regime is that the regime is based on protection of the nominal pension benefits, while it is argued that it would be better to focus on protection of the purchasing power of the retirement income of the participants. This is one of the reasons why the current supervisory regime will be changed. Every element of the current supervisory regime is reconsidered, e.g. the discount rate and the risk based capital requirements, except for the funding ratio that is and stays the key indicator of financial health of a pension fund. This is strange because there could be better alternatives than the funding ratio. As an example we mention the ‘target rate of return’. Similar to the funding ratio, this risk measure depends on the current value of the assets and future benefits of the pension fund. But one of the main advantages of the ‘target rate of return’ is that it is independent of the discount rate that is used to value the

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liabilities to obtain the funding ratio. Therefore it is more stable over time and it is easy to interpret this number.

Target rate of return The ‘target rate of return’ is defined as the minimum yearly investment return on the assets that is needed to pay all future benefits. As an example, we take a pension fund with a funding ratio which is currently 100%. In theory, this pension fund has exactly enough assets to cover the liabilities. But due to the capital requirements the pension fund should have a funding ratio of 120%.

Therefore this pension fund is subject to a recovery plan, until the funding ratio is on or above 120%. The capital requirements are chosen such that the pension fund

Econometrics

should be able to meet all future benefits with 97.5% certainty. Now we look at the ‘target rate of return’ of this pension fund, it is 2.2%. In other words, as long as the pension fund manages to get a yearly investment return of exactly 2.2% on its asset portfolio it will be able to pay all future benefits. The expected rate of return of the pension fund is, given its asset mix, 4.6%. So if the pension fund manages to realize exactly this expected return on assets, there is even (4.6%-2.2%) = 2.4% left for inflation compensation every year.

97,5% certainty level But investment returns are not constant every year, there is also volatility in the asset returns. Given the volatility of the asset returns we can calculate a ‘97.5% certainty target rate of return’ or ‘required rate of return’. This is the target rate of return that should be made on the investment portfolio to be able to pay all future benefits with 97.5% certainty. This required rate of return depends on the investment portfolio of the pension fund. The riskier the investment portfolio, the higher the required rate of return, equivalent to the current risk based capital requirements and required funding ratio. For our example pension fund the required rate of return is 4.1%.

Conclusion We think the target rate of return and the risk based required rate of return can replace the funding ratio and risk based capital requirements in the new supervisory regime. As long as the expected returns on the investment portfolio are above the required rate of return at a given required certainty level and at the chosen volatility of the pension funds’s asset-mix, the pension fund has adequate coverage of the liabilities. To prevent the pension fund of using unrealistic high expected investment returns, the supervisor could set maxima on the used return parameters, comparable with the current set of maximum parameters as used for the continuity analysis. In the example here we focused on nominal benefits, but the target rate of return and a required rate of return can also be calculated for benefits that include a compensation for inflation.

The target rate of return has many possibilities, and there will be more risk measures that could easily replace the funding ratio. When setting up the new supervisory regime these measures should also be taken into account.

Agnes Joseph Agnes Joseph is an expert advisor at Achmea.

She worked for Achmea’s investment and actuarial departments since 2003 in the area of Risk Management and Asset & Liability Management. Agnes is (co-)author of various books and articles on pension funds and pension fund regulation, see for example www.pensiondeal.nl.

Figure 1. Target rate of return as a function of the volatility of the pensions assets given a required certainty level to be able to pay all future benefits

Arno van Mullekom Arno van Mullekom works as an actuary for Syntrus Achmea since 2009. Arno started his carreer in finance in Amsterdam in 1997. He has gained broad experience in asset management and risk management as he has since worked as strategist, tactical asset allocator and owner of a hedge fund.

Different certainty levels for the required rate of return are also possible, see also figure 1 where the required rate of return and its dependence on the certainty level and the volatility of the investment portfolio of the pension fund is given. As can be seen, the higher the certainty level and/or volatility of the investment portfolio is, the higher the required rate of return.

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Avoiding Simplification Strategies by Introducing Multi-Objectiveness in Real World Problems by: Charlotte Rietveld, Gijs Hendrix, Frank Berkers, Nadine Croes and Selmar Smit In business analysis, models are sometimes oversimplified. We pragmatically approach many problems with a single financial objective and include monetary values for nonmonetary variables. We enforce constraints which may not be as strict in reality. Based on a case in distributed energy production, we illustrate how we can avoid simplification by modeling multiple objectives, solving it with an NSGA-II algorithm with a novel comparison operator. Advantages include a strengthened focus on the trade-off relation between financial and non-monetary objectives. We conclude that this approach is very applicable in a business analysis setting.

Background and Objectives When modeling problems in a real world setting, it is often necessary to find the optimum in a set of feasible solutions. In situations where this solution space is (very) large, many model builders adopt a simplification approach to facilitate analysis. Although a model is by definition a simplification of reality, models can sometimes be oversimplified even when numerous scientific methods (such as optimization techniques) could be employed.

An example of simplification is reduction of the solution space by selecting a small subset of possible scenarios. When doing this, the model builder takes the risk of ending up with a sub-optimal solution. Another form of simplification is that many problems which are modeled with a single objective are in reality multiobjective problems. All objectives are expressed in a single quantity (usually money) which fixes the trade-off between multiple objectives at a certain value, and makes further analysis of this trade- off impossible.

In this paper we address how multi-objectiveness can be introduced in seemingly single-objective realworldproblems as an alternative to the simplification approaches described above. As an example of this approach, a case study on a basic distributed energy production problem is used1, to show that this method allows for visualization and analysis beyond traditional methods. This case, which appears to be a standard single-objective optimization problem, turns out to yield far more extensive and interesting results when treated as multi-objective. Furthermore, we describe how this problem can be solved using a multiobjective evolutionary algorithm specifically designed to approximate the Pareto front as closely as possible.

The techniques that are used are not new to the industry, however only used in cases in which the

multi-objectiveness of the problem is obvious. We hope to show model builders the benefits of designing their models in a multi-objective manner, but also to point scientists to the fact that often real world problems are much more complex than is reflected in the models used in the industry. We feel that both can benefit from the application of multi-objective algorithms in real world problems to avoid simplification strategies.

Charlotte Rietveld Charlotte Smit-Rietveld MSc is consultant financial modelling at TNO Strategic Business Analysis department and joined TNO in 2007. Her focus is on strategic decision management and business modelling. She is experienced in building calculation models and also acts as a facilitator in groups and coalitions for establishing or improving their business model. Charlotte holds a master’s degree in Business Mathematics and Informatics from the Vrije Universiteit, Amsterdam.

Gijs Hendrix Gijs Hendrix MSc is Consultant Decision Support at KLM Royal Dutch Airlines. He is active in the field of airline revenue management, where he works on designing and implementing Decision Support systems which are leading in the industry.

Gijs has previously worked for TNO, in the field of business modeling and innovation management. He holds a MSc degree in Financial Mathematics from Radboud University Nijmegen.

1. Note that this case study, although representative for many real-world problems, is solely used to illustrate the approach, rather than solving problem itself

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Case Study - Distributed Energy Production In the last few years, a transition is taking place in energy networks, with an increase in development and use of distributed power generation. Some of these distributed generators (DGs) are based on renewable energy such as photovoltaic cells (PV) and wind turbines, but new technologies such as the micro Combined Heat and Power system (microCHP) are also on the rise. For more information, see Pepermans et al. (2005) and Harrison (2001). As these technologies become available to consumers, each household will make an individual choice whether or not to purchase a DG based on budget, personal preferences and circumstances. The outcomes of one’s choice are not independent of those of others, because each choice has an influence on the total ‘configuration’ of supply and demand. An unbalanced

Selmar Smit Dr. Selmar Kagiso Smit joined TNO in 2012 at the Modelling, Simulation and Gaming department in The Hague. He is specialized in machine learning and evolutionary algorithms, and currently works on healthcare design, metamodeling and environmental criminology. Selmar finished his PhD at the Vrije Universiteit, Amsterdam with his thesis entitled ‘Parameter Tuning and Scientific Testing of Evolutionary Algorithms’.

Frank Berkers Frank Berkers MSc is senior researcher at TNO Strategic Business Analysis dept. in Delft. He joined TNO in 2008. He is specialised in value networks and business modeling and is responsible within TNO for knowledge advancement on this topic. His interest is in modeling for strategic (investment) decisions in networked businesses, including qualitative aspects that influence them.

Nadine Croes Nadine Croes is research scientist at TNO Sustainable Transport and Logistics. She has experience with freight transport modelling, data analysis and sustainable logistics. Currently her main focus is on developments of freight transport models and integrating with economic trade models. Nadine studied Econometrics and Operations Research at the University of Groningen. During her internship she studied the impact of distributed generation, energy storage and electric vehicles on the electric grid.

distribution of different types of DGs might even cause instability or damage to power grids.

The question that we want to answer is: ‘What is the optimal distribution of DGs from a societal point of view?’.

In this case study we modeled an urban district consisting of 100 average households based on (Energiened (2001), Bakker et al. (2008), Menkveld (2010)). Each of these households can choose to invest in 11 different DG combinations, or to not invest at all. These 12 options each have certain costs attached and deliver a different and variable amount of energy throughout year. Houses that have surplus energy available will supply this to their neighbors, any remaining demand is supplied by a power plant, and in case the district has a surplus of energy this can be supplied back to the energy grid at a fixed price.

For each option we have a different cost price and CO2 production per kWh. We are searching for a distribution of DGs that maximizes the reduction of CO2 emission (the DGs produce less CO2 per kWh than the power plant) and minimizes the extra cost of energy for the district (the DGs produce energy at a higher price per kWh than the power plant). In addition, we assume that there is a risk of damage to the power grid involved in the use of DGs, because the unpredictability of energy production by the DGs can cause large fluctuations in grid usage.

For this reason we treat the total amount of fluctuation in the power grid as a proxy indicator for fluctuations.

We set it as a constraint on the distribution of DGs. We will not allow this fluctuation to be larger than the total fluctuation without distributed energy generation.

Solving the optimization problem Based on the description in the previous section, one could argue that this is a basic single-objective problem.

The pragmatic approach would be to find a monetary value for the overall reduction of CO2 (i.e. the cost per unit, usually measured in Euro per tonne of carbon) and find the value at which the constraint has to be fixed. We could for instance use a recent report on the social costs of carbon emission by Yohe et al. (2007) which gives a cost of one tonne of carbon (tC) of 31.50. Typically, we would create a model that converts the choices and energy consumption patterns of the households into cost, production patterns, fluctuation and CO2 emissions. We would continue to investigate several (extremum) scenarios. Next some investigations on the sensitivity of CO2 emission-costs and fluctuation constraint would be performed. If we would decide to tackle the problem by optimization, we would then typically try to solve the following optimization problem: (1) (2) where A is the proxy value of fluctuation without DGs, in this case 600. This is a basic constrained optimization problem, subject to the fluctuation constraint described in

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the previous section. As the solution space is rather large, we can either use a simplification strategy or employ a suitable optimization method to solve this problem. In either case we end up with a single proposed optimal distribution of DGs in the district, with a corresponding optimal financial result.

The multi-objective approach The traditional approach comes with a number of problems. First, the value for the fluctuation constraint could be less strict than described above. In some cases, a softened limit could lead to a much better solution to the problem which would otherwise not have been investigated because it is rejected by the constraint. If the extra monetary gain is worth the risk of such a softened limit should be the decision of the policy maker, rather than the model builder. The opposite is also possible. If the limit is already soft, an optimization algorithm could find an optimum close to this limit which financially is only slightly better than a solution with a much lower fluctuation.

In essence, the fluctuation can be seen as an objective that has to be minimized (Coello Coello (2000)). When merged into a singleobjective target function, we would have the problem of scaling. Rather than a single ‘optimal solution’, one would like to know how the amount of fluctuation interacts with the financial result; we are interested in the relation of fluctuation, CO2 emission and financial result. With such knowledge, the decision maker can select which of the solutions is optimal with respect to the profits and risk.

Second, we find a ‘hidden’ objective in the description of the constants in this business case. Like other business case models, the case model includes some fixed constants that need to be set beforehand. Although some of them are really constant, others are just an estimation of the value. Such fuzzy constants might even be found in the objective function itself. In this case, the cost of CO2 emission is more than just a monetary value. Taking a closer look at Yohe et al. we find that the value of 31.50 is an average based on a whole range of uncertainties and assumptions and it might be as much as three times this figure. With such uncertainties, a single fixed value would certainly lead to suboptimal behavior. Moreover, it does not give any insight in the dynamics of the problem.

We have now transformed this case into a problem with three objectives: we want to minimize the extra cost of energy production, maximize the reduction in CO2 emission, and minimize the fluctuation in the power grid.

NSGA-II with a Novel Comparison Operator Where single objective problems (such as the model without the ‘new’ objectives) are easily solved, solving problems with multiple objectives is, generally a very difficult goal. The most commonly used algorithms

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are the Non-dominated Sorting Genetic Algorithm - II introduced by Deb et al. (2002), and the Strength Pareto Evolutionary Algorithm-2 by Zitzler et al. (1998). Such algorithms try to approximate the Pareto optimal set by means of a generate-and-test approach. However, finding this set itself involves two objectives, namely the distance to the optimal front is to be minimized, while the diversity of the non-dominated solutions to the problem is to be maximized. In this paper, we have chosen to use the NSGA-II algorithm as a base and extended it with an novel comparison operator to overcome some difficulties that rise with the standard NSGA-II, when facing problems with 3 or more objectives. A detailed description of the algorithm without the new operator is in Deb et al. Only slight modifications are applied to ensure integer values and to make sure that the sum of the inputs is equal to the number of households in the model (since each household chooses exactly one of the 12 options given).

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Generalized Crowding Distance Deb et al. introduced the density measure ‘crowding distance’ to enforce diversity of the Pareto set. A point on a certain Pareto front is assumed to be more valuable if the distance to its neighbors on the same front is bigger than that of another individual. Eventually, this is supposed to lead to a uniform spread over the Pareto front. In Deb et al., the crowding distance of a certain point i is defined as the sum of the distances between its neighbors when projected on each of the objective-axes. In Figure 1 this crowding distance CD(i) is expressed as a + b.

Although this metric works in two dimensions, extending it to three or more dimensions raises problems.

Some points that may be close when projected onto 1 dimension, are far from each other ‘in reality’. For example, the individual i from Figure 1 and the points p1; p2; p3; p4 lead to a very small crowding distance (namely 2.2) of individual i, while we know that point i is very isolated. This effect is likely to cause the Pareto set to converge to a population of individuals that is not uniformly spread over the Pareto front as desired.

There is a range of different approaches to overcome this problem (Köppen (2007)), however none of them is a true generalization of the original crowding distance.

To generalize this more adequately, the original definition needs to be reformulated. We use the following equivalent definition of the crowding distance for individual i on objective f, with fitness values y i1..... y iD: CD(i; f) is the length of a straight line QS. Where Q , S yf , and are the two points closest to y if for which y if is on QS. Based on this definition, we can apply the standard aggregation method, namely CD(i) = CD(i, f) if CD can be calculated for all f D, otherwise CD(i) =

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Figure 1: Example in two dimensions

Table 1: Crowding Distance in three dimensions

In Figure 1, the two lines are a and b. Both connect the points that, when projected on one axis, are on either side of point i. Those are therefore the two closest points to i, that, when connected, also cover point i. This definition, however, can be naturally extended to higher dimensions without losing its properties, namely by changing ‘line’ to a different shape. In a space with three dimensions, we can project the solutions of a certain Pareto front to a 2-dimensional surface. In this 2D space, a triangle can cover any point that is not ‘on the edge’. For higher dimensions, triangular (hyper)pyramids can be used.

As length is the ‘size’ indicator of the line, for higher dimensional shapes ‘size’ can be measured by means of calculating the area of a triangle, or the volume of a (hyper)pyramid.

This generalized method of measuring crowding distance can correctly indicate the crowding in higher dimensions. For example, the points in Figure 1 lead to a GCD(i) in the order of 10:000, rather than the 2.2 of the standard approach, therefore it correctly indicates that i is a highly isolated point.

Front-Contribution Indicator Using the generalized crowding distance as a second stage comparison measure, strengthens one of the desired properties of the final Pareto set, namely the diversity.

However, it does not directly contribute to the quality of the Pareto Front. To correctly approximate the true Pareto Front, some area’s would need special attention, while other areas hardly contribute anything to the outline of the front. For example, g and i from Figure 2 have the same value for GCD, while it is clear that they do not contribute equally to the shape of the Pareto Front. As in this case, our main interest is finding the best approximation of the Pareto front, we would like to emphasize on the points with the highest contribution.

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The Front-Contribution Indicator (FCI) is such a metric.

Rather than the density around an individual, it indicates the contribution of this individual to the Pareto front. The idea is straightforward, namely to measure the change of the Pareto Front, if a certain point would be removed from the Pareto set. Figure 2 illustrates this approach.

If point i is removed from the Pareto set, points h and j would be used to approximate the values of all points in between. The difference of the approximated values, with and without i is indicated as the gray area. The size of this area can therefore be used to express the contribution of point i to the Pareto Front.

When points are isolated, the base (a) of such a triangle will be large, like similar approaches as [1]. However, if the height of the triangle is very small (the point is close to the diagonal), this will still yield in a small FCI. Figure 3 illustrates how this value can be calculated more generally.

Namely, the area of the triangle is equal to a does not only represent the base of the triangle, but is also the value of CD(i,B). Furthermore, indicates how much the estimated y-coordinate of point i, based on i and j, is either under-estimating(concave regions) or overestimating(convex regions).

Just as in the 2D case, in higher dimensions the points used to calculate GCD(i; f) can be used to estimate the value for too, in this case by using (hyper) triangular interpolation. We can therefore define the FrontContribution Indicator of an individual i as follows: (3)

Results In Figure 4 we see the distribution of solutions in the Pareto Set when looking at reduction in CO2 emission versus load fluctuation, as found by NSGA-II with FCI. This shows a curved pattern of solutions. An explanation for the existence of such a pattern is that, starting from fully centralized energy generation, a tendency towards usage of distributed generators will reduce network usage, or rather district inflow, but whenever their production cause net overproduction, the network will experience an increase in usage. This implies that, for the given network and the dimensions considered, fully distributed generation is not optimal, but a large improvement on the current situation is feasible. Note that this shape is in part created by the (scoping) assumptions in our model.

Recently there has been an increase in attention on so called Smart Grids (Lindley (2010)), which are (among other things) able to mitigate potential overloads by coordinating the distributed energy generation. Smart Grids are not included in the model.

Figure 4: 3D-Pareto front, projected on CO2 Fluctuation

Load

Figure 2: The Contribution to the Front

Figure 5: Projected on Costs

Figure 3: Base Error

In Figure 5 we displayed the Pareto Fronts for emission reduction versus the increase in production costs, for different relaxations of the fluctuation constraint. A more relaxed constraint implies we can use the quickly increasing benefits of CO2 reduction, without the costs increasing very rapidly (as a consequence of the hard limit on fluctuation). This type of pattern helps us identify the trade-off relation between these dimensions.

Based on the insights from these figures, we identified 4 different solutions (Table 2). We started off with a constrained solution to mimic the classic (pragmatic) approach and along the way relaxed both the tC price and fluctuation constraint. (Note that for simplicity we refer to solutions as if they were single solutions, whereas in fact many more solutions exist in the front.)

Solution 1 shows the solution that would typically be obtained by the traditional, single-objective approach, using a fixed value of 31.5/tC and a constraint for fluctuation. The new approach adds to this the insight that this solution is optimal at emission costs between 29/tC and 50/tC. When relaxing the 31.50/tC tradeoff we observe that the solution is more expensive, with more fluctuation but results in higher reduction and at higher emission costs (when we substitute the values of the range ends in both solutions we can see that the solution in the second run dominates the first). However, given the high uncertainty regarding the emission costs, many more equivalent or even better solutions, such as solution 2 and 3, may exist depending on the ‘true’ costs.

Therefore it pays off to maintain the emission reduction as a separate objective.

CO2

When compared to the first solution, the second solution has almost all citizens opting for distributed generation, with a combination between a small PV and a microCHP system occurring most often. This is in line with the higher reduction of emissions, but it also shows that the configurations do differ over solutions.

However, if we relax the fluctuation constraint, we can acquire a new solution, namely solution 4. This last solution is characterized by about 75% of households choosing a microCHP system and some PV and no decentralized generation devices. It is optimal in the emission-costs range 51-137, which indicates that this relaxed solution is very robust and dominates solution 2 and 3, if we can accept higher fluctuation2. However, too high fluctuations imply a risk of overload and speed up the aging (wearing) of the network, which in turn leads to investments having to be made earlier. At this point we cannot say whether or not this acceptance of 4% fluctuation will actually lead to earlier investments (and if it outweighs them). These considerations will have to be dealt with by experts, but seem worth investigating from a business analysis perspective. Using the Pareto

Table 2: Four promising outcomes of the Distributed Energy Production problem. Mind that ‘costs’ and ‘fluctuations’ are to minimized and ‘reduction’ is to be maximized.

Front, risk-strategies and policies can be chosen in order to find the ‘optimal’ solution to each particular business.

2. it should be remarked that this increase of 4% in fluctuation is rather small, but may be caused by the assumptions about this type of microCHP which is not yet available on the market

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Conclusions and Outlook When comparing this multi-objective approach with the traditional approach we see that working with multiple objectives brings a number of advantages: Robustness and range information. In the first solution we obtained range information of the tC price of the optimal solution. This raises the question if we are really certain that the emission costs are within this range (we actually are not). This range information can be used to easily assess the robustness of the solutions.

Maintain uncertain constants as dimensions. Because we found very different values for the tC price in the literature, we are very uncertain about this value. Now we can maintain this aspect and compare solutions.

We do no longer need to assume or look for values.

Constraint relaxation and pattern information. Without having to rerun we can inspect constraint sensitivities and trade them off with other dimensions, supported by inspecting the shape of the Pareto Front.

This new approach brings about some practical implications. Firstly, this approach focuses much more on the trade-off relation between the financial and non-monetary objectives. Secondly, the model can remain its pureness, because here is no need to find for monetary values of non-monetary variables and process them within the model. Thirdly, we need no longer use a simplifying strategy in scenario and sensitivity analysis. The new approach will provide us with a large set of inspectable solutions that are on the Pareto front and thus gives insights into the relation between the objectives. This implies that we have to take another approach, when developing to model in the first place.

Furthermore, in our experience, the (multi-objective EA) technique was easily integrated in our modeling environment which is dominated by the use of MS Excel.

This is an important factor in further acceptance of these techniques. Although it is computationally expensive to find the smallest triangle that encloses a certain point, from our experience evaluating an individual is the most computationalexpensive task in these kinds of real world problems. The additional costs of the new operator were therefore relatively small, and outweighed by the benefit of selecting the proper individuals.

We see several types of problems that exhibit similar properties: a complex problem with both financial and nonmonetary objectives. Examples are found in e-health technology investments (cost versus efficacy), subsidies for digitalization of cultural heritage (investment versus cultural exposure and value of conservation), investments in ITS mobility/infrastructure (investment versus mobility, exhaustion and safety), information security investments (investments versus security, ease-

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of-maintenance). Based on the experience reported in this paper, we strongly believe that application of MOEA helps us to address these problems better.

We know that decision makers do not make decisions on financial aspects only, usually other aspects are considered. We felt the need to confront decision makers with the complex trade-off between investments and non-monetary returns (or side-effects), captured in one integrated model approach allowing us to investigate the relation. Additionally, we see opportunities for scientists not only as a community supplying algorithms, but also to indicate how and when they should be used and how certain things can be overcome.

Econometrics

References Nicola Beume, Boris Naujoks, and Michael Emmerich.

Sms-emoa: Multiobjective selection based on dominated hypervolume. European Journal of Operational Research, 181(3):1653–1669, September 2007.

Carlos A. Coello Coello. Constraint-handling using an evolutionary multiobjective optimization technique.

Civil Engineering and Environmental Systems, 17:319–346, 2000.

Kalyanmoy D. Deb, Amrit Pratap, Sameer Agarwal, and T. Meyarivan. A fast and elitist multiobjective genetic algorithm : Nsga-ii. Evolutionary Computation, IEEE Transactions on, 6(2):182–197, August 2002.

G.W. Yohe, R.D. Lasco, Q.K. Ahmad, N.W. Arnell, S.J. Cohen, C. Hope, A.C. Janetos, and R.T. Perez.

Perspectives on climate change and sustainability.

In M.L. Parry, O.F. Canziani, J.P. Palutikof, P.J. van der Linden, and C.E. Hanson, editors, Climate Change 2007: Impacts, Adaptation and Vulnerability.

Contribution of Working Group II to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, pages 811–841. Cambridge University Press, 2007.

Eckart Zitzler and Lothar Thiele. An evolutionary algorithm for multiobjective optimization: The strength pareto approach, 1998.

EnergieNed. Elektriciteitsdistributienetten. Technical report, 2001.

J.D. Harrison. Micro Combined Heat & Power Potential impact on the electricity supply industry.

In 16th International Conference and Exhibition on Electricity Distribution, 2001.

M. van; Bakker E.J.; Jeeninga H.; Dam J.; Wolferen H van. Jong, Arjen de; Gastel. Energie- en co2besparingspotentieel van micro-wkk in nederland (2010-2030). Technical report, Update 2008, Werkgroep Decentrale Gastoepassingen, onderdeel van Platform Nieuw Gas, 2008.

Mario Köppen and Kaori Yoshida. Substitute distance assignments in nsga-ii for handling many-objective optimization problems. Evolutionary Multi-Criterion Optimization, pages 727–741, 2007.

D. Lindley. Smart grids: The energy storage problem.

Nature, 463:18–20, 2010.

M. Menkveld. Energietechnologie¨en in relatie tot transitiebeleid. Technical report, Energieonderzoek Centrum Nederland (ECN), 2004.

G. Pepermans, J. Driessen, D. Haeseldonckx, R. Belmans, and W. Dhaeseleer. Distributed generation: definition, benefits and issues. Energy Policy, 33:787–798, 2005.

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Puzzle

Puzzle

On this page we provide you with the answers to the puzzle of last edition and the winner of Aenorm 78.

On this page you find two challenging puzzles. Try to solve them, submit your answers and compete for a price!

Answer to “Alternative Sudoku”

Answer to “A quadruple of consecutive

New puzzles

integers” The correct answer is: 1735, 1736, 1737, 1738.

Magical Square

Solutions Solutions to the puzzles can be submitted up to August 15, 2013. You can hand them in at the VSAE room (E2.02/04), mail them to aenorm@vsae.nl or send them to VSAE, for the attention of Aenorm puzzle 79, Roetersstraat 11, 1018 WB Amsterdam, Holland. Among the correct submissions, one will be the winner. Solutions can be both in English and Dutch.

Winner Aenorm 78 Peter Hilkhuysen

Place the numbers 1 up to and including 9 in the squares in such a way that the sum of the numbers is always the samen horizontally, vertically and diagonally.

Candies A bag contains one red and one white candy. In a game a player pays €2 to take a candy at random. If the candy is white then it’s returned to the bag and one extra red candy is added, then another candy is taken. This continues until a red candy is taken.

Once the game stops the player receives an amount in euros equal to the number of red candies that were in the bag on that particular turn. Find the exact value of the expected return on this game.

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37

April, May and June were busy months for members of the VSAE. The second week of April was an interesting one, because the Econometric Game 2013 took place. 150 participants from all over the world came to Amsterdam for at least three days to take part in this competition.

With the help of a very devoted committee we managed to organize another successful edition of the Econometric Game. This year the winning team was Universidad Carlos III de Madrid, and I am sure that all teams are hoping to be able to participate again next year to bring the trophy home.

Only a few days later the yearly and long-expected soccer tournament with study association Kraket took place. The weather was rather good and the number of participations was higher than ever. Five VSAE teams and four Kraket teams battled for the everlasting honor of winning this tournament. Although the past few winners were mainly teams from Kraket, this year’s final was a match between two teams from VSAE. The final was close, but in the end the best team won. After the matches it was time for a well-deserved barbecue.

The second week of May was definitely a busy one for some members. On Tuesday a group of twentyfive selected students travelled to Lisse to participate in the Risk Intelligence Competition. In two days the participants solved three challenging cases, provided by De Nederlandsche Bank, Zanders and Deloitte. Next to the cases there were lunches, drinks and dinners to meet employees from all three companies. After two days of hard work there were two people that scored most points during the case rounds, so they were the winners of the RIC 2013.

After returning to Amsterdam close to midnight it was an early wake up the next day. Around 8 am a bus with 41 enthusiastic VSAE members departed with destination Paris for a short trip. Four days of fun, relaxing, sightseeing and clubbing were awesome. Most people slept way too little, but it was definitely worth it.

The group of people was fantastic and new friendships were made, I can’t wait for next year’s short trip!

With the exams of June and July coming up it was time for one more activity. The jaarafsluiting with over 30 participants was a good event to end the college year with. A sunny Friday afternoon and a camp site near Leiden turned out to be a perfect combination.

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After having dinner it was time to explore nightlife in Leiden. A great night was followed by a rainy morning.

Nevertheless, we travelled to Duinrell to enjoy the water slides in Tikibad.

After a well-deserved break we hope to see all of you back at the university of Amsterdam at the end of the summer holiday. The VSAE introduction days in August and the monthly drink in September will be a lot of good opportunities to meet new (and old) members of the VSAE. The soccer tournament for econometricians in September is an excellent opportunity to also meet students from other universities and to bring the cup back to Amsterdam. Furthermore, the Beroependagen in October will offer you an excellent opportunity to get in touch with various interesting employers.

Last but not least, I want to thank you for reading the Aenorm and taking part in all the projects and activities that we organized this year. I wish you a very good holiday and hope to see you all back for the new academic year.

Agenda • 21 - 23 August

VSAE introduction days • 26 - 30 August

Introduction week University of Amsterdam • 17 September

Monthly drink • 19 September

Soccer tournament for econometricians • 23 September

General members assembly • 1 - 2 October Beroependagen

Welkom in de advieswereld Jij bent een consultant in hart en nieren. Je wilt iets doen met je wiskundige achtergrond. Én je vindt het interessant contact te hebben met klanten en met collega’s over de hele wereld. Dan ben je bij Towers Watson op de juiste plek!

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