Aenorm 76

This edition:

Econometric Game 2012: How Does Maternal Smoking During Pregancy Affect Infants’ Birthweight?

76

vol. 20 aug ‘12

And:

What if?

The Theory of Interstellar Trade Pension Winds of Chance Complementary Insurance and Deductibles in the Dutch Health Care System

Jij ziet overal cijfers...

…en de bijbehorende uitdagingen.

Want jij ziet dingen die anderen niet zien. Juist dat maakt je zo’n uitmuntende consultant. Bij Mercer waarderen we dat. Werken bij deze internationale autoriteit in financieel-strategische dienstverlening betekent werken in de voorhoede. Terwijl jij samen met je enthousiaste collega’s financiële HR-vraagstukken meetbaar en tastbaar maakt, zorgt Mercer voor een ongeëvenaard klantenpakket én een direct toegankelijk, internationaal kenniscentrum. Ook onze ontspannen werksfeer – even informeel als inhoudelijk – is een begrip in de branche. Allemaal kenmerken die, volgens je toekomstige collega’s, van Mercer een topbedrijf maken.

Junior consultants m/v Die positie willen we graag behouden. We zijn voortdurend op zoek naar junior consultants die zowel individueel als in teamverband kunnen excelleren. Jonge, hoogopgeleide talenten met een flexibele geest, cijfermatig inzicht, kennis en gezond verstand. Menselijke professionals die, net als Mercer, niet terugdeinzen voor uitdagingen. Voldoe jij aan dit boeiende profiel? Dan vind je bij Mercer volop mogelijkheden. Kijk op www.werkenbijmercer.nl of bel 020-4313768.

IT’S TIME T0 CALL MERCER Consulting. Outsourcing. Investments.

Colofon Editorial Board Milan Schinkelshoek Ruben Walschot Editorial Staff Tamer Dilaver Hugo Evers Linda de Koter Milan Schinkelshoek Pranay Shetty Ruben Walschot Sina Zolnoor

Let the games continue by: Peter Boswijk

Design United Creations © 2009 Lay-out Milan Schinkelshoek Ruben Walschot Cover design ©iStock/sekulicn Edit by United Creations Circulation 2000 A free subscription can be obtained at www.aenorm.eu.

Advertisers ING Mercer PWC RiskQuest Towers Watson Information about advertising can be obtained from Kevin Weltevreden at info@vsae.nl Insertion of an article does not mean that the opinion of the board of the VSAE, the board of Kraket or the redactional staff is verbalized. Nothing from this magazine can be duplicated without permission of VSAE or Kraket. No rights can be taken from the content of this magazine.

ISSN 1568-2188 Editorial Staff adresses VSAE Roetersstraat 11, E2.02/04 1018 WB Amsterdam tel. 020-5254134 Kraket De Boelelaan 1105 1081 HV Amsterdam tel. 020-5986015

The summer of 2012 has offered a wide range of international sporting events, including the (for us ill-fated) Euro 2012 football championship and culminating in the London Olympic Games. However, the sporting season this year was opened a few months earlier in April, when the 12th edition of the Econometric Game took place in Amsterdam. As one of the case makers for the very first Econometric Game in 1999, it gives me great pleasure to see that this VSAE initiative has grown to such a well-established and wellattended international event. I attended the congress and final presentations this year, and I was positively impressed, both by the level of the presentations and by the professional organization. The international jury members that I talked to were similarly impressed. The top 3 this year was dominated by Denmark; the winning contribution from Copenhagen is included in this issue of Aenorm. It is good to see that also a US team (Harvard) made it to the top 3 this year, which confirms the global nature of the Econometric Game.

Even at such a successful event, there are always aspects that can be improved upon. A serious reason for concern is the fact that the UvA team did not make it to the final round this year, and I believe that this is not the first time this has happened. I shall not go so far as to compare this to the deplorable track record of the Netherlands in the Eurovision song contests, but I do think we need to reconsider our strategy. The usual solution for bad performance in football is to fire the coach (the effectiveness of which was analyzed in an earlier edition of the Econometric Game) but perhaps we should first start by actually appointing a coach, and doing some training. I am aware that the Aenorm also has a wide readership at the VU, so I should not go into any further details, but I trust that we shall be able to do better next year.

Another issue to think about is the choice of themes for the cases in recent years. Let me emphasize first that each of these cases have been interesting, academically challenging and relevant to society, and the organization is to be congratulated with finding such distinguished international econometricians willing to develop the case and be part of the jury. However, after studying child mortality, hiv, and the effects of drinking and smoking on early child development, one cannot help but wonder if the econometrics discipline is actually concerned with analyzing economic problems. It is a credit to the econometrics profession that the models and methods that we develop are applicable and applied in other disciplines, but it is not as if we have solved all economic problems. In particular, I think it would be great if we could set the world’s brightest young minds to analyze the current financial crisis and the effectiveness of various policy measures that Europe is using to resolve it, or the way in which pension funds should deal with the term structure of interest rates. One the other hand, I realize that it is part of the tradition of the Game that the case and case maker is kept secret and unpredictable as long as possible, so the mere fact that I am suggesting these topics is probably sufficient to guarantee that next year’s case will be in an entirely different field. In any case, I am already looking forward to next year’s Econometric Game, which I trust will be as successful as this year’s edition!

AENORM

vol. 20 (76)

August 2012

1

00 76 Winning EG paper: How does maternal smoking during pregnancy affect infants’ birthweight?

04

by: Line Elvstrøm Ekner, Andreas Noack Jensen, Anna Folke Larsen, Anders Munk-Nielsen and Rasmus Søndergaard Pedersen This April, 30 Universities participated in the Econometric Game to solve an econometric case concerning the effects of maternal smoking on an infants’ birthweight. Ten universities made it to the finals and the jury named the University of Copenhagen as overall winner.

This article gives a brief summary of their winning paper.

Interview with the EG casemakers, Geert Dheane and João Santos Silva

10

interviewed by: Misaël Belle and Daan Besamusca This interview with the casemakers took place on the third and final day of the Econometric Game.

Report: Econometric Game 2012 by: Daan Besamusca

14

On the 17th, 18th and 19th of April 2012, the study association for Actuarial Science, Econometrics and Operational Research and Management (VSAE) of the University of Amsterdam was host for the Econometric Game. Students from all over the world worked on a socially relevant and econometrically challenging case during this unique three day competition in Econometrics.

Pension winds of change by: Dennis van Putten

17

Annual review of the IAS 19 pension disclosures of companies in the Dutch AEX25 and AMX25

Dependencies and aggregations by: Matthew Cocke, Servaas Houben and Elliot Varnell

21

How does diversification in porfolios take place and what are the pros and cons of diversification? The current techniques, based on Solvency II and Monte Carlo, are being investigated and interpreted.

2

AENORM

vol. 20 (76)

August 2012

vol. 20 00 aug m. ‘12 y.

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

The Theory of Interstellar Trade

26

summarized by: Pranay Shetty

It is often said that orthodox economic theory abstracts from reality and is hence not of much use. However with recent advances in space exploration (Mars One Project, etc.)

Paul Krugman contends that Man will one day find a world to which orthodox economics applies perfectly. In this wonderfully humorous paper Krugman proves “two useless but true theorems� about interstellar trade.

What if? by: Hans Heintz and Frank Pardoel

29

What happens with a pension fund’s coverage ratio if an effective drug against cancer is found, fewer people stay smoking and at the same time the Dutch economy enters into a Japan scenario with low interests and a high equity volatility. Such a question is very relevant for Dutch pension funds. This article argues that scenario analysis is complementary to the current statistically oriented risk measurement methods.

The dynamics of financial markets and one-dimensional discontinuous piecewise-linear maps Longevity swaps: hedging longevity risk

33

by: Fabio Tramontana and Frank Westerhoff The economic and financial crisis of the last years may have at least one positive consequence: the rethinking of the economic and financial theories because those that are considered mainstream until now dramatically failed in anticipating and in remedying at the present economic scenario. An alternative consists in trying to build a brand new theory that permits to explain what is happening and which are the causes of it. A less expensive and preliminary task should be to look at what have to say all those theories that are not mainstream. Maybe some of those theories have forseen the current crisis but have not been taken into consideration by politicians and policy makers because they are not orthodox.

Complementary Insurance and Deductibles in the Dutch Health Care System

42

by: Daan Stroosnier In 2006 the Netherlands experienced a health care reform that shifted part of the health care risk from the insurer and public system to the insured and thus shifted some of the financial burden more towards the public. This shift was an attempt to reduce the steady increase of health costs during the last decades. Two of the changes were the introduction of a voluntary additional deductible and the possibility to opt for a complementary voluntary health insurance (VHI), in order to enable a rational use of health care and thereby diminishing the effects of moral hazard and adverse selection. This article addresses the choice for having a complementary voluntary health insurance and a voluntary additional deductible in the Netherlands.

Puzzle

47

Facultive

48 AENORM

vol. 20 (76)

August 2012

3

Econometrics

How does maternal smoking during pregnancy affect infants’ birthweight? by: Line Elvstrøm Ekner, Andreas Noack Jensen, Anna Folke Larsen, Anders MunkNielsen and Rasmus Søndergaard Pedersen This April, 30 Universities participated in the Econometric Game to solve an econometric case concerning the effects of maternal smoking on an infants’ birthweight. Ten universities made it to the finals and the jury named the University of Copenhagen as overall winner. This article gives a brief summary of their winning paper.

Introduction Adverse birth outcomes have large costs with respect to direct medical costs as well as long-term developmental consequences. Maternal health behaviours at conception and during pregnancy are important determinants of fetal growth and child development. Maternal smoking is one of the most commonly studied behavioural risk factors that affect fetal/child development and is often considered the single most important, modifiable factor affecting birth outcomes, see Kramer (1987)1. One way of measuring a birth outcome is the birthweight, which is considered a leading indicator of infant health. For instance, it has been shown that babies with low birthweight have higher mortality rates, are more likely to have cognition and attention problems and are more likely to be unemployed and earn lower wages later in life.

The literature on evaluating the effects of smoking on birthweight is vast and several different statistical and econometric methods have been applied. Endogenous maternal selection into smoking and biased reporting of smoking behaviour complicate the estimation of the causal effects of smoking on birth outcomes. Specifically, mothers who smoke during pregnancy are also likely to self-select into smoking based on their preferences for health and risk taking and their perceptions of fetal health

endowments. These factors, typically unobserved in available data samples, are related to fetal health through other pathways besides smoking. For example, women who smoke during pregnancy may adopt other unhealthy behaviours that may also have adverse effects on the fetus (e.g. poorer nutrition or reduced prenatal care), but may also be less likely to have a family history of poor birth outcomes.

Data and identification Unobserved heterogeneity is the main obstacle for identifying the effect of smoking on birthweight. The availability of panel data allows us to account for the time-invariant mother behaviour, such as general unhealthy behaviour and a preference for drinking alcohol, which affect birthweight and is correlated with smoking behaviour. Exploiting changes in smoking behaviour over time enables us to come closer to the effect of smoking on the weight of the newborn child. However, there are several caveats.

First, when the mother changes smoking behaviour she may also change her unobserved health behaviour such as nutrition and drinking. If the reason for the mother to quit smoking is to live a healthier life in general, the change

Team Copenhagen University The winning team of the Econometric Game 2012 consisted of the following participants: Anna Folke Larsen, whose research interests lie microeconometrics and development economics; Anders Munk-Nielsen, who is doing a PhD in structural microeconometrics and transport economics; Andreas Noack Jensen, who is interested in theoretical time-series analysis; Rasmus Søndergaard Pedersen, whose interests are in the field of financial economectrics and volatility modelling and Line Elvstrøm Ekner, who is interested in applied non-linear time series econometrics.

4

AENORM

vol. 20 (76)

August 2012

Econometrics

in smoking behaviour will be correlated with a change in the unobserved characteristics as well. Hence, a firstdifference approach will no longer provide estimates of the causal effect of smoking on birthweight. The virtue of panel data is that it allows us to take the time-invariant mother characteristics into account. However, the timevariant unobserved mother characteristics can still not be accounted for. This is a general drawback of a panel data analysis that we are not able to address with the given data. Hence, when interpreting the estimates we should keep in mind that the effect of smoking is confounded by the impact of changes in other health-related behaviour.

Thus, we are not able to estimate the direct causal effect of maternal smoking on birthweight.

Second, when exploiting panel data to account for time-invariant characteristics, the identification strategy implies that the variation in data used to estimate the effect of smoking on birthweight only stems from mothers who have changed their smoking behaviour between the different births. It does not provide an estimate of the effect of smoking on birthweight for lifetime smoking mothers, and we thus suspect that the estimated effect only is a lower bound (in magnitude) of the true effect for the full population. To shed light on the difference between the group of lifetime smokers and mothers that change smoking behaviour between their pregnancies (switchers), Table 1 shows the mean of the covariates for the two different groups.

On average, the birthweight for lifetime smokers is around 200g lower than for switchers. Moreover, lifetime smokers are likely to be less educated and receive inadequate prenatal care than switchers. Overall, lifetime smokers and switchers appear to have different

characteristics with respect to variables that may influence the birthweight. Thus, we expect first difference estimates to be lower than pooled OLS estimates simply due to the fact that the identification of the estimates stems from variation in smoking across time. That is, we would expect a smaller effect from smoking on birthweight for the subsample of women that change smoking behaviour between pregnancies, than for the lifetime smokers.

Usually, we expect first difference estimates to be smaller than pooled OLS estimates because OLS estimates are inflated by the correlation with the mother specific effects, but we here argue that this is not the sole reason for first difference estimates to be smaller than OLS estimates. If we are interested in the effect of smoking on birthweight for the full population, first difference estimates may not be accurate. However, the policy relevant estimate may well be the estimate for the subpopulation of switchers, as we would expect these mothers to be easier to influence through e.g. smoking campaigns.

Another way to obtain identification could be to pursue a instrumental variables approach, see e.g. Permutt and Hebel (1989)2 and Evans and Ringel (1999)3. However, we do not consider any of the available variables to be relevant and valid for the analysed effect.

Analysis Although the link from smoking behaviour over gestation seems to be of great importance, we have chosen not to include gestation in the analysis. This exclusion is entirely done in order to keep things simple and to, some extend, make our results more comparable to the existing literature. Moreover, in order to make a policy relevant analysis on the effect of smoking on birthweight, one might be interested in the full effect of smoking, i.e. the sum of the indirect effect, that goes through gestation, and the direct effect from maternal smoking on birthweight.

The estimation output for pooled OLS and firstdifference (FD) regressions based on the panel data is shown in Table 2. Regarding the OLS regression, we find that maternal smoking is significantly negatively associated with 1 M. Kramer: “Determinants of low birth weigt: methodological assessment and meta-analysis” Bulletin of the World Health Organization, 65 (1987): 65,663 2 T. Permutt and J. Hebel: “Simultaneous-equation estimation in a clinical trial of the effect of smoking on birth weight”, Biometrics, (1989): 619-622 3 W.N. Evans and J.S. Ringel: “Can higher cigarette taxes improve birth outcomes?”, Journal of Public Economics, 72 (1999): 135-154

AENORM

vol. 20 (76)

August 2012

5

Econometrics

birthweight with an estimate of -179.2g. This result is in line with existing literature. The output for the FD regressions suggests a much smaller, but still significant, impact of smoking on birthweight with a point estimate of -93.9g, approximately four standard errors lower (in magnitude) than the pooled OLS estimate. This is in line with the expected as discussed in the identification section, see also Abrevaya (2006)3.

In order to investigate the differences between lifetime smokers and switchers, we make OLS regressions on two subsamples; one sample containing observations for non-smokers and lifetime smokers only, and one

sample containing data for non-smokers and switchers only. These estimates are presented in Table 3. When not taking the number of consumed cigarettes into account (column 1 and 2), we find a negative impact of 333.7g for lifetime smokers and of 242.2g for switchers. Based on a formal t-test (not reported) we can strongly reject that the two estimated effects are identical. When controlling for the number of cigarettes consumed, the impact decreases to 193.6g and 166.3g respectively. This is anticipated since the number of cigarettes smoked will take some of the explanatory power from the smoking dummy. The average number of cigarettes consumed by smokers is 8, and we use this to construct the impact of smoking 8 cigarettes per day compared to none for the two groups based on the OLS estimates. The effect of maternal smoking is 306.3g for lifetime smokers and 221.8g for switchers, which appears to be quite a large difference.

Quantile regression is another method previously used in the literature on birthweight. This method is motivated by the fact that both social and health costs associated with birthweight have been found to exist primarily in the low end of the birthweight distribution.

In contrast to other methods, where low birthweight is based on a common unconditional threshold for low birthweight for the entire sample, quantile regression focuses on a particularly chosen (conditional) quantile of the conditional birthweight distribution. As a result, the quantile regression is a convenient method for determining how different factors affect birthweight at different parts of the distribution.

As a benchmark, we make a quantile regression on the pooled dataset. The results are shown in Table 4. We note that the results are in line with existing literature, see Abrevaya and Dahl (2008)4. That is, we see heterogeneous effects from smoking behaviour on birthweight on the entire conditional distribution with the largest effects on the lower tail of the distribution.

In this section we set out to argue that the identification strategy in Abrevaya and Dahl (2008)4 suffers from the problem that the smoking variable is the primary source of identification for their unobserved Chamberlain (1982)5 type component as well as for the identification of the effect of smoking itself. We run the same quantile regression as Abrevaya and Dahl (2008)4 but with three time periods instead of two and with a slightly different set of conditioning variables (most notably, we choose to include cigarettes to retain the 3 J. Abrevaya: “Estimating the effect of smoking on birth outcomes using a matched panel data approach”, Journal of Applied Econometrics, 18 (2006): 489-519 4 J. Abrevaya and C. Dahl: “The effects of birth inputs on birthweight”, Journal of Business and Economic Statistics, 26 (2008): 379-397 5 G. Chamberlain: “Multivariate regression models for panel data”, Journal of Econometrics, 72 (1982): 5-46

6

AENORM

vol. 20 (76)

August 2012

Econometrics

distinction between the intensive and extensive margin).

We estimate the model using the method outlined in Abrevaya and Dahl (2008)4. In order to keep the analysis simple, we do, however, not include all the variables that

they use. Specifically, we use smoking, cigarettes, cigarettes squared, age, age squared, the genders of each of the children as well as all prenatal care variables. The results are shown in Table 5. Most importantly, we note that although our coefficients are slightly different from Abrevaya and Dahl (2008)4, we still see a substantial drop in the coefficients to smoking in all the quantiles when we apply the Chamberlain method. The median is now -92.81 compared to the estimate in Table 4, and thus very close to the FD estimate of -93.86 reported in Table 2. We see this as an indication that the problems in the tails are not distorting the conditional mean effects listed in Table 2. There is, however, the issue that the results in Table 5 are quite noisy. One reason for this could be that individuals in the left tail of the distribution tend to be lifetime smokers. In that case, there would not be sufficient variation to identify the individual specific Chamberlain effect separately from the direct effect of smoking.

To shed light on this, we estimate the Chamberlain quantile regression where we exclude smoking from the Chamberlain effect. The results are shown in Table 6. Here, we note that the significance of smoking is restored in all quantiles and that the estimates jump up to approximately the same level as the pooled OLS results from Table 2. This indicates that most of the identification of the Chamberlain effect stems from the smoking variables.

By investigating the estimated Chamberlain coefficients both in our analysis and Abrevaya and Dahl (2008)4, we note that quite few variables are significant. Smoking, age and prenatal visits are the only ones. Since we have the others included as well, we conclude that their contribution to explaining the unobserved type is negligible compared to that of smoking.

The implication of these findings is that while it may be that the results of Abrevaya and Dahl (2008)4 get very close to those found in the first difference regressions, they rely on smoking to identify both the unobserved type and the effect of smoking. In other words, they lack what one might call the equivalent of an exclusive restriction or a relevant instrument for the direct effect of smoking.

In any case, it is unclear exactly what is identifying the effect of smoking.

AENORM

vol. 20 (76)

August 2012

7

Econometrics

References J. Abrevaya: “Estimating the effect of smoking on birth outcomes using a matched panel data approach”, Journal of Applied Econometrics, 21 (2006): 489-519 J. Abrevaya and C. Dahl: “The efects of birth inputs on birthweight”, Journal of Business and Economic Statistics, 26 (2008): 379-397 G. Chamberlain: “Multivariate regression models for panel data”, Journal of Econometrics, 18 (1982): 5-46 W.N. Evans and J.S. Ringel: “Can higher cigarette taxes improve birth outcomes?”, Journal of Public Economics, 72 (1999): 135-154 M. Kramer: “Determinants of low birth weight: methodological assessment and meta-analysis”, Bulletin of the World Health Organization, 65 (1987): 65,663 T. Permutt and J. Hebel: “Simultaneous-equation estimation in a clinical trial of the effect of smoking on birth weight”, Biometrics, (1989): 619-622

Conclusion In this paper we have tried to estimate the causal effect of smoking on birthweight. Panel data has been available which has opened an array of different methods.

With the Fixed Effects regressions, we were able to reproduce the results found in the literature. However, as we have discussed, the identification relies on a particular subset of the mothers, namely the switchers. Hence, part of the reason for the smaller estimate on the effect of smoking compared to OLS may be due to heterogenous treatment effects.

The quantile regression framework is better suited to dealing with heterogenous treatment effects across the conditional distribution, and we have pursued that approach. We have replicated the results by Abrevaya and Dahl (2008) but have further elaborated on what is identifying the unobserved mother effects in the Chamberlain approach. We found that the smoking variable was the main source of identification of the unobserved mother effect and thus, we question the variable’s ability to identify the direct effect of smoking.

However, if more variables had been available to proxy for unobserved type, this approach might very well be a feasible one.

8

AENORM

vol. 20 (76)

August 2012

69

71

vol.18 dec ‘

70

vol. 18 dec ‘10

vol. 19 may ‘11

72

vol. 19 1 aug ‘1

Are you interested in being in the editorial staff and having your name in the colofon?

If the answer to the question above is yes, please send an e-mail to the chief editor at aenorm@vsae.nl.

The staff of Aenorm is looking for people who like to: - find or write articles to publish in Aenorm; - take interviews for Aenorm; - make summaries of (in)famous articles; - or maintain the Aenorm website.

To be in de editorial board, you do not necessarily have to live in the Netherlands.

Interview with the casemakers, Geert Dheane and João Santos Silva interviewed by: Misaël Belle and Daan Besamusca This interview with the casemakers took place on the third and final day of the Econometric Game.

What is the topic of the case?

Geert Dheane: The case is about the effect that maternal smoking has on the birthweight of babies. If you look at the data, they suggest that there is a causal effect of smoking of the mother on the birthweight of the baby.

The question is, what is the difference between the average weight of babies of mothers who do smoke and the ones who don’t? And of course, is that smoking effect causal? The behavior of a mother, smoking or not smoking drinking, not drinking is correlated with many other variables that also have presumably effect on the birthweight of a baby. And the case holds also the question how to disentangle the effects on birthweight and in particular the effect of smoking.

João Santos Silva: I think that is exactly the point. If you use a standard regression for instance, it is easy to believe that the thing that you are investigating is a true causal effect, whatever that is. On the first day, the teams have only access to cross-sectional data, so I believe that the teams are not able to find any causal effect. The contestants can look at the conditions, and can see how these change when statistics change. At the second day, when they have access to panel data, they have a lot of different options. The teams can use fixed effects or, for instance, they can try to use instrumental variables. The teams have a range of methods which they can deploy to identify the causal effect. To be honest, I am still skeptical if they can find anything deeply causal.

If you look at the solutions of the first day, do you expect original and new approaches?

Geert Dhaene: We believe that with the data of the first day, you cannot interpreted the affects as causal. And most of the teams got it quite right at this point. You can look at the joint distribution of smoking, the outcome variables and the covariance but you cannot say whether or not the effects are causal. That was on the first day.

Just because it is not causal, it does not mean that it is not useful. It is useful for other purposes, a doctor can advise a smoking mother to quit. On the first day, they were very creative, some of them in the right direction. Let’s see today what they will do.

How did you came up with the topic?

João Santos Silva: Off the record?... I’m just kidding.

I was working on this dataset with a very different purpose, I was working on a paper and more or less the time you got in touch with us I realized that that paper was not going to take the flight. But I worked with the data, so I was familiar with the data and was aware that the most of the questions would come from the literature and this was an area where the students could use a wide field of techniques. Also, I could address a wide range of questions so it would be appropriate for a case.

Geert Dhaene

notes

10

AENORM

Geert Dhaene is professor of econometrics at KU Leuven. He obtained a PhD from KU Leuven in 1993 and then was a Human Capital and Mobility Fellow at Erasmus University Rotterdam and a post-doctoral researcher at FWO (Belgian Science Foundation). He taught at the University of Mons-Hainaut and Ghent University before returning to KU Leuven in 2001. He contributed to the theory of model encompassing. Currently his main interest is microeconometrics, in particular bias reduction methods for nonlinear panel models with unobserved heterogeneity. He has published in econometrics, economics and statistics journals, including Econometrica, Journal of Applied Econometrics, Games and Economic Behavior, Health Economics and Journal of Multivariate Analysis.

vol. 20 (76)

August 2012

The case of this year is related to last year, do you see a problem?

João Santos Silva: Last year was mainly focused on instrumental variables and using genetic markers. So I don’t think that the case is related to last year. This year using iv is only one of many. And no genetic markers are used this year. The topic is similar in a sense but the techniques are very wide this year. Last year it was around a specific technique and this year it was much more open.

What do you think about the current design in which two cases are made. One for all participants, one for the finalists?

Geert Dhaene: To me it is actually more impressive as expected. I was overwhelmed by the brain power that is here. Like 150 independent minds working hard on a case for at least two days because they’ve read literature on one day so they know what direction it is going. The effort is in fact unparalleled in this topic.

What do you think about the distribution of the working hours? Like first a small case and for the finalists an extra case?

Geert Dhaene: In my opinion, as it is now, it is good.

The design with three stages, reading time, first case, finalists case, is good. Because the two cases have the same subject, it is more easy to develop those two cases, if you want to give for example three different cases, you’ll need three datasets. And two cases is ideal, with one day without the data, so they can read and reflect.

How is it to be a member of the jury?

Geert Dhaene: We did have a good distribution of what we did, as a jury we focused actually on the cases that were on the border of going to the finals. Like João said it is relatively easy to select the best five and the worse five, then we concentrated on the ones who could make it to the finals. Because of different specializations, we worked in groups of two, so every paper was read by at least two jury members

and the ones close to the final at least by four.

What is your opinion about the EG? João Santos Silva: Like we said before, the game is really amazing and the organization which is absolutely faultless. And I was very impressed with the work of the participants.

What are your normal research areas or specializations?

Geert Dhaene: My focus of the last years has been on panel data and in particular on the bold problem, a parameter problem. This problem has not been solved and it cannot be solved directly , since the MLE goes wrong with the number of parameters that you have to extramit increases at the same rate as the sample size. Even the parameters that are kept constant at all the observations.

So think about the fixed effects panel model, with fixed effect, we know that the estimated slope is consistently so that’s because the linearity of the model. As soon as you do good with dynamic panel model if it’s linear, then as a number of individual units goes to infinity the MLE of the auto regressive parameter with the number of time periods fixed becomes inconsistent. The linear model can be cured but the modeling in models is much more difficult. So you can come up with approximate solutions .

João, you’re originally from Portugal and live in the UK now, why did you move?

João Santos Silva: The main reason is that the research environment is miles better in the UK than in Portugal.

In Portugal there are some good universities like Nova in Lisbon which is excellent, but in the UK you teach much less so you have more time to do research. And of course the salary is also a bit better as well. In Portugal you have much more work in administration of the university than in the UK, so that’s how I decided.

João Santos Silva João Santos Silva is professor at the Economics Department of the University of Essex since January 2007. He obtained a PhD at the University of Bristol in 1992 and then was Human Capital and Mobility Fellow at the University College London and taught at the Technical University of Lisbon. He is best known for his “Log of Gravity” paper on the econometrics of gravity equations for trade. He has contributed to various other topics and he has published in a variety of academic journals, including the Review of Economic Studies, Journal of the American Statistical Association, Review of Economics and Statistics, Journal of Econometrics, and the Journal of Business and Economics Statistics.

AENORM

vol. 20 (76)

August 2012

11

Are you planning to go back to Portugal?

João Santos Silva: Not until I retire I think. I may go to somewhere else, Southern-France or Singapore but that’s not on my agenda at the moment.

In the Netherlands you have a master program in econometrics. Is there a similair program in Portugal?

João Santos Silva: At the university of Lisbon, we have a master in economics with the possibility of a degree in mathematical methods in economics, somewhat related to what you have here, because it involves operational research actuarial science and econometrics. A strong background in mathematics and a strong background in economics is needed. One of the members of the jury, Teresa Bago d’Uva, has an undergraduate degree in this course. Students are doing great in econometrics and in finance, so the course is a quite small course but very successful. So it is more or less equivalent to what you have here.

And compared to Belgium?

Geert Dhaene: We have no separate econometric course but we have economics programs and econometrics is one of the major courses. Like micro and macro, econometrics is part of the program. I would say it is approximately the same weight.

Can students econometrics?

already

specialize

in

Geert Dhaene: No you cannot, in the bachelor, there is one introduction course econometrics and in the master several ones. In the master, you’ll get five courses in one year. Everybody who does a PhD had to do a second year one ordinary master and an advanced research master.

How does the number of foreign students change over the years?

Geert Dhaene: The number of students have been constantly increasing I think we have 40000 students in total with 6000 foreign students. But the group of foreign students grows faster, with about seven percent a year.

I think that the Dutch are the largest group now. There was a time that the Chinese outnumbered the Dutch for example. But apparently not anymore.

What are your main interests besides research?

João Santos Silva: My job is my hobby, when I am not at work, I do econometrics, think about it or whatever, most of my best ideas rise along in my free time. Further,

12

AENORM

vol. 20 (76)

August 2012

I like to visit my family walk around the country. I do not have a particular hobby, but listen to music of course is an important part of my work, musical time, I almost forgot that.

Your interest in econometrics, is that because of the econometrics itself or your interest in researching interesting topics?

João Santos Silva: It’s very creative work. You have to come up with new things and be creative, that’s exciting.

If you have an empirical problem, or whatever, you’ll have to come up with a creative solution. You don’t go through the book and see what you should do but you’ll have to come up with something new, and better, and that is challenging and interesting.

What are your interests besides economics?

Geert Dhaene: Let me first say that I very much share the view of João , I cannot distinguish between my free time and my work time even when I go home I work and read econometrics books. Besides that I also read popular science in other branches. The main try of science is, in my opinion, understanding what we see.

Report: Econometric Game 2012

Report: Econometric Game 2012 by: Daan Besamusca

On the 17th, 18th and 19th of April 2012, the study association for Actuarial Science, Econometrics and Operational Research and Management (VSAE) of the University of Amsterdam was host for the Econometric Game. Students from all over the world worked on a socially relevant and econometrically challenging case during this unique three day competition in Econometrics.

Introduction On the 17th, 18th and 19th of April 2012, the study association for Actuarial Science, Econometrics and Operational Research and Management (VSAE) of the University of Amsterdam was host for the Econometric Game. Sponsored by ING and ING Insurance, and supported by the University of Amsterdam, the Royal Economic Society and the city of Amsterdam, the VSAE has organized a successful thirteenth edition. On account of the growing reputation among students, professors and business, both home and abroad, the committee was able to put 30 contestants together that are worth mentioning.

Within our selection procedure, the committee tried to maintain the diversity and to further increase the competitiveness among the contestants. This effort has resulted in the first-time participation of McGill University from Canada, Harvard University from the U.S. and 6 other new European Universities. Newcomers, together with many loyal participants like Monash, Oxford, Cambridge and LSE have sent a team consisting of 5 master and doctoral students to Amsterdam. Geert Dhaene (Universiteit van Leuven) and João Santos Silva (University of Essex) worked together to create two cases capable of testing the participants’ creativity, intelligence, analytical skills and econometrical knowledge. It’s design such that, in order to obtain a complete solution in time, cooperation within teams was essential.

Daan Besamusca Daan Besamusca is 23 years old and currently in the process of finishing his MSc in Econometrics at the University of Amsterdam.

He obtained a minor at the University of New South Wales in Sydney and recently finished an internship at the Dutch Central Bank. He has been an active member of the VSAE since he started his BSc at the University of Amsterdam and in April 2012 he was chairman of the Econometric Game.

14

AENORM

vol. 20 (76)

August 2012

The first day Tuesday morning, the 17th of April 2012. After an early morning filled with preparations, the already exhausted committee looks upon 200 interested students, professors, anxious participants and speakers of the opening congress of the Econometric Game. De Duif, a former church idyllically located at the waterfront of one of Amsterdam’s famous canals has been fully redecorated into an Econometric Game location. The contestants are welcomed to the Econometric Game by the chairman of the committee, have their academic prospects addressed by the dean of the University of Amsterdam, and are introduced to ING by Mark Vermeule. Afterwards a presentation is given by João Santos Silva to outline the expectations of the casemakers and jury and explain the case in more detail. The coming three days, the participants will focus on the effect of maternal smoking during pregnancy on infants’ birthweight. After a lunchbreak, the Econometric Game starts in a large exam room at the University grounds. Teams have until 17:00h to do preliminary research after which they are introduced to other teams, ING employees, former participants and committee members during drinks and diner.

The second day Wednesday the 18th all teams start at 09:00h on the first case round. They are given the dataset, exact case questions and concise explanations on the dataset and regulations. They are given until 18:00h to work on their report. Punctually, the committee will gather all case solutions and hand them over to the jury consisting of 6 professors from all over Europe that have their expertise on the case’s topic and the methodologies used. Of course the temperature rose steadily as the clock ticked onwards, but all Universities were able to hand in complete reports before the deadline. While the jury discussed all anonymous case solutions in order to pick the best 10 reports, the teams were introduced

Report: Econometric Game 2012

to Amsterdam’s café-life in anticipation of their judgment. Around eleven, Santos Silva joined the 150 nervous students with ten numbers which corresponded to the ten finalists. Unfortunately, the national pride of the committee had no impact on the juries decisions and none of the Dutch Universities made it to the final.

The final After long evaluations with the non-finalists, Thursday the 19th seemed to start even earlier than the other days.

Finalists started at 09:00h again to work on a second case. They were given a new dataset and asked to prepare both a written report and a 5 minute presentation on their solution. In the meantime, non-finalists took a scenic canal tour and had lunch on the Marie Heinekenplein with students from the University of Amsterdam and ING employees. After lunch they were escorted to De Duif where an econometric congress was hosted to highlight the methodologies used in this year’s edition and the social aspect of the econometric game. At 17:00h the finalists joined the congress to present their case solutions according to the semi-anonymously system of numbers.

Afterwards all participants, clearly exhausted from three

long days were dragged along for drinks, diner and more drinks, while the jury retired to a local restaurant to discuss the 10 case solutions. Around midnight Geert Dhaene and João Santos Silva joined us at the Amstelhaven with the top three. While tension increased among all finalists and the large group of students that came over to watch the ceremony. The Econometric Game ended with a Danish lesson in econometrics, as the University of Copenhagen won the competition and is crowned best University in Econometrics among students for the coming year.

Second was the also Danish Aarhus University followed by first-time participant Harvard University who came third. Jeroen Potjes congratulated all teams with their participation on behalf of ING and with some final words of the casemakers and the introduction of the chairman of the next edition of the Econometric Game; i.e. Mara Laboyrie, the Econometric Game was officially over. ING and the VSAE can look back at an amazing successful edition. The growth of the Econometric Game is admirable and next year’s committee, who already dedicated themselves to helping the past three days, are well aware of this and will surely contribute to even further developing the Econometric Game.

AENORM

vol. 20 (76)

August 2012

15

www.werkenbijpwc.nl

Soms hou je alle opties open

Soms weet je direct waar je aan de slag wilt Kom verder op werkenbijpwc.nl

Tijdens je studie heb je een schat aan kennis opgedaan, je bent slim, sociaal en ambitieus en nu wil je aan de slag. Bij ons kun je al je kwaliteiten volop ontwikkelen.

Je ideeën zijn meer dan welkom

Ook wij zijn ambitieus. We werken in Nederland met 4.600 mensen in twaalf vestigingen op de gebieden Audit & Assurance, Tax & Human Resource Services, Advisory en Compliance Services.

We willen de beste en meest innovatieve oplossingen bedenken voor de vraagstukken van onze klanten. Dat kan alleen als onze mensen vanuit allerlei oogpunten naar die vragen kijken.

Dus maakt het minder uit wat je precies gestudeerd hebt. Het gaat om je ideeën.

Blijf je ontwikkelen

De lat ligt hoog, maar je staat er niet alleen voor. Je krijgt op dag één een coach die je begeleidt en ondersteunt bij je werk en bij het uitstippelen van je carrière. Je werkt samen in teams met inspirerende collega’s en volgt opleidingen om je vaktechnisch en persoonlijk te blijven ontwikkelen.

Zo ontdek je al doende waar je kracht ligt. Je kunt switchen tussen sectoren. Begin je bijvoorbeeld bij beursgenoteerde ondernemingen, dan kun je altijd overstappen naar de overheid. En andersom.

Je kunt ook van PwC-vestiging veranderen, binnen Nederland of over de grens.

Pak de ruimte die je krijgt

Je gaat bij ons aan de slag in een open kennisorganisatie. We werken met passie en een gezonde dosis lef; zijn open, integer en eerlijk; zeggen geen ja als het nee moet zijn. Het gaat er bij ons informeel aan toe. Je krijgt echt de ruimte. We staan open voor je initiatieven. Je start je carrière vliegend, ontwikkelt je volop en haalt het beste in jezelf naar boven. Want daar worden onze klanten, wij én jij beter van.

© 2012 PricewaterhouseCoopers B.V. (KvK 3412089) Alle rechten voorbehouden.

Actuarial science

Pension winds of change Annual review of the IAS 19 pension disclosures of companies in the Dutch AEX25 and AMX25

by: Dennis van Putten As we are living longer, more of our lives will be spent in retirement. How we plan and provide for retirement is one of the social challenges of our era. Companies play a crucial role in this as sponsors of some of the largest pension plans in the world. But this role brings a dilemma as pension risk is growing at a time of economic troubles. Companies must choose between managing the risk themselves, selling it to a third party or passing it to its members.

Dutch companies face two winds of pension change in 2013 and 2014. Under the new pension agreement, het pensioenakkoord, companies must negotiate a new pension deal with their employees to apply from the start of 2014. How a company applies the agreement will affect the cash they pay to their pension plans, the costs they include in their accounts and the long term risks they face.

Changes to the International Financial Reporting Standard (“IFRS”) for pensions, IAS19, already apply from 2013. The changes affect the company income statement and bring the ups and downs of pension deficits onto the balance sheet. On top of both changes, companies are in the middle of a difficult economy and financial markets are turbulent. In recent months IFRS pension deficits have risen above the levels during the autumn 2008 crisis.

1. The changes to Dutch pensions New Dutch pension agreement (“het pensioenakkoord”): • Agreement between employer and employee associati-

ons for a new pension framework from 1 January 2014. will need to agree changes to their pension plan by the end of 2013.

• The pension age will be increased for new pensions • Companies

Dennis van Putten My name is Dennis van Putten. I have a Master in Econometrics from the University of Maastricht and I am a qualified actuary. I have worked for PwC for over 10 years and support companies with their (international) pension challenges, from both an HR and a financial angle. This article gives some insight in part of the work we perform at PwC.

to 67, at the start of 2014, and will become flexible in future.

• Employee and employer contributions to pension plans are expected to become more stable.

• Pensions will not be guaranteed and will be subject to financial health of the fund (‘soft’ ambition).

• New funding rules are expected to apply.

• A number of elements still need to be agreed and are subject to public debate, including treatment of past accrued rights.

Changes to IAS 19 – the IFRS accounting standard for pensions: • Apply

from 1 January 2013, with early adoption possible.

• Unexpected movements in pension deficits (‘actuarial gains and losses’) must be recognised immediately on the balance sheet and can no longer be delayed to later periods.

• Companies can no longer take credit in the income statement for the equity investments held by their funds and must instead charge the ‘net interest’ on the balance sheet item.

• The company’s pension risk exposure and a sensitivity analysis must be included in increased disclosure requirements.

• Any risk-sharing arrangements, for example between employer and employees, should be reflected in the value of the defined benefit obligation (DBO) and disclosed.

2. The total IFRS deficit for AEX25 and AMX25 companies has grown by €12bn in 2011 and 2012 to €33bn IFRS pension deficits move up and down with economic and financial markets. Deficits rose in the first 10months of 2011 but then recovered in the last two months of the year. At the end of 2011 the deficit for the AEX25 and AMX25 companies was €26.2bn compared to €21.2bn at the start of the year. 2012 has been more difficult and we estimate that the deficit could now be around €33bn, a rise of €7bn so far this year.

2.1. Analysis

The link between pension deficits and financial markets is complex. Many pension plan assets are invested

AENORM

vol. 20 (76)

August 2012

17

Actuarial science

in equity markets so the rise and fall of share prices still has a big effect on asset values. 2011 saw equity markets improve and companies also paid more contributions into their plans to support their recovery.

On the other side, pension obligations are valued by discounting against the returns available on high quality corporate bonds. The lower the expected return on these bonds, or yield, the higher the value of the obligations.

High quality corporate bond yields fell during 2011. This increased the value of obligations more than the rising asset values, resulting in an increase in pension deficit.

3.1. Analysis

Changes in the value of pension assets and obligations trigger deficits and surpluses in company pension plans.

Deficits divert money from shareholders to pension plan members and affect the value of the company and its share price. The bigger the pension obligations the bigger the size of any deficits that emerge. In general, share prices are therefore more exposed to pensions the bigger pension obligations are compared to the total value of the company’s shares.

Using this measure the average company pension risk exposure is comparable to what it was after the financial crisis hit in 2008. Company share prices have improved since 2008, but pension plan obligations have increased at a comparable rate.

Figure 1: Movements in the total AEX25 and AMX25 IFRS pension deficit

2.2. Our view

There are many reasons why companies should monitor and manage their pension deficits. Changes in deficits can create cash demands from pension plans who want to protect their members by improving funding levels or need to meet regulatory rules. Analysts see deficits as a form of company debt and take this into account when assessing the company’s finances and prospects.

Movements in deficits can be reduced by changing the pension plan investment strategy so that assets more closely match obligations. Companies need to do two things: (1) analyse the impact of movements in the deficit and how this changes under different investment strategies; and (2) engage with pension plan boards to make the changes needed.

3. For every €100 of share price a company is managing €45 of pension obligations on average Comparing pension obligations to the total value of company shares gives an idea of how much those shares are exposed to pension risk. In 2011 this exposure increased compared to previous years as share prices fell but pension obligations stayed at similar levels or increased. For the AEX25 and AMX25, pension plans are managing on average €45 of pension obligations for every €100 of company shares.

18

AENORM

vol. 20 (76)

August 2012

Figure 2: Total value of AEX25 and AMX25 IFRS pension obligations as a percentage of market value of company shares 3.2. Our view

For some companies pensions can be one of the most significant risks to the business. How the company manages their exposure to pensions can be critical to its future health and success. Management should ensure they devote time and resources to their pension subsidiary that reflects this. Company annual reports and disclosures should give outsiders a clear idea of how pensions are being managed.

4. More than €2 out of every €3 of Dutch company pension obligations are for former employees Companies manage pension obligations for their former employees as well as current employees. As people live longer and workforces become smaller the size of former employee obligations compared to current employees is getting bigger. For the ten largest Dutch company pension plans only 31% of the obligation is for current employees with the remaining 69% for employees no longer providing services to the firm.

Actuarial science

4.1. Analysis

5.1. Analysis

Company’s often stay responsible for financing a pension long after the employee leaves them, sometimes for as long as 70 years. Once the employee has left it is not usually possible to go back and change the terms of the deal.

The obligations for former employees bring financial risk that companies may not want to take.

IFRS does not ask companies to split their obligations between different groups of members. Our analysis shows the split disclosed by the ten largest Dutch company pension plans in their pension fund accounts. The share of former employees has risen over the last few years.

26 out of the 50companies (52%) currently choose to delay recognition of unexpected movements in their IFRS deficit. These companies balance sheet equity will rise or fall depending on whether the movements they have not yet recognised were gains or losses. After the changes, these unrecognised items will be added to the balance sheet equity. In future the balance sheet will include the IFRS pension deficit or surplus in full.

34 of the 50 companies (68%) are affected by the changes made to income statement (profit) reporting.

Currently companies can include a credit for the expected return on their pension plan assets in the income statement. Under the new rules, they need to change this to an interest credit based on the rate used to value the obligations. The income statement will no longer be directly affected by the investment strategy of the pension plan and there will no longer be additional credit for holding equity investments.

Figure 3: Pension obligations for the ten largest Dutch company pension plans split by membership group

4.2. Our view

So far talks on the new Dutch pension agreement have focused on pensions for the future. But as these figures show the past also needs attention. These pensions were promised in very different times when their cost was thought to be much lower than it has turned out to be.

People are living longer and financial markets have not provided the returns that were needed.

As we noted above, talking to the pension plan about the investment strategy is one way of managing the pension legacy. Some companies may need to go further.

This could include transferring obligations away from the business to remove the risk altogether for an agreed amount. Members are one party that could take on the risk but this may prove too difficult to achieve. More willing parties may be found in the insurance and banking sectors through annuity-based products such as buy-outs or buy-ins and other solutions.

5. New IFRS rules will change the results of 68% of the companies in the AEX25 and AMX25 2013 sees changes to IAS 19 the IFRS standard for pensions that applies to all European listed companies. The changes affect the balance sheet and the income statement with most companies in the AEX25 and AMX25 likely to see a reduction in their equity and reported profits. Based on their latest financial statements, balance sheet equity will fall by a total of €22bn and reported profits will fall by €1.3bn.

Figure 4: Impact of IAS19 changes on Dutch AEX25 and AMX25 companies(based on 2010 and 2011 reported results)

5.2. Our view

The new IFRS rules only affect the way pensions are shown in the accounts and won’t change the underlying situation. Analysts tell us that they already make the adjustments proposed by IFRS when looking at company accounts. They already include the deficit or surplus in their analysis and adjust reported profits to take out the effect of the expected return on assets credit.

There may be indirect effects for companies for example if IFRS results are used to reward management or determine banking and debt covenants. Companies need to analyse the impact of the new rules and make the changes needed.

The new rules may also lead to pensions rise up the agenda of the company’s financial managers. Now that the balance sheet is directly affected by changes in the pension deficit, finance departments are more likely to want to have a say on how pensions are managed.

AENORM

vol. 20 (76)

August 2012

19

Actuarial science

6. Main findings Our review shows the effect pensions are having on Dutch companies and how this has changed due to financial markets and demographic shifts.

7. Conclusion The risks from these obligations stretch out way beyond the time horizons of businesses and may threaten some companies ability to stay in business without change. The new pension agreement is an opportunity for Dutch companies to start tackling this challenge. Traditional solutions may not be enough and companies may need to look for new and different ways to deal with their growing pension legacy.

Companies have three choices for dealing with their pension legacy: manage it, sell it or passing it on. In making this choice the interests of many diverse stakeholders need to be balanced.

20

AENORM

vol. 20 (76)

August 2012

Actuarial science

Dependencies and aggregations by: Matthew Cocke, Servaas Houben and Elliot Varnell

“Wide diversification is only required when investors do not understand what they are doing” - Warren Buffett Nevertheless in the insurance industry the benefits of diversification are significant: the QIS5 capital requirement decreased by 35.1% due to diversification.

Diversification is one of the most difficult topics as it needs to fulfil a wide spectrum of requirements: • Mathematical:

correlations need to be consistent: e.g. once the correlation between A&B, and B&C is defined, this defines the correlation between A&C; • Data: correlations need to withstand validation tests which are mainly based on performing historical data analysis; • Economic rationale: dependencies need to be backed up by economic rationale.

Several layers of diversification are possible within an insurance company (the following list is from complex to easy): • Geographical diversification: the interaction of different

parts within an international insurance risk group, e.g. the UK and US business unit.

• Intra risk: between risk classes. For example the interaction between US market and US life risks.

• Inter risk class: between risks within a risk class, for example within market risk (equity and property risk), or life risk (mortality, longevity).

• Inter risk: within a risk driver, for example the interaction within US equity between different US stocks. Most insurance companies won’t go into this level of detail but instead apply a benchmark to model these risks (e.g.

Servaas Houben Risk Actuary, Prudentia | Assurance

S&P500).

• Individual risk drivers: for example between UK equity

and US property risk. In practice, this is the lowest level of detail and usually the hardest to define: as the risks are very specific it will be difficult to collect sufficient data to justify extreme events.

Although agreeing on the level of diversification is doable, there is the risk of taking excess diversification benefits or double counting benefits during the aggregation process due to several layers in organisation.

Aggregation mechanisms The most common method in the insurance industry for describing dependencies is a Pearson correlation. Pearson correlation is a measure of linear dependency which is less suitable for describing non linear dependencies: for example the function y = x2 is fully dependent, however it has a Pearson correlation of zero implying no dependency. Therefore the term dependency is a more general term than (linear) correlation which also contains non-linear relationships.

An alternative to the Pearson correlation is rank correlation. This method tries to deal with the shortcoming of linear dependency by ordering each variable in the sample: when calculating a rank correlation only the degree of ordering of the sample matters. For example, the rank correlation for a polynomial (which is fully dependent) remains 1 but the linear correlation decreases as shown in the following table.

Matthew Cocke

Elliot Varnell

Consultant Actuary, Milliman

Consultant Actuary, Milliman

AENORM

vol. 20 (76)

August 2012

21

Actuarial science

Despite this, also rank correlations have difficulties with describing non linear events (e.g. also the rank correlation of y =x2 equals 0).

Current techniques Correlations are included in modelling in mainly 2 ways: • Variance

covariance methodology: used in ICA and the Solvency II Standard Formula aggregation. First the capital requirement per individual risk driver is calculated. Thereafter a correlation matrix is used to aggregate all individual capital requirements.

Variance covariance is easy to implement and to explain, however due to lack of tail data it is difficult to derive sensible correlations. Furthermore, the correlations in this method are independent on the economic cycle and hence don’t reflect any tail behaviour. Lastly, this method does not cope well with non-linearities such as options in insurance contracts.

• Monte Carlo: dependency is included in the simulations.

A number of runs are performed and a scenario giving the 1 in x capital requirement is selected. The main advantage of Monte Carlo is that it can deal with nonlinearities. The disadvantage of Monte Carlo is that one has to take the average of scenarios around the 1 in x scenario to avoid sampling error and this causes the runtime to increase substantially (required to get tail numbers; more averaging required when there are less runs).

Challenges Although these current methods are strongly embedded in the industry, they have some drawbacks: •

Positive semi definite (PSD) requirement (mathematical requirement): because of the requirement of making the correlation matrix PSD, manual adjustments might be required on top of the empirically derived correlations.

Some dependencies might not feel sensible after these adjustments and difficult to justify.

• Granularity (mathematical requirement): higher numbers of risk drivers require a larger correlation matrix and make the PSD requirement more difficult to fulfil. Also, when the level of granularity increases diversification benefits increase and will be harder to justify. Lastly, more granularity makes it more challenging to backup dependencies by empirical data.

• Allocation of diversification benefits to group and

22

AENORM

vol. 20 (76)

August 2012

business units: possible methods are proportional, and based on marginal contribution. However sampling error can de-stabilise the allocation mechanism.

• Data limitations (data requirement): little data might be available or there are stale prices (due to lack of updated data, prices remain the same over several time periods) for tail events. For example, in many countries property data is not stock traded or only provided on a quarterly or semi-annual basis leading to a sample of insufficient size.

• Changes in the data set over time (economic rationale): regime shifts (e.g. US inflation policy before and after 1982) make the choice of an appropriate time horizon to determine correlations tricky. One can attribute more weight to more recent data however this can overestimate higher correlations if the recent history was a recession and under-estimate when the recent history was a boom. When assigning more weights to recent data, pro-cyclicality increases which is not a desirable effect.

Tail dependencies Dependencies behave differently in the tail of the distribution than the body. Copulas (a copula is a generalised dependency structure) can deal with tail behaviour. The most used copula in the industry is the Gaussian copula, mainly as it is the easiest to implement: the variance covariance is an example of a Gaussian copula. However, the Gaussian copula does not model tail dependency (as it has a tail dependency of zero) or asymmetries. Other copulas (e.g. t-copula, Clayton) can have tail dependency or asymmetry.

The figures below show that a t-Copula with limited degrees of freedom has tail dependency (which is removed once the degrees of freedom increase when it becomes a Gaussian Copula):

Actuarial science

It therefore appears diversification is not there when it is needed most. The effect of this is that it is not always clear if increasing the number of counterparties (e.g. asset classes, policyholders) decreases the overall risk.

The American subprime market consisted of mortgages from people of different backgrounds. However it turned out that most securitised schemes were vulnerable to the same underlying economic factors therefore reducing the actual diversification effect.

In most calibrations we assume that equity and concentration risk decrease when we increase the number of companies we invest in therefore reducing the unsystematic/company specific risk component.

However, do diversification benefits still exist in extreme scenarios?

However, copulas are less intuitive parameterisation is not straightforward.

and

the

Left tail and right tail dependency While for some stresses (interest rate risk, inflation) we might expect a symmetrical distribution, this is not the case for dependencies that tend to differ between positive and negative stress levels and hence behave differently in the left and right tail. The scatter plot below shows that downside risks are more correlated than upside risks:

Case study Estimating correlation matrices from past data is a notoriously difficult exercise, even ignoring the impact of tail dependency. We present a simple example which demonstrates this.

The specific example is portfolio diversification where there are a range of possible assets. This example has its roots in the ground-breaking paper by Markowitz (1952).

The paper set the framework for modern portfolio theory.

In the version we consider, investors can invest in up to N risky assets. We make a number of assumptions:

AENORM

vol. 20 (76)

August 2012

23

Actuarial science

1. We

assume that the return on the assets are jointnormally distributed; 2. There are no taxes or transaction costs; 3. Securities can be bought or short sold in any quantity without restriction; and 4. All investors have the same time horizon.

Under these assumptions, the set of possible expected returns is bounded by a hyperbola in (return, standard deviation of return) space.

Suppose that we also assume that there is a unique risk free rate at which investors can borrow or lend money.

This is illustrated in the figure below.

The unique market portfolio is the point of tangency of the hyperbola and the straight line. Investing in different proportions of the risk free asset and the market portfolio achieves returns and standard deviations of returns along the straight line, with higher returns to the right of the market portfolio being achieved by borrowing money to invest in the market portfolio.

The market portfolio has the highest “Sharpe ratio”, which is a risk-adjusted measure of return.

The matrix of the correlations between asset returns and the expected asset returns are the key in determining the market portfolio. However, these cannot be known with certainty and can only be estimated from past data.

One way of testing this is comparing the performance of an estimated market portfolio with an alternative investment approach.

The alternative we consider is to invest 1/N of the portfolio in each of the N assets. We assume that the portfolio is rebalanced monthly to keep to the 1/N rule.

The 1/N strategy has a long history. Rabbi Issac bar Aha gave the earliest explanation of this strategy that we are aware of, in about 4BC: “One should always divide his wealth into three parts: A third in land, a third in merchandise and a third ready to hand.”

24

AENORM

vol. 20 (76)

August 2012

There are two possible approaches to comparing the strategies. One is empirical testing, using actual past data. The other approach is to use simulated data, and assume all the assumption we outlined above are true.

With either approach, in-sample data is used to calibrate the Markowitz approach, and out-of-sample data is then used for testing.

With empirical data, the 1/N strategy generally outperforms performs the Markowitz strategy. The following chart shows the relative Sharpe ratio of the 1/N strategy and the Markowitz strategy across 6 different sets of data:

For all 5 out of the 6 data sets, the 1/N strategy outperforms the Markowitz strategy. In the sixth data set, the Markowitz approach marginally outperforms the 1/N strategy. This investigation is described in greater detail in the paper by De Miguel, Garlappi and Uppal. The following table shows the data used:

With simulated data, the Markowitz approach may be expected to perform better. There are features of real world assets returns, such as fat tails, which are not present in the assumptions underpinning the Markowitz approach. However, it turns out that the 1/N strategy still performs remarkably well on the simulated data.

One way of measuring this is how long the time series of past data of monthly returns needs to be for the Markowitz approach to be expected to outperform the

Actuarial science

1/N strategy. With 10 assets, the Markowitz approach is expected to outperform with 6000 months’ worth of past data. However, with 25 assets 6000 months’ worth of data is not adequate and the 1/N strategy is expected to outperform. Again, the paper by De Miguel, Garlappi and Uppal has further details.

One of the key issues in the case study is that estimating large correlation matrices is extremely difficult. The amount of data required for an estimated correlation matrix to converge to the true correlation matrix can be unrealistic. The estimate matrices are quite unstable over time, and the portfolio chosen can materially change given a small change in the matrix.

Conclusion The current industry dependency methods are easy to implement and to explain. However, it appears to be problematic to fulfil both economic rationale, empirical data, and mathematical requirements. Associative measures based on historical data are prone to miss out on events that haven’t happened in the past. The level of data required for a robust calibration may be too large to be realistic. Also, standard correlation methodologies do not take into account tail behaviour which is the main focus of capital modelling as we focus on extreme events. Therefore, new ideas, like empirical copulas, are necessary to come to a better assessment of tail events.

References De Miguel, Garlappi and Uppal: “Optimal versus naïve diversification: How inefficient is the 1/n portfolio strategy?”, Review of Financial Studies, May 2009.

Markowitz: “Portfolio Selection”, The Journal of Finance, March 1952 Shaw, Smith, Spivak, “Measurement and Modelling of Dependencies in Economic Capital”, 10 May 2012 Steven Verschuren: “Copula-GARCH Models to Estimate Capital Requirements for Pension Funds”, Aenorm 74, February 2012 Stephane Loisel, Pierre Arnal, and Romain Durand: “Correlation crises in insurance and finance, and the need for dynamic risk maps”, ORSA, 15 July 2010

AENORM

vol. 20 (76)

August 2012

25

Econometrics

The Theory of Interstellar Trade Summarized1 by: Pranay Shetty

It is often said that orthodox economic theory abstracts from reality and is hence not of much use. However with recent advances in space exploration (Mars One Project, etc.) Paul Krugman contends that Man will one day find a world to which orthodox economics applies perfectly. In this wonderfully humorous paper Krugman proves “two useless but true theorems” about interstellar trade.

First Fundamental Theorem of Interstellar Trade

Introduction Interplanetary trade (within our Solar System) although more realistic in our lifetimes does not demand attention since it is but an extension of international trade. Interstellar trade on the other hand requires special attention.

Krugman theorizes in a world in which the “Warp drive” has not been invented and hence the time taken to travel between planets in other galaxies will be very large.

Due to the immense time required for interstellar trade any decision to trade will be a long term investment project and this requires that there exists extensive futures markets. Additionally there is no longer an unambiguous measure of time. To get around this problem Krugman has assumed that the trading takes place between planets (Earth and Trantor) in the same inertial frame. This requires the use of special rather than general relativity.

Those familiar with special relativity know that time dilation must be considered. For those not familiar it is suffice to know that time on board a spaceship between the two planets will appear to be less than the time that has passed on the planets. This occurs not due to any fault with the clocks but the very nature of space-time itself.

Hence if an individual travels from Earth to Trantor and comes back he would have aged less than his twin back on Earth. It is then well-known that, if the voyage from Earth to Trantor appears to take n years to observers in the Earth-Trantor inertial reference frame, it will appear to take years aboard the spaceship, where

Let us start with some notation. Let: = price of Terran, Trantorian goods on Earth = price of Terran, Trantorian goods on Trantor = interest rates on Earth, Trantor c = cost of outfitting a ship = quantity of Trantorian goods shipped N = number of years taken to travel from Earth to Trantor, as measured by an observer in the Earth-Trantor inertial frame When trade takes place between two planets in a common inertial frame, the interest costs on goods in transit should be calculated using time measured by clocks in the common frame, and not by clocks in the frame of the trading spacecraft.

To understand this we can consider the simplest kind of interstellar transaction. Consider a Trantorian merchant who decides to ships goods to Earth where they will be exchanged for Earth goods and these Earth goods will be shipped back and sold in Trantor. To know the profitability of the trip the merchant needs to access the present value of revenue to make sure it exceeds the initial cost of the trip. Since the trip took 2N years from the point of view of a stationary observer, the test criterion is: (2)

(1)

where v is the spacecraft’s velocity and the speed of light. I will now state and explain the logic behind the two theorems proved in the paper.

However if the merchant had travelled with the cargo, the trip would take only

1 This article is an summary of: ‘The Theory of Interstellar Trade’ by Paul Krugman (2010)

26

AENORM

vol. 20 (76)

August 2012

years.

Econometrics

Hence the test criterion would be:

(2’) To know which criterion is right we must consider what alternatives the merchant had to trading with Earth.

The merchant could have bought a bond on Trantor and let it mature. The value of the bond on the ship’s return does not depend on the time elapsed on board the ship itself. Hence (2) and not (2’) is the right criterion.

An objection to this line of reasoning might be that rather than traveling back to Trantor the merchant might want to settle down on Earth. We assume that transportation costs other than interest on goods in transit are negligible; and that the interstellar shipping industry is competitive, so that profits are driven to zero. Then if (2) is a correct criterion we have the relationship:

ally doubt this proposition. We can consider a particular transaction to get a clearer understanding.

Consider a Trantorian resident who carries out the following set of transactions: (i) It ships goods to Earth; (ii) It then invests the sale proceeds from selling these goods in Trantorian bonds for K years; (iii) It then buys Trantorian goods and ships them to Trantor. The return on this set of transactions, viewed as an investment, must be the same as the return on holding bonds for the same period, i.e., 2N + K years. This gives us the condition: (4) But if we use relationship (3), this reduces to . We have thus arrived at the result that interest rates will be equalized.

(3)

“In this wonderfully humorous paper Krugman proves two useless but true theorems” This shows that rather than being equal there is a wedge between the relative prices on Earth and Trantor.

We can now consider the case of a Trantorian merchant wanting to settle down on Earth. It could purchase a cargo on Trantor and sell it on Earth. Alternatively, though, it could buy a bond on Trantor and, on reaching Earth, sell its claim to a Terran planning to travel in opposite direction. This makes the requirement of a round trip not essential. All that is required is that there be a Human or Alien going in the opposite direction back to Trantor.

Conclusion

Second Fundamental Theorem of Interstellar Trade

References

If sentient beings may hold assets on two planets in the same inertial frame, competition will equalize the interest rates on the two planets.

The First Fundamental Theorem assumes that interest rates are the same on the two planets. The Second Fundamental Theorem shows that arbitrage will in fact equalize interest rates. One might initi

These two theorems set the foundation for a Theory of Interstellar Trade between planets in the same inertial frame. A possible extension of the paper could be to consider trade between planets in different inertial frames, which would require the use of general relativity. As Krugman mentions, this paper is just a foray into vastly unexplored territory and although the tribe of explorers is small the Force is strong with them.

P. Krugman: ‘The Theory of Interstellar Trade’, Economic Inquiry 48: 1119-1123 (2010).

AENORM

vol. 20 (76)

August 2012

27

RiskQuest is een adviesbureau gespecialiseerd in wiskundige modellen voor banken, verzekeraars en pensioenfondsen.

Denk hierbij aan risicomodellen (Solvency II en Basel II), waarderingsmodellen en beslismodellen. We richten ons op zowel data, modelontwikkeling, validatie, gebruik en governance.

Kunt u ons advies goed gebruiken of weet u alles van risico’s?

Speel de quiz en test uw kennis

1

U heeft een obligatie gekocht van bedrijf ABC (Standard & Poors rating A-) met vaste coupon van 5%.

De obligatie loopt af in 2020 en noteert momenteel op 101%. Welk risico is gedurende het komende jaar groter voor u als houder van de obligatie ?

A: Het marktrisico (rente- en spreadrisico) B: Het kredietrisico (default) ?

C: Beide risico’s zijn even groot

2

Wat is modelmatig gezien de kans op een aandelencrash met prijsdalingen van 25% op 1 dag. Ga hierbij uit van een normale kansverdeling en een dagelijkse standaarddeviatie van 1%.

A: Kleiner dan 1 op duizend handelsdagen B: Tussen 1 op duizend en 1 op een miljoen handelsdagen C: Tussen 1 op een miljoen en 1 op een miljard handelsdagen D: Minder dan 1 op een miljard handelsdagen

3

Is een gemiddelde Nederlandse verzekeringsmaatschappij meer blootgesteld aan verzekeringstechnische, operationele of aan marktrisico’s? Baseer uw antwoord op de hoeveelheid kapitaal welke volgens Solvency II naar verwachting zou moeten worden aangehouden.

A: Verzekeringstechnische risico’s B: Operationele risico’s C: Marktrisico’s

Speel de hele quiz op www.riskquest.nl/quiz en maak kans op een fles Veuve Cliquot champagne!

Kijk voor de voorwaarden op www.riskquest.nl/quiz RiskQuest, Weesperzijde 33, 1091 ED Amsterdam, telefoon 020-6932948, email: info@riskquest.nl

Actuarial science

What if? by: Hans Heintz and Frank Pardoel What happens with a pension fund’s coverage ratio if an effective drug against cancer is found, fewer people stay smoking and at the same time the Dutch economy enters into a Japan scenario with low interests and a high equity volatility. Such a question is very relevant for Dutch pension funds. Although financial institutions apply scenario analysis1 like stress testing within the framework of enterprise risk management (ERM), this is mostly done in an ad hoc and not very structured way.

This article argues that scenario analysis is complementary to the current statistically oriented risk measurement methods.

Current risk measurement methods During the last decades the financial world has applied mathematical models to estimate risk. In the beginning of the seventies of the last century Black and Scholes introduced their model for option valuation. In 1994 JP Morgan introduced the Value-at-Risk concept as part of RiskMetrics2. Since then the use of risk measurement methods was accelerated. Many of the currently used methods are based upon probabilties, e.g. the possible loss will not exceed y with a probability x %.

Shortcomings of current methods Working with probabilities gives false precision. This reminds of a joke in which someone is looking for his house key in the light of a street lamp. When after a long period of searching another one asks him if he has indeed lost his key at that particular spot, he answers:’’No, but in the light it is easier to search’’. Much is being invested in the further perfectioning of existing methods (e.g. think of the use of copulas). May be it is better to look elsewhere for the key. Not all risks are measurable with probability calculus. For instance the abolishment of mortgage tax deduction or the election victory of socialist parties.

Moreover the calculus methods have known deficiencies.

For variables for which historical values are available, value-at-risk-method are often applied3. These methods are based upon percentiles (and implicitly on averages).

If one bets 1,000 times at the roulette table, the ball hits zero on average 27 times (where you loose the bet).

However, what to do if you can bet only one time? In which case probability calculus is not very helpful.

Moreover a percentile doesn’t exclude the occurrence of an extreme event. If your loss at your equity portfolio is less than x with a certainty of 95%, it may nevertheless happen that you loose all money the other day. A black swan4 can always occur.

Mostly there is also too few history to find the real ‘probability distribution’ which may form the base of a once in 200 years value. The longest existing financial time series have a length of about 100 years. Moreover long time series are more sensitive to regime shifts.

Another welknown shortcoming of statistical methods is the fact dat they are based on the past, or as Warren Buffet says it:’In the business world, the rear view mirror is always clearer than the wind shield‘’.The last disadvantage of these methods is that small probabilities are hard to interprete.

Despite the above mentioned deficiencies, statistical risk methods are useful. They however form a necessary condition for good ERM, not a sufficient one. If well embedded and used, scenario analysis is a perfect

Hans Heintz

Frank Pardoel

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.

Frank graduated in 2009 from the University of Amsterdam as M.Sc. in Econometrics, track Mathematical Economics. Frank started his career within Hewitt Associates in 2007, working as an actuarial consultant and member of the Asset Liability Management team. In 2010 he decided to join RiskQuest. Frank currently joins the postgraduate program Risk Management for Financial Institutions at the VU Graduate School of Economics and Business. Frank is an associate at RiskQuest.

AENORM

vol. 20 (76)

August 2012

29

Actuarial science

complement to the mentioned methods. For an effective scenario analysis the following conditions are important:

Transparency

themselves. It is a challenge to design good and meaningful scenarios. Some of the criteria they must fulfill are: realistical, relevant, challenging, complete and structured. A well known method to design scenarios is the PEST method:

Both the scenario identification, underlying assumptions and the results must be very clear. This makes it possible for the manager to get a good overview.

Nearly good is sufficient For an effective ERM predicting the risk with high accuracy is not necessary. The philosopher Carveth Read wrote in 1898:’’It is better to be vaguely right than exactly wrong’’.

Top down To prevent users from not seeing the wood for the trees, it is important to start at a high level (for instance not individual stocks but an equity index and groups of pension contracts rather than individual contracts).

Speed To assess risks direct feed back is important. Users must be able to directly see the effect of hanges.

Herefore a large calculating capability is required.

Holistic Catastrophes nearly always occur at diverse aspects.

Therefore it is important to analyse more risks at the same time, for instance liquidity risk and market risk.

The PEST-method distinguishes the macro surrounding, the meso surrounding and the institution itself. The macro surrounding consists of Political, Economical, Social and Technological factors. These are translated to the direct surrounding of a company. A technological invention of a cancer medicine and a social change like a healthier way of life lead to a longer life expectancy. The core question is wether the cancer medicine results in an increased expectancy of 1 year or of 3 years.

Flexible It is important to be able to adjust scenarios in a simple way. What if life expectancy increases by 1.5 year instead of by 1 year?

The main input of scenario analysis are the scenarios

How to use the results of the analysis?

1 A company like Shell has applied advanced scenario analysis for over 50 years for planning, see also the book “The art of strategic conversation” by Kees van der Heijden 2 Please note that, Louis Bachelier, student of Henri Poincaré, wrote a revolutionary thesis back in 1900, titled “theorie de la speculation. This thesis included many modern concepts of risk measurement.

3 Think of Solvency II which applies a 1-in-200 year stress level 3 The term “Black Swan” stems from the Latin expression “rara avis in terris nigroque simillima cygno” which means something like “a strange bird looking like a black swan”. People used to think that such did not exist. However, explorer Willem de Vlamingh actually discovered Black Swans in 1697 in West-Australia

30

AENORM

vol. 20 (76)

August 2012

Actuarial science

As soon as the impact of scenarios has been determined, the question rises what to do with the results. A meaningful method is to arrange the scenarios in two dimensions: Impact and probability.

Therafter a selection can be made on the base of which management actions can be formulated. The selection focuses on scenarios that have some probability of occurrence in combination with a high (negative) impact. Welknown instruments for the management of pension funds are hedges (derivates), premium increases, indexation, operational cost reduction, investment policy and pension claims.

Although no scenario will ocur exactly in the pre-defined way, preparation and awareness are important conditions for effective risk management. Put differently:’’by failing to prepare, you are preparing to fail’’.

Example of SCENARIO analysis Consider a small pension fund with a coverage ratio of 100%. The investment mix consists of 10 % real estate, 30 % equity (15 % developed markets, 15 % emerging) and 60 % fixed income . The interest curve lies between 2.5 % (short interest) and 4.5 % (long). The liabilities amount tot 94 million euro. The average age is 55 years.

Management wants to assess the scenario as mentioned in the introduction with a 5 years horizon. Therefore the following steps must be made: Graphically, the translation looks as follows:

After having pressed the right buttons, the impact can be

AENORM

vol. 20 (76)

August 2012

31

Actuarial science

determined as follows: Base case (year 5) Coverage ratio (2.5th percentile) 85% Reserves (2.5th percentile) € -2.5 million Value of liabilities € 94 million

Scenario (year 5) 57% € -55 million € 175 million

Suppose management wants to know what is going to happen if the scenario changes a little. Equity volatility does not increase to 30%, but to 40 %, the life expectancy of men increases with 4 years (for women it still increases with 3 years). By pressing the right buttons the impact can be simply calculated.

Base case (year 5) Coverage ratio (2.5th percentile) 85% Reserves (2.5th percentile) € -2.5 million Value of liabilities € 94 million

Scenario (year 5)

Modified scenario (year 5)

57% € -55 million € 175 million

50% € -80 million € 193 million

If you want to see for yourself how this example works, please go to website www.iscenario.nl and login with ID: “Hans” and password: Ce-r3t.

The word scenario comes from the Latin word “scaena” which means scene. A formal definition is:’’ Scenarios are consistent and coherent descriptions of different imaginary future situations that reflect a different perspective of historical, current and future developments that can form the base for action 5 Although there are different interpretations of scenario analysis unanimity exists about one aspect: Scenarios do not intend to predict the future6.

5 See Ph.W.F. van Notten: “Writing on the wall: scenario development in times of discontinuity“, 2005 6 See van der Heijden et al.: “The Sixt sense: accelerating organisational learning with scenario’s”, Wiley & Sons, Chichester (2002)

32

AENORM

vol. 20 (76)

August 2012

Econometrics

The dynamics of financial markets and one-dimensional discontinuous piecewise-linear maps by: Fabio Tramontana and Frank Westerhoff 1. Introduction The economic and financial crisis of the last years may have at least one positive consequence: the rethinking of the economic and financial theories because those that are considered mainstream until now dramatically failed in anticipating and in remedying at the present economic scenario. An alternative consists in trying to build a brand new theory that permits to explain what is happening and which are the causes of it. A less expensive and preliminary task should be to look at what have to say all those theories that are not mainstream. Maybe some of those theories have forseen the current crisis but have not been taken into consideration by politicians and policy makers because they are not orthodox. This is exactly the case of Behavioral Economics and in particular Behavioral Finance, whose representative researchers warned against the real estate bubble that was at the origin of the crisis (see Shiller 2005). One of the core assumptions of Behavioral Economics is that people do not always make rational choices, but they use simple rule of thumbs that sometimes permit them to achieve a good result and, other times, not. As a consequence, models based on the neoclassical assumption of a representative, perfectly rational economic agent is no more acceptable and should be replaced by agent-based models with boundedly rational agents.

Agent-based financial market models have been proposed for a number of years now (for surveys, see Chiarella et al. 2009, Hommes and Wagener 2009, Lux 2009 and Westerhoff 2009). These models study interactions between heterogeneous market participants who rely on simple technical and fundamental trading rules to determine their orders. It should be noted that the key building blocks of these models are supported by empirical evidence. Most importantly, there are numerous survey studies (see the review of Menkhoff and Taylor 2007) and laboratory experiments (see the review of Hommes 2011) which clearly confirm that financial market participants do indeed rely on trend-extrapolating and meanreverting trading strategies.

Some agent-based financial-market models can be studied analytically. These models are usually deterministic, and reveal that nonlinear trading rules, switching between (linear) trading rules and/or market interactions,

may lead to irregular endogenous price dynamics. Contributions in this direction include Day and Huang (1990), Kirman (1991), de Grauwe et al. (1993), Lux (1995), Brock and Hommes (1998), Chiarella et al. (2002) and Westerhoff (2004).

Analytically tractable models are usually represented by smooth dynamical systems. However, there are also a few examples where the dynamical system is discontinuous (e.g. Huang and Day 1993, Huang et al. 2010, Tramontana et al. 2010, 2011a, 2011b). One advantage of these models is that they allow a deeper analytical understanding of the underlying dynamical system. Another advantage is that discontinuous maps also offer interesting and sometimes quite peculiar bifurcation phenomena, enriching our understanding of what may be going on in financial markets. For instance, in some of these models fixed point dynamics may turn directly into (wild) chaotic dynamics once a model parameter has crossed a certain bifurcation threshold, implying that even a tiny parameter change may have a dramatic impact on dynamics.

In addition to deterministic agent-based financial market models, stochastic versions also exist. While deterministic models usually generate complex dynamics, thereby mimicking the stylized facts of bubbles and crashes and excess volatility, they usually have difficulties in reproducing the finer details of stock market dynamics, such as fat tails, volatility clustering and long memory effects. Stochastic versions of agent-based financial market models are able to mimic these statistical features quite well and these are the features of our model.

2. A simple financial market model Within our model, prices adjust with respect to excess demand. We use the following (standard) log-linear price adjustment rule, where P is the log of price .

(1)

The four terms in bracket on the right-hand side of (1) capture the transactions of the four groups of speculators, that is, the transactions of type 1 chartists, type 1 fundamentalists, type 2 chartists and type 2 fundamen-

AENORM

vol. 20 (76)

August 2012

33

Econometrics

talists, respectively. Parameter is a price adjustment parameter which we set, without loss of generality, equal to =1. Therefore, (1) states that excess buying drives the price up and excess selling drives it down.

. Hence, with reaction parameter , transactions of type 2 chartists can, in such a situation, either be increased or decreased, in the latter case down to zero .

Orders by type 1 chartists are formalized as

Orders by type 2 fundamentalists are based on the same principles, i.e. we have

(2) The four reaction parameters of (2) are non-negative, i.e.

(5)

. Note first that type 1 chartists optimistically buy (pessimistically sell) if prices are in the bull (bear) market, that is, if log price P is above (below) its log fundamental value F. Reaction parameters and capture some general kind of optimism and pessimism, respectively; reaction parameters and indicate how aggressively type 1 chartists react to their perceived price signals. Obviously, type 1 chartists may treat bull and bear markets differently with respect to their trading intensity.

where restrictions , and apply.

In a serious bull market, given by , type 2 fundamentalists submit selling orders ; in a pronounced bear market, given by , they submit buying orders .

Orders by type 1 fundamentalists are written as

2.1. The model’s law of motion (3)

where

the

reaction parameters fulfill . Type 1 fundamentalists always trade in the opposite direction as type 1 chartists.

They sell in an overvalued market and buy in an undervalued market. The trading intensity of type 1 fundamentalists may also differ in bull and bear markets: a certain overvaluation may trigger a larger or smaller absolute order size than an undervaluation of the same size.

Type 2 chartist are only active if prices are at least a certain distance away from their fundamental value.

The threshold in the bull market is given by ; the threshold in the bear market is denoted by . Orders by type 2 chartists may therefore be expressed as

Two simplifying assumptions which we make throughout the rest of the paper are that (i) type 2 chartists and type 2 fundamentalists share the same market entry levels and that (ii) their upper and lower market entry levels are equally distant to the fundamental value. Formally, we thus have .

Moreover, it is convenient to express the model in terms of deviations from the fundamental value by defining . Combining (1) to (5) then yields (6) which is a one-dimensional discontinuous piecewiselinear map. To make the notation more convenient, let us introduce

(4) Here we make the following assumptions. We assume that , i.e. the trading intensity of type 2 chartist increases with the distance between prices and fundamentals. In addition, we assume that , i.e. the upper market entry level, indicating a robust bull market, is above the fundamental value and the lower market entry level, indicating a robust bear market, is below the fundamental value. Finally, we assume that and . The transactions of type 2 chartists are therefore non-negative in the bull market and non-positive in the bear market. For instance, if were equal to zero, then transactions of type 2 chartists at the market entry level would be given by

34

AENORM

vol. 20 (76)

August 2012

(7)

What can we say about the signs of these eight aggregate parameters? Given the assumptions we have made about the 16 individual reaction parameters, it is clear that each of the eight aggregate parameters can take any value.

With the help of (7), our model can be simplified to

(8)

Econometrics

The map representing our financial market model is extremely flexible – since there are no restrictions on the eight aggregate parameters, each of its four branches can be positioned everywhere in -space – and thus incorporates a number of potentially interesting subcases.

The properties of this deterministic model has been analyzied in detail in various paper in collaboration with Laura Gardini (see. Tramontana et al. 2010, 2011a, 2011b). They are able to replicate qualitative features of financial markets like bubbles and crashes and excess volatility. In the next section we develop and study a stochastic version of this model.

3. A stochastic model version We seek to show that the models in the previous section, which are relatively simple and rely only on a minimum set of economic assumptions, are not only able to replicate certain stylized facts such as bubbles and crashes and excess volatility – they also mimic the finer statistical details of actual stock prices.

First of all, let us assume that type 1 speculators treat bull and bear markets symmetrically. Technically, we thus have m1 = m2 and s1 = s2, and the map reduces to

would be the case, for instance, if we assumed a positive mean for m1. This could have been interpreted as a general kind of optimism of type 1 chartists, leading to systematic buying pressure. However, from period to period there may be some unsystematic (random) optimism and pessimism, and the variability of speculators’ sentiments is given by the standard deviations of the distributions. Note here that the degree of randomness of type 1 speculators is larger than the degree of randomness of type 2 speculators. This seems to be reasonable since type 2 speculators perceive clearer trading signals than type 1 speculators.

The assumptions about the distribution of the slope parameter of the inner regime imply that type 1 chartists trade, on average, more aggressively than type 1 fundamentalists. However, the joint trading intensity of type 1 and type 2 fundamentalists dominates the joint trading intensity of type 1 and type 2 chartists. Note that the dominance of fundamental trading is highest in the lower regime. By setting the standard deviation in the inner regime higher than in the outer two regimes, we assume that the inner regime is subject to stronger random influences than the two outer regimes. Of course, assuming Z=0.2 implies that type 2 speculators enter the market if prices are either 20 percent below or 20 percent above the fundamental value. Without loss of generality, we also set F=0. As a result, we have , thus can be interpreted as the log price and changes of as returns.

(9) Moreover, speculators may randomly deviate from their trading strategies, i.e. all model parameters are from now on regarded as random variables. As a result, both the location and the slope of the model’s three branches change randomly over time. Economically, this assumption seems to be quite natural. Speculators do not always follow exactly the same deterministic trading rule. Their mood and aggressiveness depend on a number of factors.

Instead of modeling them in detail, we introduce, for simplicity, a degree of randomness to capture unsystematic deviations from the trading rules (2)-(5).

To be precise, we make the following assumptions

(10) Before starting to explaining the economic meaning of (10), we note that (10) is the result of a trial and error calibration process. As we will see in more detail in the sequel, parameter setting (10) is able to generate reasonable dynamics and is thus (indirectly) supported by the data.

What can we say about the economic implications of these assumptions? Let us start with the distributional assumptions concerning m1, m2 and m3 and observe first that all their means are zero, implying that there is no systematic optimism or pessimism amongst speculators. This

3.1 A typical simulation run Figures 1-6 show the outcome of a “typical” simulation run of 3392 iterations. Figure 1 presents the evolution of the price. Recall that the fundamental value is equal to 1.

As can be seen, the model is able to generate bubbles and crashes. For instance, around time step 2000, the market is overvalued by about 70 percent, and crashes immediately afterwards. Figure 2 shows that, despite having a constant fundamental value and there being therefore no fundamental reason for price changes, prices nevertheless fluctuate strongly. Extreme price changes can easily be higher than 5 percent and up to 10 percent; there is also visual evidence of volatility clustering.

The two panels of Figure 3 compare the distribution of the simulated returns with the results one would obtain from normally distributed returns (based on the same mean and standard deviation). Note first that the distribution of the simulated returns is well behaved: it is unimodal and bell-shaped. Compared to the normal distribution there is, however, less probability mass in the shoulders and more probability mass in the center and the tails. The same feature can be observed in real stock markets.

Figures 4 and 5 present the autocorrelation function of the returns. Since the autocorrelation coefficients are insignificant, prices are very close to a random walk. And, indeed, it would be hard to predict future price movements from Figure 4. Figure 5 displays the autocorrelation function of absolute returns. These autocorrelation

AENORM

vol. 20 (76)

August 2012

35

GET A FR SUBS E CRIP E TION NOW ! www . aeno

rm.eu

DOWNLOAD and READ published articles online

title

www.aenorm.eu

Econometrics

Figure 1 - Figure 6

coefficients are highly significant, and decay slowly over time. Even after 100 lags, we find significant autocorrelation coefficients and, thus, evidence of long memory effects. Finally, Figure 6 represents a typical log prices evolution.

Let us next endeavor to understand how the model works. Suppose first that the market is slightly overvalued. As a result, the market is, on average, dominated by type 1 chartists and there is a tendency for prices to rise. However, the dominance of type 1 chartists over type 1 fundamentalists is rather weak and, since the reaction parameters are stochastic, we have (almost) erratic switches between a monotonic convergence towards the fundamental value and a monotonic departure from the fundamental value. Prices are therefore close to being unpredictable. Assume next that prices move away from the fundamental value. If market entry level Z is crossed, type 2 speculators enter the scene. We now have a situation where type 1 and type 2 fundamentalists jointly dominate the trading behavior of type 1 and type 2 chartists. Since the dominance is weak, prices may first move further away from the fundamental value, but are eventually driven back towards more moderate levels. What happens then? Prices could again be pushed upwards; however, due to the stochastic nature of the model, prices may also decrease and even drop below the fundamental value. If this is the case, chartists become pessimistic and tend to drive prices down even further. At some point, it may be the case that the lower market entry level –z is crossed. Then we again have a situation where type 2 speculators become active. Since type 2 fundamentalists are rather aggressive compared to type 2 chartists, prices eventually recover.

What about the other stylized facts? As prices run away from the fundamental value, both chartists and fundamentalists receive stronger trading signals – their trading rules are just a linear function of the mispricing. Excess demand in the market therefore also increases, triggering larger price changes. Since bull and bear markets are persistent to some degree, we have regular periods of high volatility, alternating with periods of low volatility where prices are closer to their fundamentals. Periods of high volatility also render the distribution of the returns fat tailed.

3.2. A Monte Carlo Study So far, our analysis has been restricted to one particular simulation run. Now we attempt to evaluate the model in a more serious fashion. To this end, we first estimate certain summary statistics (or moments) of the Italian and German stock market indexes in order to have two benchmarks. Then, on the basis of 1000 simulation runs, we check whether our model produces comparable figures for these statistics. Two things should be noted. First, all times series comprise 3392 observations (or 13 years), i.e. the times series are rather short. Second, it seems that the period from 1998 to 2010 was a rather volatile

AENORM

vol. 20 (76)

August 2012

37

Econometrics

period. Both markets displayed two major crises and thus volatility may have been above its long-run level.

With the first two statistics, rmin and rmax, we look at the most negative and the most positive daily log price change, respectively. As reported in Table 1, both the FTSE MIB and the DAX produced extreme returns of around Âą10 percent between 1998 and 2010. In comparison, the extreme returns of our model seem to be somewhat lower on average. For instance, the median negative and positive extreme returns are given by 6 percent and 5 percent,

use the statistic, which measures the average absolute distance between log prices and log fundamentals. Apparently, this statistic is an indicator of the distortion in the market and quantifies, at least partially, the size of bubbles and crashes. Unfortunately, this statistic cannot be computed for actual markets, at least not as long as there is a reliable indicator of the markets’ fundamental values. For our model, however, we find that 90 percent of the simulation runs have a distortion between 8 and 15.5 percent. Hence, bubbles and

Table 1: Summary statistics for the FTSE MIB and the DAX. Daily data between 1998 and 2010, 3392 observations.

respectively. However, at least 5 percent of the simulation runs produce extreme returns larger than Âą10 percent.

We obtain a similar result when we look at volatility estimates. For this reason, we introduce the volatility estimator , measuring the average absolute return (T is the sample length, given here by T=3391 observations). The median volatility estimate we obtain for our model is approximately 0.75 percent. For the Italian and German stock markets, we find volatility estimates of around 1 percent. Given this evidence, we may conclude that our model is able to produce excess volatility, and that its volatility is roughly comparable to what we observe in actual stock markets (taking into account that the period 1998 to 2010 was, presumably, more volatile than the long-run average).

To capture the phenomenon of bubbles and crashes, we

38

AENORM

vol. 20 (76)

August 2012

crashes seem to be present in almost all simulation runs.

Estimates for the kurtosis K are given by 8.21 for the Italian and 7.11 for the German return distribution. The median value we obtain for our model is 5.38, which is close to these values. Moreover, 95 percent of our simulation runs have a kurtosis of 4.3 or more. Since the kurtosis of a normal distribution is given by 3, this can be regarded as a safe indicator of excess kurtosis. A better indicator of the fat-tailedness of a return distribution is the Hill tail index H, which we compute on the basis of the largest 5 percent of the absolute returns. For actual markets, this statistic tends to hover between 3 and 4 and, indeed, for the Italian and German stock markets they are given by 3.18 (FTSE MIB) and 3.06 (DAX). Our model comes quite close to these figures. As we can see, 70 percent of the simulation runs yield Hill estimates between

Econometrics

2.93 and 4.11. In other words, there is ample evidence that our model is able to generate fat-tailed return distributions.

A further important stylized fact of financial markets concerns their unpredictability. Table 1 presents the autocorrelation coefficients of the returns for the first six lags. These autocorrelation coefficients are quite small, and imply that neither the Italian nor the German stock market can be predicted, at least not based on past returns

and linear methods. This important feature is matched by our model quite nicely. The autocorrelation coefficients of the simulated returns are essentially insignificant.

Finally, we turn to the markets’ tendency to produce volatility clustering and long memory effects, two other closely related universal features of financial markets.

The predictability of the volatility can be detected via the autocorrelation coefficients of the absolute returns (which we compute for lags 1, 5, 10, 25, 50 and 100). In real markets, these autocorrelation coefficients are highly

Table 2: Summary statistics for the model. The quantiles of the summary statistics are calculated on the basis of 1000 simulation runs with 3392 each.

AENORM

vol. 20 (76)

August 2012

39

Econometrics

significant and decay slowly. Again, this also is the case for the Italian and German markets, and for our artificial market.

4. Conclusions Obviously, our model is not perfect. However, given the simplicity of our setup, it is surprising to see how closely the data generated by our model comes to actual data.

Overall, our model has at least a certain ability to generate bubbles and crashes, excess volatility, fat tails for the distribution of returns, uncorrelated returns and volatility clustering and long memory effects – which are frequently regarded as the most important stylized facts of financial markets.

We think that the main contribution of this paper is to show that a stochastic version of our model – in which we assume that speculators may randomly deviate from their core trading principles – is able to generate quite realistic dynamics. Responsible for this outcome is the fact that the dynamics result from a mixture of different dynamic regimes, including fixed point dynamics, (quasi-)periodic dynamics, chaotic dynamics and divergent dynamics.

References Brock, W. and Hommes, C. (1998): Heterogeneous beliefs and routes to chaos in a simple asset pricing model. Journal of Economic Dynamics Control, 22, 1235-1274.

Chiarella, C., Dieci, R. and Gardini, L. (2002): Speculative behaviour and complex asset price dynamics: A global analysis. Journal of Economic Behavior and Organization, 49, 173-197.

Chiarella, C., Dieci, R. and He, X.-Z. (2009): Heterogeneity, market mechanisms, and asset price dynamics. In: Hens, T. and Schenk-Hoppé, K.R. (eds.): Handbook of Financial Markets: Dynamics and Evolution. North-Holland, Amsterdam, 277-344.

Day, R. and Huang, W. (1990): Bulls, bears and market sheep. Journal of Economic Behavior and Organization, 14, 299-329.

Fabio Tramontana Dr. Fabio Tramontana (1979) is an Assistant Professor of Economics at the University of Pavia (Italy) where he teaches a course in Behavioral Economics and Finance.

He received a Ph.d degree in Economics at the University of Ancona (Italy). His research interests include: Bounded Rationality, Agent-based modeling, Game Theory and Nonlinear Economic Dynamics. He is a member of the MDEF (Dynamic Models in Economic and Finance) research group, headed by Professors Bischi and Gardini of the University of Urbino (Italy)

Frank Westerhoff Frank Westerhoff obtained his doctoral degree from the University of Osnabrück in 2002, followed by a habilitation degree in 2005. After a brief stint at the University of Bonn, he joined the University of Bamberg in 2006 where he was appointed Professor of Economics and currently holds the Chair of Economic Policy. Frank Westerhoff develops, calibrates and estimates small scale, behavioral, agent-based models to investigate the dynamics of financial markets and the macroeconomy. He is on the editorial boards of the Journal of Economic Behavior and Organization and the Journal of Economic Dynamics and Control

40

AENORM

vol. 20 (76)

August 2012

De Grauwe, P., Dewachter, H. and Embrechts, M. (1993): Exchange rate theory – chaotic models of foreign exchange markets. Blackwell, Oxford.

Hommes, C. and Wagener, F. (2009): Complex evolutionary systems in behavioral finance. In: Hens, T. and Schenk-Hoppé, K.R. (eds.): Handbook of Financial Markets: Dynamics and Evolution. North-Holland, Amsterdam, 217-276.

Hommes, C. (2011): The heterogeneous expectations hypothesis: Some evidence from the lab. Journal of Economic Dynamics and Control, 35, 1-24.

Huang, W. and Day, R. (1993): Chaotically switching bear and bull markets: the derivation of stock price distributions from behavioral rules. In: Day, R. and Chen, P. (eds): Nonlinear dynamics and evolutionary economics. Oxford University Press, Oxford, 169-182.

Huang,W., Zheng, H. and Chia, W.M., (2010): Financial crisis and interacting heterogeneous agents. Journal of Economic Dynamics and Control, 34, 1105-1122.

Econometrics

Kirman, A. (1991): Epidemics of opinion and speculative bubbles in financial markets. In: Taylor, M. (ed.): Money and Financial Markets. Blackwell: Oxford, 354-368.

Lux, T. (1995): Herd behaviour, bubbles and crashes.

Economic Journal, 105, 881-896.

Lux, T. (2009): Stochastic behavioural asset-pricing models and the stylize facts. In: Hens, T. and SchenkHoppĂŠ, K.R. (eds.): Handbook of Financial Markets: Dynamics and Evolution. North-Holland, Amsterdam, 161-216.

Menkhoff, L. and Taylor, M. (2007): The obstinate passion of foreign exchange professionals: technical analysis. Journal of Economic Literature, 45, 936-972.

Shiller, R.J. (2005): Irrational Exuberance. Princeton University Press. Princeton USA. Tramontana, F., Westerhoff, F. and Gardini, L. (2010): On the complicated price dynamics of a simple onedimensional discontinuous financial market model with heterogeneous interacting traders. Journal of Economic Behavior and Organization, 74, 187-205.

Tramontana, F., Gardini, L. and Westerhoff, F. (2011a): Intricate asset price dynamics and one-dimensional discontinuous maps. In: Puu, T. and Panchuck, A. (eds): Advances in nonlinear economic dynamics.

Nova Science Publishers.

Tramontana, F., Gardini, L. and Westerhoff, F. (2011b): Heterogeneous speculators and asset price dynamics: further results from a one-dimensional discontinuous piecewise-linear map. Computational Economics, 38, 329-347.

Westerhoff, F. (2004): Multiasset market dynamics.

Macroeconomic Dynamics, 8, 596-616.

Westerhoff, F. (2009): Exchange rate dynamics: A nonlinear survey. In: Rosser, J.B., Jr. (ed): Handbook of Research on Complexity. Edward Elgar, Cheltenham, 287-325.

AENORM

vol. 20 (76)

August 2012

41

Econometrics

Complementary Insurance and Deductibles in the Dutch Health Care System by: Daan Stroosnier In 2006 the Netherlands experienced a health care reform that shifted part of the health care risk from the insurer and public system to the insured and thus shifted some of the financial burden more towards the public. This shift was an attempt to reduce the steady increase of health costs during the last decades. Two of the changes were the introduction of a voluntary additional deductible and the possibility to opt for a complementary voluntary health insurance (VHI), in order to enable a rational use of health care and thereby diminishing the effects of moral hazard and adverse selection. This article addresses the choice for having a complementary voluntary health insurance and a voluntary additional deductible in the Netherlands.

Introduction In theory, complementary health insurance and deductibles are methods to influence the “unnecessary” demand for health care induced by moral hazard (Barros, Machado, & Sanz-de-Galdeano, 20081; Schellhorn, 20012). If the difference between the expected use of health care with and without complementary insurance is large, then individuals are less likely to take a complementary insurance because it might bring them financial gain by means of lower insurance premiums. This means the complementary insurance ensures that, at least a part of, the unnecessary use of health care disappears. In case of the additional deductible the difference between expected health care usage under having no deductible and having one should also be large to ensure that the unnecessary use of health care disappears. This is because individuals are more likely to accept an additional deductible because it might bring them financial gain by means of reduction of insurance premiums. In both cases unnecessary health care usage partly disappears, because the problem of moral hazard is tackled, one of the reasons the new health care system in the Netherlands has been introduced (Schäfer et al., 20103; van Ophem & Berkhout, 20104).

Daan Stroosnier Daan Stroosnier finished his Master’s degree in Econometrics last March. He wrote his thesis, under supervision of Dr. Hans van Ophem, about the choice for having a complementary voluntary health insurance and a voluntary additional deductible in the Netherlands. The thesis was nominated for the UvA Thesis Prize 2012. As from 1 September, Daan will be Analyst at the Quantitative Analysis division of PwC.

42

AENORM

vol. 20 (76)

August 2012

On the other hand individuals will also consider their health status when having to choose for a complementary insurance and a deductible or not (Godfried, Oosterbeek, & Tulder, 20015; van Ophem & Berkhout, 20104). The consideration of health status reflects adverse selection.

The aim of this article is to examine what the determinants for the choice of taking a complementary insurance and accepting an additional deductible are and how health care demand influences these choices. On top of that the relation with moral hazard and adverse selection is modeled. To achieve this, the simultaneity between the choice for having a complementary health insurance, having a deductible and health care demand has to be modeled. Therefore possible dependence between health care demand and these choices has to be taken into account as well as dependence between the choices themselves.

In the remainder of this article, an econometric model which reflects the choice for a voluntary additional deductible and a complementary VHI is developed. The general model was split up into three separate estimable models (Stroosnier, 20126). Only the first model is presented in this article, because it is the most important model for the research and less known in literature.

Furthermore, the main emperical results, following from the estimations of the first model, and their implications are presented.

Econometric model The health status and especially health care demand, approximated by the expected number of physician visits, are expected to be considered by an individual in the decision to take an additional voluntary deductible and a complementary VHI. Individuals opt for a

Econometrics

deductible if they believe that the expected utility of this insurance option is higher than the alternative of no deductible . In similar fashion, individuals opt for a complementary insurance if they believe that the expected utility is higher than if they take no complementary insurance . Taking the possible dependence between the choice for a deductible and the choice for a complementary insurance into account, an econometric model for these choices is specified in eq. (1) and eq. (2) under the assumption that the utility functions can be approximated by a linear function:

(1) The tendency to accept a deductible, denoted by , is made dependent on health indicators, collected in Hi, and other explanatory variables, indicated by Xi. Furthermore, depends on the difference in expected number of physician visits with and without a deductible. The expected number of physician visits with a deductible is composed by the expected number of physician visits with a complementary insurance and without, denoted by and . The same holds for the expected number of physician visits without a deductible where and denote the expected number of physician visits with a complementary insurance and without. The probability of occurrence of complementary insurance is reflected in and .

visits with and without a complementary insurance.

The expected number of physician visits with a complementary insurance consists of and which are the expected number of physician visits with a deductible and without.

The expected number of physician visits without a complementary insurance is composed by the expected number of physician visits with a deductible and without, denoted by and .

The probability of occurrence of the deductible is indicated by and . The error terms in eq. (1) and eq. (2) are reflected in and and they are distributed as follows:

(3) Because in both equations the difference in expected number of physician visits is decomposed into four regimes, possible dependence between the choice for a deductible and the choice for a complementary insurance has to be considered in estimating the model.

Unfortunately, estimating this general model in eq. (1) and eq. (2) appeared not to be feasible if endogeneity of expected health care demand is taken into account.

Monte Carlo simulations showed that under different assumptions this model cannot be estimated properly with the estimation techniques at hand. Therefore the above discussed model was split up into three separate models.

The first model, which is presented in this article, does take endogeneity of expected health care demand into account, but does not consider dependence between the two insurance choices. The model is a switching count model (van Ophem & Berkhout, 20104).

Switching count model (2)

Eq. (2) reveals three aspects. First, the tendency to choose for a complementary insurance, , depends on health indicators, collected in Hi, and other explanatory variables, indicated by Xi. Second, is made dependent on the difference in expected number of physician

Applying the switching count model leads to the following simplification of the general model described in the previous section.

1 P.P. Barros, M.P. Machado and A. Sanz-de-Galdeano: “Moral harzard and the demand for health services: a matching estimator approach“, Journal of health economics, 27 (4) (2008): 1006-25 2 M. Schellhorn: “The effect of variable health insurance deductibles on the demand for physican visits“, Health economics, 10(5) (2001) : 1006-25 3 W. Schäfer, M. Kroneman, W. Boerma, M.V.D. Berg, G. Westert, W. Devillé and E.V. Ginneken: “The Netherlands: Health system review“, Health Systems in Transition, 12 (1) (2010): 1-229 4 H. van Ophem and P. Berkhout: “The deductible in healt insurance: do the insured make a choice based on the arguments as intended by the polici makers?” Working paper QE 2010/07 University of Amsterdam 5 M. Godfried, H. Oosterbeek and F.V.A.N. Tulder: “Adverse selection and the demand for supplementary dental insurance“, De Economist , 2 (2001): 177-190 6 D.M. Stroosnier: “Complementary insurance and deductibles in the Dutch health care system“ MSc-thesis, University of Amsterdam 2012

AENORM

vol. 20 (76)

August 2012

43

Econometrics

(4) The inclination to accept a deductible does not depend on the choice for a complementary insurance anymore (5) and vice versa. This means the difference in the expected number of physician visits (yi) with and without a deductible is simplified to .

The difference in the expected number of physician visits with and without a complementary insurance is given by . Furthermore, and are, contrary to the general model, not dependent and have zero mean and constant variances. Other possible factors influencing the choice for a deductible and a complementary insurance i.e. health indicators (Hi), socio-economic explanatory variables (Xi) are still present. The unknown parameters and need to be estimated.

To complete the model presented above one more aspect has to be noted. In eq. (4) and eq. (5) and are not observed. Only under one of the regimes the number of physician visits is observed. The latent variable determines under which regime the number of physician visits is observed viz. or . The number of physician visits observed under or is determined by :

(6) where and are the cumulative (7) distributions of the counts and with expectations and under regime j. Say, health care demand, approximated by physician count, depends on a variety of explanatory variables. Suppose these explanatory variables are collected in a vector Zi, then the model is completed by assuming and .

This model can be estimated by employing the copula estimation technique. This method takes full account of the possible dependences between the random variables , and in eq. (4) and eq. (6) and between the random variables , and in eq. (5) and eq. (7)7.

The copula estimation technique can be employed if the exact marginal distributions are specified. This article assumes Poisson or Negative Binomial (NB2) distributed counts and normally distributed error terms. The variance of the error terms and can only be estimated up to a scaling factor and will therefore be put equal to 1.

Results In the empirical research a number of different specifications of the switching count model are employed for both the deductible and complementary VHI choice. On top of that two different copulas are used in estimating this model i.e. the Frank copula and the Gaussian copula. It was shown that the specification with Negative Binomial 2 distributed physician counts, which treats the groups of individuals with and without a deductible completely separate, should be preferred compared to the other specifications. Whether the estimates using the Frank copula should be preferred to the ones using the Gaussian copula is ambiguous. Both copulas produce very similar estimation results across the specifications.

These findings are the same for the complementary VHI choice.

Table 1 shows the estimation results of the aforementioned specification using the Gaussian copula. The only significant adverse selection found is that individuals who have had a flu vaccination are less likely to opt for a deductible. The results do not exhibit effects of moral hazard. Further determinants are being a breadwinner and the number of children in the household. For the factors influencing health care demand, considerable differences are distinguished between the group of individuals with a deductible and without. This indicates that the underlying process governing the amount of health care used is different for these groups. Finally, significant negative dependence between the choice for a deductible and health care demand is found. This suggests that individuals take account of their (expected) health care demand in their decision to take a deductible or not, although the relevant explanatory variables are not observed.

Table 1 also shows the results of the switching count model relating to the complementary VHI choice. It shows significant adverse selection in terms of a negative effect of self-assessed health. Self-assessed healthier individuals are less likely to opt for a complementary insurance. Moral hazard is found to play a role in the choice for having a complementary VHI. Other determinants are age, being a breadwinner, income, the number of children in the household and having a partner. The effect of age has an inverted U-shape. For the factors influencing health care demand, some differences are distinguished between the group of individuals with a complementary VHI and without, although these differences are small compared to the deductible case. This indicates that the underlying process governing the amount of health care used is to some extent different for these groups. Finally, dependence between the probability of choosing for a complementary insurance and health care demand under having a complementary insurance is found positive and significant. This suggests that individuals take account of their (expected) health care demand under having a complementary insurance in their decision to take a

7 Since yd1i and yd0i are not observed simultaneously, the dependence between these counts is not identifiable. The same holds for yc1i and yc0i.

44

AENORM

vol. 20 (76)

August 2012

Econometrics

AENORM

vol. 20 (76)

August 2012

45

Econometrics

complementary insurance or not, although the relevant explanatory variables are not observed.

Conclusion The results indicate that the choice for a complementary health insurance depends on the health status of individuals and the difference between expected health care demand with and without having a complementary insurance. Consequently, adverse selection and moral hazard appear to be relevant in the choice for a complementary insurance. Other determinants are age, being a breadwinner, income, number of children and having a partner. In the choice for a deductible moral hazard does not appear to be relevant and the effect of adverse selection is limited. Determinants are being a breadwinner and number of children. Finally, the underlying process governing the amount of health care used is different for different insurance schemes.

Subsequent research can focus on a number of issues. First, the switching count model distinguishes only two regimes, but there are many more possible choices in the deductible and complementary insurance choice. A research taking more choices into account could prove interesting results. Second, investigating the behavior of the switching count model under different specifications, misspecification or under estimation using a two-step method might show useful results. Third, further research may use other marginal distributions or copulas for estimation. For example, zero-inflated Poisson distributed counts might lead to better estimations. Another option is semi- or nonparametric estimation of the marginal distributions. Finally, only the number of physician visits is used as a measure of health care demand, leaving other measures unexplored.

References P.P. Barros, M.P. Machado and A. Sanz-de-Galdeano: “Moral hazard and the demand for health services: a matching estimator approach“, Journal of health economics, 27(4) (2008): 1006-25 M. Godfried, H. Oosterbeek and F.V. Tulder: “Adverse selection and the demand for supplementary dental insurance“, De Economist, (2) (2001): 177-190 M. Schellhorn: “The effect of variable health insurance deductibles on the demand for physician visits“, Health Economics, 10 (5) (2010): 441-56 W. Schäfer, M. Kronema, W. Boerma, M.V.D. Berg, G. Westert, W. Devillé and E.V. Ginneken: “The Netherlands: Health system review“, Health Systems in Transition, 12(1) (2010):1-229

46

AENORM

vol. 20 (76)

August 2012

D.M. Stroosnier: “Complementary insurance and deductibles in the Dutch health care system“ MScthesis Econometrics, University of Amsterdam (2012) H. van Ophem and P. Berkhout: “The deductible in health insurance: do the insured make a choice based on the arguments as intended by the policy makers?“ Working papar QE 2010/07, University of Amsterdam

On this page you find a few challenging puzzles. Try to solve them and compete for a prize! Submit your solution to Aenorm@vsae.nl.

Answers to puzzles Aenorm 75

Winner Aenorm 75

The race of the econometrician and the actuary The hands will next come together, at 5 minutes, 27 and 3/11 seconds past 1 o’clock.

The winner of Aenorm 75 is: Bas Kunst.

Congratulations!

Dividing farmers earnings Each man would have accomplished the same amount of work during the eight hours it took them to complete the field, so each is entitled to $2.50 for his labours.

Solutions

The canals on Mars All the readers who submitted answered “There is no possible way” which is indeed correct.

Solutions to the two puzzles above can be submitted up to October 31st 2012. 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 76, Roetersstraat 11, 1018 WB Amsterdam, Holland. Among the correct submissions, one will be the winner. Solutions can be both in English and Dutch.

Olympic Games 2012: The fastest man in the world The whole world will watch the 100 metres sprint during the Olympic Games in London. Who will become the fastest man in the world? Due to a severe foodborne illness only four men compete in this year’s final. The odds are as follows. Yohan Cake: 2 to 1, Tusain Gold: 3 to 2 and Gyson Tay: 11 to 4.

The question is: what are the changes for Murandy Chartina to become the fastest man in the world?

Baseball Game One day we went to Walibi Theme Park and noticed this game where you had to knock the men over with baseballs.

The man said: “You can take as many throws as you like.

Each throw costs you 1 euro. Add up the numbers on all the men you knock down. When your score exactly sums up to 50 you win an inflatable crocodile.

Unfortunately our money gave out before we learned how to win. Can you show us how we could win the inflatable crocodile?

AENORM

vol. 20 (76)

August 2012

47

The last few months, it has been a quiet period for the VSAE. After the drink on the last day of the academic year and the succesfull end-of-the-year-activity, our members enjoyed their summer holidays. Of course, the organization of our upcoming events continued.

Every year, we welcome our new first year students on the VSAE Introduction Days. This year, we will take off to Friesland with seventy freshman, the board and the organizing committee. In three days, they will get to know each other and the VSAE. The Beroependagen, organized in cooperation with the Financial Study association Amsterdam (FSA), will take place on the 3th and 4th of October. Students with a quantitative or financial background can enjoy presentations, workshops, lunches and dinners in Hotel Sofitel Amsterdam The Grand. A broad selection of more than 25 leading companies will present themselves, so there is something for everyone.

On the 7th of November we will head to London with 24, last year bachelor or master, students for the International Study Project 2012. At the office of KPMG these 24 students will try to solve a challenging case about Financial Risk Management.

We have a lot more activities ahead, like our monthly drinks, the National Econometricians Soccer Tournament in Utrecht and the traditional pool tournament in October.

We look forward to seeing you there!

Agenda •

22 - 24 August

Agenda •

20 - 23 August

VSAE Introduction Days

IDEE Week

•

Monthly Drink

18 September

•

Introduction Weekend

•

48

Once again a year of studying hard ended and we’ve celebrated this with several informal activities, including the famous, annual Kraketweekend, which took place at a lovely location near Apeldoorn, where we’ve visited the Apenheul, lasergamed and had several outdoor activities.

After the examweek Kraket organized a creative day of painting in the Vondelpark followed by a barbecue in the sun and later the - now traditional - beachvolleybal tournament in Zandvoort.

This summer we, the new board, are already working hard to come up with and organize some new, impressive activities and will do our best to set up a stylish ball.

However we will also keep or try to improve some of the succesfull events of previous years, like the very much loved partyish activity at the end of each examweek.

Besides this all, we will be upgrading our Introduction Weekend to a higher level with new extras to show our fresh members what we can and will offer as a studyassociation coming academic year!

We are very excited to let our new and older members experience the new activities and will do our utmost to make it an awesome academic year and hope to see you there!

24 September

General Members Meeting

•

Beroependagen

•

Inhouse Day MIcompany

•

International Study Project 2012

2 - 3 October 12 October

7 - 11 November

AENORM

vol. 20 (75) (76)

August 2012

31 August - 2 September

If you ask for it, you will get responsibility Robert Steemers, trainee Risk, ING

Where do you want to go?

ING wants Risk Management trainees. If you have the hands-on mentality and skills to back it up, you’ll find the bank to be a world of opportunity. Try, practice and discover what you’re good at. Like redeveloping the corporate LGD model.

We’ll throw you in at the deep end, but not without a coach, a lifeline and ample rewards. Join the ING International Talent Programme at ING.nl/graduates

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!

smar t phone

Scan deze

QR code met je

Benefits | Risk and Financial Services | Talent and Rewards werkenbijtowerswatson.nl