Aenorm 74

This edition:

It’s Not the Economy, Stupid!

It’s All About Well-being

74

vol. 20 feb. ‘12

And: Optimizing the Healthcare System for Alcohol Use Disorders Copula-GARCH Models to Estimate Capital Requirements for Pension Funds

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In this edition of Aenorm one of the articles argues that GDP per capita is a futile wellbeing measure. While I agree that countrywide well-being is far from the same as a high per capita GDP and it is well-being that should be the main focus of policy, I believe that in most situations increasing the per capita GDP will lead to more well-being. For example, looking at the current economic situation it is very important for the well-being of our country that the economy starts to grow again and that unemployment rates are reduced.

Another article in this edition deals, amongst other things, with the problem of the possibility of the default of a country. While there currently is much active debate about the possibility of the default of Greece, I think it is highly unlikely that countries such as Holland, Germany or the US will ever default. Taxes can always be raised if our government’s ability to pay back its loans comes into question. With this in mind, the European rules regarding budget deficits, which our country fought so hard for, are quite unnecessary for Holland and hinder its policy making.

This brings me back to the getting our economy out of the recession. The mainstream view is that this should be achieved with monetary policy. Lowering the interest rates will stimulate economic activity, raising investments and thus raising aggregate demand to a good level. What has rarely been suggested the past two or three decades is fiscal policy as an active tool to stimulate the economy when it is in the downturn of a business cycle.

According to Keynes the government should step in when investment of the private sector is too low, by raising government expenditure and lowering taxes to stimulate aggregate demand. Several arguments against this theory have been made. It is said, for instance, that a higher deficit will not lead to higher aggregate demand but to lower investment and/ or an increase in the current account deficit. It is further argued that consumers know that a lowering in taxes will eventually have to be compensated by a raise in taxes and that companies and civilians will start saving for that raise (which may not be implemented for hundreds of years) instead of consuming more.

These “crowding out” arguments are, however, heavily debated and I believe that in the short run (which is what we care about when aiming to get out of a recession) fiscal policy will work to stimulate aggregate demand. Fiscal policy should, therefore, seriously be considered as a tool to get the economy out of a downturn and much less emphasis should be laid on the balancing of the budget of a government, whose financial position is sound enough. As long as a budget surplus is run when the economy comes into a boom there is no reason for concern about Hollands public debt. Requiring the deficit to be less than 3 percent of GDP completely takes away the power of fiscal policy to act as a countercyclical tool and makes it much harder for our government to get the economy back on track.

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00 74 Optimizing the Healthcare system for Alcohol use Disorders

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by: Joran Lokkerbol Alcohol use disorders are a leading cause of disease burden and are associated with substantial economic costs. Therefore, curbing alcohol use has long been recognized as an important public health objective. Healthcare systems play a crucial role in achieving this objective, and most healthcare systems offer room for improvement in terms of greater efficiency. This poses the question of what type of healthcare system, in terms of the mix of interventions, is optimal. Finding a mix of interventions that is acceptable to its recipients, scalable to absorb increasing demands, effective in generating health gains and economically affordable to be sustainable, can be a daunting task. This article describes the use of a health economic model to aid in the search for the optimal healthcare system.

Sovereign Credit Risk

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The Forgotten Risk

by: Servaas Houben Although the world history contains many examples of countries which haven’t (fully) honoured their obligations, this risk seems to be underestimated in the QIS5 and the level 2 text (especially for European countries). A better understanding what causes a sovereign default and how to determine the capital requirement, will lead to a better internal model and to better risk management. However, due to limited data, there is currently no uniform approach.

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vol. 20 00 feb m. ‘12 y.

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

Copula-GARCH Models to Estimate Capital Requirements for Pension Funds

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by: Steven Verschuren Recently there is a growing attention for the capital requirements in the financial world.

Specifically, for the capital requirements for pension funds. Many Dutch pension funds have a coverage ratio below the minimum standards set by the regulator, making the future pension payments uncertain. The discussion about the financial buffers that pension funds have to hold is therefore a very relevant topic.

It’s Not the Economy, Stupid! It’s All About Well-Being

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by: Ruth van de Belt Traditionally, Gross Domestic Product (GDP) has been used for designing and assessing policies aimed at advancing the progress of societies. The use of GDP as a measure of well-being is based on the conviction that people are better off when more GDP growth is realised. If GDP per capita increases people will, on average, have a higher income and are assumed to be more able to satisfy their needs and derive a higher level of satisfaction.

Therefore, it is unsurprising that most governments strive to push their country’s GDP to ever higher levels. Although, GDP per capita is often used as a proxy for well-being, it was never intended to measure such a thing. Kuznets (1934), the original architect of GDP, already mentioned that: “the welfare of a nation can scarcely be inferred from a measurement of national income as defined by the GDP”.

Puzzle

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Facultive

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Optimizing the Healthcare System for Alcohol Use Disorders by: Joran Lokkerbol

Alcohol use disorders are a leading cause of disease burden and are associated with substantial economic costs.

Therefore, curbing alcohol use has long been recognized as an important public health objective. Healthcare systems play a crucial role in achieving this objective, and most healthcare systems offer room for improvement in terms of greater efficiency. This poses the question of what type of healthcare system, in terms of the mix of interventions, is optimal. Finding a mix of interventions that is acceptable to its recipients, scalable to absorb increasing demands, effective in generating health gains and economically affordable to be sustainable, can be a daunting task. This article describes the use of a health economic model to aid in the search for the optimal healthcare system.

Method Modeling current healthcare and comparing this with possibly more optimal alternatives, immediately poses a number of questions: what is healthcare? How do we define it in our model? In what unit do we measure the effectiveness of a healthcare system? What timeframe do we use? This section describes the assumptions on which our economic modeling is based.

Healthcare system The healthcare system is defined as the mix of interventions that are offered to people who suffer from alcohol use disorder, ranging from anything like brief face-to-face intervention to complete detoxification (see table 1).

Every intervention is defined in terms of its effects and costs and the extent to which patients adhere. Effects and costs are mapped from the healthcare perspective, which means that outcome in terms of effects are purely health related, and costs only hold direct medical costs,

Joran Lokkerbol Joran Lokkerbol got his Masters degree in Mathematical Economics in 2008 at the University of Amsterdam. After working as an economic consultant for two years he found his way back into the academic world. Currently he is working on his PhD at the VU University of Amsterdam (VU) and holds a position as researcher at Trimbos Institute, where he specializes in health economics.

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as opposed to effects in terms of productivity or costs due to time lost by the patient.

Effects The effect of an intervention depends on multiple aspects.

First of all, the number of patients to which it is offered, also called the coverage rate. Second of all, to the extent to which patients adhere to the offered intervention.

When a patient does not adhere to a therapy, for example by flushing his pharmaceutics through the toilet, costs are made without any effect on health. This shows the importance of offering interventions that are acceptable to patients.

Next to coverage and adherence, the last aspect determining the effect of an intervention is the actual effect it has on the health of an individual patient. The model aims to project the health-related effect of interventions on individuals onto a corresponding disability weight in the total population. The individual disability weight is defined as DW = 1 – U, where U stands for utility, which is 1 for a perfectly healthy individual, and 0 for someone who, somewhat crude, has a quality of life equal to death.

To serve as a reference point; problem drinking, for example some physical, psychological or social problems caused by excessive alcohol intake is considered to give an average utility of 0.89, whereas manifest alcoholism, being severe social problems caused by excessive alcohol intake, is considered to give an average utility of 0.45. The effect of an intervention on an individual is expressed in a so called effect size d, which stands for the increase in health for that individual person. Multiplying this individual effect with the number of people receiving this intervention and the extent to which they adhere to the intervention, as well as taking into account the time they

Econometrics

would be suffering from alcohol use disorder, this gives the decrease in disability weight in the total population.

Or the increase in the quality of life of the population.

Adding to this the number of deaths prevented because of less alcohol intake, we get the total increase of life years due to the healthcare system. This total amount is called DALY averted, Disability Adjusted Life Years averted, and is one of the main outcome measures of our model, representing both the quality of life as well as the extension of years lived. In our model however, the emphasis is mainly on quality while living, since our short term time horizon (12-months) causes mortality to play only a minor role. In a longer term model, mortality would eventually dominate.

The last step in translating the effect of a healthcare system into an economic viable outcome measure, is to value health in terms of Euros. This is done using the ‘Willingness-to-Pay’ for one year of perfect health. This is a measure that represents the value that we, as a society, are willing to pay for one individual who lives one year in perfect health, represented by a score of 1 on the Quality of Life scale. Needless to say, this Willingnessto-Pay generates a healthy amount of discussion among stakeholders. In health economic modeling, a Willingness to Pay ranging from 20,000 to 80,000 is common. This amount is in line with the economic value added by a healthy person to a nation’s economy, though the link with individual productivity is not generally accepted. In our modeling, we work with the average willingness to pay of 50,000 for averting one DALY, that is, for gaining one year of good health.

Cost effectiveness Placing a Euro value on health gain allows us to evaluate the cost of offering interventions and benefit of health gains in straightforward return on investment. This enables us to compare the return on investment of the current healthcare system with alternative healthcare systems.

Our model provides for this by simulating cost effectiveness of the current set of interventions with an alternative set of interventions, which could consist of the current set augmented with additional interventions, or which could be the result of a substitution of different forms of interventions. After each scenario is defined in terms, of coverage, adherence, effect and costs, our model simulates 1000 runs of each scenario, where both costs as well as effects are drawn from a distribution, to represent the uncertainty around such parameters. After simulating the 1000 runs for both scenarios, median costs and effects are used to compare both scenarios in terms of cost effectiveness.

Results The underlying research (Smit, Lokkerbol et al, 2011) aimed to evaluate the cost effectiveness of offering

Table 1. Interventions offered to different target groups with alcohol use disorder.

Target group alcohol use disorder

Intervention

Heavy drinking Brief face-to-face intervention

Online brief intervention Hazardous drinking

Brief face-to-face intervention Online brief intervention Behavioral intervention Online self-help intervention

Harmful drinking

Behavioral intervention Online self-help intervention Online therapist-led intervention Detox and acamprosate Aftercare and rehab with AA

Alcohol dependence

Behavioral intervention Online therapist-led intervention Detox and acamprosate Aftercare and rehab with AA

online intervention by comparing the base scenario of current healthcare with the alternative scenario of current healthcare augmented with online interventions. The interventions that were used in the scenarios are presented in table 1.

The base scenario consisted of all interventions that were ‘offline’, where the alternative scenario augmented these interventions with online forms of interventions.

Return on investment in the base scenario was 1.04, indicating that costs are somewhat lower than the effects, and every Euro spent gives an expected return of an additional 4 cents. In the alternative scenario however, the return on investment increases to 1.62, indicating that a healthcare system for alcohol use disorders including online interventions is much more cost effective than a healthcare system without online interventions. Current healthcare could thus be made much more cost effective by augmenting it with online interventions.

Discussion Online interventions are a very likely candidate for improving current healthcare. For one thing due to their desired scalability in times of recession in combination with the strongly increasing costs in healthcare. Online interventions have the additional advantage in dealing with alcohol use disorders of being anonymous and easily accessible, where people might find it too confronting to go to their General Practitioner with alcohol problems.

On top of the fact that online interventions are an obvious extension of healthcare with respect to alcohol

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use disorders, the above analysis shows that it also makes a lot of sense from a health economic point of view.

Augmenting current healthcare with online interventions increases the return on investment by more than 50%, from 1.04 to 1.62 per Euro spent.

Multidisciplinary research is always subjected to numerous assumptions on the way in which different fields of science interact. In our model, this is best seen in the use of the controversial value of the willingness to pay for a healthy life year. Where combining different fields of science often leads to valuable new insights, this is sometimes obscured by the fact that they usually go hand in hand with numerous assumptions. We therefore stress the fact that this type of healthcare modeling is by no means an autopilot for creating the optimal healthcare system. Instead, we wish for the model to be used by various stakeholders in working out various scenarios for improving healthcare, thereby stimulating an objective discussion between everyone involved in healthcare.

Finally, it is important to emphasize the fact that the economic perspective is only one aspect that policymakers take into account. We highly recommend online interventions to be considered for inclusion in the healthcare system for patients with alcohol use disorders, and recommend policymakers to investigate this type of intervention from different viewpoints, to see whether it is a desirable addition for society as a whole.

References Smit F, Lokkerbol J, Riper H, Majo C, Boon B, Blankers M (2011). “Modeling the Cost-Effectiveness of Health Care Systems for Alcohol Use Disorders: How Implementation of eHealth. Interventions Improves Cost-Effectiveness.� Journal of Medical Internet Research; 13(3):e56

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De generatiekloof binnen het pensioenstelsel Actuariaatcongres 2012 Presentaties van:

Prof.dr.ir. M.H. Vellekoop Mr. A.J.Kellermann Martin Pikaart Dagvoorzittter:

Ir. Drs. J. Breen AAG

Verder zullen er verschillende keuzemogelijkheden zijn voor het middagonderdeel van het programma. In twee rondes van elk drie mogelijke keuzes worden er door verschillende actuarissen presentaties gegeven. De presentaties geven een volledig beeld van de meest recente ontwikkelingen rondom het Nederlandse pensioenstelsel. Er is ruimte voor discussie over solidariteit en de houdbaarheid van het stelsel. Op het programma staan onder meer:

Fiscale aspecten van het pensioenakkoord Solidariteit tussen jong en oud Paneldiscussie

9 mei 2012 Felix Meritis Amsterdam

Ga voor meer informatie naar www.actuariaatcongres.nl

Actuarial Sciences

Sovereign Credit Risk The Forgotten Risk by: Servaas Houben

Although the world history contains many examples of countries which haven’t (fully) honoured their obligations, this risk seems to be underestimated in the QIS5 and the level 2 text (especially for European countries). A better understanding what causes a sovereign default and how to determine the capital requirement, will lead to a better internal model and to better risk management. However, due to limited data, there is currently no uniform approach.

Historical defaults

Spread components

Reinhart and Rogoff provide a detailed overview of sovereign defaults (including 1 Dutch default in 1814!) starting from the Napoleonic wars. The authors show that defaults occur in “waves” where long periods without defaults, are followed by periods with a sharp increase in defaults. Hence, looking at historical data, one cannot speak of a “new era” in which a lower number of defaults are applicable. They also point out that defaults are not limited to Latin American and African countries, but have happened in Europe and Asia as well, as shown in Table 1.

They also observe that defaults happen both through impairment of assets, or by the excessive increase of money supply (seignorage). Furthermore, opinions differ if delaying payments automatically triggers a default or if the intention behind a default should be taken into account as well (the Venezuelan default of 1998 did not happen because the government refused to honour payments voluntary, but because the official who was responsible for signing the checks was not present causing delays and hence an automatic default).

The yield (return) on corporate bonds is higher than the return on government bonds as the latter are less risky: in the worst case, the government can decrease its spending and raise taxes to meet its obligations or employ seignorage. Companies are less flexible because a substantial increase in their product prices and reduction of expenditure is usually not an option. The difference in yield between government and corporate bonds is referred to as the spread.

However, before looking into the spread components, one has to agree on a risk-free asset. The AG position paper concludes that a government curve or a swap curve with a credit adjustment is the closest approximation to a risk-free return: the government curve is a natural fit (as a government can fund its way out of a default), the swaprate is more liquid than the government market which is an attractive characteristic for a risk-free rate.

Of course we can not assume that every government bond is risk-free: a government bond with a low credit rating does have default risk!

The difference between the risk-free rate and the yield on corporate bonds is explained on the basis of the following factors (as outlined in Churm & Panigirtzoglou):

Servaas Houben Servaas Houben studied econometrics at the University of Maastricht and economics at the University of Glasgow. Thereafter he studied actuarial sciences, CFA, and FRM. He has worked in the Netherlands for the first 4 years of his career and then 2 years in Ireland. He currently works in London.

For any questions or information please contact me: servaashouben@gmail.com Visit my blog: http://actuaryabroad.wordpress.com/

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1. Credit risk factors: 1.1 Expected default: this is the extra return investors require on corporate bonds as compensations for the increased risk of default.

1.2 Downgrade risk: the compensation investors require for the risk that a corporate bond is downgraded (e.g. from A to BBB) leading to a decrease in value.

1.3 Increase in credit spread: the risk that although a corporate bond retains the same rating, the difference in yield between corporate bonds and risk-free bonds increases, therefore leading to a decrease in value of the corporate bonds.

Actuarial Sciences

Table 1. Default and re-scheduling. Source: Reinhart and Rogoff.

Default and re-scheduling

1800-24 Africa Asia Europe Latin America

NA NA 13 NA

1825-49

1850-74

1875-99

1900-24

1925-49

1950-74

1975-2006

NA NA 9 15

1 NA 7 10

1 NA 5 22

1 1 2 13

0 2 12 18

1 4 0 11

21 7 7 36

2. Non-credit risk factors: 2.1 (Il)liquidity: the market for government bonds is deeper and more liquid than the corporate bond market. Therefore, investors usually incur higher costs when trading corporate bonds. For these additional costs investors require an additional return also known as (il)liquidity premium.

2.2 Tax: government bonds (e.g. municipal bonds) have a preferential tax treatment. Investors require a compensation when investing in corporate bonds instead.

2.3 Regulations: government bonds are more widely accepted than corporate bonds or there might be a preferential treatment towards government bonds.

E.g. Solvency II exempts some government bonds from capital charges making them more attractive for insurance companies. Also, in some countries pension funds are required to hold a certain percentage of their assets in (local) government bonds.

An overview of spread-decomposition is given in Figure 1.

Figure 1.

England.

Spread-decomposition.

Source:

Bank

of

In the insurance industry, non-credit risk factors belong to the yield pickup of the insurer: for some products with a predictable cash flow pattern (e.g. annuity) the insurer is able to hold the corporate bond until maturity while matching its liability cashflows. Therefore, the insurer has no need for interim trading and can benefit from the non-credit factors.

This article elaborates on the spread elements of an increase in spread and default.

Spread risk Because the swap market is more liquid than the government bond market, most insurers use a swaprate, with a credit adjustment to discount liability cash flows. Nevertheless, if these obligations are backed by government bonds this creates the risk that the interest rate on government bonds in some scenarios is higher than the swap rate. Figure 2 below shows how a 1 x scenario is determined for Philippine swaps and bonds.

However, this method has its limitations: • A liquidity and credit adjustment is required to compare swaps with government bonds; • The swap market is still not fully developed everywhere (e.g. Asia), and therefore a lack of appropriate data can occur; • Lack of data requires a subjective duration choice or the need to apply inter/extrapolation; • This method calculates the risk in the reduction of spreads and not the probability of a default.

Default model When a government defaults, this does not automatically result in complications for an insurer: the value of the liabilities decreases proportionally with the bond values.

However, when an insurer’s assets and liabilities are denominated in foreign government bonds, there is less certainty that the foreign government/regulator uses the same principle. Besides the standard currency risk, there is now a risk of a government default as well. Due to reputational risk, it is not always possible for the insurer to (partially) write down its obligations.

The default risk for corporate bonds is usually estimated by the Probability of Default (PD) and the Recovery Rate (RR) once default has occurred. Structural form models

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Figure 2. Spread 7 year PHP swap over 7 year PHP government bond. Source: Bloomberg.

assume a threshold (also called default boundary) after which default occures. The loss is calculated as follows:

A simple historical average hence does not sufficiently identify the potential future risks;

Loss amount = PD x Loss given default = PD x (1 - RR)

• Lack of transparency on one-year default probability calculation: specific descriptions of the methods which rating agencies apply are not available. Comparing the 1-year default probabilities of different rating agencies is thus difficult; • Differences local and foreign defaults: the local credit rating is usually higher than the foreign credit rating because governments can print money to avoid a local default, and because the political and economical costs of a local default are higher. Although the difference between the number of foreign and local defaults declined over the years, the choice between the two ratings remains subjective; • No historical 1-year investment-grade defaults: the use of a longer history (5 or 10 years) default probability (PDi) therefore leads to better risk assessment. The following formula determines the 1-year default probability (δi): ln(1 − PDi ) 1 − PDi = e− tδi ⇒ δ i = − t • The lowest rating category, CCC-C, is a “mixed bag” that contains both countries with a high default chance in the near future (e.g. by end of 2011 Greece) and countries that have already defaulted and have returned to the capital market.

For the PD a standard normal distribution is appropriate and a beta distribution for the RR is common. A Monte Carlo simulation creates random numbers for PD and RR from which you can determine VaR outcome. Rating agencies provide annual reports with PD and RR for each asset type and rating.

Rating data unfortunately have several limitations: • Lack of historical defaults: Moody’s mentions only 15 defaults between 1983-2010, hence derived PD and RR values might not be robust; • Changing data set: in 1990 the majority of Moody’s government bonds consisted of investment grade bonds (BBB and higher). As more emerging markets have entered the bond market, the proportion of speculative bonds (BB and below) has increased, as shown in Figure 3. The increase in the number of defaults over time (the first default in the Moody’s data set was only in 1998), shows that counterparties are less risk-free than before.

Figure 3. Changing Moody’s government bond dataset.

Rating agencies claim that their procedure for assigning ratings is on the same basis for companies and countries. As there is more data available for corporate bonds than sovereigns, the PD and RR corporate data are used instead of the government bond data. Also there are one-year historical defaults for investmentgrade corporate bonds which are not available for government bonds. The only adjustment that remains is for the CCC-C rating: countries can default, re-structure and return to the capital market while companies often don’t have that option. A reduction of the CCC-C rating

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PD for sovereigns compared to corporates is therefore appropriate.

Moody’s. Sovereign Default and Recovery Rates, 19832010. Moody’s, New York, 2011.

Solvency II

Reinhart, C.M. and K.S. Rogoff. This time is different: A Panoramic View of Eight Centuries of Financial Crises. NBER working paper, 2008.

The standard formula in Solvency II has no spread capital requirements for AAA and AA-rated government bonds issued in domestic currency. Especially European government bonds are given a preferential treatment under the standard formula as a capital exemption is given independent of the rating: e.g. both German (AAA-rated) and Greece (CCC) sovereign bonds are capital exempted although the underlying risks differ significantly. However, an internal Solvency II model can make an exception for this and include a sovereign credit capital charge.

Solvency II seems to have an odd relationship with sovereign default risk: QIS5 excludes government bonds in the counterparty default module and instead assigns them to the spread module, which indirectly implies that there is no default can take place on government bonds.

Under the current economic climate this seems to be far too optimistic!

Remolona, E.M., M. Scatigna and E. Wu (2008). “A ratings-based approach to measuring sovereign credit risk.” International Journal of Finance and Economics, volume 13.

Standard & Poor’s. Sovereign Defaults And Rating Transition Data, 2010 Update. Standard & Poor’s, New York, 2011.

Webber, Lewis (2007). “Decomposing corporate bond spreads.” Bank of England Quarterly Bulletin, Winter, pages 533-541.

Conclusion Ratings have a prominent role in the Solvency II framework (counterparty, credit spread, and concentration risk). In the default model ratings play a crucial role as well. However, the rash use of ratings is similar to the blind crossing of a busy street when the light is on green: it seems safe until one day it goes wrong, as investors in AAA-rated American mortgage backed securities found out in 2008. The actuarial profession should adopt a more market-based instrument to estimate counterparty risk: market ratings, such as spreads, or CDS, are available for this, although this leads to more volatility.

In the meantime, the use of an average rating of different agencies would be the most practical solution.

References Actuarieel Genootschap & Actuarieel Instituut. Rapport: Principes voor de Rentetermijnstructuur. “Dé juiste curve bestaat niet”. Actuarieel Genootschap & Actuarieel Instituut, Utrecht, 2009.

Churm, Rohan and Nikolaas Panigirtzoglou.

Decomposing credit spreads. Bank of England, London, Working paper no. 253, 2005.

Moody’s. Corporate Default and Recovery Rates, 19832010. Moody’s, New York, 2011.

Moody’s. Narrowing the gap – a clarification of Moody’s approach to local versus foreign currency government bond ratings. Moody’s, London, 2010.

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

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Econometrics

Copula-GARCH Models to Estimate Capital Requirements for Pension Funds by: Steven Verschuren

Recently there is a growing attention for the capital requirements in the financial world. Specifically, for the capital requirements for pension funds. Many Dutch pension funds have a coverage ratio below the minimum standards set by the regulator, making the future pension payments uncertain. The discussion about the financial buffers that pension funds have to hold is therefore a very relevant topic.

Current model The regulator, the Dutch Central Bank (De Nederlandsche Bank, DNB), publishes the financial requirements for pension funds in the Financial Assessment Framework (Financieel Toetsingskader, FTK) (see DNB, 2006).

These rules are currently under evaluation. The benchmark model that is used nowadays tries to ensure that pension funds have enough capital to cover losses in the upcoming year with a (theoretical) probability of 97.5%. This is equivalent to the one year 2.5% Value-atRisk. In the context of Dutch pension funds, the 2.5% VaR is generally given as a percentage of the pension liabilities and is called the required capital (Vereist Eigen Vermogen, VEV).

To calculate this VEV, DNB published a standard model (DNB, 2006). This standard model works with shocks to calculate the required capital per risk class.

These shocks are based on a confidence level of 97.5%.

The formula to aggregate these risk classes and to obtain the VEV is: St = S12 + S 22 + S32 + S 42 + S52 + S62 + 2 Ď S1 S 2

(1.1)

Steven Verschuren Steven Verschuren is currently finishing a double master degree in Actuarial Sciences and Mathematical Finance, and Financial Econometrics at the University of Amsterdam. He wrote his Econometrics thesis about the impact of the distributional assumptions on the capital requirements for pension funds. Dr. Simon Broda from the University of Amsterdam supervised his master thesis, as well as ir. drs. Martijn Euverman AAG CFA and ir. Bertjan Kobus from Sprenkels & Verschuren, a Dutch actuarial consultancy company, where Steven works part time as a working student.

where Si is the quantile for the risk classe i. S1 involves the interest rate risk, S2 the equity risk, S3 the currency risk, S4 the commodity risk, S5 the credit risk and S6 the technical insurance risk. Ď is the correlation between S1 and S2, the correlations between the other risk classes are assumed to be zero. In this article, the technical insurance risk (S6) is left out of the analysis and therefore assumed to be zero. The shocks to calculate the individual Si are published by DNB. The DNB standard model is based on a couple of assumptions. The first assumption has to do with the assumed distribution of the risks, namely a multivariate normal distribution. There exists however a large literature about the non-normality of financial returns (Fama, 1965, Behr & Potter, 2009, Rosenberg & Schuermann, 2006).

The probability mass in the tails of the distribution is important to estimate tail risks (kurtosis). Allowing for skewness in the distribution is also an important property as we will discuss later on. Furthermore, the phenomenon that assets move in the same direction on an extreme trading day can also not be modeled by the multivariate normal distribution (Longin & Solnik, 2001). These pitfalls of the multivariate normal distribution suggest to investigate other multivariate distributions.

The second assumption involves the parameters of the multivariate distribution function. The data that is used to estimate these parameters can be argued. At least it is arguable that these parameters are fixed and the same for all pension funds. A pension fund specific approach may be more appropriate. Also the data sample used by DNB (for example, 1970-2002 for equity) might be not representative for today’s risks.

To investigate the impact of these assumptions on the estimated capital requirements, this article suggests to use copula models and a different data sample.

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Copula

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Figure 1. Gaussian copula.

Bivariate density function Gaussian copula

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According to Sklar (1959), any multivariate distribution can be decomposed into a dependence structure, modeled by the copula function, and marginal distributions: ∀x ∈

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Figure 2. Student’s t copula.

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Bivariate density function Student’s t copula

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Bivariate density function Clayton copula

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where C (⋅) is the copula distribution function and Fi(xi)‘s are the marginal distribution functions. This approach makes it possible to estimate lots of different and possibly unknown multivariate distributions (Lee & Long, 2009).

The copula functions that are investigated in this thesis are the Gaussian copula, the Student’s t copula and the Clayton copula. These three copulae all have different properties with respect to their tail dependence, which is easiest explained by some plots of the distribution functions of the copulae, as shown in figures 1, 2 and 3.

From these plots, we can see that the behavior in the tails of the distributions is different. The behavior in the tails of the distribution is captured by the so called tail dependence property of the distribution. Upper (lower) tail dependence measures the probability that one variable is observed in the upper (lower) tail of the distribution conditional on the fact that the other variable is also observed in the upper (lower) tail of the distribution. This property can be used to model joint movements of assets on extreme trading days. We see that the Gaussian copula does not have this property (tail dependence of zero). The Student’s t copula (symmetric) and the Clayton copula (asymmetric, lower tail) have this property.

The choice of a particular copula function is not the only ‘variable’ that determines the dependence structure.

The structure of the copula function can also be changed (Aas et al., 2000, Czado & Min, 2007, Berg & Aas, 2007). We only consider two possible structures, here mentioned as the standard copula construction and the pair copula construction (PCC). The differences between these two are again most easily shown in a figure (see Fischer et al., 2009).

Figures 4 and 5 contain respectively the structure of the standard copula construction and the PCC. C123 (⋅) is the three dimensional copula distribution function and Fi(xi)‘s are the marginal distribution functions. C12 (⋅) and C23 (⋅) are bivariate copula distributions and C13|2 (⋅) is the conditional distribution function of x1 and x3, given x2.

Figure 4 contains an ordinary multivariate copula distribution functions, which forms the dependence structure of the marginal distributions. Figure 5 contains a series of bivariate copula functions. The advantage of the latter is that it is even more flexible. In every node of the tree, another copula function can be chosen and estimated. Both the standard copula construction and the PCC are investigated in this thesis.

To complete the multivariate distribution functions, we still need to choose our marginal distribution functions. To get a wide range of parameters to estimate, the Normal,

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Figure 4. Standard copula construction.

Table 1. Balance sheet.

Assets

Liabilities

Equity 20 Pension Liabilities 90 Real estate 5 Equity capital 10 Credits 40 Commodities 5 Government bonds 25 Currency 5 Figure 5. Pair copula construction (PCC).

Total

100

100

1 is given in table 2.

From these data sources, the monthly returns are calculated. These are then used in the actual estimation.

The sample period is chosen to be from the introduction of the Euro, 31-1-2001 until 30-6-2011, which yields 115 data points.

Estimation techniques Student’s t and skewed Student’s t distribution are chosen (Chan et al., 1993). The most general distribution, the skewed Student’s t (Hansen, 1994), has four parameters to be estimated and nests the other two distributions. In total, we now have 18 multivariate distributions to use in the estimation of the VEV. One combination, the Gaussian copula with the normal marginal, yields the multivariate normal distribution which is used in the DNB standard model.

Virtual pension fund and data To see what implications the different models have on the estimated capital requirement of a pension fund, we need to make assumptions about the pension fund’s balance sheet. The financial position of our virtual pension fund is shown in table 1.

Our virtual pension fund has a coverage ratio of 111.11%. The position of Currency is formed by investments in foreign currency. The equity capital is the surplus of the balance sheet.

The data that is used to model the positions from table

After investigating the time series of the different assets, periods of high and low volatility were discovered, a phenomenon which is also known as volatility clustering.

A multivariate GARCH model would therefore be very useful to account for this. To keep a small and simple model, according to Hansen & Lunde (2005), a GARCH(1,1) model is a good choice (also see Lee & Long, 2009).

Because we assume that we know the joint distribution function of our balance sheet, the obvious estimation method is maximum likelihood. The joint distribution function however has many parameters to be estimated, what can result in long estimation times and possibly infeasible solutions. Therefore, a special case of maximum likelihood estimation is often used in the context of copula functions. Namely the Inference Function for Margins (IFM) method (Durrleman et al., 2000). The IFM method consists of a two-step procedure.

First, the marginal distributions are separately estimated.

Then, the copula function is estimated conditional on the marginal estimates. This method comes at a cost, because it only yields asymptotically consistent and efficient

Table 2. Data sources.

Asset Classes

Specific asset

Ticker

Equity Real estate Commodities Currency

MSCI World MSCI Real Estate Europe Dow Jones UBS commodity index EUR/US Dollar

mxwo index mxeuOre index DJUBS index eurusd curncy

Pension liabilities Credits Government bonds

DNB zero coupon term structure DNB zero coupon term structure + credit spread DNB zero coupon term structure

IBoxx Euro Corporates A 5-7 -

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estimates. However, we get around the problems of ordinary maximum likelihood.

To estimate the VEV of the pension fund’s position, we need to calculate the quantiles of the future distribution of that position. An analytical expression of the joint distribution function is however often not possible, so therefore we use the technique of simulation in this thesis.

A random sample of 100.000 observations is computed to estimate the required quantiles.

Results Now we know the theoretical background, we proceed to the results. First, we present the estimated quantiles (shocks) based on the multivariate normal distribution.

These estimates can then be compared to the parameters that DNB publishes in the FTK. Secondly, the fit of the 18 different multivariate distributions is considered. Finally, we look at the estimated required capital (VEV) of the different distributions and draw our conclusions.

But first we present the results of the estimated quantiles of the multivariate normal distribution. These results are shown in table 3. All the estimated quantile values are equal to or higher than the quantiles given by DNB. This is probably caused by the relatively volatile sample that is used. DNB uses a larger and less recent sample which causes the estimated quantiles to be somewhat lower than our estimates, which are based on the last ten (volatile) years. The large difference for real estate is caused by the fact that DNB used a non-listed index and here a listed index is used.

The fit of the estimated models is presented in table 4.

This gives some interesting insights. First, the standard

Econometrics

Table 3. Estimated quantiles (shocks).

Asset classes

Quantile value

DNB

Equity Real estate Credits Commodities Government bonds Currency Pension liabilities

-30.19% -41.15% -8.67% -31.15% -19.17% -20.00% -20.44%

-25% -15% -3% -30% -17% -20% -16%

copula constructions perform better than their PCC equivalents. The PCC models are more general, what results in a higher loglikelihood. But when we look at the information criteria, which are the Akaike- and Bayesian Information Criteria (resp. AIC and BIC), the standard copula models are chosen in front of the PCC models.

So the additional parameters of the PCC models come at a cost and don’t add a significant gain to the fit of the models. The AIC chooses the standard Student’s t copula with the skewed Student’s t marginals as the best model.

The BIC chooses the same copula, but then with ordinary Student’s t marginals. The loglikelihood of the first is however higher, which makes that one our preferred model.

The preferred models are also tested with a likelihood ratio test against the benchmark model, the Gaussian copula with normal marginals. For both information criteria, the null hypothesis of the Gaussian copula with normal marginals is strongly rejected in favor of the models chosen by the AIC and BIC. The implications of the models are now discussed. To

Table 4. Goodness-of-Fit.

Margins

Copula

Loglik. total

AIC

BIC

Normal

Gaussian Student’s t Clayton Gaussian Student’s t Clayton Gaussian Student’s t Clayton

-1954.45 -1951.61 -2012.16 -1937.17 -1933.29 -1998.23 -1923.47 -1920.69 -1988.68

3972.9 3969.22 4060.32 3952.34 3946.58 4046.46 3938.94 3935.38 4041.36

4060.74 4059.8 4109.73 4059.39 4056.38 4115.08 4065.21 4064.39 4129.2

Normal

PCC- Gaussian PCC-Student’s t PCC-Clayton PCC- Gaussian PCC-Student’s t PCC-Clayton PCC- Gaussian PCC-Student’s t PCC-Clayton

-1954.45 -1942.97 -1980.85 -1937.17 -1924.51 -1964.66 -1923.47 -1916.7 -1949.57

3972.9 3981.94 4025.7 3952.34 3959.02 4007.32 3938.94 3957.4 3991.14

4060.74 4113.7 4113.54 4059.39 4109.99 4114.37 4065.21 4127.59 4117.41

Student’s t

Skewed Student’s t

Student’s t

Skewed Student’s t

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Table 5. VaR and VEV.

Margins

Copula

VaR portfolio (%)

VEV (%)

Normal

Gaussian Student’s t Clayton Gaussian Student’s t Clayton Gaussian Student’s t Clayton

7.28 7.16 7.95 7.16 6.98 8 9.39 9.16 10.48

15.37 15.11 16.78 15.1 14.74 16.89 19.8 19.32 22.11

Normal

PCC- Gaussian PCC-Student’s t PCC-Clayton PCC- Gaussian PCC-Student’s t PCC-Clayton PCC- Gaussian PCC-Student’s t PCC-Clayton

7.23 6.8 7.94 7.19 6.68 7.99 9.43 9.12 10.65

15.26 14.34 16.74 15.17 14.09 16.86 19.89 19.23 22.47

Student’s t

Skewed Student’s t

Student’s t

Skewed Student’s t

keep the benchmark model in mind, the estimated VEV from the DNB standard model, for this virtual pension fund, is 10.31%.

We now compare this with the estimates of our 18 models, which are presented in table 5. The first thing to notice is that the estimated quantiles from the Gaussian copulae are a bit higher that those of the Student’s t copulae, conditional on the marginal distributions. We would however expect that the estimates of the Student’s t copulae are higher, due to the thick-tailedness of the Student’s t copula. The reason for this is the relatively high quantile level (2.5%). At a lower quantile level, the differences become visible. The Clayton copula, which gives greatest importance to the lower tail of the distribution, gives the highest estimates. Furthermore, we see that the choice of the marginal distribution is quite important. The Normal and Student’s t marginals give similar results, but the skewed Student’s t marginal distribution gives higher estimated VEV’s.

Furthermore, we can see that the estimated VEV’s of these models are much higher than the DNB standard model. For the distribution that is used by the DNB model, the Gaussian copula with normal marginals, the difference is around 50%. This is completely caused by the use of different parameters, formed by the correlations and the parameters of the marginal distributions. For the other models, the difference is at a minimum around 50%, which indicates that the pension funds have to hold, at a minimum, around 50% more buffer than the DNB standard model according to these models.

The difference with our preferred model is however even more striking. The estimated VEV is around 87% higher than when the DNB standard model is used.

Conclusions In general, we can conclude the following. The data that we used leads to higher quantiles (shocks) than those from DNB. This seems clear, because we used a more volatile sample, which leads to higher estimates.

When we consider the fit of the estimated models, we strongly reject the distribution of the DNB standard model, the Gaussian copula with normal marginals. This thesis suggests to use the standard Student’s t copula with skewed Student’s t marginals.

However, on a 2.5% quantile level, we can conclude that the differences between the resulting capital requirements for our estimated models (not including the DNB model) are not that striking. The Clayton copula always gives the highest estimate, but the Gaussian copula gives similar and slightly higher estimates than the Student’s t copula, conditional on the marginal distributions. For the marginal distributions, the skewed Student’s t distribution gives the highest estimated quantiles.

Compared to the DNB standard model, our estimated models give a VEV that is at a minimum around 50% higher than the DNB standard model (which gives a VEV of 10.31%). For our preferred model (standard Student’s t copula with skewed Student’s t marginals), the difference is even larger (87%), which is caused by the use of a different multivariate distribution.

As a concluding remark, I should say that these results are sensitive to the data used. For future research I would suggest to estimate these models with a larger sample and maybe at another data frequency. It would also be interesting to investigate the effects of different models on a lower quantile level (0.5% for example). But at least

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a discussion about the parameters of the current standard model would be appropriate according to the results of this thesis.

References Aas, K., Czado, C., Frigessi, A., & Bakken, H. 2000.

Pair-copula constructions of multiple dependence.

Insurance: Mathematics and Economics, 44(2), 182– 198.

Behr, A., & Potter, U. 2009. Alternatives to the normal model of stock returns: Gaussian mixture, generalised logF and generalised hyperbolic models. Annals of Finance, 5, 49–68.

Berg, D., & Aas, K. 2007. Models for construction of multivariate dependence. Insurance: Mathematics and Economics, 44(2), 182–198.

Chan, K., Pan, M., & Wu, H. 1993. An investigation of the empirical distribution of bond returns. Journal of Economics and Business, 45(2), 159–167.

Czado, C., & Min, A. 2007. Bayesian Inference for Paircopula Constructions of Multiple Depence.

DNB. 2006. Advies inzake onderbouwing parameters Financieel Toetsingskader.

Durrleman, V., Nikeghbali, A., & Roncalli, T. 2000. Which copula is the right one? Insurance: Mathematics and Economics, 44(2), 182–198.

Fama, E. 1965. The behavior of stock-market prices. The Journal of Business, 38(1), 34–105.

Fischer, M., Kck, C., Schlter, S., & Weigert, F. 2009. An Empirical Analysis of Multivariate Copula Models.

Quantitative Finance, 9(7), 839–854.

Hansen, B. 1994. Autoregressive Conditional Density Estimation. International Economic Review, 35(3), 705–730.

Hansen, P., & Lunde, A. 2005. A Forecast Comparison of Volatility Models: Does Anything Beat A Garch(1,1)?

Journal of Applied Econometrics, 20(7), 873–889.

Lee, T., & Long, X. 2009. Copula-based multivariate GARCH model with uncorrelated dependent errors.

Journal of Econometrics, 150(2), 207–218.

Longin, F., & Solnik, B. 2001. Extreme Correlation of International Equity Markets. The Journal of Finance, 56(2), 649–676.

Rosenberg, J., & Schuermann, T. 2006. A General

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Approach to Integrated Risk Management with Skewed, Fat-tailed Risks. Journal of Financial Economics, 79(3), 569–614.

Sklar, A. 1959. Fonctions de repartition a n dimensions e leurs marges. Publications de l’Institute de Statistique de l’Universite de Paris, 8.

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It’s Not the Economy, Stupid!

It’s All About Well-Being by: Ruth van de Belt

Traditionally, Gross Domestic Product (GDP) has been used for designing and assessing policies aimed at advancing the progress of societies. The use of GDP as a measure of well-being is based on the conviction that people are better off when more GDP growth is realised. If GDP per capita increases people will, on average, have a higher income and are assumed to be more able to satisfy their needs and derive a higher level of satisfaction. Therefore, it is unsurprising that most governments strive to push their country’s GDP to ever higher levels. Although, GDP per capita is often used as a proxy for well-being, it was never intended to measure such a thing. Kuznets (1934), the original architect of GDP, already mentioned that: “the welfare of a nation can scarcely be inferred from a measurement of national income as defined by the GDP”.

Introduction GDP is only a measure of economic performance and does not accurately measure whether our lives are on an improving trend in both material and immaterial terms.

This becomes immediately clear when one looks at the world today. While more and more countries move from a situation of scarcity to a situation of plenty, the improvements in GDP do not yield to the same improvements in life satisfaction, at least according to the reliable surveys. For this reason, the use of GDP as a measure of well-being is being increasingly scrutinised.

Many alternative measures have been developed in the recent past, all of which take different aspects of wellbeing into account.

Based on academic research, Stiglitz et al. (2009) concluded that the following eight dimensions matter most for the way in which people enjoy their lives: material living standards, health, education, personal activities including work, political voice and governance, social connections and relationships, present and future environmental conditions and insecurity of an economic as well physical nature. We build an ordered-probit

Ruth van de Belt Ruth van de Belt works as an economist for the Economic Research Department at Rabobank.

Her main area of expertise is the Dutch economy, especially macroeconomic developments in the business cycle and forecasting. She is also responsible for the Corporate Social Responsibility strategy of the Economic Research Department. Current research topics include the movement towards a biobased economy and the measurement of economic performance and social progress. Ruth studied at the University of Amsterdam and holds both a Master’s Degree in Econometrics and Economics.

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model to explain some of the cross-national differences in reported levels of satisfaction with life collected in the last three waves of the World Values Survey. Our results strongly echo the conclusions drawn by by Stiglitz et al.

(2009), since we find that the dimensions reported by the authors are more highly related to self-reported life satisfaction than GDP per capita.

GDP is a futile well-being measure A quite extensive theoretical and empirical literature exists in which the shortcomings of per capita GDP are described. In the empirical literature it is shown that in certain periods or regions a positive correlation exists between per capita GDP and life satisfaction, but this is not the case for all periods and in all regions. While GDP can be on an upward trend, human welfare cannot reach infinitely higher levels. Because of the well-known concept of diminishing marginal utility of income, one can expect somewhere a delinking to take place.1 If income rise higher and higher, people are less able to transform the extra purchasing power into higher living standards. Essentially Maslow’s hierarchy of needs plays a role here (Maslow, 1943). According to this hierarchy, an individual must first satisfy his physiological needs (health, food, sleep etc.) before he can move on to higher levels of needs, including safety, love, (self-)esteem and self-actualisation. In meeting the physiological needs income plays an important role, but in order to satisfy the ‘higher’ needs income matters less.

In the theoretical literature many shortcomings of GDP as a measure of well-being are put forward. We will describe a list of arguments below. First, GDP does not 1

Helliwell (2003) estimates that the delinking takes place around a per capita GDP of 15.000 USD.

Econometrics

take all production into account. Domestic and personal services by members of the household are excluded since they are hard to value and the impact on the economy is assumed to be negligible. However, domestic work, caring for children, the elderly and the ill at home, subsistence farming and voluntary work are very valuable for society and may have a significant impact on the way in which people value their lives. Second, a lot of non-economic factors that matter for well-being are not taken into account. These include, amongst others, leisure and the quality of the environment. Moreover, GDP is also not corrected for changes in stocks and resource supplies. This implies that changes in the underlying capital, such as non-renewable resources, may be overlooked for a long time. As a consequence, consumption may increase beyond a sustainable level and future economic growth is jeopardised at the expense of higher short-term growth. Also no distinction is made between costs and benefits. In the calculation of GDP, it is simply assumed that all monetary transactions boost the well-being of people, while this is clearly not the case. Cobb et al (1995) describe this as quite striking.

They mention that “by the curious standard of GDP, the nation’s economic hero is a terminal cancer patient that is going through a costly divorce and the happiest event is an earthquake or a hurricane”. Due to these events money is spent and the economy will grow, but it is clear that these events do not lead to a greater satisfaction with life. A further difficulty with using GDP per capita as a measure of well-being is that it strongly emphasises on average income, while the income distributions in some cases can be highly unequal. A rising tide does not lift all boats. This becomes painfully clear when one looks at the growth experiences of many developing countries during the 1950s and 1960s. Most of these countries reached their growth targets, but only the people in the highest income brackets profited while the life satisfaction of the masses of people remained almost unchanged. It can be concluded that GDP is a weak measure of human welfare, at best. Therefore, governments should not use GDP as a yardstick. Instead, they should “pursue the elaboration of additional measures that better capture the importance of happiness and well-being in development with a view to guiding their public policies” (UN, 2011).

Many factors affect well-being In order to analyse which well-being dimensions matter for human welfare, we build an ordered-probit model (Van de Belt, 2011). Below, the main results are discussed.

Living standards, measured by the logarithm of per capita GDP, matter for well-being. An individual who lives in a country with a higher per capita GDP, has a higher probability to report satisfaction with his/her life, ceteris paribus. A good health, measured by the subjective health 2

status, is also important, because it strengthens human development. Education enhances human capital and contributes to an individual’s well-being, as it generates (non)economic benefits. Labour market earnings often increase with the level of education and more educated people are often healthier than less educated people.

In addition, education leads to productivity growth, the easiness with which a society can absorb advanced technologies, a higher political and social engagement, a higher level of trust, tolerance of diversity, commitment to equality of opportunities and resistance to anti-social behaviour. People engage in all kinds of personal activities on a daily basis, such as paid work, leisure and domestic work. The quality of these activities also matters for life satisfaction. Although being employed does not seem to have a significant positive impact, being unemployed does have a significant negative impact. It is a damaging experience to have to go through both pecuniary and psychologically. Leisure is also essential for people’s wellbeing. People who value leisure more also have a higher probability of stating that they are satisfied with their life.

People also spend a lot of time on domestic and personal services. Unfortunately, no data on unpaid domestic work are available so we are not able to take this into account.

Good governance also has a positive effect on the way in which people enjoy their lives. People who feel that they have much more freedom of choice and control over their lives, have a higher probability of reporting a high level of life satisfaction. The same is true for people who are of the opinion that there is respect for human rights in their country. In line with previous research, confidence in the government turns out to be important as well.

Social capital, measured by the level of trust in people you know2 and whether or not you are a volunteer, also increases the propensity to say that one is satisfied with his life. This may be caused by the fact that social capital lowers transaction costs and increases the likelihood of finding employment. Besides these personal advances, a higher level of social capital may also generate benefits for the society as a whole. It generates economic growth, leads to more investment in human capital, higher levels of financial development and a lower incidence of crime.

The impact of environmental conditions, proxied by per capita carbon dioxide emissions in metric tons, on wellbeing is negative, because environmental conditions influence human health in a direct (e.g. air, water and noise pollution etc.) and indirect (e.g. climate change, loss of biodiversity, natural disasters etc.) way. Personal and economic insecurity also have a negative impact on the well-being of (risk-averse) people, because it is a source of fear and anxiety and leads to uncertainty about the future.

Besides the aforementioned factors, individual characteristics are important as well. Therefore, we have included several control variables in our model. For example, a U-shaped relationship exists between life

Trust in general does not have a significant impact.

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satisfaction and age. People in their middle ages generally report lower levels of life satisfaction, everything else constant, than people who are younger or older. This U-shaped pattern may be caused by the fact that those in their middle ages are often burdened with difficult decisions and have to think about their family instead of themselves. Other explanations could be that individuals learn to adapt to their strengths and weaknesses as they age, that happier people may live longer than sad ones (selection effect) and that people see their friends pass away and are happier with what they have at an older age (comparison effect). The marital status seems to matter too. In comparison with single people, marriage goes hand in hand with higher levels of life satisfaction for both men and women. In literature this is explained by the fact that marriages boost the self-esteem of people and leads to support and companionship. Being a male decreases the odds of saying that one is satisfied. This is a rather surprising result, because in many other studies it is found that the men are, on average, happier than women. The observed difference in those studies is often explained by gender inequality and the fact that women are typically more critical of themselves and do not appreciate themselves as much as men do. An explanation for our result is lacking. We also find that the life satisfaction of individuals increases with the number of children that they have.

Based on de pseudo R2, it can be concluded that the model including all eight well-being dimensions identified

by Stiglitz et al. (2009) is slightly favourable to a model that only contains per capita GDP as an explanatory variable. However, given the small differences, the evidence in favour of the use of multiple dimensions is far from convincing and further research on the underlying determinants of life satisfaction is needed.

Least developed versus most developed countries Our result does not imply that per capita GDP is completely useless. Aside from the fact that per capita GDP is an indicator for the economic activity within a country, it is also not a bad starting point for measuring well-being.

This is especially true for the least developed countries, i.e. the bottom 25% of the countries in terms of per capita GDP, in our sample. In these countries a small increase in income usually leads to huge increases in satisfaction with life. For more developed countries it makes sense to look at other dimensions as well. Governments in advanced countries should not simply follow (economic) policies that maximise economic growth at any cost. Instead, they should focus on the optimisation of the well-being of their citizens. Following a policy that improves life satisfaction holds a much greater potential. Rather than economic growth figures, human welfare should be used as a measure that dictates how well policy makers are living up to the society’s expectations. In this respect, the

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developed world could learn something from the poor, but happy, Kingdom of Bhutan, where the government strives to maximize the well-being of its citizens.

References Cobb, C., Halstead, T. and Rowe, J. (1995). If the GDP is Up, Why is America down? Atlantic monthly, October 1995.

Kuznets, S. (1934). National Income 1939-1932. Senate document no. 124, 73d Congress, 2d session.

Mashlow, A. (1943). A Theory of Human Motivation.

Psychological Review, 50, pp. 370-396.

Stiglitz, J.E., A. Sen and J. Fitoussi (2009). Report by the Commission on the Measurement of Economic Performance and Social Progress. Paris: The Commission on Economic Performance and Social Progress.

Van de Belt, R. (2011). Special 11/08 It’s more than the economy, stupid! It’s all about well-being. Utrecht: Rabobank Nederland.

Puzzle On this page you find a few challenging puzzles. Try Lead to solve them and compete for a price! But first we will provide you with the answers to the puzzles of last edition.

Answer to “Math Maze” Basistekst

Dog’s Mead.

10. The age of farmer Dunk.

11. The year in which Mary was born.

14. The circumference of Dog’s Mead (in yards).

15. The walking speed (in miles per hour) of farmer Dunk, to the power of three.

16. 15 horizontal minus 9 vertical.

Dog’s Mead It’s the year 1939. The farm of the family Dunk is situated in the south of England. The rectangular piece of land on which the farm stands is called Dog’s Mead.

The goal is to complete the cross-number puzzle on basis of the next hints. In each box of the cross-number puzzle, one digit (0-9) must be placed (and none of the numbers starts with the digit 0).

A Hint: In 1939, England had not changed to the metric system and the “decimal” subdivision of the pound yet.

Therefore, this puzzle still uses the old English units: 1 rood = 1210 square yards.

1 mile = 1760 yards.

1 pound = 20 shillings.

Horizontal: 1. The area of Dog’s Mead (in square yards).

5. The age of Martha, the aunt of farmer Dunk.

6. The difference between the length and width of Dog’s Mead (in yards).

7. The number of roods in Dog’s Mead multiplied by 8 vertical.

8. The year in which the Dunk family became owner of

Vertical: 1. The value of Dog’s Mead (in shillings per rood).

2. The square of the age of the mother-in-law of farmer Dunk.

3. The age of Mary, the daughter of farmer Dunk.

4. The value of Dog’s Mead (in pounds).

6. The current age of Ted, son of farmer Dunk, who will be in 1945 twice as old as his sister Mary will be in that year.

7. The square of the width (in yards) of Dog’s Mead.

8. The number of minutes in which farmer Dunk walks 11/3 times around Dog’s Mead.

9. 10 vertical divided by 10 horizontal.

10. See 9 vertical.

12. The sum of the digits of 10 vertical plus 1.

13. The number of years that Dog’s Mead is owned by the Dunk family.

Solutions Solutions to the puzzle above can be submitted up to May 1st 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 73, Roeterstraat 11, 1018 WB Amsterdam, Holland. Among the correct submissions, one book token will be won.

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In February, the new board consisting of Ruben Walschot (Chairman), Kevin Weltevreden (External Affairs), Lennart Niezen (Treasurer) and Milan Schinkelshoek (Secretary and Internal Affairs) has started. They presented their plans for this year on their first General Members Meeting on the 20th of February. It looks like it will be another action-packed year for the VSAE. Some big events will be organized in the next few months.

On the 28th of February, the National Econometricians Day (LED) took place. This year, it was organized by Kraket and the VSAE. 380 students from all over the country came to the RAI in Amsterdam to meet three of 24 companies during two cases and a dinner.

The Marketing Intelligence Competition is scheduled for the 13th of April. MIcompany will provide two interesting cases and the participating students will form teams and compete for a prize.

On the 17th, 18th and 19th of April, Amsterdam will host the thirteenth Econometric Game. For three days, the participating universities from all over the world will work on a case at the University of Amsterdam. The case topic will remain secret until the opening of the Econometric Game.

Last but not least, our yearly Actuarial Congress will take place on the 9th of May in Felix Meritis. The theme will be the generation gap in the Dutch pension system.

Agenda •

24

We live in vibrant times. At the moment of writing the general members meeting has just taken place and the energy that erupted inspires us to do the best job we can.

The search for new active members for our committees has begun, as well as the startup of the search for our successors.

The organization of the activities planned in the second half of this academic year excites us.

We are looking forward to the next few months.

Which will bring great opportunities for our members in the form of orientation on the business world as well as a great time to make friends, sit back and relax from all the hysteria that surrounds us.

We are grateful for what the LED 2012 committee has realized, and want to thank them for their perseverance and enthusiasm. It has been a great event, and we wish the LED 2013 committee the best of luck in organizing it next year in the beautiful city of Tilburg. We hope to experience the great ‘gezelligheid’ the south is known for.

Agenda

0 March 2 Monthly drink

•

0 March 3 Monthly drink

• 13 April Marketing Intelligence Competition

• 4 April Optiver Inhouse day

• 17 - 19 April Econometric Game

• 19 April Active members activity

•

19 April

•

24 April

•

9 May

•

4 May

•

11 - 14 May

Econometric Game Congress Actuarial Congress Short Trip Abroad

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February 2012

Poker tournament Monthly drink

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