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The effect of measured risk aversion on wealth : the relationship between risk aversion measured in an experiment and wealth on an individual level

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Bachelor of Science Thesis Econometrics

The Effect of Measured

Risk Aversion on Wealth

The relationship between risk aversion measured in an experiment and

wealth on an individual level.

In this paper I make use of data of the LISS (Longitudinal Internet Studies for the Social sciences) panel administered by CentERdata (Tilburg University, The Netherlands).

Acknowledgements

I want to thank Zhenxing Huang and Jan Tuinstra for supervising and giving feedback during the process of writing this thesis. I also want to thank Rob van Hemert and Kees Jan van Garderen for the feedback on the presentations and literature review, and finally I want to thank Yoram Vanmaekelbergh for the final review of my thesis.

Joppe Arnold, 10067639

Supervisors: Zhenxing Huang and Jan Tuinstra

27-6-2014

Abstract

This research examines whether higher levels of risk aversion lead to lower wealth, lower variance in wealth and smaller changes in wealth over time, as can be expected from previous research on risk aversion and economic choices and their outcomes. Using data consisting of a sample of the Dutch population it is found that almost none of these relationships are significant, although the signs indicate there is an effect of risk aversion on several wealth variables. The results remain insignificant despite excluding subgroups, including control variables and using auxiliary models. This

insignificance might be caused by measurement errors, a wrong experimental setup, causality issues, small sample size or a misspecification in the used models.

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Table of contents

1. Introduction ... 3

2. Previous research and theory ... 4

2.1 Theory of risk aversion ... 4

2.2 Factors influenced by risk aversion and influencing wealth ... 5

2.3 Hypotheses ... 8

2.4 Causality problems ... 8

3. Research method ... 9

3.1 Dataset and variables ... 9

3.2 Measuring risk aversion ...11

3.3 Subsamples ...13

3.4 Models ...15

4. Results ...16

4.1 Descriptive statistics ...16

4.1.1 The wealth distribution ...17

4.1.2 Differences within a specific year ...18

4.1.3 Robustness check using entrepreneurship ...21

4.1.4 Differences over time ...22

4.2 Differences in the wealth distribution and deviation ...22

4.2.1 Differences in the wealth distribution ...23

4.2.2 Deviations in the wealth distribution ...25

4.2.3 Robustness checks using entrepreneurship ...27

4.3 Differences in changes over time ...28

5. Conclusions ...31

6. Discussion ...32

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1. Introduction

Recently, more and more research has become available on the influence of an individual’s risk attitude on his or her economic choices. Studies on for example how risk aversion affects the probability of becoming an entrepreneur, investment behavior or the kind of job one chooses to do. The outcome of these economic choices has a large effect on an individual’s financial situation. Risk averse people may tend to make safer choices that have a lower expected monetary value. More risk seeking people tend to choose the opposite, taking more risk. This risk taking allows for a higher average outcome, but also entails a larger variance in the range of possible outcomes.

In experimental and behavioral economics, the risk-behavior of a person is frequently measured by looking at choices in a range of lotteries. More risk averse people are expected to take a safer lottery, with lower (or even zero) variance and lower (more certain) expected outcome. The measured risk behavior of a person has shown to have an influence on all kinds of choices. These choices have shown to be of a big impact on the wealth of a person, as taking more risky economic choices in real life also usually gives a higher return, albeit with a high variance in the possible returns.

While quite some research is already available on specific relationships of risk aversion on one economic choice, this research is about the greater relationship between risk behavior and wealth. Using data on the Dutch population, gathered from the LiSS panel, the influence of risk-behavior on a person’s wealth and the changes in that wealth over two two-year periods will be investigated.

In the following part of this paper a short general introduction on the theory of risk aversion will first be given. Following, previous research about the relationship between risk behavior within an experimental context, choices in real life and the outcomes of these choices will be addressed. This theory and previous research is used as a base for the hypotheses that will be tested. After that the data and methods of analyzing will be

introduced, which is followed by the results. The first part of the results will use descriptive statistics, while the second part uses regression analysis. Finally the results will be

summarized in the conclusion and suggestions for further more detailed research will be provided in the discussion.

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2. Previous research and theory

In this part a short theoretical introduction on risk aversion will be given in the first subsection. In the following subsection several previous results on specific relationships between risk aversion and economic choices will be mentioned. These results are used to construct the hypotheses which are introduced in the third subsection. In the last subsection of this part the possible causality problem that occurs for the given hypotheses is addressed.

2.1 Theory of risk aversion

Wakker (2010) gives an introduction on risk aversion, which holds only when the expected utility assumption is assumed. In the simplest version of the theory, all economic agents are presumed to either have a convex, linear or concave utility function. When an agent then has to choose between an uncertain outcome (either α or β) or a certain fixed amount computed by taking the weighted average of all uncertain outcomes and the respective probabilities, the risk aversion and type of utility function of this agent is exposed. An agent who prefers the uncertain choice is risk seeking, an agent who prefers the fixed amount is risk averse and an indifferent agent is said to be risk-neutral. Consider for example the graph of a risk averse person, which has concave utility. It can be seen that the expected utility of a fixed amount consisting of the average of the uncertain outcomes,

u(p * α + (1 - p) * β)1, is higher than the linear combination of those outcomes with uncertainty, p * u(α) + (1 - p) * u(β). This agent will only start to choose the uncertain outcome if the fixed amount (which is no longer a weighted-average of those uncertain outcomes) gets under d (see figure 1), or when the expected outcome of the uncertain choice will be e while the fixed amount will not change.

Figure 1

A concave utility function facing a choice between a lottery with outcomes α and β and a certainty equivalent.

© 2010, Cambridge University Press. Original by Wakker (2010, p. 92).

1 Where u(x) is the utility function for a given person with wealth x and p is the chance on

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For risk seeking persons the utility graph is convex and the results are opposite. They will normally pick the lottery and in this example end up with either high payoff β or low payoff α. For risk-neutral people having a linear utility graph both lines would be the same, making them indifferent between the lottery and the fixed choice.

Lots of influences of risk aversion on economic choices have been found throughout the years, implying that the theoretical model of risk aversion indeed applies in real life. As different empirical researches shows there is indeed usually a higher variance in the

outcomes of choices picked by risk seeking persons, which will be elaborated on in the next section. However, there is an excess demand for risk seeking people, as can be seen in for example King (1973) and Harrison and Rutström (2008). This implies that there is usually a premium for the risk seeking group, giving them higher expected outcomes for income and wealth. This happens even when those agents do not necessarily require the higher expected payoff to make that specific choice with higher variance in possible outcomes.

2.2 Factors influenced by risk aversion and influencing wealth

In this subsection several widely ranging relationships between risk aversion and economic decision making will be given, as found in previous literature. The outcomes of these choices on income and thus wealth will also be addressed. These choices include the choice of becoming an entrepreneur, working in the private or public sector, the way people search for jobs, lottery participation and investment behavior.

One of the most investigated relations is that of risk aversion and entrepreneurship. Being an entrepreneur gives higher volatility in income, as De Wit (1993) shows. However, entrepreneurs also have a higher average income than non-self-employed people, which is shown by Merz (2000). Combining these two outcomes implies that being an entrepreneur requires more risk-taking behavior, as the rewards, but also the risk incurred, are higher than for people working on contracts. Kihlstrom and Laffont (1979) therefore state that the choice of starting a new firm is influenced by the willingness to take risks of the decision-makers. Cramer et al. (2002) were the first to put this relationship to an empirical test and found evidence that risk averse people are less likely to become an entrepreneur. Van Praag and Cramer (2001) have developed a theoretical model earlier that was also tested empirically on Dutch data. This research shows that the choice of becoming an entrepreneur depends on both one’s ability and again on the willingness to take risks. Combining the economic

decision to become an entrepreneur with the effect of income suggests that risk aversion has an indirect effect on income and therefore on wealth.

Another effect that influences the wealth of an individual is that of the choice between working in the private or the public sector. Bellante and Link (1981) provide evidence that working in the public sector gives a higher certainty of keeping a job. They show that there is a significant link between the level of risk aversion of an individual and the probability that

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this individual will choose the public over the private sector. They also state that, ceteris paribus, there will be an excess supply of workers in the public sector when the payment in both sectors would be equal, explaining lower wages in the public sector. However, it is assumed that the market is dominated by risk averse people, as for example King (1973) states. Therefore, risk averse people are expected to get an even lower pay because as a reaction the wages in the public sector can be lowered to get rid of this excess supply. This implies that risk averse people that do go on the labor market also get a lower wage because they are more likely to seek a job in the public sector, where there is an excess supply. Risk seekers2 however are more likely to choose a job with less certainty giving a higher expected level of wealth in return. In return though, because of this uncertainty in the private sector, those workers are also more likely to lose their jobs and end up with a lower level of wealth.

A further factor affecting wealth occurs during the search for a new job when an individual is unemployed. Kohn and Shavell (1974) and Pissarides (1974) show, using an optimal job-search model, that more risk averse people have a lower reservation wage when searching for new jobs, because of the fear for being jobless for another period. More risk seeking people have higher wage demands which in the end could pay off for the uncertainty in the period of looking for a job when they find their new job. However, because of the high requirements of the risk seekers the possibility exists that they will stay jobless for a long time and end up spending their wealth during the jobless period. Empirical evidence on this link between risk aversion and duration of unemployment has been given by Feinberg (1977). He shows that an individual’s expected duration of unemployment increases when the variance in the distribution of possible wages increases. He also gives numerical proof that because of this effect, risk averse people tend to have a shorter expected period of unemployment.

A last job-related factor influencing the income and wealth of a person is the wage structure of an employee. Both King (1973) and Bonin et al. (2007) show that people with a lower degree of risk aversion are also likely to get a contract with a higher variance in earnings. This is caused by for example a bonus scheme in these contracts. King (1973) mentions that the expected value of the income is higher for a job with a high pay-variance. This implies that risk averse people have a lower average income, but that this also gives lower variance within earnings.

Outside the labor market there are also several relations between risk aversion and wealth to be found. The first is the investment behavior of an individual. Intuitively, and by the definition of risk aversion, it is to be expected that risk averse people invest more in low risk

2 In this section, comparisons are being made between risk averse and risk seeking people.

Risk neutral people are usually expected to be indifferent in choices which yield equal expected outcomes, as is also shown by Wakker (2010). In the real world the scale of risk aversion is continuous and has endless options instead of the mentioned three.

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investments such as safe government bonds and a savings accounts. Risk-seeking persons will be more tempted to invest in a higher risk portfolio, containing assets as company stocks. Kapteyn and Teppa (2002) compare different ways for finding out one’s risk aversion and show that some measures of risk aversion (the more simple) give good predictive results on the amount of a portfolio being high-risk and low-risk. As Dimson et al. (2009) show, the more risky investments tend to pay an investor significantly more in the long run. However they are also more volatile, allowing for negative real returns for periods as long as 40 years in a worst-case scenario. However, on average the returns are indeed higher, but if one has invested risky in a period of economic downturn or financial turmoil this may largely decrease wealth.

A second aspect to consider, outside of the labor market, is that of the decision to buy insurance to decrease risk. Insurance companies make money by applying the law of large numbers, as is explained by Wakker (2010). Because risk averse people want to insure themselves for the risk of losing a lot of money on incidents that happen with a very low probability (e.g. a fire, traffic accident) the insurer jumps into this gap and sells insurance. An insurance company has a large portfolio, which allows those companies to insure and payout in the case of an unlikely event, but still make a profit, by asking a risk-premium and applying the law of large numbers. Risk averse people tend to buy insurance, as is also shown by Dionne and Eeckhoudt (1985). Risk seeking and risk neutral people have a smaller

probability to buy this insurance, which gives them higher expected wealth, as they don’t pay this risk-premium to an insurance company. However, in the event of an incident they also lose a lot more money, making their wealth decrease significantly.

The third and last non job-related factor that will be discussed is that of participating in a lottery. However, a lottery differs from previous discussed effects in one way, which is that participation actually gives a negative expected value. This means that risk seekers that join a lottery in the long run lose money by participating, albeit usually small amounts of money. However, the large variance is still present here, as one can win huge amounts of money. Wärneryd (1996) gives evidence that risk seeking people are more likely to participate in lotteries, again increasing the variance of their possible-outcomes-range. The lottery is one of the few known cases where despite the negative expected outcome (the usually risk seeking) people still participate for this small chance for a large prize.

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2.3 Hypotheses

Combining all previous research and theories discussed above allows constructing

hypotheses on the influence of risk aversion on wealth. The first hypothesis is that more risk averse people have lower wealth because of this premium for risk seekers. In almost all mentioned empirical research, except for the lottery case, more risk seeking persons get on average the higher expected payoffs as some sort of compensation for taking the risk and facing higher variances in the range of possible outcomes.

The second hypothesis is that more risk averse people are more likely to be found inside the center of the wealth distribution, while more risk seeking people will be more in the tails. This is caused by the suggestion that risk averse individuals will likely make

comparable choices in the real world as they do in the experiment. These choices give them a lower expected outcome, but also a lower variance in the range of outcomes. If the first hypothesis holds it is necessary to correct for this by running analysis on the deviation to the mean and median of the specific subsample of people with the same level of risk aversion. If the first hypothesis is not shown to be significantly present within the dataset, it is possible to act as if there is one wealth distribution for all groups of risk behavior instead of correcting for the differences of the first hypothesis.

The last hypothesis is that it is expected that the changes in wealth over time tend to be lower for risk averse people and higher for risk seeking people, as risk averse people invest their money in less volatile ways and have decreased their risks of losing money or jobs.

2.4 Causality problems

One problem arising is that of the causality between risk aversion and wealth. Previous research indicates that quite some risk measurements used in economics are changing with an individual’s wealth. Cohn et al. (1975) find that people with a higher level of wealth make more risky investments. A person with a lot of money can act more like an insurance

company and invest in a lot of securities. This allows them to apply the law of large numbers, lowering the risk of losing relatively large amounts. Therefore, the risk aversion that is

measured for an individual with more wealth might be different than that for the same individual having lower wealth. This is caused by the fact that the (possible real) incentive is relatively smaller for a wealthier person. Another result in line with this is that of Guiso and Paiella (2008), who also find that more wealthy persons have a higher absolute tolerance of risk than those with a smaller wealth. Contrary to these results is the paper by Brunnemeier and Nagel (2006). They use empirical data to show that fluctuations in wealth do not

influence the portfolio choice of an agent in the short run. Rabin (2008) shows that the effect of wealth on risk aversion might be smaller than expected from theory. He states that for wealthier individuals the changes in risk aversion are less than could be expected based on

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the literature, and that this is not explained by the diminishing marginal utility of wealth. It can be concluded that the causality between risk aversion and wealth is complicated. A lot of possible reasons for a relationship from risk aversion to wealth have been shown in earlier research, as was discussed in the section 2.2. However, other research has also shown that wealth has an influence on the degree of risk aversion of an individual.

A way to deal with this problem in this research is to include several risk

measurements in the model, to compare the results for absolute and relative risk aversion measures. Also, by using several fluctuations in the model and in groups included in a regression it is possible to see if the results vary or whether they are consistent with each other. Other possible solutions for looking into this causality are given in the discussion part, as they fall beyond the scope of this research.

In the part of the research that focuses on changes in wealth over time the causality issue is less present as it is then possible to include the wealth in the previous year as an explanatory variable. By doing this it is possible to compare people that have more or less the same initial wealth in the first year of measurement. This gives the opportunity to look into the relationship between risk aversion and changes over wealth in those periods, as people with the same initial wealth but different levels of risk aversion might show different changes in wealth.

3. Research method

In this part the methods used to research the hypotheses are introduced. In the first

subsection the dataset and variables included in the models will be introduced. In the second subsection the three used measurements of risk and their derivation from the dataset will be explained. In the third subsection several possible differences in subsamples in the dataset are mentioned to introduce the subsamples that will be included in the analysis. Finally, in the last subsection of this part the models that will be used for testing each of the hypotheses are introduced and elaborated on.

3.1 Dataset and variables

The data used to test the hypotheses is from the LiSS panel. This panel is a true probability sample of individuals in the Netherlands, meaning that the sample is representative for the Dutch population. Households are drawn randomly using the population register. The panel also controls for individuals not having access to the internet or a computer by supplying these to participants not in the possession of one. A longitudinal survey is given to the panel on a yearly base. This survey covers topics such as work, education, income, personal background and more. Next to the yearly longitudinal survey the LiSS panel also has a wide range of data collected using other questionnaires on for example risk aversion.

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For this research data from the two-yearly asset panel3 is combined with a questionnaire on risk behavior4 and background information5. Next to measures of risk aversion, which will be elaborated on in section 3.2, other variables will also be included to predict wealth. To determine which variables to include in the model to control for it is necessary to look at previous literature. Variables that are known to influence both risk aversion and wealth should be included to control for their effects.

Riley and Chow (1992) argue that risk aversion is a function of age, education, wealth and income. Eckel and Grossman (2008) find that the gender is also a factor influencing risk aversion. Other researches indicate that age, education and gender also influence wealth. Mirer (1979) shows that age influences wealth and Hartog and Oosterbeek (1998) show the same for education. Both age and education should therefore be included by themselves and age possibly also quadratic, as quite some literature mentions that this effect is non-linear. It has also been shown that gender affects income and wealth through for example the glass ceiling. Therefore education, age and gender will be controlled for in the results. Education and gender are supplied as discrete variables, age is in years. Gender will be included as a dummy variable that is one for women and zero for men. Education will be recoded to dummy variables, where the completion of primary education or lower is taken as control group. Higher levels of completed education, being vmbo (preparatory middle-level applied education), havo/vwo (higher general continued education/preparatory scholarly education), mbo (middle-level applied education), hbo (universities of applied sciences or vocational university) and wo (university) will be included as dummy variables.

In the previous paragraph the reverse causality problem of wealth and risk aversion was already discussed. It is the question in what way wealth has a real influence on results in a more laboratory-like session. Because a lot of ways that risk aversion influences wealth go through occupation and therefore income, the variable income will not be included in the models. In this research, the focus is on whether the intuition that risk averse people are more in the center of the wealth distribution and on average on a lower wealth level than risk seekers, because of the factors discussed in the literature review. The focus is not on the nominal effects for the specific measures taken from a single experiment but on the sign of the coefficient for risk aversion and the significance.

The dependent variable in all three hypotheses is wealth. Data on this subject is available per individual in a panel about assets, which gives detailed information about different sources of wealth such as bank accounts, investments, housing, cars, debts and more. Participants are required to give a monetary value for those categories. Combining all those questions could provide an accurate view of the wealth of a person. However, because

3 Panel 9. 4 Panel 38. 5 Panel 1.

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these measurements are quite prone to measurement errors, only the questions on liquid assets, investments, assurance policies and housing will be used to compute wealth. These categories function as good proxies for wealth and cover the major part of personal monetary assets. The questionnaire about assets is first conducted in 2008 and then repeated in 2010 and 2012, allowing to compare the changes in assets over time. The wealth variables are built up by first removing all observations of individuals that answered that they do not know the value in one specific category or that did not want to share the value with the panel, despite it being anonymous. In the leftover data, some individuals answered that they did not know the exact amount of a specific asset category. In that case they could pick a range, which was converted to an exact value by taking the average of that range. Liquid assets, investments and assurance polices are then taken directly from either the exact filled in value or the average of the given range. The housing variable is constructed by taking the given value of property and deducting the outstanding mortgage. The total assets value in a given year is then computed by summing all these categories.

For the first and second hypothesis it is important to note that the control variables of the January 2010 wave will be used, as well as the asset dataset of 2010. This is done because the experiment on risk aversion is conducted in December 2009, and the assets dataset asks participants to fill in their assets value as of the 31th of December in the foregoing year. This means that by combining these three datasets the difference in time is kept as small as possible, allowing for more accurate results. For the differences over time the asset datasets of 2008, 2010 and 2012 are combined with the participant’s background data of January of those years.

3.2 Measuring risk aversion

To have a model that actually says something about the real world, it is necessary to include a valid measure of risk aversion in the models. Kapteyn and Teppa (2002) and Harrison and Rutström (2008) find that different ways of measuring risk aversion might lead to different results when involved in modelling. Because it is useful to compare these outcomes several measurements will also be used in this research. In the LiSS panel participants had to choose between a lottery and a certain fixed amount. The possible outcomes in the lottery are € 65 and € 5, both with equal probability, and the certain amount is ranging from € 20 to € 40 in steps of € 5, or € 40 to € 20 for another group. At one moment a participant switches to the safe amount, and this moment will be used to calculate the certainty equivalent of the lottery, by taking the average of the two fixed amounts in which between the participant switches. For individuals that always choose the certain option this equivalent is taken as 42.5, while for individuals that always pick the lottery the equivalent is taken as 17.5. For some groups, these choices had the chance of being paid off for real, while for other groups all payoffs were purely hypothetical. Also, one group had the hypothetical payoff with all

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amounts scaled up by a factor 150, which directly influences the exponential risk measure. The certainty equivalent of the lottery will be transformed into an absolute and a relative measurement of risk. The relative measure will be calculated by means of the power utility family6, while the absolute measure will be calculated using the exponential utility family7. The relative measure increases in wealth, while the absolute decreases, as is shown in Wakker (2010). Both these risk measures can be calculated by solving the family of functions for the risk degree when filling in the certainty equivalent for the lottery. The utility functions that are used represent the utility for different levels of wealth. The power utility function measure remains constant when all payoffs are scaled by a factor. The exponential utility function does not remain constant when the absolute risk changes but the relative risk remains constant (thus scaling all values by a constant).

A more simple measurement of risk will also be included in this research. As Kapteyn and Teppa (2002) show, a simple measure of risk derived directly from the experiment may prove to be a better estimator for risk aversion than more theoretical measures8. Therefore, the total number of safe choices for a certain payoff made in all five choices will also be used as a measurement of risk aversion.

By including those three measurements of risk, all three increasing in risk aversion, it is possible to look into differences in causality, by comparing the findings and running

regressions on all three measures9. Also, when all three measurements give the same result, it makes the findings in this research more robust. Because of the relative risk aversion that stays the same for power utility there are no changes between an individual that had a hypothetical high payoff and one with a normal payoff. However, because the absolute amount and risk changes this difference does occur in the exponential measure, meaning that there is a real difference between the different measures for risk, as the exponential measure is influenced by the scaling factor in the experiment, which is why that measure is also included among the other two measures of risk aversion.

6 By numerically solving u(certainty equivalent) = ½ * u(5) + ½ * u(65) where u(x) = xθ for θ > 0,

u(x) = ln(x) for θ = 0 and u(x) = -xθ for θ < 0, and then taking as risk measure θreal = -θ to ensure all estimates

using different risk measures have the same sign.

7 By numerically solving u(certainty equivalent) = ½ * u(5) + ½ * u(65) where u(x) = 1-e-x * θ for

θ > 0,

u(x) = x for θ = 0 and u(x) = e-x * θ -1 for θ < 0.

8 As is also shown by Guiso and Paiella (2008).

9 The number of safe choices is referred to as ‘nosafe’, the exponential utility as ‘exp’, the power

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3.3 Subsamples

In the experiment on risk aversion the moment that a person switches between the certain payoff and the uncertain lottery is used to determine the certainty equivalent of the lottery. This certainty equivalent is then used to compute an individual's risk aversion using power and exponential utility functions. However, a small group of people switches from the safe amount to the lottery when the safe amount increases. This violates the assumption of rationality and risk aversion and therefore these individuals will be excluded in all analysis. In the experiment one group received hypothetical payoffs, without being informed of this, while a second group had an actual chance of receiving a monetary reward for the outcome of their choices and was told about it. As shown in literature this can cause

differences in the outcome, because an incentivized individual may perform differently from a non-incentivized one. Using a two-sample Wilcoxon rank-sum Mann-Whitney test it is

possible to compare and look for differences between these two samples. The z-value of this test with the number of safe choices as dependent variable is -3.920, which means there is a highly significant difference. Using the total wealth in 2010 as dependent variable the z-statistic is -1.552 which is not significant but gives a clear indication that there is also a difference here.

This idea can further be tested by running a two-group t test on the different groups and comparing the found results. As is shown in table 1 the means differ significantly. Where this is logical for exponential utility, where an increase in absolute risks means different values for the risk measurement10, this result is also found for the number of safe choices and power utility measurement. When looking at the difference in standard deviations this result can only be found in the exponential measure, which tells that the standard deviation for the hypothetical group is significantly smaller than for the real payoff group. This is possibly caused by the fact that the differences between the different values for the exponential measure prove to be smaller for the subsample that was shown hypothetical payoffs scaled up with a factor of 150.

Table 1

Means and two group mean-comparisons for different payoff situations.

risk measure \ value mean (hypothetical) mean (real) difference t-value diff > 011

# safe choices 3.611538 3.340302 -0.271236 -3.5120***

exponential utility 0.0132519 0.0264659 0.013214 12.8030***

power utility -0.3901774 -0.4764589 -0.0862815 -3.5453***

10 Note that the group with scaled up outcomes 150 times was part of the hypothetical payoff

group.

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From table 1 and the foregoing statistics it can be concluded that there are actual differences present between the different groups of payoffs. Therefore it makes sense to take a look at the subsample with only incentivized payoffs, as it can be expected that people show more of their behavior in real life where there is also money at stake when in an incentivized

experiment. This has also been shown by for example Holt & Laury (2002). The direction of these differences are not consistent for all risk measures though. This is caused by the fact that only the exponential risk measure is affected by scaling up by a constant, which is done for part of the hypothetical payoff group. The power utility risk measure remains constant if the relative risk stays the same and the measure of number of safe choices is not affected at all by the amounts offered. For the scaled up subsample the computed exponential risk measure becomes a lot smaller for all choices, as this utility function is decreasing in the amount of absolute risk. As there are more risk averse people, this causes the change to be in the opposite direction than the change for other risk measures.

When looking at the dataset of wealth for 2010, there is another possibly disturbing problem. A group of 218 out of the 1595 total observations reports a wealth of 0 in this year. Although it is possible that a person has 0 assets, it seems highly unlikely that this group consists of almost 14% of the sample. Almost all individuals have a bank account and it is more likely that individuals that fill in 0 for all their assets don't want to tell their wealth. Although an option was available for persons not wanting to share this information and these persons were excluded, it seems that there is still a large group that did not do this but still filled in wrong information. Therefore the wealth is subject to severe measurement errors and it seems logical to also take a look at the subsample where those individuals are excluded. The last subsample with both groups excluded seems the most valid based on theory, and this group will thus mostly be used when running regressions. The number of useful observations is shown in table 2.

Table 2

Number of useful observations when dropping certain subsamples in 2010 and for which data is available in all three consecutive years.

# observations excluding

subsamples total set risk averse risk neutral risk seeking

observations for all 3 years

Total 1595 1131 186 278 640

+ exclude wealth of 0 1377 980 169 228 481

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3.4 Models

To find empirical evidence to test the different hypotheses it is necessary to have a fitting model and appropriate method to analyze the data and different subsamples. It is also useful to take the logarithmic value12 of wealth in all models, as the wealth distribution is far from linear. This favors different ways of measuring wealth instead of using the real numerical value, also decreasing the influence of outliers. By applying this transformation ordinary least squares will also yield better results, as this method has more power when used in linear models.

The first hypothesis is that risk aversion has a negative effect on wealth. This can be modelled easily because the tails don’t really matter for this hypothesis, while the mean does. Therefore a model will be used to predict wealth using risk aversion and the earlier explained explanatory variables, as is shown in equation (1).

WEALTHi = c + β * RAi + γ * Xi + εi where εi ~ N(0, σ2) (1) If the hypothesis holds β should be negative, indicating lower wealth for risk averse

individuals. All earlier explained explanatory variables are part of the X-matrix in all mentioned equations.

The second hypothesis is that the higher the level of risk aversion, the greater the probability of being in the middle (presumably near the median13) of the wealth distribution is. This can be modelled in one model by taking the absolute deviation of the wealth from the median or average wealth for each individual. By then running a regression with that deviation or its logarithmic conversion as dependent variable the hypothesis can be tested. The model for this can be found in equation (2).

|ΔAVGWEALTHi| or |ΔMEDWEALTHi| = c + β * RAi + γ * Xi + εi where εi ~ N(0, σ2) (2) If the hypothesis holds the sign of β will be negative for all measures of risk aversion.

Assuming that hypothesis 1 holds, the median and average are differing for varying levels of risk aversion. This means that the dependent variable should be computed on a group level using the specific average and median from the subsample of persons with the same risk aversion.

Another way to look into this hypothesis is by running a logit regression with the person being in the 20% highest or lowest wealth groups as dependent variable. The regression to run is then as in (3).

P[TAILi = 1] = F(α * RAi + γ * Xi + εi) where εi ~ N(0, σ2) (3)

12 All conversions to logarithmic values in the proceedings of this paper are done by taking the

logarithmic value for x > 1, 0 for -1 < x < 1 and -log(-x) for x < -1 to smoothly transform into a less linear distribution.

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Would the findings be robust, then the sign for α will be negative, indicating a higher likelihood of being in the tails for lower levels of risk aversion.

The third hypothesis is that risk aversion has a negative effect on the magnitude of changes in wealth over time. Here the wealth of the first period can be included, because the focus is on the change in wealth caused by risk aversion and not on the wealth itself. The dependent variable is then the absolute change in wealth between year t -1 and t. The equation to estimate is equation (4).

|ΔWEALTHi,t| = c + αt * |WEALTHi,t-1| + βt * RAi + γ * Xi,t-1 + εi,t where εi,t ~ N(0, σ2) (4) The α in this equation can be interpreted as the general change in wealth while the β

explains the part caused by risk aversion. Because the absolute change in wealth is taken as dependent variable, the absolute value of wealth at the start of the period should also be used, as change in wealth is obviously heavily correlated with the amount of wealth one has at the start, be it negative or positive. If the hypothesis holds β should have a negative sign, indicating a lower change in wealth for more risk averse people. This model does not support a way to research the direction of changes over time, as the focus is on differences in

magnitude. The direction might also be prone to the level of risk aversion, which is a relationship to investigate in further research.

4. Results

Following the introduction of the models in the previous section, the data will now be analyzed. In the first subsection the dataset will be analyzed using descriptive statistics, to allow for a simple insight in the data. In the second subsection the first and second

hypothesis will be tested using data for the specific year 2010. In the third subsection the changes over time will be addressed to test the third hypothesis. In parts on the first and second hypothesis a look at the influence of self-employment on wealth will be included to allow looking into this specific relationship which is mentioned in the literature review. This allows making the findings more robust.

4.1 Descriptive statistics

This subsection will elaborate on the dataset and functions as an introduction into the data. Using standard methods as mean comparisons the hypotheses are tested and the dataset is introduced. In the first paragraph the wealth distribution will be explained in more detail. In the second paragraph the differences within a specific year will be shown. After that the example of entrepreneurship and the effect of being an entrepreneur on wealth will be introduced and finally the differences over time will be shown using simple statistics.

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4.1.1 The wealth distribution

The best way to characterize the wealth distribution is by looking at the logarithmic

transformation of the total assets of an individual in a given year. The distribution of wealth within the dataset used is shown in figure 2. Additionally, the mean and median for the

different groups of risk aversion are reported in table 3. Using the number of safe choices it is possible to divide the dataset into three different groups. One group consists of risk averse people (more than two safe choices in the experiment), one group of risk neutral people (two safe choices) and one group of risk seeking people (less than two safe choices).

Figure 2

The logarithmic transformation of the wealth distribution.

Table 3

Statistics on wealth distribution for different risk groups and nominal and log wealth.

nominal Log

variable \ value # observations mean median mean median

Total 1595 52996 8000 7.4174 8.9872

risk averse (# safe = 5) 742 49053 6525 7.1411 8.7834

risk averse (# safe = 4) 172 44940 8875 7.2041 9.0909

risk averse (# safe = 3) 217 44029 12750 8.1691 9.4533

risk neutral (# safe = 2) 186 72795 13000 7.988 9.4727

risk seeking (# safe = 1) 96 64726 11587 8.0252 9.357

risk seeking (# safe = 0) 182 60957 6000 6.9453 8.6995 As mentioned before, there is a problem with the number of people reporting zero wealth. This group is quite large in the dataset as can be seen in figure 2. On the positive side (wealth > 0) of the figure the wealth distribution shows to indeed have one high peak as expected with density quickly decreasing for higher wealth levels. Another problem can be seen immediately, which is that individuals with a negative wealth are far away from individuals with positive assets, which means that persons with negative wealth may be overly represented when running OLS and therefore influential to the OLS estimates. This

0 .0 5 .1 .1 5 .2 D e n si ty -10 -5 0 5 10 15 logwealth

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can also be seen when comparing means and medians for both nominal as log values of wealth in table 3. In the nominal distribution, the mean is far higher than the median, while in the logarithmic transformation the opposite occurs. This indicates that the negative values could have a high effect on the findings for the first hypothesis. Therefore, robustness checks can be added in by also looking at a new subsample of persons with only positive wealth. For hypotheses 2 and 3 this is not necessary as the model is specified as the logarithmic

transformation of the absolute difference. By doing this there exist no negative values and this gap in the logarithmic scale is non-existent.

4.1.2 Differences within a specific year

The dataset for the year 2010 consists of data on risk aversion, assets, age, gender,

education and of course wealth. Without excluding any of the subsamples, except the for the people that switch to the lottery when the safe amount increases, the dataset consists of 1595 observations for which background, wealth and risk variables are all available.

Table 4

Summary for all observations and variables in the 2010 dataset

variable \ value mean standard error variable \ value mean standard error

female 0.4891 0,50 invest assets 12843 97536

age 49.73 17.68 housing assets 5437 42860

vmbo 0.2408 0.4277 total assets 52996 254619

havovwo 0.1260 0.3320 log total assets 7.417 4.6947

mbo 0.1875 0.3904 # safe choices 3.4589 1.7732

hbo 0.2483 0.4322 exponential risk measure 0.01808 0.02436

wo 0.09530 0.2937 power risk measure -0.4388 0.5595

liquid assets 29268 201339 hypothetical payoff 0.6069 0.4886

fixed-end assets 5448 29087

Table 4 shows that in 2010 the average asset value for an individual is 52996, however there is a large spread present, which can also be seen when looking at the minimum and

maximum values of wealth, respectively -445000 and 7612147. The mean of number of safe choices is around what can be expected when looking at the share of individuals receiving a hypothetical payoff and comparing this with the reported means in table 1. It can be seen that the standard deviation decreases when taking the log of wealth, which shows that the

distribution is indeed more normalized after the transformation.

The main focus of this paper is the differences in the wealth distribution that are caused by the risk aversion of individuals. Looking at the means of the different groups of risk aversion for our variables, creates an insight into possible results of the analysis. This is shown in the following table. Table 5 yields some first interesting results. First of all, when looking at the total assets it can be seen that the mean of real wealth for risk averse people

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is indeed lower as is expected by theory. However, the log of total assets is lower for risk seeking individuals than for risk averse persons. These two contrary results indicate that there are possibly a lot more outliers in the risk seeking group, because effects of outliers are smaller in more normalized distributions. This is in line with hypothesis 2.

Table 5

Means for different variables and risk categories in the year 2010 and the t-statistic for the two-group test for equal means for mean (risk averse) – mean (non-risk averse).

variable \ group risk averse risk neutral risk seeking t-statistic

# observations 1131 186 278 N/A female 0.531 0.360 0.406 -6.2066*** age 49.1 48.1 53.3 2.4044*** wo 0.0822 0.172 0.0971 2.8488*** liquid assets 29160 33273 27024 0.0332 fixed-end assets 4272 6276 9683 2.5269*** invest assets 10506 27629 12458 1.4946* housing assets 3526 5618 13094 0.0027*** total assets 47463 72795 62259 1.3553*

log total assets 7.348 7.988 7.318 0.9227

# safe choices 4.464 2.000 1.009 N/A Contrary to what is expected by hypothesis 1, risk neutral individuals have even higher levels of real wealth than risk seeking persons. In the experiment, being risk neutral is the most rational as the expected payoffs are highest in this case. This indicates that risk neutral persons might behave in a way that gives them the highest expected payoff while risk seekers take risks even if the expected payoff is lower than for a certain choice, as is the case in the used experiment. In table 3 in section 4.1.1 it can also be seen that the risk neutral group has the highest mean and median of wealth, and for the median this even seems to be somewhat parabolic when comparing with different number of safe choices made. This is in line with a direct translation from experimental choices and their outcomes to economic choices and their outcomes and a theoretical framework where all possible

outcomes and their probabilities are known to each individual. This suggests a non-linear effect of risk aversion on wealth. However it is impossible to know by just looking at this table what really causes the shown differences, as it might be that other variables than risk

aversion (for example schooling) cause deviations in wealth. Therefore a more detailed look into what is the cause of these differences is done using regression techniques in the next section. Some further discussion about a possible non-linear relationship is done in section 6.

Looking into the standard deviations for the different groups, no real significant differences are found between different groups, which is contrary to what is to be expected

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by hypothesis 2. This might be solved by controlling for education, age and gender. One last meaningful way to look into hypothesis 1 and 2 is by looking at the density plot of the logarithmic transformation of wealth for the different categories of individuals. It can be seen in figure 3 that each line has a peak around zero, showing people that reported a wealth of 0. However, more to the right in the graph it can also be seen that both risk seeking and risk neutral individuals have a lower peak and a slightly higher variance near the peak of the wealth distribution as their peaks are slightly wider. This figure does not give any proof but it suggests that some differences do occur between the various risk groups. This can be tested by running a two-sample Kolmogorov-Smirnov test for equality of distributions and comparing the risk averse group with the other two groups. The corrected p-value of this test is 0.427, indicating a non-significant difference in distribution functions.

Figure 3

The kdensity plot of log wealth for different levels of risk aversion.

0 .0 5 .1 .1 5 kd e n si ty lo g 1 0 -20 -10 0 10 20 x

Risk seeking Risk neutral

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4.1.3 Robustness check using entrepreneurship

An example that also allows looking into robustness of the hypotheses is that of

entrepreneurship. By declaring a dummy variable that is one if someone is self-employed and zero otherwise it is possible to look into this specific relationship. Adding this dummy reduces the total observations that all information is known for to 1540.

Figure 4a (left) & 4b (right)

Left: The number of safe choices made in the experiment by entrepreneurs and non-entrepreneurs.

Right: The kdensity plot of the logarithmic transformation of wealth for (non-)self-employed where the x-axis represents wealth.

Figure 4a gives an indication that entrepreneurs are more likely to take risk. This is also confirmed by running a test on the equality of means for the number of safe choices. Although not significantly at the 10% level (t = 1.1514) this value shows that there is quite a large probability entrepreneurs take less safe choices, although the causal direction of this relation is not known. Figure 4b shows that self-employed persons have a smaller peak in the distribution of wealth and that the peak is more to the right, indicating higher levels of wealth for self-employed individuals. This is also confirmed by running a test on the equality of means on wealth, which shows that the wealth for self-employed persons is significantly higher (t = -1.39*). The lower peak also indicates a difference in variance between the two groups, which is confirmed by running a variance ratio test (f = 0.8177*), meaning a significantly higher variance for self-employed individuals. This gives good indication that hypotheses 1 and 2 seem to hold because of the fact that self-employed persons also have a lower level of risk aversion.

14 Assuming normality. 0 .1 .2 .3 .4 .5 D e n si ty 0 2 4 6 nosafe

Non self-employed Self-employed

0 .0 5 .1 .1 5 .2 kd e n si ty lo g 1 0 -20 -10 0 10 20 x

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4.1.4 Differences over time

For the third hypothesis it is necessary to look over changes in time. Using the same groups as in the first part of this section it is possible to construct a table of differences over time. Only individuals on which both background and asset data is available on for all three years will be included. This means that the dataset used for testing the third hypothesis is reduced to 640 individuals.

Table 6

Means for (logarithmic transformations of) differences over in wealth over years for different risk categories and the t-statistic for equal means of risk averse and non-risk averse.

variable \ group total risk averse risk neutral risk seeking t-statistic

# observations 640 453 81 106 N/A

absolute value of assets change

2008-2010 42791 34578 80760 48876 1.8544**

log of absolute value of assets

change 2008-2010 8.0076 7.8966 8.7192 7.9384 1.3482*

absolute value of assets change

2010-2012 39285 33729 60108 47117 1.3485*

log of absolute value of assets

change 2010-2012 7.9475 7.9375 8.0411 7.9186 0.1252

absolute value of total change 82076 68307 140868 95992 1.8766**

log of absolute value of total change 9.1313 9.0736 9.658 8.9752 0.7982 Table 6 clearly shows that differences arise in the changes over time for different levels of risk aversion. As expected the absolute change for risk averse persons is lower, but the logarithmic values of the changes are higher for risk averse than for risk seeking individuals. This might be due to outliers in the data, because the absolute differences are more

significant than those of the logarithmic transformation, and the average absolute change in the risk neutral group seems highly unlikely as opposed to the other groups.

It can be concluded from this section that the descriptive statistics give some

evidence that the proposed hypotheses hold. Some of these first results are contrary to what can be expected based on the literature review though. To be more certain about the power of the findings it is necessary to analyze the data with a more sophisticated method which will be done in the next section using regressions.

4.2 Differences in the wealth distribution and deviation

In this subsection the first two hypotheses will be tested using regression techniques. The first paragraph goes into detail on the first hypothesis, the second paragraph addresses the second hypothesis and the final paragraph elaborates more on this using the entrepreneur example introduced in the previous part.

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4.2.1 Differences in the wealth distribution

The first hypothesis states that the wealth of individuals with a low level of risk aversion tends to be higher, caused by the risk premium paid in different ways as a compensation for taking the risk. As shown in the earlier part, using descriptive statistics, there does seem to be an effect of risk aversion on wealth. Running a regression on the (logarithmic transformation of) wealth using just the measure of risk as explanatory variable is a first introduction to

(in)validate the hypothesis. The results of this regression are shown in table 7. Table 7

Regression results for regressing nominal and log wealth on risk measures only.

dependent variable:

wealth nominal wealth log wealth

value \ risk measure nosafe pow exp nosafe pow exp

estimated coefficient -3495.36 -10773 -122277.5 -0.0822 -0.2183 -13.9682

t-stat coefficient -0.97 -0.95 -0.47 -1.24 -1.04 -2.9***

adjusted R-squared 0 -0.0001 -0.0005 0.0003 0 0.0046 It can be seen that, although the values of R-squared are very low, all signs match with the expectations from theory. This is a first indication that people with a higher degree of risk aversion prove to have higher wealth. However, in this model the proposed control variables are not present, which might disturb the results as highly educated persons show other degrees of risk aversion but also have on average a higher income. The t-statistics indicate that these findings are not significant though.

The logarithmic values show a higher significance, but are still not robust near the 10% confidence level. The reason for this higher significance is that, as was shown in section 4.1.1, the wealth distribution is very prone to outliers, which can have a huge influence on the estimates when running simple ordinary least squares. The logarithmic transformation of wealth is then a better measure as outliers are more normalized and have a smaller influence on the results. The exception when looking at significance is the exponential measure of risk, which is significant at the 1% level and shows the highest R-squared for all tested models. The reason why this measure is significant is unknown, but it might indicate that there is some randomly-caused correlation between wealth and whether a participant was offered hypothetical high payoffs.

By including control variables and looking at several of the subsamples proposed earlier on, the first found results can be checked for robustness and the significance levels might change. Table 8 shows the results for various setups of the model and subsamples.

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Table 8

Regression results for log wealth on risk measures and control variables with several groups.

dependent variable:

wealth log wealth

value \ risk measure nosafe pow exp nosafe pow exp nosafe pow exp

estimated coefficient -0.0291 -0.0552 -9.218 -0.0791 -0.2336 -7.0749 -0.0863 -0.2481 -6.878

t-stat coefficient -0.45 -0.27 -1.99** -1.34 -1.25 -1.66* -1 -0.91 -1.13

adjusted R-squared 0.0935 0.0934 0.0956 0.0899 0.0897 0.0905 0.0902 0.0899 0.0907

include control variables yes yes yes yes yes yes yes yes yes

exclude wealth of 0 no no no yes yes yes yes yes yes

exclude hypothetical

payoffs15 no no no no no no yes yes yes

sign as expected? yes yes yes yes yes yes yes yes yes It can be seen in table 8 that the signs of all coefficients are in line with the derived

expectations from the theory. Again, the found results are statistically insignificant for most measures of risk aversion and subsample, but the fact that the sign of the coefficients is consistent throughout the table does support the hypothesis that more risk aversion leads to lower levels of wealth, albeit with low levels of significance. The probability that all signs are coherent with the expectations for all subsamples without a causal relationship existing is assumed to be very small.

As mentioned in 4.1.1, the high spread of the logarithmic values caused by negative wealth and the flaw in the transformation process might need checking. Running some side regressions leaving out the subsample of individuals with negative and zero wealth it is found that the signs stay in line with theory and expectations, albeit with an even lower significance, indicating that there might be proportionally less risk averse than risk seeking persons with negative wealth than with positive wealth.

It can thus be concluded that although the significance of the found results is far from satisfying, the consistency does support the expectations of hypothesis 1. As seen in table 8 the reported coefficients and their t-statistics fluctuate quite a lot for different models and subsamples. This supports the idea that real differences between different samples do exist and the method used to measure risk aversion might not be sufficient. Also, the sample might have become too small to allow the model to have real power. The exclusion of individuals reporting a wealth of zero also clearly influences findings, supporting the notion that measurement errors in the data on wealth might disturb the results.

15 Each time the hypothetical payoffs are excluded the risk measures using the power and

exponential utility function tend to yield around the same results, as the variance with this group included is caused by the hypothetical high payoffs causing different levels of risk.

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4.2.2 Deviations in the wealth distribution

From the previous paragraph it is not entirely clear whether hypothesis 1 holds, therefore in this paragraph the case where hypothesis 1 is not valid will also be looked at more deeply, as will be made clear later on. By running a regression on the absolute difference of an individual’s wealth from the median or average (and taking the logarithmic transformation of that) the hypothesis that more risk averse people are more likely to be in the center of the wealth distribution can be put to the test. This would imply a greater variance for more risk seeking individuals. Although the descriptive statistics are not convincing, literature still suggests that there are differences present between different levels of risk aversion.

As explained in section 3.4 the dependent variable will be calculated firstly using the specific mean and median per group of risk aversion, which assumes that hypothesis 1 holds. The results for this model, introduced as model (2) are shown in table 9.

Table 9

Regression results for absolute nominal deviation from average and median wealth on risk measures and control variables under assumption that hypothesis 1 holds, including control

variables, excluding wealth of 0 and excluding hypothetical payoffs.

dependent variable: absolute deviation

nominal wealth

deviation from average deviation from median

value \ risk measure nosafe pow exp nosafe pow exp

estimated coefficient -12860.96 -40534.25 -869144.1 -7083.871 -22234.94 -485593.6

t-stat coefficient -5.06*** 5.05*** -4.85*** -2.48** -2.46** -2.41**

adjusted R-squared 0.0835 0.0834 0.08 0.083 0.0829 0.0825

sign as expected? yes yes yes yes yes yes In this table it can be seen that when looking at nominal values, the deviation from both the average and the median matter significantly in the expected way. More risk averse people are estimated to be closer to both the median and the average of the wealth distribution, even with hypothesis 1 in place. Although this could be caused by a few outliers that really affect the average (and thus the deviation for all other individuals) and estimations within a subsample this is a first proof for hypothesis 2. The signs of models without the exclusions of individuals with a reported wealth of 0 or hypothetical payoff are also consistent with the results found here in almost all cases. As stated earlier, the logarithmic transformation is less prone to outliers. The results of running regressions on this transformation of the absolute nominal deviations are given in table 10.

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Table 10

Regression results for logarithmic transformation of the absolute deviation from average and median wealth on risk measures and control variables under assumption that hypothesis 1 holds, including control variables, excluding wealth of 0 and excluding hypothetical payoffs.

dependent variable: log of absolute deviation

log wealth

deviation from average deviation from median

value \ risk measure nosafe pow exp nosafe pow exp

estimated coefficient -0.207 -0.6453 -13.7054 -0.0001362 0.004224 0.01468

t-stat coefficient -8.04*** -7.93*** -7.52*** 0 0.03 0.01

adjusted R-squared 0.1276 0.1248 0.1151 0.0717 0.0717 0.0717

sign as expected? yes yes yes yes no no The deviation from the average is in line with the previous findings and also indicates that more risk averse persons are estimated to have a significantly smaller absolute deviation from the average reported wealth. However, the logarithmic transformation of the absolute nominal deviation from the median is contrary to all earlier findings. The significance has dropped to almost zero and the signs are no longer as expected. The significance is so low that no real power can be given to the estimated signs of the coefficients. This could be caused by the fact that more individuals are situated near the median, as was also shown in 4.1.1, thus resulting in lower variance and smaller differences. Another possible factor causing these opposite results is that there might be a difference in only one part of the distribution, below the median. This is confirmed by running two regressions, one for the deviation from the median < 0, and one for that deviation > 0. For the first regression the risk aversion has a negative influence on the absolute deviation (t = -1.35), while for the second regression the results are less significant (t = -1.00). Although not mentioned in the

hypothesis, this does show that differences might vary depending on the side of the distribution an individual is on.

The last case to look at is that when hypothesis 1 does not hold. In this occurrence the deviations from the average and median from the whole sample can be used, instead of that from the subsample an individual is in. The reports of these regressions are shown in table 11. The results of this regression are more or less in line with earlier results. The deviation from the average is significant, but the deviation from the median of wealth is insignificant, although the signs are as expected the by theory and hypotheses this time, contrary to those found earlier and reported in table 10.

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Table 11

Regression results for logarithmic transformation of the absolute deviation from average and median wealth on risk measures and control variables under assumption that hypothesis 1 does not hold, including control variables, excluding wealth of 0 and excluding hypothetical

payoffs.

dependent variable: log of absolute deviation

log wealth

deviation from average deviation from median

value \ risk measure nosafe pow exp nosafe pow exp

estimated coefficient -0.46367 -0.1424 -3.208 -0.01523 -0.04505 -0.9953

t-stat coefficient -2.02** -1.96** -1.99** -0.46 -0.43 -0.43

adjusted R-squared 0.0085 0.0081 0.0083 0.0965 0.0964 0.0964

sign as expected? yes yes yes yes yes yes By ordering all reported values for wealth and creating a dummy variable that is 1 when an individual’s reported wealth is either in the top or bottom 20% of the wealth distribution and regressing that on risk measures and control variables the findings might become more robust. Although having low explanatory power these results are in line with the hypothesis, reporting a z-value of -0.51 and a coefficient of -0.02379 for the number of safe choices. This indicates that the probability of an individual being in the tails is higher for people with a lower degree of risk aversion.

Concluding this paragraph, no real proof has been given for the hypothesis in a clear meaningful way. The majority of the results point to the direction that, despite whether hypothesis 1 holds or not, there is a negative relationship between risk aversion and the deviation from the median and average wealth in the population. For all measures of wealth the deviation from the average has proven to be significantly influenced (on the 5% level) by the level of risk aversion, but for the median this result is less clear. Running the alternative logit regression also gives some support to the hypothesis that risk averse people are less likely to be found in the tail of the wealth distribution, but this is also not on a significant level. 4.2.3 Robustness checks using entrepreneurship

The case of the entrepreneur is again a meaningful way to give more power to earlier literature. As mentioned in section 2.2 risk aversion has proven to be of big influence on the choice to become an entrepreneur. It can be assumed that entrepreneurs are more risk seeking, as starting a business is a gamble and gives uncertainty, especially in the first years. This means that under the assumption that entrepreneurs are more risk seeking, hypotheses 1 and 2 should hold when replacing the risk measure by an entrepreneurship dummy.

Although it might be expected that the decision to become an entrepreneur is strongly influenced by the amount of wealth an individual possesses, Hurst and Lusardi (2004) find

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