The Effect Of An Unexpected Wealth Shock On Willingness To Takes Risks

Graduate School

Master Thesis

The Effect Of An Unexpected Wealth Shock On Willingness To Takes Risks

Erik Haglund Johansson Tim Straßburger Supervisor: Conny Wollbrant

June 15, 2017

Abstract

In this thesis we investigate how an exogenous wealth shock in the form of an

unexpected inheritance or gift affects individuals’ self-reported willingness to take

risks. We apply a quasi fixed effects ordered probit model using the large panel data

set from the German Socio-economic Panel (SOEP), which enables us to control

for observed and unobserved individual characteristics. Our results suggest that an

unexpected wealth shock affects willingness to take risks negatively. Furthermore,

these findings contradict the assumption of constant relative risk aversion.

Contents

1 Introduction 2

2 Literature Review 4

3 Theoretical Background 6

4 Data 8

4.1 Variables . . . . 9

4.1.1 Dependent Variable . . . . 9

4.1.2 Independent Variables . . . . 10

4.1.3 Control Variables . . . . 11

4.2 Descriptive Statistics . . . . 12

5 Identification Strategy 14 5.1 Econometric Framework . . . . 14

5.2 External Validity . . . . 16

5.2.1 Risk measure . . . . 17

5.2.2 Windfall . . . . 17

6 Results 19 6.1 Non-linear Estimation . . . . 19

6.2 Linear Estimation . . . . 21

6.3 Investigating Income Groups . . . . 23

6.4 Further Robustness Checks . . . . 24

7 Discussion and Conclusion 25

A Appendix 29

1 Introduction

Economic decision making often contains risk and uncertainty, meaning that outcomes of decisions are unknown. ¹ Different decisions come with different levels of risk. Usually higher risks, which implicates a higher probability of an unwanted outcome, will be rewarded with a higher expected value. Risk preferences describe how much risk an individual is willing to take under certain circumstances. Knowledge about people’s risk preferences is important to predict economic behavior and to implement correct policies.

As a simple example, insurances need to know which group of people are risk-averse so they can implement insurances for them.

This thesis extends the literature that studies changes in people’s willingness to take risks with increasing wealth. Particularly, we exploit panel data to study the effect of an unexpected monetary inheritance or gift on self reported risk attitudes. We implement the unexpected windfall as a significant exogenous wealth shock to overcome the common problem of reversed causality. As argued by Dohmen et al. (2011), a high level of wealth could affect the willingness to take risks, but at the same time risk behavior and decisions can be the reason for higher accumulated wealth.

One can account for this issue by constructing controlled lab experiments. However, these experiments often suffer from small sample sizes and low monetary rewards. We benefit from using real life behavior by a large representative population and a significant change in wealth. Self reported risk is an easy to implement risk measure which allows for a large sample size, but despite simplicity proven to be a valid measure for risk taking behavior in various fields like finances, traffic or health. Inheritances (and connected gifts) are for many people the largest wealth increase during their life time. The panel structure of our data allows us to use an econometric framework that exploits within individual changes and by this controls for unobserved heterogeneity. Existing panel data studies on risk, analyses portfolio compositions and so only sample a fraction of

1 When economists speak about risk, the probabilities of outcomes are known, while uncertainty

means that the probabilities are unknown. For simplicity reasons we do not distinct between risk and

uncertainty in this thesis.

the whole population (e.g Sousa 2007; Chiappori and Paiella 2011; Brunnermeier and Nagel 2008. We therefore contribute by deploying a far different approach which allows us to study a large representative sample in which a large group is exposed to a non- hypothetical exogenous wealth shock, where we apply panel-data methods to observe within individual changes and therefore control for unobserved heterogeneity.

It is an ongoing discussion of how risk preferences are formed. Often economic models assume risk preferences to be a given personality trait that is stable over a lifetime. In the expected utility theory, risk preferences are described through the difference between expected value and expected utility of uncertain outcomes. Since one cannot observe the utility function, it remains unclear if a change in observed willingness to take risks implies a change of the utility function. However, our analysis can be helpful to test for properties of an utility function that describes real life behavior of decisions under risk.

The general risk question has explanatory power for choices in financial lotteries (Dohmen et al. 2011). This enables us to test for the widely made assumption that an individual’s risk preferences can be described by an isoelastic utility function which implies constant relative risk aversion (CRRA). (Chiappori and Paiella 2011).

We use data from the German Socio-Economic Panel (SOEP) which include a broad range of variables on both individual and household level. Containing a large sample size, it is composed to be a representative sample of the German population. Our dependent variable is the self-reported ”willingness to take risks”, where participants indicate their general willingness to take risks on a zero to ten scale. This variable has been included in the SOEP data-set from 2004 and onward. For every year in which the risk question was asked we have additional information of inheritances and gifts received by the household, which we match to the individuals.

In order to confirm the hypothesis, that an individual’s behavior can be described by

an isoelastic utility function with constant relative risk aversion, we would expect our

risk measure to increase after a positive wealth shock. Our results suggest that a positive

wealth shock has a negative impact on willingness to take risks. Applying a quasi fixed

effect ordered probit model we find a significant decrease in self reported risk attitudes

after receiving an unexpected inheritance or gift. We include controls for observable socio-demographics and control for unobservable heterogeneity. These findings are robust to different types of model specifications (linear or non-linear, (quasi) fixed or random effects) and we therefore reject the hypothesis of CRRA utility. We can furthermore confirm findings of studies that suggest decreasing risk taking with increasing age and decreasing health statuses, as well as a higher level of risk aversion for females.

The structure of the thesis is as follows: Section 2 presents a literature review of related studies. Section 3 develops the theoretical background of relative risk aversion and how our method is a convenient tool to make inferences in this framework. In section 4 we present our data, discuss our main variables and present descriptive statistics. Section 5 describes the identification strategy and discusses external validation. Results are presented in section 6 and discussed in section 7.

2 Literature Review

In this part we review close related literature that either uses a similar risk measure, exploits panel data to test for CRRA or focus on inheritances as a unexpected wealth shock.

The study by Jung and Treibich (2015) investigates the matter of time variant self

reported risk attitudes using Japanese panel data collected by the University of Osaka,

Ritsumeikan University and Waseda University. The dataset contains eight waves for

the years 2003 to 2010. The results of a correlated random effects regression suggest

that there is a time-variant part in individuals’ self stated risk attributes. As a further

implication of these results, they stress out the importance of measuring several points

of risk aversion and not only once as a baseline measure. The general willingness to

take risks measure from the SOEP-dataset has been used by Schurer (2015) with the

purpose of examining changes in risk aversion over the life-cycle. Findings suggest that

controlling for age cohorts, risk tolerance is affected negatively with increasing age until

middle-age, where only lower socio-economic status individuals continue having a negative

relationship with age.

A paper by Sahm (2012) uses American panel data from the Health and Retirement study for the years 1992 to 2002 in order to examine variation in risk tolerance over time, as well as differences between individuals. In order to derive a risk measurement, she uses a hypothetical gamble question on lifetime income, where the respondents are asked to indicate their preferences over different save and a risky income flows. The results suggest that there is a small negative change in risk tolerance by age and a small positive effect on risk tolerance when macroeconomic conditions are improved. However, no significant results are found regarding how wealth and income shocks are affecting willingness to take risks.

A bunch of literature investigates risk attitudes by studying portfolio compositions, where the principle is to examine how the proportion of risky to non-risky assets change with increasing wealth. These studies often directly test for constant relative risk aver- sion. Sousa (2007) uses macroeconomic U.S. quarterly data on Flow of Funds Accounts provided by Federal Reserve System for the years 1953 to 2004 and unexpected variations in housing prices to indicate wealth changes. He concludes that risky assets allocations are significantly and positively correlated with wealth shocks. He concludes that prefer- ences with habit-formation or wealth- dependent utility functions are better fitting than preferences with the assumption of constant relative risk aversion.

Chiappori and Paiella (2011) exploit panel data from the Survey of Household Income

and Wealth, an Italian household survey. They use eight waves covering the years of 1989

to 2004. They test for CRRA in individual’s portfolio compositions with a regression in

first differences. The regression estimates a small and statistically insignificant elasticity

of the risky asset share to total wealth and CRRA property is not rejected. Furthermore,

they find a small but significant negative correlation between wealth and risk aversion in

cross sectional regressions. Their findings are consistent to a similar study by Brunner-

meier and Nagel (2008) on U.S. data from the Panel Study of Income Dynamics for six

waves between 1984 and 2003. Their results also suggest that relative risk aversion is not

varying with changes in wealth.

The use of an unexpected inheritance as an exogenous source of wealth shock has been central to several studies. One example is Andersen and Nielsen (2011), who use inheritances in due to the death of an individual’s parents as a natural experiment for stock market participation. They argue about the importance of having a true unex- pected windfall in order to be able to draw causal inference. In order to be certain that the inheritance is unexpected, they make sure that all included inheritances are due to unexpected and sudden deaths. Thy find a positive effect of an unexpected windfall on stock market participation.

The existing literature generally agrees that risk tolerances have a time varying com- ponent. Yet, there is no common census of how increasing wealth affects willingness to take risks and if risk preferences with constant relative risk aversion are realistic. The objective of this study is to add new knowledge to this field by applying a measure of risk which samples a more representative general population and a wealth increase that is exogenous.

3 Theoretical Background

Partly because of reasonable intuition, but also partly because of subsequent easy math-

ematical implications, theoretical models as well as empirical studies often assume a

utility function with constant relative risk aversion (CRRA), as discussed by Chiappori

and Paiella (2011). The concept of CRRA is part of the theoretical framework of the

expected utility theory (EUT), which is due and despite its simplicity popular when it

comes to modeling risk preferences. The EUT states that in situations which require

decisions with an uncertain outcome, an individual does not decide according to the ex-

pected value (e.g. money in financial decisions or life years in medical decisions) of the

possible outcomes, but rather to the expected utility of these outcomes. The relation-

ship between expected value and expected utility of uncertain outcomes defines ones risk

preferences. Diversity between individual risk preferences are described through different

individual shapes of the utility function, which can imply risk averse, risk neutral or risk

seeking behavior. Since a common finding suggests that people are in average risk averse, literature often talk about the degree of risk aversion when referring to risk attitudes, even when the observed behavior is risk seeking.

Arrow (1965) and Pratt (1964) developed a measure of an agent’s risk aversion, de- pending on his or her utility function. The Arrow-Pratt-Measure of relative risk aversion is defined as follows:

RRA(x) := − u ⁰⁰ (x)

u ⁰ (x) ∗ x (1)

This corresponds to the marginal utility of the outcome. It shows the change of risk aversion if the outcome variable x changes. The higher the coefficient of RRA, the higher the degree of risk aversion. If the relative risk aversion is constant, changes in x do not affect the coefficient of relative risk aversion. A linear relative risk aversion implies increasing/decreasing aversion with change in the outcome variable. The derivate of relative risk aversion RRA ⁰ (x) gives information about the sign of change.

Often implications of constant, increasing or decreasing relative risk aversion are pre- sented in a scenario where an individual invests its wealth in a portfolio only with one risky and one risk-free asset. Decreasing relative risk aversion implies that with increasing wealth the share of the total amount that is invested in the risky asset increases. Increas- ing relative risk aversion would result in investing a smaller share in the risky asset, while constant absolute risk aversion would not affect the share spent in the risky asset.

As stated before, theoretical models as well as empirical studies often assume a utility function with constant relative risk aversion. The isoelastic utility function u(x) = ^x _1−γ

exhibits these properties (Ljungqvist and Sargent 2012).

Dohmen et al. (2005) show that the general self reported risk measurement is a valid

predictor of investment choice experiments by analyzing the same dataset as in this

thesis. By making use of an investment choice question asked in the SOEP in 2004,

where participants were asked what fraction of a hypothetical lottery win they would

invest in a risky asset, the authors show a significant correlation between the two risk

measurements. Furthermore, they show how this information makes it possible to derive

coefficients of CRRA from the general self stated risk attitudes. They match each answer

to the general risk question to the average amount invested in the risky asset. Together with information about an individual’s endowment in wealth, they are equipped with the necessary input to calculate the CRRA parameter. Holding the wealth level constant, stating a higher willingness to take risks goes along with a CRRA coefficient decrease.

Holding risk taking constant, a higher wealth level results in a larger CRRA coefficient.

(Dohmen et al. 2011).

This relationship allows us to test the hypothesis of CRRA utility by applying panel analyses on the self reported risk measure. Assuming that the wealth shock through in- heritance or gift is a notable change in an individual’s wealth, we would expect individuals to report higher risk attitudes after the wealth shock as a necessary condition to support CRRA utility. Reporting the same or lower risk attitudes after a wealth increase would imply that individuals have a higher CRRA parameter than before. This would be a violation of CRRA, suggesting to reject the hypothesis that individuals can be described by a isolelastic utility function that implies constant relative risk aversion.

4 Data

The data used is gathered from the German Socio-Economic Panel (SOEP), which is representative of the German population. It is one of the longest term and most complete data-sets available to model risk taking processes using within-person data (Josef et al.

2016). The survey is household-based, re-interviewing adult household members annually.

The data-set is based on a large sample, starting with 12290 sampled individuals in 1984 and currently containing 27183 individuals. The questionnaire gathers information on finances, occupation and many other subjects on individual and household level. It also includes questions on various subjective measures such as life satisfaction and health.

The high variety of questions asked in the survey allows us to expand our model with

the necessary controls. The next section presents our key- and control variables.

4.1 Variables

4.1.1 Dependent Variable

In 2004, the SOEP questionnaire began including questions regarding willingness to take risks. One measure constantly included until 2015 (with exceptions of 2005 and 2007) asks about ”willingness to take risks, in general” on an 11-point scale. The exact question is shown in Figure 1.

Figure 1: Risk measure

The simplicity of the measure made it easy to implement the question into the ques- tionnaire. As a consequence, the data on the self reported general willingness to take risks is consistent over 11 years (with 9 actual measuring points) and answered constantly by over 20000 individuals in all years. This provides us with a large sample size. The same self reported risk measure is used by Dohmen et al. (2011), validating that the simple measurement significantly is a good predicator for actual risk taking. In some years, even more context specific data about risk attitudes was gathered in the SOEP. In 2004, 2009 and 2011 individuals were asked about their willingness to take risks while driving, in financial matters, leisure and sports, in occupation, health and in trusting other people.

Dohmen et al. (2011) show that the general risk question is able to predict behavior in all these contexts while a standard lottery measure does not.

All these properties leave us confident that the general willingness to take risks ques-

tion serves as a sufficient dependent variable for our purposes.

4.1.2 Independent Variables

Our main independent variable is a windfall of wealth; more specific we elicit the windfall through an inheritance or gift. For every year where the questionnaire asks for general risk attitudes, questions regarding received inheritances and gifts are included. Figure 2 displays the inheritance question. (The question regarding a gift is stated exactly the same.)

Figure 2: Question about inheritance

The questions are included in the household questionnaire and ask if one of the house-

hold members received a large sum of money or other assets as an inheritance/gift during

the last calendar year and if so what the monetary value was. Since inheritances/gifts are

collected on household level we cannot distinguish which exact household member actu-

ally received the inheritance/gift. This is of course no problem in a one-person household,

for bigger households we match the inheritance/gift to the head and the spouse of the

head of household. We argue that married/together living couples likely have a shared

economy and are affected by a windfall of the other person in a similar way. Our ex-

planatory variable is an indicator, meaning that the variable indicates if a windfall for an

individual occurred. The variable has the value 1 for every year after the windfall (includ-

ing the windfall year itself), and 0 otherwise. In order to distinguish between two types

of windfalls, expected and unexpected, we are matching the individuals who received an

inheritance with their expectation of a substantial inheritance or gift. We make use of a

question regarding expectations which was included in the 2001 wave (Figure 3).

Figure 3: Question about expectation of a windfall

We consider an later received inheritance or gift as expected when the individual answered with ”Yes, that is certain” or ”Yes, probably”. Since there is no data of risk attitudes available for the years before 2004, we exclude the individuals who in- herited/received a gift between 2001 and 2004, since these individuals might have a non-observable already adjusted willingness to take risks.

4.1.3 Control Variables

In our specification we add a number of variables, controlling for what could possibly affect the self reported level of risk. Firstly, we suspect gender to affect willingness to take risks, where females often are found to be more risk averse than men are (e.g. Croson and Gneezy (2009)). Furthermore, level of risk is also found to be dependent on age, e.g.

in Dohmen et al. (2011), where risk aversion is increasing with age. Our dataset has a rich set of socio-economic variables, which could be determinants of level of risk and thus useful to control for. For example, Hanewald and Kluge (2014) find that household composition and relationship status is affecting the same risk measure as we use. We also suspect job marked participation to affect willingness to take risks. We control for income by using household net income as a variable. Since income is skewed over our sample, we choose to use the logarithm of income in order to correct for the skewness.

Another control which we include in our models is the case of the death of a close family

member, which is likely correlated with an inheritance. In conclusion the true channel of

how an inheritance affects willingness to take risks could be the loss of a family member,

rather than a wealth shock. In order to address this problem, the data set allows us to

control for a parent’s death. In addition, since individual level of risks could be affected by time specific events or conditions such as financial crises. We include year fixed effects to control for these possible unobserved variations over time. Furthermore, it is likely that due to the history and size of Germany we observe regional differences. We control for regional differences by including dummies for every German state.

4.2 Descriptive Statistics

Taking all these factors in consideration, we are left with an (unbalanced) dataset with in total 232715 observations of self reported risk for the years 2004, 2006 and 2008 to 2015.

The mean risk level is 4.563 with a standard deviation of 2.371, supporting general risk aversion. Table 1 shows the distribution of answers to the general risk question.

Table 1: Distribution of General Willingness to Take Risk

Risk 0 1 2 3 4 5 6 7 8 9 10 Total

N 13,260 11,786 24,994 30,845 23,398 48,677 25,856 27,310 18,450 4,804 3,335 232,715

% 5.70 5.06 10.74 13.25 10.05 20.92 11.11 11.74 7.93 2.06 1.43 100

Cum. % 5.70 10.76 21.50 34.76 44.81 65.73 76.84 88.57 96.50 98.57 100

In table 2, we further investigate our risk measurement. For each year, we present

the percentage of individuals who states higher or lower risk attitudes compared their

previous answer. In line with Jung and Treibich (2015), we only account for changes

larger than two steps from the previous observed level of risk in order to minimize possible

measurement error from the respondents. Additionally, we report mean risk and total

number of observations for each year. We observe that each year around 30 to 40 percent

of all individuals adjust their statement on the willingness to take risks question. We are

therefore confident that the data shows enough variation for the following analyses. We

also see significant differences of mean risk aversion between the years, probably due to

different macroeconomic events occurring, such as financial crises. Noticeable is the much

lower mean risk for the year 2009. While the second lowest year is 2004 with a mean of

4.41 on the 1 to 10 scale, we have an average risk of only 3.74 in 2009. It supports to

include year fixed effects in our regressions.

Table 2: Changes of General Willingness to Take Risk

% 2004 2006 2008 2009 2010 2011 2012 2013 2014 2015

Share of individuals

with lower risk 15.4 26.5 28.9 10.4 12.8 13.6 19.0 18.9 16.7

with higher risk 21.4 16.6 12.4 20.2 16.6 19.2 12.8 22.0 18.5

Mean 4.41 4.77 4.45 3.74 4.43 4.53 4.86 4.52 4.77 4.87

#Observations 20993 21453 18980 20107 26062 20515 27432 23602 26847 26724

In table 3 we present further information of our windfall variable. In total we have 4,737 cases of inheritances with a mean of 62710.3 Euro and 4,997 cases of gifts with a mean of 27659.7 Euro. Taking the in 2001 asked question about expectation of future inheritances or gifts into account, we can state that (at least) 2,470 of these windfalls were unexpected. Unexpected windfalls have a lower mean of 33097.28. Since our main dependent variable is an indicator variable that takes the value 1 if a windfall occurred for every year after the windfall, we do not take multiple windfalls from one individual into account. Therefore it is of interest how many ”first” windfalls our sample experiences.

Thus, our variable switches from 0 to 1 in 1,856 cases, where the mean is 34758.21 Euro.

Table 3: Cases of Windfall

Pooled Unexpected

N Mean Median N Mean Median

Inheritance 4,737 62710.3 20000 1,349 47453.95 18000 First 3,436 64092.02 20000 1,151 47284.82 15000

Gift 4,997 27650.7 5000 1,121 18648.55 5000

First 2,706 28989.19 5000 705 20101.97 5000 Windfall 9,652 43429.87 10000 2,470 33097.28 10000

First 6,142 46831.95 10000 1,856 34758.21 10000

Table 4, shows the distributions of expectations of inheritances of gifts in the future.

These are the answers to the question in figure 3. We can observe that with 13,452

individuals (63.55%), it is a majority stating that they not expect to receive an inheritance

or a gift in the future. We further consider an answer of ”do not know” as an indicator that the individual is not expecting an inheritance or gift in the future.

Table 4: Expectations of Windfall

N %

Yes 1,131 5.34

Yes, Probably 1,956 9.24

No 13,452 63.55

Do Not Know 4,628 21.86

5 Identification Strategy

5.1 Econometric Framework

The longitudinal structure of the data-set allows us to apply an econometric framework that controls for unobserved heterogeneity. Crucial for the choice of model is the assump- tion whether the observed individual characteristics are correlated with the unobserved characteristics or not. If we assume that the unobserved individual characteristics are correlated with observed individual characteristics, the conventional approach is an OLS estimation with individual fixed effects, otherwise a random effects model would be prefer- able (Greene 2011). In the fixed effects model we basically estimate a constant for every individual and capture the average within variation. By this we control for all possible time independent variables. Our individual fixed effects regression model is:

Risk∗ _it = β ₀ + β ₁ · W indf all _it + X _it ⁰ · γ + α _i + µ _t + µ _s + ε _it (2)

where Risk∗ _i,t is the risk attitude of individual i at time t. The first variable W indf all _i,t

is an windfall indicator consisting of unexpected inheritances and gifts, which equals zero

when the individual did not get any windfall until this point and equals one for the year

of windfall and every year afterwards. It measures the average within individual effect of

an unexpected windfall on willingness to take risks. The vector of control variables X _it ⁰

includes time variant variables. We control for health statuses, number of children living in the household, martial status, household size, labor status, household income, parent death and years of education. Time invariant effects are captured by the individual fixed effects α _i . So α _i is a constant for each individual α ₁ , α ₂ ,..., α _N . µ _t and µ _s capture year and state fixed effects, respectively. Although we think that the assumption of correlation between observed and unobserved characteristics is reasonable, we will estimate a random effects model as a robustness check.

However, using a linear model might yield problems due to the nature of our dependent variable. The self reported willingness to take risks is ordinal, reported on a 11-point scale ranging from 0 to 10. A linear regression assumes cardinality of our dependent variable.

In our case this means that it treats the difference between answering 5 and 6 the same as that between 9 and 10. Since the different points on the scale de facto only represent a ranking, this assumption is violated. (Greene 2011)

In order to account for the ordinal discrete nature of the variable, an econometric model based on an ordered probit approach can be used (Akay and Martinsson 2009).

The nonlinear nature of the ordered probit model implies the use of a maximum likelihood method. In the MLE, individual fixed effects may not be consistent due to the inciden- tal parameters problem, as shown by Neyman and Scott (1948). Therefore, we apply a quasi-fixed effects ordered probit model instead. This so called correlated random-effects model was suggested by Chamberlain (1984) and uses an auxiliary distribution for the unobserved individual characteristics. Similar to the fixed effects model it allows corre- lation between observed and unobserved individual characteristics. Different though we do not include a control for each individual, yet here the α _i is specified as α _i = x ⁰ _i φ + v _i where x is the within-mean of the time-variant variables and v _i becomes the normally distributed unobserved individual effects. (Akay and Martinsson 2009)

The model estimated then is:

Risk∗ _it = β ₀ + β ₁ · W indf all _it + X _it ⁰ · γ + x ⁰ _i φ + v _i + µ _t + µ _s + ε _it (3)

Risk attitudes of every individual i at time t Risk _it ∗ itself is latent, meaning it is

unobservable. However, we can observe the self reported risk attitudes Risk it of every

individual and when it crosses a threshold. Since we have in total 11 possible outcomes, we have 10 thresholds that can be crossed (µ ₀ , µ ₁ ,..., µ ₉ ). The definition of our observed self reported risk attitudes Risk _it becomes:

Risk _it = 0 if Risk∗ _it ≤ µ ₀ Risk _it = 1 if µ ₀ <Risk∗ _it ≤ µ ₁ Risk _it = 2 if µ ₁ <Risk∗ _it ≤ µ ₂

.. .

Risk _it = 10 if Risk ∗ _it >µ ₉

(4)

The probability of stating one of the 11 risk attitudes j for an individual i at time t then is (Φ is the standard normal distribution function) (Greene 2011)

P r(Risk _it = j) = Φ(µ _j − β ₀ − β ₁ · W indf all _it − X _it ⁰ · γ − x ⁰ _i φ − v _i − µ _t − µ _s )

−Φ(µ _j−1 − β ₀ − β ₁ · W indf all _it − X _it ⁰ · γ − x ⁰ _i φ − v _i − µ _t − µ _s ) (5)

Since the quasi fixed effects ordered probit model accounts for most of the character- istics of the underlying data, our focus will be on this model. We will include a random effects ordered probit for comparison. As stated before we estimate the linear fixed effects and random effects as well.

5.2 External Validity

In this section we discuss benefits and drawbacks of our approach and data. It will

elucidate to what extent our results can contribute to identify a causal effect of wealth on

people’s real willingness to take risks. Therefore, we elaborate validity of the self reported

risk measure in the SOEP to realistically represent individuals ”true” risk behavior and

we discuss the validity and exogeneity of our wealth shock.

5.2.1 Risk measure

The simplicity of the general willingness to take risk question from the SOEP results in a large sample measured over nine points in time. This is a big benefit compared to experimental data, where the complexity of conducting experiments results in much smaller samples Hardeweg et al. (2013). The consistency of the same measurement over a long time span and the large sample from the SOEP gives us a valuable opportunity to use extensive panel data methods and thus minimize omitted variable bias. The most important question is how well the self-reported measure of willingness to take risks can portray the subjects’ true risk-behavior. In purpose to examine this question, Dohmen et al. (2011) investigates the SOEP-dataset on this general risk question. Compared to context-based questions on risk, the general risk measure is the only one which is able to predict all tested risky behaviors such as portfolio choice, occupational choice or smoking, concluding that this measure is the best ”all-round” measurement. The general risk question is furthermore validated by experiments conducted on a representative group of 450 individuals, confirming that the general risk attitude can predict actual lottery behavior well. Supplementary Hardeweg et al. (2013) confirm these findings in a similar study with more than 900 respondents in rural Thailand and conclude that the simple self indicated risk attitude is a useful measure.

The correlation found between self assessed risk and objective measures, validates that individuals know and state their risk attitudes correctly. Despite the positive validation, the subjectivity of the measure bears possible limitations. Comparisons between subjects are limited. However, since we apply a within subject variation approach, this limitation does not affect us.

5.2.2 Windfall

Although our research questions the relationship between wealth and willingness to take

risks, we prefer a wealth shock rather than (total) wealth or income as our explanatory

variable. A true wealth shock is not influenced by the individual. If we were to use total

wealth or income as our main independent variable, we would have large issues regarding

reverse causality, not knowing if the income itself is affecting the risk or if the risk is affecting the income.

We identified inheritances and gifts as a valid exogenous shock. A change in the will- ingness to take risks can very unlikely influence the probability of getting an inheritance or gift. In addition we focus on unexpected windfalls, which guarantees that individuals do not include the future income flow into their current wealth. A good wealth shock should of course also have a sufficient number of cases. We identified 1,856 cases of (first) unexpected windfalls, which we confidently consider as satisfactory.

In order to draw conclusions that are not only about a wealth shock, we need to assume that our wealth shock is a significant increase of total wealth. As shown in table 5, the mean value of an unexpected windfall is 34758.21 Euro. To unexpectedly receive this large amount of money very likely has an impact on the average individual. Although we are confident that this shock is a sufficient indicator for a wealth increase for most individuals, it is not a perfect measure. Not knowing the initial wealth makes it not possible to control for this issue.

A possible limitation using an unexpected inheritance as a wealth shock is that for many cases it is caused by the death of a near relative of the recipient. The issue is that the death itself could affect the willingness to take risks of the recipient. As it is important to ensure that the possible change in risk taking of the individual is driven by the windfall of money, and not by the death of parents, we control for the cases of parents’ death in the regressions and minimize this issue to some extent.

We are faced with one more problem, since the SOEP data-set has only one year

in which individuals were asked if they expect an inheritance or gift in the future. We

therefore have missing information on expectations for individuals that were not part of

the 2001 wave of the panel. Therefore, we might miss out some unexpected windfalls and

by not assigning them to the not treated group, we might underestimate the effect of an

unexpected windfall.

6 Results

Table 5 and 6 show our main regression results, where the columns in table 5 include the results from the non-linear models: random effects ordered probit and quasi fixed effects ordered probit. The columns in table 6 display estimations of the linear random effects and fixed effects. For all specifications and for all variables we present the estimated coefficients and standard errors clustered at individual level. Recall that the dependent variable for all models is the self reported general willingness to take risks, spanning between zero and ten, where zero is defined as ”not at all willing to take risks” and ten is ”very willing to take risks”. The linear models in table 6 have the advantage that the coefficients can be interpreted as marginal effects. Since the specifications in table 5 are non-linear, we can only comment on the sign and size of the coefficient.

In order to test for correlation between observed and unobserved characteristics, we run a Hausman test both for the linear and non-linear models. Since the null hypothesis of no correlation is rejected for both tests, we do not know if the random effects models are consistent and/or efficient. The fixed effects models are always consistent and therefore the Hausman tests suggest that the (quasi) fixed effects models are the most suitable for our case.

6.1 Non-linear Estimation

We start by commenting table 5 which includes the ordered probit regressions. Firstly investigating our main independent variable, the unexpected windfall, we can observe that the coefficient is negative and significant at a 1%-level for the random effects model.

Controlling for the panel average of the time-variant variables in the quasi fixed effects

model yields similar results with the difference of a slightly smaller magnitude. It is also

less significant. Our dependent variable is defined as increasing in willingness to take

risks and thus the interpretation of the negative coefficients for the unexpected windfall

is that in the years after the wealth shock, the self reported level of risk is lower compared

to the years before the windfall.

Investigating the logarithm of household net income yields opposite results compared to the unexpected wealth shock. For the two models, the household income has a positive sign, significant to a 1%-level in both the random effects model and in the quasi fixed effects model.

Other control variables of interest are firstly the case of a parent’s death, which has a

negative value for both specifications, however not significant for any of them, suggesting

that the effect on risk is through the wealth shock and not caused by the death of a

parent. Age is highly significant at 1%-level for both specifications with a negative sign,

so that willingness to take risks decreases with age, which is consistent with many other

studies. Furthermore, the variable female is negative and highly significant for both

specifications, meaning that females have a lower willingness to take risks, confirming

what several other studies have found on differences in risk taking behavior between

genders. Number of years of education affects the willingness to take risks, for both

specifications the coefficient is highly significant at 1%-level, however in the random

effects model we can observe a positive effect, whereas in the quasi fixed effects model we

can see a negative effect.

Table 5: Ordered Probit Regressions

Random Effects Quasi Fixed Effects

General Willingness to Take Risks β ˆ se β ˆ se

Unexpected Windfall -0.0635 0.0207 ^∗∗∗ -0.0419 0.0245 ^∗ Controls

Age -0.0147 0.000483 ^∗∗∗ -0.0313 0.00236 ^∗∗∗

Female -0.539 0.0109 ^∗∗∗ -0.528 0.0110 ^∗∗∗

log HH Income 0.104 0.00928 ^∗∗∗ 0.0330 0.0122 ^∗∗∗

Years of Education 0.0138 0.00208 ^∗∗∗ -0.0270 0.00604 ^∗∗∗

Household Size -0.0209 0.00552 ^∗∗∗ -0.00912 0.00735

Parents Death -0.0140 0.0190 -0.0190 0.0197

One Child -0.0187 0.0120 -0.0278 0.0152 ^∗

Two Children -0.0297 0.0159 ^∗ -0.0385 0.0213 ^∗

Three Or More Children 0.00449 0.0238 -0.0542 0.0335

Not In Labor Force -0.0653 0.0120 ^∗∗∗ -0.0138 0.0150

Unemployed 0.00994 0.0162 0.00449 0.0185

In School 0.0190 0.0224 0.0445 0.0261 ^∗

Martial Status Controls (Married omitted)

Single 0.135 0.0143 ^∗∗∗ 0.0999 0.0226 ^∗∗∗

Widowed -0.0546 0.0226 ^∗∗ -0.0258 0.0373

Divorced 0.200 0.0174 ^∗∗∗ 0.0805 0.0275 ^∗∗∗

Separated 0.198 0.0240 ^∗∗∗ 0.113 0.0286 ^∗∗∗

Health Status Controls (Very Good omitted)

Good -0.0456 0.0113 ^∗∗∗ -0.0179 0.0126

Satisfactory -0.118 0.0126 ^∗∗∗ -0.0714 0.0142 ^∗∗∗

Poor -0.208 0.0146 ^∗∗∗ -0.136 0.0166 ^∗∗∗

Bad -0.421 0.0230 ^∗∗∗ -0.298 0.0260 ^∗∗∗

State Fixed Effects Yes Yes

Year Fixed Effects Yes Yes

N 206476 206476

∗

p < 0.10,

p < 0.05,

p < 0.01 Standard errors clustered at individual level

6.2 Linear Estimation

Since our dependent variable is of ordinal scale, our first focus are on the ordered probit

models. However, as discussed by Ferrer-i-Carbonell and Frijters (2004), in reality the

assumption of cardinality is not an extreme assumption having ordinal data with a large

scale. Estimating the linear models function as a robustness check and it is also valuable

to directly observe the marginal effects of the coefficients. Therefore, in this section, we

include linear estimations of the random effects model and since we are not faced with a

incidental parameters problem we are able to apply individual fixed effects.

The overall results are similar to our non-linear estimations. As can be observed in table 6, for an unexpected windfall the linear models yield the same sign on the coefficient as the non-linear models, they are all negative. Also similar is that the magnitude of the coefficients varies between the models, where the fixed effects suggests a smaller impact.

These results are significant at a 1% level for the random effects and to a 10% level for the

fixed effects model. The interpretation of this result is that after an individual receives

an unexpected windfall, on average they answer 0.104 (RE) and 0.0676 (FE) units lower

on the 0 to 10 scale of willingness to take risks. As in the non-linear models, household

income has an opposite effect compared to the unexpected windfall, where a one percent

increase in household income yields on average a 0.0016 increase of risk in the random

effects and a 0.0004 increase of risk in the fixed effects model (significant to 1%-level

(RE) and to 5%-level (FE)). Also gender and age show the same sign in the random

effects model compared to the probit models. Note that gender is dropped out in the

fixed effects model since it is time invariant, as well as age since the collinearity to the

year dummies.

Table 6: Linear Regressions

Random Effects Fixed Effects

General Willingness to Take Risks β ˆ se β ˆ se

Unexpected Windfall -0.104 0.0331 ^∗∗∗ -0.0676 0.0392 ^∗

Controls

Age -0.0227 0.000748 ^∗∗∗

Female -0.847 0.0168 ^∗∗∗

log Household Income 0.164 0.0145 ^∗∗∗ 0.0464 0.0193 ^∗∗

Years of Education 0.0228 0.00329 ^∗∗∗ -0.0433 0.00970 ^∗∗∗

Household Size -0.0322 0.00866 ^∗∗∗ -0.0124 0.0118

Parents Death -0.0202 0.0303 -0.0249 0.0313

One Child -0.0311 0.0189 -0.0460 0.0241 ^∗

Two Child -0.0487 0.0251 ^∗ -0.0670 0.0339 ^∗∗

Three Or More Children 0.000282 0.0374 -0.0911 0.0533 ^∗

Not in Labor Force -0.103 0.0189 ^∗∗∗ -0.0212 0.0237

Unemployed 0.0121 0.0253 0.00796 0.0290

In School 0.0377 0.0355 0.0738 0.0424 ^∗

Martial Status Controls (Married omitted)

Single 0.219 0.0224 ^∗∗∗ 0.163 0.0361 ^∗∗∗

Widowed -0.0768 0.0348 ^∗∗ -0.0330 0.0583

Divorced 0.312 0.0272 ^∗∗∗ 0.130 0.0432 ^∗∗∗

Separated 0.311 0.0377 ^∗∗∗ 0.183 0.0450 ^∗∗∗

Health Status Controls (Very Good omitted)

Good -0.0632 0.0177 ^∗∗∗ -0.0236 0.0199

Satisfactory -0.177 0.0196 ^∗∗∗ -0.108 0.0224 ^∗∗∗

Poor -0.320 0.0227 ^∗∗∗ -0.210 0.0260 ^∗∗∗

Bad -0.641 0.0351 ^∗∗∗ -0.458 0.0400 ^∗∗∗

State Fixed Effects Yes Yes

Year Fixed Effects Yes Yes

N 206476 206476

∗

p < 0.10,

p < 0.05,

p < 0.01 Standard errors clustered at individual level

6.3 Investigating Income Groups

A higher income group is likely to be less affected by a windfall of money than lower

income groups. Table 7 in the appendix shows the results of our favored quasi fixed

effects ordered probit model for different subgroups of household income. Column 1

includes only individuals who have a panel average household income of lower than 2000

Euro, column 2 includes individuals with a panel average household income of 2000-3000

Euro and column 3 contains the subsample with an average household income of 3000

Euro or more.

The regression results support our expectations. The subgroup with the lowest average income is affected most of an unexpected windfall. The highest earning group shows no significant effect. This furthermore underlines that increasing total wealth is the driving force for the adjustment of willingness to take risks after an unexpected inheritance or gift.

6.4 Further Robustness Checks

In this section, we present regression results with adjusted data-sets. We identified two problems that might affect our estimations in coherence with our main independent vari- able.

Inheritances or gifts that are expected might have a similar effect as an unexpected windfall when individuals do not integrate their future income flows into their current wealth. In our main regressions we treated the windfalls that were not indicated as unexpected as if no windfall occurred. Including the group with expected windfalls in the ”baseline” might affect our results. Therefore, we adjust our data-set by excluding all windfalls other than unexpected windfalls from the sample. The results can be observed in table 8 in the appendix.

As discussed earlier, the SOEP dataset has only one year in which individuals where asked if they expect an inheritance or gift in the future. We therefore have missing information on expectations for individuals that were not part of the 2001 wave of the panel. In our previous regressions we might have missed out some unexpected windfalls and by assigning them to the not treated group we might underestimate the effect of an unexpected windfall. Table 9 shows regressions results for a sample with only individuals that answered the expectation question.

The estimations in the adjusted data-sets confirm our main regression results, sug-

gesting that the mentioned limitations of the underlying data is of no concern.

7 Discussion and Conclusion

The results in section 6 show that individuals exhibit a lower grade of willingness to take risks after they received a valuable inheritance or gift. This is a rather interesting finding, considering that wealthier people are in average shown to be more risk taking. In fact, our regressions support that there is indeed a positive correlation between (household) income and risk attitudes. As both variables indicate a wealth increase we would expect a similar effect. The contradicting effects could be explained by the suspected endogeneity problem of income as a wealth measurement. This would imply that the correlation between risk and income is driven by an income increase after individuals adjust their willingness to take risks. As discussed, we do not see the possibility that a change in willingness to take risks could affect the probability of getting an unexpected inheritance or gift. Therefore, we conclude that the effect of wealth on willingness to take risks is negative as suggested by our exogenous wealth shock.

A similar argumentation is applicable when we interpret our results in the framework of constant relative risk aversion. If we look at the income variable, we cannot reject the hypothesis that individuals can be described by a utility function with CRRA. However, as stated in section 3, we would expect an increase in the self reported risk measure after a windfall for CRRA to hold. We therefore reject the hypothesis that a utility function which implies constant relative risk aversion is a good description of individuals utility.

Note that we cannot make statements to the general validity of EUT. The simplicity of the one parameter model of EUT is often criticized when it comes to modeling real life behavior. However, since it is far more complex to test for stability of parameters in a more descriptive multi-parameter model like in prospect theory (Zeisberger et al. 2012), this analysis goes beyond this thesis. ²

It is disputable to what extent our empirical results allow us to make implications and predictions of individuals’ behavior. As discussed in section 5.2.1, the self reported risk measure is a good ”all around” measurement of individuals’ risk behavior and it

2 Concepts of prospect theory as that utility is derived from gains and losses in wealth (rather than

total wealth) and loss aversion in gains are however potential explanations of our findings.

is correlated to risk attitudes in various categories. This could suggest that a negative change in general risk attitudes also implicates lower willingness to take risks in domains like traffic, health or occupation. However, we can not completely unravel the general risk into different subjects, which could imply that a lower general willingness to take risks after a financial shock only is driven by lower willingness to take risks in financial questions.

Although we are convinced of the overall validity of an unexpected inheritance or gift as an exogenous wealth shock, there are still some limitations. One limitation is that we do not know the wealth of the individuals before inheriting. This makes it impossible to create thresholds in order to test for shocks larger than a certain threshold of the individuals’ total wealth. However, instead of including initial wealth, we made an assumption that household net income could reflect the individuals’ wealth level.

Results from these regressions support our expectation that the largest effect of the unexpected windfall is in the subgroup with the lowest average income. It underlines that increasing total wealth is the reason for the adjustment of willingness to take risks after an unexpected inheritance or gift.

The main purpose of this study is to use the benefits of a simple risk measure and

the exogeneity of increasing wealth through an unexpected inheritance or gift in order to

add knowledge about the relationship of willingness to take risks and wealth. For further

research we suggest to extend this method by e.g. including more detailed controls for

background wealth.

References

Akay, Alpaslan and Peter Martinsson (2009). Sundays Are Blue: Aren’t They? The Day- of-the-Week Effect on Subjective Well-Being and Socio-Economic Status. IZA Discus- sion Paper 4563. Institute for the Study of Labor (IZA).

Andersen, Steffen and Kasper Meisner Nielsen (2011). “Participation Constraints in the Stock Market: Evidence from Unexpected Inheritance Due to Sudden Death”. In: The Review of Financial Studies 24.5.

Arrow, Kenneth J (1965). Aspects of the theory of risk-bearing. Helsinki: Yrj¨ o Jahnssonin S¨ a¨ ati¨ o.

Brunnermeier, Markus K. and Stefan Nagel (2008). “Do Wealth Fluctuations Generate Time-Varying Risk Aversion? Micro-Evidence on Individuals’ Asset Allocation”. In:

The American Economic Review 98.3.

Chamberlain, Gary (1984). Panel data. Handbook of Econometrics Vol. 2, edited by Zvi Griliches and Michael Intriligator. Amsterdam: North Holland.

Chiappori, Pierre-Andr´ e and Monica Paiella (2011). “Relative Risk Aversion Is Constant:

Evidence from Panel Data”. In: Journal of the European Economic Association 9.6.

Croson, Rachel and Uri Gneezy (2009). “Gender Differences in Preferences”. In: Journal of Economic Literature 47.2.

Dohmen, Thomas et al. (2005). Individual Risk Attitudes: New Evidence from a Large, Representative, Experimentally-Validated Survey. DIW Discussion Paper 511. Berlin:

German Institute for Economic Research.

— (2011). “Individual Risk Attitudes: Measurement, Determinants, and Behavioral Con- sequences”. In: Journal of the European Economic Association 9.3.

Ferrer-i-Carbonell, Ada and Paul Frijters (2004). “How Important is Methodology for the estimates of the determinants of Happiness?*”. In: The Economic Journal 114.497.

Greene, William H. (2011). Econometric Analysis. 7th Revised edition. Boston: Prentice

Hall.

Hanewald, Katja and Fanny Kluge (2014). The Impact of Family Structure on Risk Atti- tudes and Financial Decisions during the Financial Crisis. Working Paper 2014/03.

ARC Centre of Excellence in Population Ageing Research.

Hardeweg, Bernd, Lukas Menkhoff, and Hermann Waibel (2013). “Experimentally Vali- dated Survey Evidence on Individual Risk Attitudes in Rural Thailand”. In: Economic Development and Cultural Change 61.4.

Josef, Anika K. et al. (2016). “Stability and change in risk-taking propensity across the adult life span”. In: Journal of Personality and Social Psychology 111.3.

Jung, Seeun and Carole Treibich (2015). “Is Self-Reported Risk Aversion Time Variant?”

In: Revue d’´ economie politique 125.4.

Ljungqvist, Lars and Thomas J. Sargent (2012). Recursive Macroeconomic Theory. 3rd Revised edition. Cambridge: Mit Press Ltd.

Neyman, J. and Elizabeth L. Scott (1948). “Consistent Estimates Based on Partially Consistent Observations”. In: Econometrica 16.1.

Pratt, John W. (1964). “Risk Aversion in the Small and in the Large”. In: Econometrica 32.1.

Sahm, Claudia R. (2012). “How Much Does Risk Tolerance Change?” In: The Quarterly Journal of Finance 2.4.

Schurer, Stefanie (2015). “Lifecycle patterns in the socioeconomic gradient of risk prefer- ences”. In: Journal of Economic Behavior & Organization 119.

Sousa, Ricardo M. (2007). Wealth Shocks and Risk Aversion. NIPE Working Paper 28/2007. NIPE - Universidade do Minho.

Zeisberger, Stefan, Dennis Vrecko, and Thomas Langer (2012). “Measuring the time sta-

bility of Prospect Theory preferences”. In: Theory and Decision 72.3.

A Appendix

Table 7: Quasi Fixed Effects Ordered Probit by Income Groups

(1) (2) (3) HHIncome < 2000 2000 ≤ HHIncome < 3000 HHIncome ≥ 3000 General Willingness T o T ak e Risks

ˆ β

se

ˆ β

se

ˆ β

se Unexp ected Windfall -0.0987 0.0523

-0.0701 0.039 5

0.0349 0. 0406 Contr ols Age -0.0396 0.00387

-0.0239 0.0042 5

-0.0256 0.00414

F emale -0.436 0.0185

-0.545 0.0197

-0.612 0.0194

log HH Income 0.0334 0.0214 0.0216 0.021 9 0.0575 0.0204

Y ears of Education -0.0173 0.0125 -0.0376 0.0104

-0.0267 0.00955

Household Size -0.0231 0.0162 -0.0131 0.0132 -0.000583 0.0110 P aren ts Death 0.0114 0.03 87 0.00179 0.0364 -0.0557 0.0300

One Child -0.0256 0.0340 0.00685 0.0272 -0 .0615 0.0224

Tw o Children -0.0204 0.0516 -0.0197 0.0383 -0.0720 0.0311

Three Or More Children -0.0919 0.09 03 0.0174 0.0609 -0.110 0.0467

Not In Lab or F orce -0.0352 0.0245 -0.000704 0.0272 0.00337 0.0256 Unemplo y ed 0.00182 0.0231 0.0284 0.034 1 -0.0328 0.0493 In Sc ho ol 0.0657 0.0434 0.0296 0.0470 0.0254 0.0453 Martial Status Contr ols (Married omitted) Single 0.0558 0.0512 0.0859 0.0371

0.125 0.0358

Wido w ed -0.00706 0.0484 -0.142 0.0673

-0.0470 0.0962 Div orced 0.0664 0.0496 0.0651 0.042 9 0.0912 0.0513

Separated 0.114 0.0543

0.0603 0.0459 0.163 0.0490

He alth Status Contr ols (V ery Go o d omitte d) Go o d -0.0462 0.0269

-0.00622 0.0239 -0.0106 0.0 185 Satisfactory -0.0905 0.0292

-0.0687 0.0265

-0.0634 0.0214

P o or -0.159 0.0320

-0.123 0.0306

-0.133 0.0265

Bad -0.303 0.0411

-0.323 0.0478

-0.276 0.0545

N 65167 64374 76935

p < 0 .10,

p < 0 .05,

p < 0 .01 Standard errors clu stered at individual lev el

Table 8: Ordered Probit Regressions (expected windfalls dropped)

Random Effects Quasi Fixed Effects

General Willingness to Take Risks β ˆ se β ˆ se

Unexpected Windfall -0.0704 0.0215 ^∗∗∗ -0.0519 0.0254 ^∗∗

Controls

Age -0.0145 0.000498 ^∗∗∗ -0.0301 0.00240 ^∗∗∗

Female -0.529 0.0110 ^∗∗∗ -0.520 0.0111 ^∗∗∗

log Household Income 0.107 0.00973 ^∗∗∗ 0.0291 0.0131 ^∗∗

Years Of Education 0.0161 0.00215 ^∗∗∗ -0.0259 0.00678 ^∗∗∗

Household Size -0.0229 0.00573 ^∗∗∗ -0.0107 0.00779

Parents Death -0.00879 0.0205 -0.0135 0.0214

One Child -0.0125 0.0126 -0.0182 0.0163

Two Children -0.0268 0.0165 -0.0305 0.0226

Three Or More Children 0.0175 0.0247 -0.0332 0.0356

Not In Labor Force -0.0739 0.0125 ^∗∗∗ -0.0262 0.0158 ^∗

Unemployed 0.0112 0.0165 0.00336 0.0190

In School 0.0311 0.0243 0.0578 0.0288 ^∗∗

Martial Status Controls (Married omitted)

Single 0.136 0.0149 ^∗∗∗ 0.104 0.0249 ^∗∗∗

Widowed -0.0539 0.0227 ^∗∗ -0.0394 0.0380

Divorced 0.199 0.0177 ^∗∗∗ 0.0766 0.0285 ^∗∗∗

Separated 0.198 0.0248 ^∗∗∗ 0.112 0.0298 ^∗∗∗

Health Status Controls (Very Good omitted)

Good -0.0482 0.0121 ^∗∗∗ -0.0182 0.0137

Satisfactory -0.118 0.0133 ^∗∗∗ -0.0683 0.0154 ^∗∗∗

Poor -0.210 0.0154 ^∗∗∗ -0.135 0.0178 ^∗∗∗

Bad -0.419 0.0235 ^∗∗∗ -0.293 0.0268 ^∗∗∗

State Fixed Effects Yes Yes

Year Fixed Effects Yes Yes

N 187730 187730

∗

p < 0.10,

p < 0.05,

p < 0.01

Standard errors clustered at individual level

Table 9: Ordered Probit Regressions (only 2001 sample)

Random Effects Quasi Fixed Effects

General Willingness to Take Risks β ˆ se β ˆ se

Unexpected Windfall -0.0454 0.0264 ^∗ -0.0428 0.0228 ^∗

Controls

Age -0.0261 0.00429 ^∗∗∗ -0.0156 0.000795 ^∗∗∗

Female -0.486 0.0174 ^∗∗∗ -0.498 0.0172 ^∗∗∗

log Household Income -0.0123 0.0187 0.0738 0.0149 ^∗∗∗

Years of Education -0.0322 0.0125 ^∗∗∗ 0.0365 0.00354 ^∗∗∗

Household Size 0.00176 0.0103 -0.0148 0.00829 ^∗

Parents Death -0.00764 0.0259 -0.00326 0.0254

One Child -0.00632 0.0212 -0.000907 0.0184

Two Children -0.0664 0.0290 ^∗∗ -0.0535 0.0240 ^∗∗

Three Or More Children -0.0709 0.0494 -0.0429 0.0409

Not in Labor Force -0.0171 0.0207 -0.0607 0.0175 ^∗∗∗

Unemployed -0.0102 0.0263 -0.00688 0.0241

In School -0.0174 0.0598 0.0480 0.0522

Martial Status Controls (Married omitted)

Single 0.169 0.0353 ^∗∗∗ 0.0981 0.0237 ^∗∗∗

Widowed -0.0195 0.0451 -0.0440 0.0292

Divorced 0.103 0.0368 ^∗∗∗ 0.162 0.0260 ^∗∗∗

Separated 0.113 0.0388 ^∗∗∗ 0.164 0.0343 ^∗∗∗

Health Status Controls (Very Good omitted)

Good -0.0244 0.0221 -0.0295 0.0210

Satisfactory -0.0594 0.0241 ^∗∗ -0.0842 0.0226 ^∗∗∗

Poor -0.132 0.0267 ^∗∗∗ -0.188 0.0247 ^∗∗∗

Bad -0.302 0.0373 ^∗∗∗ -0.431 0.0341 ^∗∗∗

State Fixed Effects Yes Yes

Year Fixed Effects Yes Yes

N 97128 97128

∗

p < 0.10,

p < 0.05,

p < 0.01

Standard errors clustered at individual level