Influence of gender and education on risk aversion

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Bachelor of Science thesis Econometrics

Influence of gender and

education on risk aversion

In this paper use is made of data of the LISS (Longitudinal Internet Studies

for the Social sciences) panel administered by CentERdata (Tilburg

University, The Netherlands)

Written by: Margot van Moll 6148883

Supervised by: Zhenxing Huang and Jan Tuinstra

June 2014

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Abstract

Economic research often focuses on risk aversion. In this paper the effect of gender and education on three measures of risk aversion is explored via two ways 1) OLS and 2) TSLS. OLS indicates a significant negative correlation between gender and risk aversion by which one can conclude women are more risk averse than men. However, one failed to find significant results of education. The variable education appeared to be endogenous which resulted in a broader research by TSLS. The instruments gender, categorised groups of age and urbanity were used in the TSLS regression. Via TSLS a significant negative correlation between gender and risk aversion was detected again, while one failed to detect a significant result of education on risk aversion.

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Chapter title

Page

Title page _i

Abstract _ii

Table of contents _iii

1 Introduction ₁

1.1 Introduction to research ₁

1.2 Research question and hypotheses ₂

2 Theoretical framework ₃

2.1 Utility and risk aversion ₃

2.2 Determinants gender and education of risk aversion ₅

2.3 Empirical models ₆

2.4 Choice of instrumental variables ₈

3 Participants and methodology ₉

3.1 Participants ₉

3.2 Measurement risk attitudes ₁₀

3.3 Measurement gender, education, age category and urbanity ₁₂

4 Results ₁₃

4.1 Summary of variables ₁₃

4.2 Effect of gender and education on three measures of risk aversion by OLS ₁₄ 4.3 Results from tests for homoscedasticity, multicollinearity, and exogeneity ₁₅

4.4 Instrumental variables ₁₇

4.5 Effect of gender and education on three measures of risk aversion by TSLS ₂₃

5 Conclusion 24

6 Discussion 25

7 Bibliography 26

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1 Introduction

1.1 Introduction to research

A lot of research has focused on risk attitudes and risk aversion. Risk attitudes are characterised by the choices that an individual makes in situations, while exposed to uncertainty. Someone is said to be risk averse if he is trying to reduce uncertainty in these types of situations (Arrow, 1965). In economic research, risk aversion is often linked to economic decision making. By investigating this link, one can understand the effect of risk aversion on economic outcomes.

Several factors influence risk behaviour, or in particular risk aversion. Dohmen et al. (2005) have found that risk attitudes correlate with age and gender. Other research by Sapienza et al. (2008) reported a connection between testosterone levels and risk aversion. In both cases researchers concluded that women are more risk averse than men. Other research has shown that there exists a correlation between education and risk aversion (Dohmen et al, 2005; Hyrshiko et al., 2011; Jung, 2014). In the case of Jung, (2014), this correlation was positive. Hence, it was concluded that he more education a person has enjoyed, the more risk averse a person becomes. Interestingly, Dohmen et al. (2005) concluded the exact opposite, as they found that education reduces risk aversion. Hence, as the existing literature is conflicting, further research is required to conclude if the correlation between schooling and education is positive or negative.

An explanation for these conflicting conclusions could be that there is reversed causality between education and risk aversion. This would imply that education has an effect on risk aversion, but also the other way around: risk aversion has an effect on education. Different problems could arise with the estimation model if this appears to be true (Jung, 2014). In the case of reversed causality, education will appear to be endogenous and the estimates will no longer be consistent (Heij et al., 2004). Hence, in the latter case a significant effect via ‘OLS’ will be difficult to find.

The main aim of this paper is to describe the way education and gender influence one’s risk behaviour. This research will attempt to estimate the effect of education and gender on risk aversion by means of 1) ordinary least squares (‘OLS’) and 2) two staged least squares (‘TSLS’). By testing the variables on exogeneity, one can conclude which of the two is the best according to the theory. Firstly, OLS will be applied, whereby

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education and gender will be regressed on three measures of risk aversion. Subsequently, the research will check for heteroscedasticity, perfect multicollinearity and endogeneity of the regressors. Heteroscedasticity will be tested by means of the Breusch-‐Pagan test, there will be checked for perfect multicollinearity by calculating the variance inflation factors (‘vif’) and finally, exogeneity of the variable education will be tested by means of the Hausman test (Heij et al., 2004). If education appears to be endogenous, different instrumental variables will be taken into account. The exogeneity of the instrumental variables will be checked by means of the Sargan test. Relevance will be checked by looking at the results of the first stage of the TSLS regression. Ultimately, the outcomes of the different tests will be interpreted in order to draw a conclusion about the estimate that is most accurate according to theory.

It is expected that TSLS estimates the effect of education on risk aversion more accurately, as existing literature has found that there exists a reversed causal relationship between education and risk aversion (Jung, 2014). It is therefore expected that education will be endogenous (Heij et al., 2004). In case the correlation is positive, this research will be in line with the research of Jung (2014).

1.2 Research question and hypotheses

As there are conflicting conclusions made in the current literature about risk behavior, the following research question will guide this research:

RQ: How does gender and education influence risk behaviour?

Based on the literature about risk aversion, the following hypotheses are formulated about the relationships between the variables of this study, which are gender, education and risk aversion.

H1: The average person is risk averse

H2: The correlation between gender and risk aversion is negative

H3: The correlation between education and risk aversion is positive

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This paper is structured as followed: first the theory on utility and risk aversion will be explained. Subsequently, the link between the determinants gender, education and risk aversion will be explored. Thereafter, the theoretical estimation model, the choice of instruments and a data analysis will follow. Thenceforth, conclusions will be made in the results and conclusion sections.

2 Theoretical framework

2.1 Utility and risk aversion

Economists often study the characteristics of risk behaviour, as this knowledge is of importance for the prediction of economical choices. One’s risk behaviour can be analysed by means of a utility function. A utility function assigns values to certain decisions. An option or consumption bundle is said to be better, or preferred, if its utility is higher (Jehle & Reny, 2011). In other words, a choice with higher utility is always preferred over one with lower utility. Based on the utility function of a person, one can decide which are the best choices for him. Hence, a utility function can be seen as a device to summarize information contained in a person’s preferences (Jehle & Reny, 2011).

An important property is the Expected Utility property (‘EU’). According to Jehle & Reny (2011, p. 98), EU states that a ‘utility function u: 𝒢 → ℝ has the expected utility property if, for every g ∈ 𝒢,

u(g) = !_!!!𝑝I *u(ai)

where (𝑝1 ∘ 𝑎1, . . , 𝑝𝑛 ∘ 𝑎𝑛) is the simple gamble induced by g and ai the outcomes’. Thus,

by stating that the expected utility property applies to u, it can be concluded that the expected utility property ‘assigns to each gamble the expected value of the utilities that might result, where each utility that might result is assigned its effective probability’ (Jehle & Reny, 2011, p. 98). This paper assumes that every utility function has the expected utility property.

Risk behaviour theory generally refers to three sorts of risk behaviour: 1) risk seeking; 2) risk neutral; and 3) risk averse (Wakker, 2008). Jehle & Reny (2011) &

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Wakker (2008) state that for a simple gamble g, in which a person can make two kinds of decisions, one risky and one non-‐risky (g = (p * w1, (1-‐p)*w2), with 0<p<1 the chances

of being rewarded with wi (i=1,2):

-‐ A person is said to be risk averse if u(E(g))>u(g). In other words, if his utility function is concave. This is the case if u(p * w1 + (1-‐p)*w2)> pu(w1)

+ (1-‐p)u(w2) for all 0<p<1, w1.w2

-‐ A person is said to be risk averse if u(E(g))>u(g). In other words, if his utility function is linear. This is the case if u(p * w1 + (1-‐p)*w2) = pu(w1)

+ (1-‐p)u(w2) for all 0<p<1, w1.w2

-‐ A person is said to be risk averse if u(E(g))>u(g). In other words, if his utility function is convex. This is the case if u(p * w1 + (1-‐p)*w2)< pu(w1)

+ (1-‐p)u(w2) for all 0<p<1, w1.w2

The main focus of this paper is risk aversion. In order to analyse risk aversion more accurately, the amount of risk aversion could be of importance. Arrow (1970) and Pratt (1964) proposed a measure for risk aversion. This so-‐called Arrow-‐Pratt measure of absolute risk aversion is calculated by Ra(w) = !!!!(!)_!!(!) (Jehle & Reny, 2011). The sign

of Ra(w) indicates whether a person is risk loving, risk neutral or risk averse. If Ra(w) is

positive, a person is risk averse. If it is zero, a person is neutral and if it is negative, a person is risk seeking. Another measurement is the measure for relative risk aversion (Wakker, 2008). This relative risk aversion is calculated by: 𝑤 ∗!!!!(!)

!!(!) . Relative risk

aversion has as advantage that c can vary while the function remains a valid measure for risk aversion in the case that the utility varies from risk averse to risk seeking.

In his book ‘Prospect Theory for Risk and Ambiguity’, Wakker (2008) describes different families of the utility function. For example, the family of power utility functions is characterised by the parameter denoted as:

𝜃, on ℝ!_{:
for
𝛼>0
by:}

For 𝜃>0, u(𝛼) = 𝛼!

For 𝜃=0, u(𝛼) = ln (𝛼) For 𝜃<0, u(𝛼) = −𝛼!

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This family is also referred to as the family of constant relative risk aversion (CRRA), in which 𝜃 can be seen as the ‘anti-‐index of concavity’ (Wakker, 2008, p. 101). The bigger 𝜃, the less concave u is, and therefore less risk aversion will be generated. Wakker (p. 101, 2008) states that under EU, the ‘functions u are interval scales and therefore replaceable by any function 𝜏 + 𝛼𝑢 for 𝜏 ∈ ℝ, 𝛼 > 0 and therefore concludes:

For all 𝜃 ≠ 0, 𝑢 𝛼 = !_!!, which amounts to scaling u’(1) = 1’. The family of constant relative risk aversion is characterised by the multiplication of both prospects by a same positive number, which does not affect one’s preferences.

Wakker (2008) also describes the family of exponential utility functions. This utility function is characterised by the parameter denoted 𝜃, on the entire outcome set ℝ by: For 𝜃>0, u(𝛼) = 1 − 𝑒!!" For 𝜃=0, u(𝛼) = 𝛼 For 𝜃<0, u(𝛼) = 𝑒!!"_{− 1}

in which the first implies concave utility, the second linear utility and the third convex utility. In this case, 𝜃 can be seen as the ‘index of concavity’. The bigger 𝜃, the more risk concave u is, and therefore the more risk aversion will be generated (Wakker, 2008, p.104) Again, Wakker (p. 101, 2008) states that under EU, the ‘functions u are interval scales and therefore replaceable by any function 𝜏 + 𝛼𝑢 for 𝜏 ∈ ℝ, 𝛼 > 0 and therefore concludes: For all 𝜃 ≠ 0, 𝑢 𝛼 = !!!_!!!". This family of utility functions is mostly used in data fitting theories, since adding a number does not affect a person’s preferences.

2.2 Determinants gender and education of risk aversion

Many variables determine a person’s risk aversion. Some personal characteristics are positively correlated with risk aversion, while others are negatively correlated. Firstly the link between gender and risk aversion will be discussed. Hyrsko et al. (2011) found that females are more risk averse. This fact was confirmed by the research by Charness and Gneezy (2012), who found in their experiment that women were making

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lower financial risk investments than men. Considering this fact, this research concluded that women are more financially risk averse than men.

The second variable in this paper for the estimation of risk aversion is education. The link between education and risk aversion has been broadly explored without definite results. This could be due to the fact that the direction of the causality remains unclear (Jung, 2014). Jung (2014) collected data from schools before and after the 1973 British reform whereby the compulsory years of schooling were increased by one year. He found that the change in compulsory years of schooling increased the subjects’ risk aversion. This would imply a positive correlation between education and risk aversion. Dohmen et al. (2005) concluded the exact opposite. In their research they used data retrieved from the German Socio-‐Economic Panel (‘SOEP’). Via this panel risk attitudes of more than 22,000 subjects were collected. They looked at the link between a person’s risk aversion and years of education and found a negative correlation between schooling and risk aversion. Hryshko et al. (2011) concluded the same. In their research they used data from the Panel Study of Income Dynamics. In this panel, individuals and their children are followed over time. By the use of compulsory schooling laws as instruments, they showed that policies that increase schooling tended to make future generations less risk averse. This implies a negative correlation between education and risk aversion.

Hence, as existing research has found conflicting results with respect to the sign of the correlation between education and risk aversion, this paper will further explore this. Thereby, the aforementioned variables (i.e. education, gender and age) will be taken into consideration, as they all appear to be correlated to risk aversion.

2.3 Empirical models

Ordinary Least Squares (‘OLS’)

To estimate the model, with dependent variable Risk Aversion (RAi) and independent

variables gender, education and a constant 𝛽1 one fits the following model:

RAi = 𝛽1 + 𝛽2 Dgender i + 𝛽3 educi + 𝜀

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In OLS the coefficients will be estimated by the following formula: b = (X’X)-‐1_{X’y,
in}

which b are the estimated coefficients, X are all the variables collected in the model, in this case a constant, gender and educ, and whereby y is the dependent variable, RA. Via OLS 𝛽1,.., 𝛽3 will be estimated in STATA.

OLS estimates must meet several conditions to be called optimal and consistent. An estimate b is called consistent if all regressors in X are exogenous and there is no perfect multicollinearity. An estimate b is optimal if the errors are not heteroscedastic and not serially correlated.

Testing perfect multicollinearity

Multicollinearity will be checked by the variation inflation factors (‘vif’) (Heij et al., 2004). This is a factor that calculates by which the variance of the regressors increases because of multicollinearity. Vif’s that are greater than 10 indicate severe multicollinearity. Vif’s of 1 indicate an absence of multicollinearity.

Testing exogeneity

The OLS estimates will be tested on exogeneity via the Hausman LM-‐test. According to literature, especially the variable educ has a chance of being endogenous (Jung, 2014). If educ turns out to be endogenous, there must be a reversed causal relationship between education and RA, in other words:

educ = 𝛾1 + .. + 𝛾n RA + 𝜉 with 𝛾n ≠ 0.

In the Hausman test, firstly, an OLS regression of RA on a constant, gender and educ is done. After that, residual vector eOLS will be saved. Subsequently, the regression

of educ on its instrumental variables is done. The residuals are saved under the name V. After these operations, the first stage of TSLS is completed.

Secondly, a regression of eOLS is done on a constant, gender, educ and V. This

regression therefore looks like: eOLS = 𝛿1 + 𝛿2 gender + 𝛿3 educ + 𝛼V + 𝜂. The hypotheses

are: H0: 𝛼 = 0, education is exogenous, vs. Ha: 𝛼 ≠ 0, education is endogenous Under H0

LM = nR2_{≈
χ}2_{(m-‐k)
holds,
with
m
being
the
amount
of
instruments
and
k
being
the}

amount of regressors in X. For values of nR2_{>
χ}2_{(m-‐k),
H}₀_{of
exogeneity
will
be
rejected.}

STATA will calculate the value, allowing for a conclusion on the endogeneity of education (Heij et al, 2004).

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Testing heteroscedasticity

Heteroscedasticity will be tested via the Breusch-‐Pagan test for homoscedasticity. In the test, one will check if the p-‐value is small enough to reject H0 of homoscedasticity.

Two Staged Least Squares (‘TSLS’)

If educ turns out to be endogenous, TSLS will be applied instead of OLS. In two staged least squares, instrumental variables are used. An instrumental variable must satisfy three conditions (Heij et al., 2004). The three conditions are: it must be exogenous, it must be relevant and there must be at least as much instruments as regressors (Heij et al., 2004). In this analysis the X stands for exogenous variables used in the RAi model, and the Z represents the matrix with instruments. In stage 1, each

column of X is regressed on Z, with the fitted values 𝑋 = (Z’Z)-‐1_{Z’X.
In
stage
2,
y
is}

regressed on 𝑋 with parameter estimates bIV = (𝑋′ 𝑋)-‐1 𝑋′y.

2.4 Choice of instrumental variables

The first instrumental variable used in this paper is the variable ‘urbanity’. This variable refers to the urbanity of the residency of the subjects. Since universities and other forms of higher education are mainly located in a city, a place with a high level of urbanity, one could conclude there might be a correlation between the level of education and the urbanity of the residency of the participant. Therefore urbanity will be used as an instrument if it appears to be a correct variable to use as instrument.

Age appears to be another suitable instrument for education. Age is exogenous and also appears to be relevant. There are indications of a negative correlation between education levels and age, since the percentage of higher educated individuals rises (Increasing levels of education around the world, 2012). This would mean individuals nowadays are higher educated than older individuals. One has to check if this relationship is true, which could imply that age is a relevant instrumental variable for education.

Gender is the third instrumental variable used in this paper. King (2000) found that women earn increasingly more degrees each year compared to men. She found that this gap between men and women with regards to education degree was related to race,

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ethnicity and social class (King, 2000). Gender is therefore correlated with education, which makes it an instrumental variable.

For an instrument to be correct it must also relevant and exogenous. In this thesis the instruments are a constant, gender, and urbanity. To check for exogeneity, a Sargan test is applied. First, a regression of education on a constant, gender, age and urbanity is completed. Subsequently, the fitted values are saved under the name 𝑒𝑑𝑢𝑐𝑎𝑡𝚤𝑜𝑛 . Secondly, a regression of RA on a constant, gender and 𝑒𝑑𝑢𝑐𝑎𝑡𝚤𝑜𝑛 is done. The coefficient values bIV are saved and the IV residuals are calculated: eIVi = RA -‐ bIV1 -‐

bIV2 𝑒𝑑𝑢𝑐𝑎𝑡𝚤𝑜𝑛. Subsequently, a test regression is done: eIVi is regressed on a constant,

gender, age and income, after which the test LM = nR2_{≈
χ}2_{(4-‐3)
will
be
calculated.
If}

nR2_{>
χ}2_{(1),
H}₀_{of
exogeneity
will
be
rejected.
STATA
will
calculate
the
value,
and}

conclusion can be drawn upon the exogeneity of the instruments (Heij et al., 2004).

3 Participants and methodology

3.1 Participants

This research will make use of the data retrieved from the LISS-‐panel. The LISS-‐ panel is a panel linked to the Tilburg University. In this LISS panel, approximately 9000 subjects complete a questionnaire each month. In order to make the experiments as accurate as possible, an attempt was made to simulate the real world by rewarding the subjects in some tasks with real money. In the data, several observable background characteristics are taken into account, which results in a representative reimbursement of the Dutch population.

People participating in the LISS panel were categorised according to certain background variables, allowing for the controlling of certain conditions. This research will make use of the data from the panels ‘work and schooling’, ‘economic situation: income’, and ‘measuring higher order risk attitudes of the general population’. The information on gender and age will be retrieved from the panel ‘background variables’.

Since the panel on risk attitudes was conducted in 2009, the data in this research stems from 2009. By merging the datasets there will be approximately 1004 subjects,

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which will allow for an accurate estimation. Answers to the relevant questions from the data will be selected to estimate the effect properly.

3.2 Measurement risk attitudes

Subjects in the risk measurement panel had to complete five trials in which they had to choose between two options: one safe option and one risky option. The trials were presented by hypothetically rolling a dice. If the value of the dice was 1, 2 or 3, the payoff was 65, if the value of the dice was 4, 5 or 6, the payoff was 5. Therefore the payoffs for option 1 were a 50% chance of earning 65 and a 50 % chance of earning 5. The second option was a sure payoff varying from 20 to 40 in steps of five. Therefore, a rational, or risk neutral person, would be indifferent at the expected value of option 1, being 35. Subjects did not learn the actual outcome of any of the lotteries presented in the different trials.

The trials were counterbalanced in several ways. With the first being the varying kind of task. Half of the subjects were given a trial in which they had a 1/10 chance of actually winning the amount presented, the other half were given a trial in which there were purely hypothetical payoffs. The amounts presented in the tasks also varied. The amounts were varying by the standard payoffs, varying from 20 to 40 in steps of five, multiplied by a factor K, in which K could be larger or smaller than 1. The second factor that was taken into account was the position of the options on the screen. For half of the subjects, option 1 was on the right and option 2 on the left. For the other half this was mirrored: with option 1 being on the left and option 2 being on the right. The final factor was the order in which the sure payoffs were presented. Half of the subjects were presented with increasing sure payoffs, starting at 20 and increasing with 5 each trial, and the other half with decreasing sure payoffs, starting at 40 and decreasing with 5 each trial.

In order to measure the risk attitudes, the theory of Wakker (2008) will be applied. Thereby, three types of risk measures will be used: the first one is the amount of sure payoffs the subject made in the risk task, the second one is according to the power utility, and the third one is according to the exponential utility.

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Amount of safe choices:

The amount of safe choices can vary from 0 to 5. A rational person would be indifferent at the break-‐even point of 35, and therefore only make 1 or 2 safe options with sure payoffs of 35 and 40. In the other three cases it would choose the unsure payoffs, since the expected payoffs of those options is higher. Therefore, if more than 2 safe options were chosen, the subject was said to be risk averse. The amount of risk aversion increased with the amount of safe choices made in the task.

Power utility:

In order to calculate the amount of risk aversion the questions and corresponding answers from the risk task will be considered. A person was said to be indifferent between two options, if the utility was equal. For example, if a subject was not willing to accept 20, but was willing to accept 25, the least amount of money was said to be

!"!!"

! = 22.5. So at 22.5 the utility of both options must be equal.

To find the amount of risk aversion the following equation must be solved:

0.50*u(65) + 0.50*u(5) = u(22.5) ⇔ u(65) + u(5) = 2 * u(22.5) ⇔!"_!! + !_!! = 2 * 22.5!_è

solve to risk aversion measure 𝜗.

If a subject only made safe choices, his break even point was said to be 17.5, if a subject only made risky options, his break even point was said to be 42.5.

Table 1: 𝜗 solved for the different break-‐even points in power utility

Break even _17.5 _22.5 _27.5 _32.5 _37.5 _42.5

𝜗 -‐0.0361423 0.274986 0.554813 0.842792 1.17245 1.59206

Exponential utility:

The same risk task is used for the exponential utility, for which the following equation must be solved:

0.50*u(65) + 0.50*u(5) = u(22.5) ⇔ u(65) + u(5) = 2 * u(22.5) ⇔!!!_!!!"! + !!!_!!!! = 2 ∗!!!!!!.!!_! è solve to risk aversion measure 𝜗

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Break even _17.5 _22.5 _27.5 _32.5 _37.5 _42.5

𝜗 0.0519937 0.0316247 0.0174043 0.00558144 -‐0.00558144 -‐0.0174043

The three measures will be referred to as Risk Aversion Safe (‘RAS’), which represents the risk aversion measured by the amount of safe choices, Risk Aversion Power (‘RAP’), which represents the risk aversion measured by the power utility function and finally Risk Aversion Exponential (‘RAE’), which represents the risk aversion measured by the exponential utility function.

Table 3: Means of the different RAi

Variable #obs Mean

RAS 1004 3.467 (.054) RAP 1004 .478 (.018) RAE 1004 .026 (.001)

All three estimated risk aversions 𝜗 will be used in analysing the model.

3.3 Measurement of gender, education agecat and urbanity

The variables agecat, education and gender of the variables will be calculated from the dataset, whereby gender can be male, denoted by 0, or female, denoted by 1. To test the effect of age on education, the variable agecat is created. The subjects will be divided into several age categories. Category 1 consists of subjects varying from 17-‐24 in age. Category 2 will consist of people varying from the ages of 25-‐34 and so on. The final category will be category 6, which consists off all subjects above the age of 64.

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Education will be referred to as ‘educ’. Educ will be categorised into three categories: 1 for lower education, 2 for medium education and 3 for higher education. Lower education consisted of people with a highest completed education level with a diploma of VMBO, HAVO, VWO or MBO. The medium level of education consisted of people who finished HBO as the highest level of education, and the higher level of education consisted of people who graduated from university. The level of urbanity will be conducted from a question of the LISS-‐panel. This question asked the subject to grade the urbanity of their residency. They could chose grades varying from 1 to 5 with 1 representing high urbanity and 5 representing low urbanity. Therefore this variable was already suitable for the regression.

4 Results

4.1 Summary of variables

First an overall correlation between risk aversion and education is considered. In this measure the mean of every form of risk aversion is calculated for each level of education. In table 4 an overview of the means of the risk aversions is given. The first thing that is indicated, is that the average person appears to be risk averse. With the first measure of risk aversion, the amount of safe choices, the mean is varying from about 3.37 to 3.50. A risk neutral agent would make a maximum of 2 safe choices. Therefore it can be concluded the average person is risk averse by the first measurement of risk aversion. With the risk aversion abducted via the power and the exponential utility function, a person is said to be risk averse if 𝜃 > 0. The mean of both measures is >0 and therefore the average person also appears to be risk averse via these measures of risk aversion.

One can state that for the power and the exponential utility risk aversion, it looks like risk aversion increases as education levels increase. However, for risk aversion measured by the amount of safe choices, one cannot draw a conclusion since the means appear to increase alongside education at first, but decrease again in the final stage. If one looks at the means in each category, one can state that in all three cases women appear to be more risk averse than men. In the risk task, women made on an

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average 0.5 more safe choices than men, and with the power and the exponential utility women also appear to be more risk averse.

Table 4: Summary statistics

Variable #obs Mean RAS Mean RAP Mean RAE

Education 1 Low levela ₆₉₄ _3.4669 _0.4897 _0.0260 2 Medium levelb ₂₃₁ _3.5022 _0.4523 _0.0270 3 High levelc ₇₉ _3.3671 _0.4521 _0.0274 Gender 0 Male 501 3.2216 0.5350 0.0234 1 Female 503 3.7117 0.4215 0.0292

a_{participant
finished

primary
school,
VMBO,
HAVO,
VWO
or
MBO
as
a
highest
degree}

b_{participant
finished
HBO
as
a
highest
degree}

c_{participant
finished
University
or
higher
as
a
highest
degree}

Result 1: The average person appears risk averse

4.2 Effect of gender and education on three measures of risk aversion by OLS

Now OLS regressions of the three measures of risk aversion will be considered with independent variables age, gender and education. One can conclude the regressor gender significantly differs from zero in the regression on all three measures of risk aversion. However, the sign of the estimate gender is positive with a regression on RAS and RAE, but it is negative when one looks at the regression with RAP. But since an increase in 𝜃 in the power utility function means a decrease in risk aversion, one can conclude the results are not conflicting.

Result 2: Regression by OLS shows that in all three measures of risk aversion, women are significantly more risk averse than men.

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Table 5: OLS regression of a constant, gender and educ on RAi

Variable RAS RAP RAE

Constant 3.205*** .582*** .022*** (.144) (.047) (.002) Gender .491*** -‐.117*** .006*** (.107) (.035) (.002) Educ .011 -‐.328 .001 (.144) (.028) (.001) R-‐squared .021 .012 .013 Adj. R-‐squared .019 .010 .012 No. observations 1004

Standard errors are reported in the parentheses */**/*** indicate significance at 10%, 5% and 1% level.

As for the other regressor and education, one is inconclusive, since significance levels are higher than the allowed 0.05. As mentioned above, the fact that the results are not significant could be due to several reasons.

Result 3: Regression by OLS fails to significantly clarify the relationship between education and risk aversion

4.3 Results from tests for homoscedasticity, multicollinearity, and exogeneity

First heteroscedasticity will be tested via the Breusch-‐Pagan test. The test statistic is asymptotically distributed as 𝜒!_{(1)
under
H}₀_{of
homoscedasticity.
This,
since}

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First the OLS regression RAi = 𝛽1 + 𝛽2 Dgender i + 𝛽3 educ + 𝜀 is applied, followed by

the computation of the regression residuals. Then an auxiliary regression of the square residuals is done on the differences in variance of the observations. Then LM=nR2_leads

to the test statistic.

In none of the three regressions on the measures of risk aversion H0 of

heteroscedasticity could be rejected. Therefore one cannot conclude there is significant heteroscedasticity in the estimated model.

Table 6: Breusch-‐Pagan test for heteroscedasticity with H0: constant variance

𝜒!₍₁₎ _1.67 _.28 _.01

𝑝 > 𝜒!₍₁₎ _.196 _.594 _.943

Reject H0

𝛼 = 10% No No No

𝛼 = 5% No No No

𝛼 = 1% No No No

Subsequently, a test for serial correlation will be considered by the vif’s. All three vif’s are 1.01, which indicates hardly any multicollinearity. Therefore, multicollinearity will not be causing the problems in the results.

Next, endogeneity of education on all three measures of risk will be tested via the Wu-‐Durbin-‐Hausman test. Hausman test shows endogeneity for all measures of education, namely in the regression of gender and education on RAS and on RAE are significant at a level of 1% and 5% respectively. In the case of RAE, H0 of exogeneity of

regressors can be rejected at a significance level of 10%. The analysis via TSLS will be applied to all three measures of risk aversion.

Educ is endogenous in all three measures of risk aversion (at different significance levels)

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Table 7: Wu-‐Durbin-‐Hausman test with H0 exogenous regressor education

𝐹(1,998) 6.98 3.51 5.06

𝑝 > 𝐹(1,998) .01*** .06* .025** Reject H0

𝛼 = 10% Yes Yes Yes

𝛼 = 5% Yes No Yes

𝛼 = 1% Yes No No

*/**/*** indicate significance at 10%, 5% and 1% level.

4.4 Instrumental variables

If one looks at the variables in table 7, there are several things one can see. The first thing is that education levels appear to be higher for people stating to live in an area with high urbanity. With, apart from the two levels 3 and 4, the levels of education decrease alongside the decrease of urbanity.

Second conclusion one can draw, is that men appear to be higher educated than women. If one looks at the variables, there are several things one can see. The first thing is that education levels appear to be higher for people living in an area with high urbanity. Apart from the two levels 3 and 4, the levels of education decrease alongside the decrease of urbanity. The second conclusion one can draw, is that men appear to be higher educated than women. If one looks at the variable age, a pattern appears to be present. Education levels appear to decrease as age increases, apart from the first and fourth category. In the category 17-‐24 education levels are much lower than in the other categories. This is partly due to the fact that someone in the category 17-‐24 years old simply has not finished his education. Therefore the results are not completely representing somebody’s education level. In order to prevent this from interfering with the results, it is decided to drop the first category of age. This means that 106 observations are dropped in the analysis.

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Table 8: Summary instruments all agecat

Variable #obs Mean Mean educ

Urbanity 1004 3.0986 -‐ 1 Extremely urbana ₁₁₂ _-‐ _1.7054 2 Very urbanb ₂₆₁ _-‐ _1.4215 3 Moderately urbanc ₂₂₀ _-‐ _1.3091 4 Slightly urband ₂₃₈ _-‐ _1.3529 5 Not urbane ₁₇₃ _-‐ _1.2775 Gender 1004 0.5010 -‐ 0 Male 501 -‐ 1.4371 1 Female 503 -‐ 1.3380 Age 1004 48.7679 -‐ 1 17-‐24 106 -‐ 1.1321 2 25-‐34 110 -‐ 1.7182 3 35-‐44 179 -‐ 1.4134 4 45-‐54 198 -‐ 1.4646 5 55-‐64 224 -‐ 1.3482 6 65 + 187 -‐ 1.2781

a _{Urban
character:
Surrounding
address
density
per
km}2_>2500

b_{Urban
character:
Surrounding
address
density
per
km}2_1500-‐2500

c_{Urban
character:
Surrounding
address
density
per
km}2_1000-‐1500

d_{Urban
character:
Surrounding
address
density
per
km}2_500-‐1000

e_{Urban
character:
Surrounding
address
density
per
km}2_<500

To check if this does not affect the other variables in the model, means from all the variables are recalculated, starting with the means of all the risk aversion measures.

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Table 9: Summary statistics agecat, agecat>1

Variable #obs Mean #obs Mean (age>25)

RAS 1004 3.467 898 3.437 (.054) (.058) RAP 1004 .478 898 .475 (.018) (.019) RAE 1004 .026 898 .026 (.001) (.001)

Standard errors are reported in the parentheses

If one looks at the differences in results, it appears no significant changes occurred. All new means of the measures are in the confidence interval of the old means. Because of the empirical rule, confidence intervals are calculated by adding or detracting the standard errors, multiplied by 2 (Bain&Engelhardt, 1992). This leads to confidence intervals of approximately 95%. One is allowed to do this, since the assumption of normally distributed data can be done, as the data sample is large enough. For RAS the confidence interval is calculated by: (3.467 – 2*.054; 3.467 +2*.054) = (3.359; 3.575). One can conclude there is no significant different mean for RAS as 3.437 ∈ (3.359; 3.575). The same holds for RAP and RAE with for RAP .475∈ (.442; .514) and for RAE .026 ∈ . 025; .027 . New means of the instruments are calculated in the table below.

Influence of gender and education on risk aversion

Bachelor of Science thesis Econometrics