the effect of risk aversion on self- employment status

The Effect of Risk Aversion on Self-

Employment Status A review of this relationship using risk aversion measures derived from a partly incentive

compatible lottery experiment.

by YORAM VANMAEKELBERGH 10003416

Supervisors:

ZHENXING HUANG JAN TUINSTRA

Bachelor thesis econometrics

June, 2014

Abstract In this study is examined whether a high degree of risk aversion has a negative effect on the

propensity to become self-employed. Three different measures of risk aversion are derived from a

partly incentive compatible lottery experiment. Each measure is included in different reduced form logit

regressions proposed by previous research. None of the measures seems to have a significant effect,

contradictory to most previous research. Insignificance appears invariant to the definition of self-

employment, the included control variables, splitting up the sample by different payoff conditions and

leaving out individuals whose job status is unknown. Moreover, the final model is clearly misspecified.

This may be caused by reverse causality issues, heteroskedasticity because of an omitted main

control variable, the design of the experiment or construct invalidity of the risk aversion measures.

Keywords: Risk Aversion, Self-Employment, Entrepreneurship, Lottery Experiment, Incentives. In this study use is made of data of the Longitudinal Internet Studies for the Social sciences (LISS) panel administered by CentERdata (Tilburg University, The Netherlands). Acknowledgements I would like to thank Zhenxing Huang and Jan Tuinstra for their feedback on earlier drafts of this thesis. I would like to thank Rob van Hemert for teaching me academic writing skills and his extensive feedback on the theoretical part of this thesis. I would like to thank Thomas Dohmen from the University of Maastricht for sending me an important discussion paper for this thesis. Finally I would like to thank Joppe Arnold for peer reviewing my work.

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Contents 1. Introduction ....................................................................................................................... 2

2. Theory ............................................................................................................................... 5

2.1 Relating risk aversion to utility functions ....................................................................... 5

2.2 Relating the derived degree of risk aversion to risk taking behavior ............................. 6

2.3 Possible relationships between risk aversion and self-employment ............................. 8

2.3.1 A theoretical model ................................................................................................ 8

2.3.2 Risk aversion as a determinant of self-employment probability .............................. 8

2.3.3 Available variables and their effect on self-employment probability ......................10

2.3.3.1 Gender ...........................................................................................................10

2.3.3.2 Age ................................................................................................................11

2.3.3.3 Marital status and number of children ............................................................11

2.3.3.4 Level of education ..........................................................................................12

2.3.3.5 Wealth and capital constraints .......................................................................12

2.3.3.6 Family background, not in the LISS panel ......................................................13

2.3.3.7 Unemployment status ....................................................................................13

2.4 Research question and hypotheses ............................................................................14

3. Data and methods ............................................................................................................14

3.1 Data: the LISS panel ...................................................................................................14

3.2 Deriving different measure of risk aversion based on the LISS lottery experiment ......15

3.3 Procedure to derive a model for the relationship between risk and self-employment ...17

3.4 Operationalization of the variables ..............................................................................17

3.5 creating subsamples for robustness checks ................................................................18

4. Results .............................................................................................................................20

4.1 Comparing the derived risk aversion measures by payoff condition ............................20

4.2 Differences between self-employed and not self-employed individuals .......................21

4.3 The final model ...........................................................................................................23

4.4 Results found using the final model ............................................................................25

4.5 Detecting influential observations ................................................................................29

4.6 Heteroskedasticity and its possible solutions ..............................................................31

5. Conclusion .......................................................................................................................33

6. Discussion ........................................................................................................................33

References ...........................................................................................................................38

Appendix I ............................................................................................................................... i

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1. Introduction Recently, a lot of research has been done on why individuals choose for self-employment

rather than a normal job. This is interesting for society because starting an own business

potentially creates new jobs and can therefore decrease currently high unemployment rates.

Moreover, the topic is interesting for the academic world, because of the complex nature of

self-employment. This interest is reflected in the fast increasing number of studies on this

topic.

Research on self-employment has resulted in a wide range of explanations for this

phenomenon. In the past, self-employment was explained by access to capital, links between

generations and fiscal reasons (Brown et al., 2011). Nowadays research on this topic

focuses on the differences in personal characteristics between self-employed individuals and

individuals who are not. Previous studies found evidence that one of the main differences is

that self-employed workers are more able and more willing to take risks (see for example,

Brown et al., 2011; Ekelund et al., 2005; Dohmen et al., 2011). Modern economics regards

an individual’s attitude towards risk as a main determinant for all kinds of behavioral choices,

including the choice to be(come) self-employed.

For example, Hartog et al. (2002) and Masclet et al. (2009) provide evidence that self-

employed workers have a significantly lower degree of risk aversion than their not-self-

employed counterparts. This view is supported by Ekelund et al. (2005) and Brown et al.

(2011), who find that a low degree of risk aversion increases the probability of self-

employment, ceteris paribus. However, Miner and Raju (2004) find evidence for the reverse

relationship, i.e. self-employed workers are more risk averse than wage employed workers.

Contrary to this, Tucker (1988) and Parker (2008) find that risk attitude has no significant

effect on the decision for self-employment. Finally, Caliendo et al. (2009) find that risk

aversion is only a significant explanatory variable in explaining the self-employment decision

when an individual has already been employed before becoming self-employed.

Although more supportive than counter supportive literature can be found,

significance of the risk aversion variable is not invariant to the used models and the way the

degree of risk aversion is measured. The models differ with respect to the direction of the

relationship between the two variables. In some models the degree of risk aversion is used

as an explanatory variable for the probability of self-employment (see for example, Dohmen

et al., 2011), while in other models self-employment status is used as an explanatory variable

for the degree of risk aversion (see for example, Masclet et al., 2009). Previous research

also differs in the way in which risk aversion is measured. Four possible derivations of the

degree of risk aversion are used most frequently; based on a hypothetical gamble, based on

experiments with real payoffs, based on a psychological measure and based on a self-

assessment risk question.

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All the above measures of risk aversion have one thing in common: they are all

proxies for an individual’s degree of risk taking behavior. Whether the derived proxy for risk

aversion is a good predictor for the decision of self-employment is examined in Dohmen et

al. (2005). One of their results is that responses to lottery questions with hypothetical payoffs

are not able to predict self-employment status. This finding contradicts many of the results of

the aforementioned researches, but comparison is complicated due to the different used

models and different measures of risk aversion.

A possible explanation for the contradictory result of Dohmen et al. (2005) is that

responses to their used hypothetical risk question are not incentive compatible. This makes it

unclear to what extent the derived degrees of risk aversion translate into actual risk-taking

behavior, like the choice to become self-employed (Dohmen et al., 2011). Therefore, in this

study a risk aversion measure derived from a partly incentive compatible lottery experiment

is included in a model explaining the probability of self-employment. The question is whether

this degree of risk aversion is a significant explanatory variable in such a model. A negative

answer to this question is found in the present study, as will be shown in the results section

in paragraph 4.4.

However, on beforehand an affirmative answer to this question is expected because

of three reasons. Firstly, Masclet et al. (2009) find that a degree of risk aversion based on an

incentivized lottery experiment is significantly explained by self-employment status.

Therefore, it seems natural to expect significance in a model in which the dependent and

explanatory variables are exchanged, as used in this paper. Secondly, Dohmen et al. (2011)

find that the results of an incentive compatible lottery experiment are strongly correlated with

an individual’s general risk measure, which proved able to predict self-employment status.

This together implies that it should as well be possible to predict self-employment status from

the experimental measures used in this study directly. Thirdly, Camerer and Hogarth (1999)

state that adding incentives to a risky choice question reduces the variance of the results.

This reduced variance may increase the likelihood of significant results.

In this study three different degrees of risk aversion are derived from a partly

incentive compatible lottery experiment of the LISS panel1. These degrees of risk aversion

are used among other variables of the LISS panel to estimate an appropriate reduced form

model to answer the question whether the derived risk aversion coefficient is a significant

explanatory variable for the probability of self-employment. To the author’s knowledge, the

combination of risk aversion derived by a partly incentive compatible lottery experiment and

risk aversion as an explanatory variable for the probability of self-employment is unique and

never researched before.

1 40% of the participants were in a condition that they were able to make money.

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The proceeding of this thesis is organized as follows. In chapter two the theory about

risk aversion and its influence on self-employment status found in previous research are

addressed. Chapter three discusses the data, methods, used model and used samples. In

chapter four the results of this study can be found. Chapter five summarizes the conclusions.

Finally, in chapter six an extensive explanation for the found results and forthcoming advises

for future research are discussed.

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2. Theory

In this chapter the theory of risk aversion is related to utility functions firstly. Secondly, risk

aversion derived by the used lottery experiment is linked to risk taking behavior. Finally,

existing models to explain self-employment status and determinants of self-employment

status are reviewed.

2.1 Relating risk aversion to utility functions

This paragraph gives a brief explanation of all relevant aspects of utility theory and risk

aversion necessary for this research. It’s important to note that all statements in this

paragraph are only valid within the expected utility framework. All concepts in this paragraph

are retrieved from Wakker (2010).

A well-known measure of risk aversion is the Pratt-Arrow measure, also called the

absolute measure of risk aversion:

(1)

In this measure U is a utility function which is twice continuously differentiable. Another

frequently used measure is the relative measure of risk aversion:

(2)

In this measure x is an individual’s wealth.

An individual A is said to be more risk averse than another individual B if and only if

A’s absolute (relative) measure of risk aversion, exceeds B’s everywhere. This also applies

to all the risk aversion measures used in this study: a higher value means a higher degree of

risk aversion.

Empirical observations often have properties which can be derived from two different

families of utility functions, introduced in what follows. The first family of utility functions is the

power family, which has the property of constant relative risk aversion. That family is defined

on as follows:

(3)

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In the family of equations of (3), θ can be considered as an anti-index of risk aversion: the

smaller its value, the more concave the utility function, the more risk aversion is generated.

Based on this family a relative degree of risk aversion, necessary for the present study, is

computed (see 1) to correspond with the common empirical finding from previous research of

increasing relative risk aversion with increasing wealth.

The second family of utility functions is the exponential family which has the property

of constant absolute risk aversion. That family is defined on as follows:

(4)

In the family of equations of (4), θ can be considered as an index of risk aversion: θ > 0

results in a concave utility function implying risk aversion, θ = 0 results in a linear utility

function implying risk neutrality, θ < 0 results in a convex utility function implying risk seeking.

Based on this family an absolute degree of risk aversion, necessary for the present study, is

computed (see 2) to correspond with the common empirical finding of decreasing absolute

risk aversion with increasing wealth.

2.2 Relating the derived degree of risk aversion to risk taking behavior

Previous research about the relationship between risk aversion and self-employment status

uses different measures of risk aversion to examine their potential relationship. For example,

Hartog et al. (2002) deduce their measures of risk aversion from an individual’s reservation

price for a lottery ticket and from the answer provided on an income shift question. In

addition, Brown et al. (2011) use a six point risk aversion scale which is based on classifying

individuals by their risk attitude according to answers they provided on a hypothetical gamble

with their income. Furthermore, Ekelund et al. (2005) use a psychological measure of risk

aversion, based on harm avoidance. Finally, Masclet et al. (2009) and Dohmen et al. (2011)

use an incentive compatible lottery to reveal an individual’s degree of risk aversion.

All these measures for risk aversion are quite complicated to obtain: they require

understanding of probability theory by the participants, strong imaginary power or they are

expensive to carry out. However, risk aversion measures which are easy to obtain also exist.

For example Dohmen et al. (2011) use a question which directly asks survey participants

about their willingness to take risks: “How do you see yourself: are you generally a person

who is fully prepared to take risks or do you try to avoid taking risks?”. Participants provided

answers to this general risk question on a 10-ladder Likert scale (i.e. 0 means ‘Not at all

willing to take risks’ and 10 means ‘Very willing to take risks’).

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An interesting question for this paper arises with respect to measuring the degree of

risk aversion: what is the relationship between the answer provided on the above general risk

measurement question and the measure derived by an incentive compatible lottery

experiment? Dohmen et al. (2005) find that the degree of risk aversion derived from a

hypothetical lottery question is highly correlated with the degree of risk aversion derived from

this general risk question. Moreover, they find that this last mentioned risk measure is able to

predict self-employment status, while the first measure is not. This is noteworthy because the

general risk question aims to measure an individual’s degree of risk perception, which can be

related to an individual’s risk taking behavior in real life according to Weber et al. (2002), like

the choice to become self-employed (Dohmen et al., 2005). The same variable, to wit the

individual’s degree of risk aversion, should therefore lie underneath both the answer of the

general risk question, the decision to become self-employed and the results of the

hypothetical lottery experiment.

In Dohmen et al. (2011) is found that, when the above lottery question is incentivized,

its results are not only highly correlated with the general risk measure, but also able to

predict the general risk measure and vice versa. Combining this last result with the

aforementioned result that the general risk measure is able to predict self-employment

status, it seems natural to assume that a risk aversion measure derived from an incentive

compatible lottery experiment is able to predict self-employment status directly. This study

sought to examine this last question. The complete reasoning of this paragraph is

summarized in figure 1.

Figure 1

Left: Results of Dohmen et al. (2005). Right: hypothesis of this paper (in green) combined

with the results of Dohmen et al. (2011).

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2.3 Possible relationships between risk aversion and self-employment

Previous research provides many explanations why an individual chooses to become self-

employed. A low degree of risk aversion appeared to be one of the main determinants in this

choice. In general two approaches to model this relationship can be distinguished, a

theoretical model and a reduced form equation. These models and their included variables

are elaborated respectively in the next paragraphs.

Of course no real model for the choice of self-employment exists. Previous research

dealt with this fact by considering reduced form equations for this relationship, which do not

take all influencing variables into account. In this study the same strategy is employed: the

purpose is not to find a structural model for the probability of self-employment2, but to find an

appropriate reduced form equation containing risk aversion to review the relationship

between risk aversion and self-employment.

2.3.1 A theoretical model

Praag and Cramer (2001) developed a theoretical model in which an individual chooses for

self-employment based on his risk attitude and entrepreneurial ability. An individual is said to

know the labor demand and profit for both occupational choices and compares the expected

utility of the profit of self-employment with the utility of wage employment based on these

values. He occupies himself in the sector with the highest utility.

This model’s strong and unrealistic assumptions, e.g. single wage rate, only full-time

employment and a closed economy, make it not suitable for empirical analysis with data from

a real economy as in the present study. But the model does contribute to this research by

giving insight in which factors influence the probability of self-employment. By their model,

including the variables level of education, gender and risk attitude to model the probability of

self-employment is both theoretically sound and empirically underbuilt. The inclusion of other

influencing variables relies on common sense, sociological arguments and empirical

evidence, rather than on a theoretical model, as will be discussed in paragraph 2.3.3.

2.3.2 Risk aversion as a determinant of self-employment probability

The paper of Cramer et al. (2002) was the first that examined the relationship between risk

aversion and self-employment in an empirical way. Previous research has suggested that

individuals with a low degree of risk aversion are more likely to choose for self-employment.

To test this hypothesis empirically they built a relatively simple model with self-employment

status as the dependent variable and a risk aversion measure among the independent

variables in a probit model. Their results show that risk aversion is a significant explanatory

2 The words self-employment status, probability for self-employment and decision to become self-

employed are all used together without distinction in meaning.

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variable with a negative sign, but because of different timing of the data3, nothing concerning

causality is claimed.

In addition, Ekelund et al. (2005) state that, because earnings of a self-employed

individual have greater variance than the earnings of a wage employed individual, it seems

natural to assume that self-employed workers are less risk averse. In both the logit model

with and without possible endogenous variables, their risk aversion measure based on harm

avoidance appeared to be a significant explanatory variable with the expected negative sign.

Furthermore, Brown et al. (2011) include even more possible explanatory variables to

model the choice for self-employment. Finally they estimate a probit model with many control

variables, family background covariates and a risk aversion measure based on a gamble with

an individual’s income. They find a significant negative relationship between risk aversion

and the probability of being self-employed.

Finally, Dohmen et al. (2005) use a probit model with self-employment status as the

dependent variable and a risk aversion measure based on a hypothetical investment

question among the independent variables. They find that this risk aversion measure does

not have a significant influence on self-employment status. A possible explanation for

insignificance of this risk aversion measure is the aforementioned lack of real payoffs

resulting in high variance of the derived risk measures.

In the aforementioned studies endogeneity of the risk aversion measure may be a

problem. This problem is addressed in Brown et al. (2011), who wonder whether their risk

aversion measure is not simply capturing the individual’s unobserved characteristics which

are not included in their model. In accordance with the assumptions of previous literature

they find that this is not the case.

This is not the only endogeneity issue; the direction of causality between the degree

of risk aversion and self-employment status is not self-evident. Perhaps an individual

chooses to become self-employed and this decision influences his degree of risk aversion,

instead of the other way round, as assumed in most previous studies. This reverse causality

issue is investigated in different ways in Brown et al. (2011) and Ekelund et al. (2005)4. In the

end both conclude that the risk aversion coefficient measured in the past is influencing

current employment status. This is consistent with risk aversion as a causal determinant for

future self-employment status, as is also assumed in the present study. Therefore, any

endogeneity issues will not be taken into account in the final model of this study.

3 In the study of Cramer et al. (2002) the degree of risk aversion is derived long after the occupational

choice has been made 4 Ekelund et al. (2005) investigate whether a longer tenure in self-employment would result in a lower

degree of risk aversion. Because data of tenure in self-employment was not available, they approximated this relationship with tenure in current employment as a proxy for tenure in self-employment. Brown et al. (2011) were able to measure an individual’s risk attitude prior and after becoming self-employed.

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However, research based on the reverse relationship, i.e. in which way self-

employment status influences risk attitude cannot be ignored at this point (see for example,

Hartog et al. (2002) and Masclet et al. (2005)). The main difference between the two

approaches can be explained by different research interests in the papers employing the

different models. When self-employment status is used as a determinant for risk aversion, it

is just a control variable in order to get a clear view of the effect of another variable on risk

aversion5. This is not the case in the present study, but the model is used in the discussion of

chapter 6.

2.3.3 Available variables and their effect on self-employment probability

After the above literature investigation, the following variables (among a degree of risk

aversion) are selected from the LISS panel to be included in a reduced form equation to

estimate the probability of self-employment: gender, age, marital status, number of children,

level of education and whether an individual owns a dwelling. Why these variables are

included is discussed in what follows and how these variables are included is addressed in

paragraph 3.4.

2.3.3.1 Gender

In previous research, gender appeared to be a main determinant of the probability to become

self-employed: men are significantly more often self-employed than women. This is explained

in many ways; only the main reasons are highlighted here. Rosa et al. (1995) find that

businesses of self-employed females underperform compared to men-owned businesses by

looking at standard performance measures. This may decrease the likelihood to survive for a

self-employed female and therefore decreases the probability that a female is self-employed.

Burke et al. (2001) suggest that the social implications of gender (still) play an important role:

women are regarded as responsible for the upbringing of the children and other domestic

commitments. Women make occupational choices to complement with these duties, which is

better possible with (part-time) wage-employment than with self-employment. Another

argument is given by Georgellis and Wall (2005): men are more willing to give up wage-

employment just because of the difference in earnings with self-employment, while women

attach more value to non-wage aspects of a job. Simoes et al. (2013) complement this

argument by stating that women are engaged in different sectors with fewer possibilities to

become self-employed and with a higher job satisfaction, resulting in a lower probability of

self-employment. Finally, Koellinger et al. (2014, in press) state that even after controlling for

all the aforementioned effects women still show a lower propensity to become self-employed

because of different subjective perceptions, for example about their entrepreneurial ability,

5 In these papers the reverse causality issue is not mentioned.

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than men. All in all a gender dummy variable should be included in the final model of the

present study.

2.3.3.2 Age

Age is a possible determinant for the probability of self-employment as an approximation for

labor market experience: self-employment probabilities increase with labor market

experience. Le (1999) gives two possible explanations for this effect. Firstly, as labor market

experience increases, accumulated capital also increases. This makes it possible to

overcome the liquidity constraints associated with setting up one’s own business. Secondly,

labor market experience increases entrepreneurial ability and hence, according to the model

by Praag and Cramer (2001), an individual is more likely to become self-employed. Previous

research did indeed provide evidence that labor market experience, approximated by age,

has a significant positive effect on the probability of self-employment.

Moreover, according to Simoes et al. (2013) a real age effect can also be attached to

the age variable. A positive sign for this variable is explained by a strong desire for more

flexible employment, a way to avoid mandatory retirement and limiting health status that

makes it impossible to have a full-time job. In some research a negative sign above a certain

threshold value is also found. This can be explained by a higher level of risk aversion, not

being able to work many hours associated with self-employment and less time to recover the

invested capital in one’s own business. The different found signs could imply a non-linear

relationship and therefore encourage including both an age term and a quadratic age term in

the final model of the present study.

2.3.3.3 Marital status and number of children

In previous research a married individual appeared to have a higher probability to be self-

employed. This can be explained in several ways according to Le (1999). Firstly, marriage is

associated with stability and emotional support and therefore a good background for the risk

bearing entrepreneur. Secondly, entrepreneurs face the possibility that their employees shirk.

Employing one’s spouse in the business prevents this last phenomenon because both the

spouse and the entrepreneur have the same incentive of maximizing family profit. Thirdly, a

married individual faces less financial constraints to start a business because of possible

sharing of their accumulated capital.

However, also a negative effect for married individuals on self-employment probability

is found. According to Simoes et al. (2013) this can be explained by the specialization

hypothesis of the neoclassical theory of family interpreted in a self-employment context.

According to this hypothesis, a married couple maximizes joint utility if one of them

specializes in domestic work and the other in self-employment. This implies a negative sign

for the individual who is specializing in domestic work and may encourage including an

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interaction term between gender and marriage, next to a married dummy variable, in the

used model of the present study.

Previous research found another family characteristic that affects the probability of

self-employment, namely the number of children. A positive sign for this variable is found by

Connelly (1992): women with young children are more likely to choose for self-employment

to lower the cost for child care and to be able to spend time with their children while still

engaging in the labor market. Besides, teenage children are able to help in the parent’s self-

employed business (Georgellis & Wall, 2005). However, a negative sign is also found, for

example by Hundley (2001): when the number of children increases, the amount of time

related to bringing them up may increase, and less time remains to run a business. These

studies encourage that the number of children is included in the final model of the present

study.

2.3.3.4 Level of education

In previous research the level of education comes out as a determinant for the probability of

self-employment. Several channels exist through which this variable affects this probability

(Le, 1999). One possibility, implying a positive sign, is that if the level of education increases,

an individual’s entrepreneurial ability might also increase. According to the model of Praag

and Cramer (2002) this then raises the probability of self-employment. Another possibility,

implying a negative sign, is that higher educated individuals earn higher salaries in the labor

market, which decreases their probability to choose for self-employment. Hence, the net

effect of the level of education variable for the propensity to become self-employed is not

clear at first sight. This is reflected by previous research that reports ambivalent results for

the sign of the level of education variable. According to Simoes et al. (2013) a u-shaped

relationship is found most often: self-employment probability is high in both ends of the level

of education distribution. This implies that in the present study dummy variables should be

included for different levels of education.

2.3.3.5 Wealth and capital constraints

An individual’s availability to capital influences the decision to become self-employed: an

individual who wishes to start up a business has to overcome the financial constraints

associated with establishing one’s own business6. The importance of this has been shown in

previous research by significance of variables approximating an individual’s wealth (Le,

1999). Perhaps this effect is also partly captured by the age variable because a higher age

implies more accumulated capital to overcome the financial constraints.

6 For example high initial investment, uncertainty in the first period etc.

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In the present study, inclusion of the financial constraints associated with self-

employment is done by including a dwelling owner dummy variable: owning a house can be

regarded as a proxy for accumulation of necessary wealth to become self-employed.

Moreover, an own dwelling can be used as collateral which increase possibilities for external

funding (Simoes et al., 2013). The same strategy is also carried out in Ekelund et al. (2005)

who find that home ownership is a significant variable with a positive sign in explaining the

probability of self-employment. However, they note that it is hard to distinguish between

home ownership as a cause or as a consequence of self-employment.

Wealth can also be included directly in the model, in the form of the accumulated

value of assets. However, Hartog et al. (2002) showed that this variable is prone to severe

measurement errors. This issue is discussed more extensively in the discussion of chapter 6.

Another problem with including wealth in the model is that wealth influences risk

aversion, as was also mentioned in paragraph 2.1. In this study this problem is partly solved

by comparing the results found using an absolute measure of risk aversion with the results

found using a relative measure of risk aversion, because both measures display different

reactions to changing wealth. This will be discussed more extensively in paragraph 3.2.

2.3.3.6 Family background, not in the LISS panel

Previous research often includes variables about an individual’s family background (see for

example Brown et al., (2011), Dohmen et al., (2011) and Ekelund et al., (2005)). However

these variables appear insignificant most of the times. This suggests that either family

background variables do not approximate one’s character well or that these variables have

also other influences on self-employment status in the opposite direction. However, self-

employment status of an individual’s father is an exception to this. An explanation for

significance of this variable is that either the individual takes over the family business of his

father or that a self-employed father reduces the psychological barrier to become self-

employed. Nonetheless, according to Skriabikova et al. (2014) it is not a problem that the

self-employment status of an individual’s father is not available in the present study. They

find that there is a strong causal relationship between risk attitude and the decision to

become self-employed and that this relationship is not driven by parental background

variables, like a self-employed father.

2.3.3.7 Unemployment status

Caliendo et al. (2009) find that the effect of risk aversion differs between individuals

becoming self-employed out of salaried work and individuals becoming self - employed out of

unemployment. They find that risk aversion is a significant variable only for the first group.

This can possibly be explained by the fact that already employed workers have more to lose

by giving up their job for self-employment and they can therefore be considered as more

14

willing to bear risk. In the present study this is partly taken into account by comparing the

results found using subsamples with and without unemployed individuals, as will be

discussed in paragraph 3.5.

2.4 Research question and hypotheses

The present study sought whether it is possible to predict an individual’s self-employment

status based on the aforementioned characteristics and a measure of risk aversion derived

from a partly incentive compatible lottery experiment. An affirmative answer can be expected

from previous research, as can be read in paragraph 2.3.2 and from the close relation

between risk taking behavior and an experimentally derived risk aversion measure, as is

discussed in paragraph 2.2. This induces the following two hypotheses:

A risk aversion measure from an incentive compatible lottery experiment is a significant

explanatory variable in predicting self-employment status (I) with a negative sign (II) in a

reduced form equation for this relationship.

3. Data and methods

Chapter 2 gives a good theoretical base to estimate a reduced form equation with the data

available in the LISS survey. In this section firstly the used LISS data sample is described.

Subsequently, the design of the conducted experiment and how a risk aversion measure can

be derived from that experiment is discussed. Thereafter follows the maintained approach to

find the final model for the probability of self-employment and the operationalization of the

included variables in that model. Lastly, the creation of subsamples for robustness checks is

considered.

3.1 Data: the LISS panel7

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). The LISS panel is a representative sample of Dutch individuals who participate

in monthly internet surveys. The panel is based on a true probability sample of households

drawn from the population register. Households that could not otherwise participate are

provided with a computer and internet connection. This procedure increases external validity

of research results based on the LISS panel by trying to prevent a biased main sample. In

this paper the data of the surveys of the year 2010 about background characteristics, work,

education, housing and assets are used. Moreover, the results of an experiment of the LISS

7 Based on obligatory description from CentERdata retrieved from:

http://www.lissdata.nl/assets/uploaded/References_LISS.pdf

15

panel conducted in December 2009 are used to derive three degrees of risk aversion for

each individual, which is discussed in paragraph 3.28.

3.2 Deriving different measure of risk aversion based on the LISS lottery

experiment

The experiment of the LISS panel aims to measure a participant’s attitude towards risk by

letting him choose five times between a varying sure payoff and a lottery that pays €65 or €5

with equal probability, so with an expected pay off of €359. The sure payoff varied from €20

to €40 in steps of €5. It was not possible to select indifference between the lottery and the

sure payoff.

This experiment is varied in a few ways to make sure that the derived degrees of risk

aversion are not measured with any systematic errors. Firstly, approximately 30% (10%) of

the participants made their choices for potentially normal (low) real payoffs and 30% {30%}

for hypothetical pay offs {scaled up by a factor of 150}. At the beginning of the experiment

the participants in the real payoff condition were encouraged to choose the option they really

preferred by a message that the decision in every option could determine the compensation

for the experiment. Only at the end of the experiment the participants in the real payoff

condition were told whether they won a prize and how much the prize was, this to ensure

incentive compatibility during the entire experiment. Noussair et al. (2013) use the data of the

same experiment and state that there are no differences between the results of the different

payoff conditions, which is in line with the results of previous incentive compatible lottery

experiments (for example Dohmen et al, 2011). This is discussed more extensively in

paragraph 4.1.

Moreover the side of the screen on which the lottery and sure payoff appeared is

varied. The lottery was displayed on the right side for one half of the subjects and on the left

side for the other half of the subjects. Furthermore one half of the subjects started with the

choice between the lottery and a sure payoff of €40 (€20) which decreased (increased) in

five steps to the sure payoff of €20 (€40).

From the choices of each subject three measures for the degree of risk aversion are

derived. The first measure of risk aversion is the frequency a participant chose the sure

payoff. This number can vary from zero to five, because the participant has to decide five

times between the lottery and the sure payoff. The higher the number, the more risk averse

the participant is. This measure is a simple measure, i.e. it is not derived using the utility

8 Data are retrieved from panel 1, 6, 9, 11, 38 and 81.

9 Harrison and Rutström (2008) find that this kind of experiment is reliable to determine a participant’s

coefficient of risk aversion. However, some discrepancy between the derived degree of risk aversion and an individual’s “real” degree of risk aversion will of course exist.

16

theory in paragraph 2.1. However, Kapteyn and Teppa (2011) show that a simple measure

may represent an individuals’ degree of risk aversion better than a sophisticated measure

based on economic theory, because the last measure makes unlikely assumptions about the

financial capabilities of an individual.

The other two measures are based on the following principle. Each participant

switches between the lottery and the sure payoff at a specific amount. For example, a

random selected participant preferred the lottery above a sure payoff of €25, but preferred a

sure payoff of €30 above the lottery. Due to the fact that the experiment did not collect data

about the sure payoff which made a participant indifferent between the lottery and the sure

payoff, the participant’s certainty equivalent is set to €27.5. This is the average of the last

value at which the participant preferred the lottery and the first value at which the participant

preferred the sure payoff. The bias which is created by this procedure can be considered as

normally distributed and is therefore not influential to the results.

Perhaps some extreme risk averse (risk loving) participants preferred the sure payoff

rather than the lottery in all instances. For these participants the certainty equivalent is set to

€42.5 (€17.5), the average of the highest (lowest) sure payoff and the logical next sure payoff

which was not included in the experiment. It’s unknown whether the switching point of these

participants would still be the same if the next option had been included.

Subsequently, the following equation is solved for each participant10:

(5)

The chosen utility function which is substituted for u in equation 5 is from both the power

utility family (see 3) and the exponential utility family (see 4). Equation 5 is solved for the

parameter θ. Then, using the found θ of the exponential (power) utility family, the coefficient

of absolute (relative) risk aversion is computed. These two different measures are derived to

take into account the common empirical finding of increasing relative risk aversion and

decreasing absolute risk aversion in wealth (Pratt, 1964). Moreover, all three risk aversion

measures can be used to check the robustness of the findings. This is useful because

Kapteyn and Teppa (2011) state that the way risk is measured may influence the found

results.

10

For participants in the high hypothetical payoff condition these numbers are scaled up with a factor k=150.

17

3.3 Procedure to derive a model for the relationship between risk and self-

employment

A top-down approach is used to see which of the explanatory variables of paragraph 2.3 are

included in the final model: the first model includes all variables which are meaningful

according to that paragraph and at the same time available in the LISS panel. This model is

refined to the final model with diagnostic tests indicating whether these refinements are

improvements.

The choice to become self-employed is modeled in the following way:

[ ] ) with )

(6)

In equation 6 is the systematic part in which is a vector summarizing the

different control variables and is one of the above three measures of risk aversion11. is

the individual specific effect which takes the possibility into account that individuals with the

same value of the systematic part may choose differently about becoming self-employed. For

the density function F either the standard normal density function (probit model) or the logit

density function (logit model) is chosen. Both models are non-linear and therefore the

method of maximum likelihood is used to estimate the coefficients.

3.4 Operationalization of the variables

To estimate equation 6, the dependent, control, and risk aversion variables are

operationalized as is shown in table 1.

11

So each equation is estimated three times, each time with a different measure of risk aversion for r i.

18

Table 1

Variables used to estimate the reduced form equation

Dependent variable Operationalization

SE Self-employment dummy: is one if an individual

answered affirmative on the question “Are you self-

employed or do

you work in a family business, or are you a

freelancer?

Independent variables: control

variables

MALE Dummy variable which is one for males.

AGE The age of an individual.

AGESQ The quadratic age of an individual.

MARRIED Is one for a married individual.

NUMCHILD12 The number of children of an individual.

VMBO, HAVOVWO, MBO, HBO,

WO 13

Dummy variables for the highest attained grade; is

one when the highest level of education is of that

type. Reference group: primary school.

HOMEOWNER Is one when an individual owns a home.

Independent variable: risk aversion

measures

NUMSAFE, ARE, RRP Degree of risk aversion, respectively: NUMber of

SAFE choices, Absolute Risk aversion measure

based on Exponential utility, Relative Risk aversion

measure based on Power utility.

3.5 Creating subsamples for robustness checks

5788 LISS panel data members were selected to participate in the lottery experiment

described in paragraph 3.2. 3457 members completed the part of the experiment (59.2%)

used in this paper. The 464 participants (13.4% of the complete responses) who switched

more than once between the sure payoff and the lottery are deleted from the sample.

Furthermore, the 103 participants (2.9%) who preferred a certain payoff above the lottery at

12

As will be discussed in paragraph 4.3 this variable is not included in the final model because it does not measure the number of children of the individual i but the number of children of the household head. 13

Dutch educational grades, respectively: preparatory intermediate vocational school (VMBO), junior/senior high school (HAVOVWO), intermediate professional education (MBO), higher professional education (HBO), academic education (WO).

19

one point in the experiment, but switched to the lottery when the sure payoff increased are

eliminated as well. Both behaviors violate the assumption of rational preferences. This

procedure results in 2890 useful observations. After merging the experimental results with

the participant’s personal characteristics necessary for the analysis, 2651 observations

(76.7% of the complete responses) are left. There are no signs that the unmerged and

eliminated observations differ in some important way from the kept observations. The sample

contains sufficient observations to say that the study is set up successfully for testing the

hypotheses.

From the primary sample of 2651 observations, five subsamples are created. First,

the sample is split by creating two subsamples consisting of 1043 (1608) participants who

were in the real (hypothetical) payoff condition. Another three subsamples are created out of

these two subsamples and the primary sample by eliminating the individuals whose job

status is unknown14. In the primary (real payoff condition) {hypothetical payoff condition}

sample 819 (322) {497} of those individuals are present. For 693 (272) {421} of those

individuals can be derived that they can be classified as unemployed. This means that they

have not had a job for at least four years or that they are studying and older than 26, but that

they used to work in the past.

As discussed above, many observations are lost by creating the subsamples. In order

to take advantage of the high number of observations in the primary sample, this sample is

considered as the basis of a more thorough analysis for the relationship between self-

employment status and risk aversion15.

The reason for the creation of the subsamples is threefold. Firstly, Caliendo et al.

(2009) found that the effect of risk aversion on the decision to become self-employed is

different for unemployed individuals as compared to wage-employed individuals16. Because

the group whose job status is unknown consists mainly of unemployed individuals, a different

result might be found by analyzing a subsample without them. Secondly, several reasons

exist for the fact that an individual does not report its job status. This makes the interpretation

of the effect of the risk aversion measure on self-employment status unclear in the full

sample, because in that case the group of individuals who is not self-employed is a mixture

of wage-employed individuals, unemployed persons, pensioners, workers in the black

14

This means that both unemployed individuals and individuals that did not report their job status are left out. 15

However, by using the full sample the incentive compatible aspect of the risk aversion measures is partly decayed. This implies that the argument based on incentives in favor of the hypotheses becomes less strong. 16

In the present study the real influence of this cannot be measures because no data are available of individuals transitioning to self-employment from unemployment. However, the effect may still be present by a smaller degree of risk aversion of the unemployed individuals.

20

economy etcetera17. Thirdly, it may be possible that the degrees of risk aversion of the

participants are influenced by the payoff condition of the experiment, as was also found by

Holt and Laury (2002), and hence the observations from the different conditions are

separated. The differences between the samples are summarized in table 2, which can be

found in the appendix.

4. Results

Now that the methods are discussed, it is time to see what results are found using these

methods. Firstly, the derived degrees of risk aversion are compared between the

experimental payoff conditions. Secondly, sample characteristics of self-employed individuals

are compared with those of not self-employed individuals. Thirdly, the final model is derived

and some diagnostic tests are carried out to review the performance of that model. Fourthly,

it is checked whether the found results hold in the created subsamples and robustness with

respect to the operationalization of the self-employment variable is discussed. Fifthly, the

influence of potential outliers on the results is considered. Finally, the problem of and

potential solutions for heteroskedasticity are addressed.

4.1 Comparing the derived risk aversion measures by payoff condition

Regarding the derived degrees of risk aversion is expected that these may differ between the

experimental payoff conditions. This expectation is confirmed18 by t-tests as displayed in

table 3. Moreover, results of the non-parametric Wilcoxon rank-sum test, carried out

because normality of the data is doubtful, agree with this (r = number of safe choices: W = -

4.660, p < .000, r = relative risk aversion: W = 4.636, p < .000, r = absolute risk aversion W =

-13.426, p < .000).

In the introduction was mentioned that Camerer and Hogarth (1999) found that

adding incentives to a risky choice question reduces the variance of the results. This

statement implies a lower variance for the degrees of risk aversion derived from the real

payoff condition in comparison with those from the hypothetical payoff condition. This

statement appears untrue for all derived risk aversion measures, as can be seen in the last

column of table 6 (r = number of safe choices: F(1043, 1608) = 1.079, p < .914, left-tailed, r =

relative risk aversion: F(1043, 1608) = 1.310, p < 1, left-tailed, r = absolute risk aversion

F(1043, 1608) = 1.088, p < .935, left-tailed). Results of the non-parametric Kruskal Wallis

variance test, again carried out because normality of the data is doubtful, show that the

variance does differ between the payoff conditions (r = number of safe choices: K = 19.112, p

17

So eliminating them makes the group of not self-employed more homogenous, which is also done in for example Brown et al. (2011). 18

Assuming the 5% significance level for this entire paper.

21

< .000, r = relative risk aversion: K = 173.767, p < .000, r = absolute risk aversion K =

18.912, p < .000). However, by the bigger standard errors in the real payoff condition

displayed in table 3 can be derived that this difference is not in the direction expected from

the research of Camerer and Hogarth (1999).

The above results have the following implications for this research. Testing whether

the results found in the primary sample still hold in a subsample split up by payoff condition

matters, because both parametric and non-parametric test statistics indicate that there may

be differences between the samples. However, results with a higher level of significance

because of incentives in the lottery experiment are not expected anymore since the incentive

compatibility appears not to have reduced the variance of the derived risk aversion

measures, as confirmed by both parametric and non-parametric test statistics.

Table 319

Summary statistics of the risk aversion measures for the different payoff conditions

4.2 Differences between self-employed and not self-employed individuals

In table 4 within sample differences between self-employed and not self-employed

individuals are summarized. In the last column of this table the p value for equal means

based on the Wilcoxon rank sum test is displayed. This test is used instead of the regular t-

test because the number of self-employed individuals is small and therefore it is risky to

assume normality. Moreover, in the third column is displayed whether the difference between

the means of self-employed and not self-employed individuals are in line with the theoretical

part of this paper. In this case the words “Yes and No” mean that previous research found

ambivalent results with respect to the sign of this variable.

19

* means significant at a 10% level, ** means significant at a 5% level, *** means significant at a 1% level.

Only hypothetical Only Real

N 1608 1043

Risk aversion measure Mean Std. Err. t (∞) p Mean Std. Err. F (1043, 1608) p (H1: F<1 )

Number of safe choices 3,632 1,730 4,139*** 0,000 3,340 1,797 1,079 0,914

Absolute (exponential utility) 0,014 0,001 -13,371*** 0,000 0,027 0,001 1,310 1,000

Relative (power utility) -0,615 0,014 4,075*** 0,000 0,525 0,018 1,088 0,935

22

Table 4

Comparison between self-employed and not self-employed individuals20

From table 4 can be derived that the means of all background characteristics between

the group of self-employed individuals and the group of not self-employed individuals are in

line with theory. However, none of the differences is significant, except for the difference in

level of education (p < .005, two-tailed).

It will be recalled that self-employed individuals are expected to be less risk averse

than their not self-employed counterparts. As can be seen in figure 2, the distribution of the

relative risk aversion measure tends to be slightly more left skewed than for not self-

employed individuals, indicating that this expectation may be right. The means of all risk

aversion measures in table 4 are also in accordance with that expectation: self-employed

individuals do make less safe choices in the lottery experiment (3.33) than those who are not

(3.53) and have a slightly lower degree of absolute and relative risk aversion (-0.002 and -

0.062 difference respectively). But as mentioned before the differences are not statistically

significant. However, fitting the data in a binary choice model may give different results for

the signs and significance of these variables, because this technique takes into account all

side effects caused by the background characteristics.

20

Level of education is measured as an ordinal variable as maintained by Statistics Netherlands, ranging from 1 (primary school) to 6 (university degree).

Not self-employed Self-employed Expected from theory? p value Wilcoxon statistic

N 2522 129

% Male 48,4% 56,6% Yes 0,0687*

Age 48,955 49,829 Yes and No 0,654

% Married 59,4% 62,0% Yes and No 0,555

% Partnered 76,5% 74,4% Yes and No 0,590

% With children 39,1% 40,3% Yes and No 0,769

Number of children 0,798 0,829 Yes and No 0,784

Education level 3,508 3,891 Yes and No 0,005***

% Own dwelling 74,8% 79,1% Yes 0,281

Number of safe choices 3,527 3,333 Yes 0,221

Absolute risk aversion 0,019 0,017 Yes 0,515

Relative risk aversion 0,582 0,520 Yes 0,219

23

Figure 2

Distribution of the relative risk aversion measure21 for self-employed and not self-employed

individuals

4.3 The final model

Before the final model can be used, some decisions have to be made. Firstly, a decision

about which distribution function F to use has to be made. Unreported results show that in a

model with only the exogenous covariates22 age, squared age and a male dummy the logit

and probit model fit the data on average equally well, regardless the used measure of risk

aversion. Because the choices are very unbalanced, i.e. there are far more not self-

employed individuals in the sample than self-employed individuals, the logit function is

chosen as the cumulative density function in the final model23, since this function has larger

values in its both tails.

Secondly, a decision regarding whether to use normal or robust standard errors has

to be made. Unreported results show that in none of the used models a variable changes

from significant to insignificant or the other way round by changing the used type of standard

errors. Moreover, using normal standard errors increases joint significance and goodness of

fit of the models in some cases, but decreases those in other cases. Because of a lack of a

compelling reason to use robust standard errors, normal standard errors are used. This topic

is elaborated more extensively in paragraph 4.6.

Thirdly, a top down approach is used to derive which control variables to include in

the vector X of equation 6. This approach requires that in the first estimate X contains all

control variables from table 1. The estimation is carried out separately for each measure of

21

The result that the distribution is more left skewed for self-employed individuals is valid for all risk aversion measures. 22

Only purely exogenous variables are used in order to prevent any interfering influences on the model shape function from possibly endogenous variables. 23

Unreported results show that all results of the present study are the same if the probit model had been used.

0.1

.2.3

.4.5

Frac

tion

-.5 0 .5 1pown

self-employed not self-employed

24

risk aversion24. The estimation results of this model, from now on called the full model, are

shown in column 1 to 3 of table 5. From this table can be deduced that only the age and

squared age variable are significant in explaining self-employment status. The other control

variables in X and the risk aversion measure are highly insignificant and some have the

wrong sign. The dummy variables for level of education all have a different effect which was

expected from the theory. However, a likelihood ratio test on joint significance shows that

these dummies are jointly insignificant regardless the risk aversion measure used (r =

number of safe choices, χ2 (5) = 7.17, p < .21, r = absolute risk aversion, χ2 (5) = 7.28, p <

.20, r = relative risk aversion, χ2 (5) = 7.18, p < .21). As can be seen in column 4 to 6 in table

5, leaving out these dummy variables results in a significant male dummy variable at a 10%-

level with insignificant other control variables, regardless the used measure of risk aversion.

The top down approach now requires that the own dwelling dummy is eliminated. As can be

seen in column 7 to 9 this doesn’t result in a significant married variable, so lastly this

variable is left out as well, resulting in the purely exogenous model.

Table 5

Results of the different models proposed by the top down approach

To see whether the top-down approach has resulted in a well-specified model, a logit

regression of self-employment status on the by the exogenous model predicted value (ŷ) and

on the squared predicted value (ŷ2) is carried out. The results of this test are striking: ŷ is

insignificant in the exogenous model, regardless the used degree of risk aversion (r =

number of safe choices, Z = 0.01, p < .99, two-tailed, r = absolute risk aversion, Z = -0.31, p

< .67, two-tailed, r = relative risk aversion, Z = 0.03, p < .97, two-tailed). This indicates that

there is a severe misspecification problem present in the exogenous model. Adding back all

the control variables from the first estimation slightly improves the results of this test, but ŷ

remains highly insignificant. Another possible solution is to add some interaction variables to

account for different effects of the risk aversion measure between groups, as was also done

24

Please note that the number of children variable is not in X because after inspection this variable appeared insolvably distorted.

1 2 3 4 5 6 7 8 9

Risk aversion measure NUMSAFE ARE RRP NUMSAFE ARE RRP NUMSAFE ARE RRP

Coefficient -0,0301733 -0,9298816 -0,1034671 -0,03662 -1,32409 -0,12255 -0,036849 -1,41454 -0,1228

p - value risk aversion measure 0,552 0,806 0,519 0,468 0,726 0,441 0,464 0,708 0,439

Covariate included? Significance(1%/5%/10%-level)

Exogenous variables (AGE, AGESQ, MALE) Yes; Except MALE Yes; Except MALE Yes; Except MALE Yes; 10% Yes; 10% Yes;10% Yes; 10% Yes; 10% Yes; 10%

5 level of education dummies Yes; No Yes; No Yes; No No No No No No No

Married dummy Yes; No Yes; No Yes; No Yes; No Yes; No Yes; No Yes; No Yes; No Yes; No

Own dwelling dummy Yes; No Yes; No Yes; No Yes; No Yes; No Yes; No No No No

MC Fadden's R squared 0,0296 0,0293 0,0297 0,0227 0,0223 0,0228 0,0221 0,0218 0,0228

25

in previous research (see for example, Hundley, 2001). Based on previous research

interaction terms between the risk aversion measure and the different educational

categories, degree of urbanization categories, civil status and gender are added.

Nonetheless, this still results in a misspecified model according to insignificance of the

predicted value of ŷ (results of these tests are available upon request). This might indicate

that the real explanatory variable for predicting self-employment status is missing in all

previous tried out models. Considering the theoretical part this may be a variable which

measures entrepreneurial drive, the ability to overcome the financial constraints associated

with becoming self-employed or some family background characteristic, which are all not

available for this sample. Another explanation could be that the risk aversion measures

derived from the lottery experiment are not a good proxy for real risk taking behavior. This is

discussed more extensively in chapter 6.

But not all is lost for the full model. Perhaps its goodness of data fit is better than that

of the exogenous model. In table 6 both models are compared by several data fit diagnostics.

As can be derived from this table, some statistics support the exogenous model and other

statistics support the full model. But all in all a conclusion can be drawn from table 6: the

difference in the Bayesian information criterion of approximately 47 between the two models

gives strong support for using the exogenous model (Kass & Raftery, 1995), regardless the

used risk aversion coefficient.

Table 6

Comparison of goodness of data fit between the full model and the exogenous model

4.4 Results found using the final model

The results found by using the exogenous model proposed by the top down approach are

displayed in table 7. As can be seen, the signs of the three different risk aversion measures

are in line with theory and confirm the second part of the hypothesis. This could already be

NUMSAFE ARE RRP

Full model Exogenous model Difference Full model Exogenous model Difference Full model Exogenous model Difference

Log-Likelihood Full Model -500,499 -504,652 4,153 -500,644 -504,855 4,211 -500,468 -504,621 4,153

Likelihood ratio (d.f.) 30,524 (11) 22,217(4) 8,307(7) 32,070(11) 23,707(4) 8,362(7) 30,585(11) 22,280(4) 8,305(7)

Prob > LR 0,001 0,000 0,001 0,001 0,000 0,001 0,001 0,000 0,001

McFadden's R2 0,030 0,022 0,008 0,029 0,021 0,008 0,030 0,022 0,008

McFadden's Adj R2 0,006 0,012 -0,006 0,006 0,011 -0,005 0,006 0,012 -0,006

Maximum Likelihood R2 0,011 0,008 0,003 0,011 0,008 0,003 0,011 0,008 0,003

Cragg & Uhler's R2 0,036 0,026 0,010 0,035 0,025 0,010 0,036 0,026 0,010

McKelvey and Zavoina's R20,087 0,071 0,016 0,087 0,070 0,017 0,087 0,071 0,016

Efron's R2 0,011 0,008 0,004 0,011 0,007 0,004 0,011 0,008 0,003

Variance of ŷ 3,604 3,540 0,063 3,602 3,538 0,065 3,604 3,541 0,063

AIC 0,387 0,384 0,002 0,387 0,385 0,002 0,387 0,384 0,003

BIC -19801,427 -19848,299 46,872 -1980,137 -19847,849 46,757 -19801,489 -19848,362 46,874

26

expected from the results in table 4, which display the same pattern of lower risk aversion for

self-employed individuals. However, all risk aversion coefficients are insignificant when

tested with the regular t-test, which rejects the first part of the hypothesis. This may be

caused by the large standard errors due to the misspecified model. Furthermore, MC

Fadden’s R2 is very low while the likelihood ratio test on joint significance indicates that the

used model is statistically significant (r = number of safe choices, χ2 (4) = 22.22, p < .000, r =

absolute risk aversion, χ2 (4) = 22.28, p < .000, r = relative risk aversion, χ2 (4) = 22.41, p <

.000). This combination of statistical significance with a low R2 is typical for binary choice

models about individual behavior: the model does not work well in describing individual

decisions but is able to show an overall pattern of the behavior. Besides, the (unreported)

classification table of this model reflects very small predictive power: the complete sample is

classified as not self-employed, i.e. none of the self-employed individuals is classified as self-

employed, regardless the used measure of risk aversion.

Table 7

Results final model

It is interesting to see whether the aforementioned results are robust when the final

model is estimated using the different subsamples described in paragraph 3.5. As shown by

table 8, eliminating the observations with missing job status does not alter the signs of the

risk aversion measures. However, not displayed in table 8, this makes the exogenous

variables insignificant.

Table 8

Robustness checks for the results of the final model using a subsample without individuals

with missing job status

Risk aversion measure NUMSAFE ARE RRP

Coefficient risk aversion measure -0,039 -1,613 -0,129

Sign in line with theory Yes Yes Yes

p value risk aversion measure 0,439 0,668 0,415

Joint significance (p value LR-test) 0,000 0,000 0,000

Goodness of fit (p value Pearson chi squared) 0,968 0,979 0,846

Mc Fadden's R squared 0,022 0,021 0,022

Subsample Full no job status excl. Full no job status excl. Full no job status excl.

Risk aversion measure NUMSAFE ARE RRP

Coefficient risk aversion measure -0,035 -0,636 -0,119

p value risk aversion measure 0,501 0,707 0,464

Mc Fadden's R squared 0,033 0,032 0,033

Result in line with results of the full sample yes yes yes

27

The same applies when only participants of the real payoff condition are considered25,

as can be seen in table 9. Deleting the observations with missing job status from this sample

does not make a difference with respect to the sign or significance of the risk aversion

measure26, as the values in the table 9 show.

Table 9

Robustness checks for the results of the final model using the real payoff condition

subsample

If merely the participants within the hypothetical payoff condition are considered the

age and squared age variables remain significant27, but the male dummy variable becomes

insignificant. In addition, all signs of the risk aversion measures change from negative to

positive, but still all risk aversion measures remain insignificant, as can be seen in table 10.

Deleting the observations with missing job status from this sample does not alter these

results, except for an insignificant squared age variable.

Table 10

Robustness checks for the results of the final model using the hypothetical payoff condition

subsample

Because the number of safe choices variable has a straightforward interpretation and

showed the best performance in previous research, this variable is investigated more

thoroughly. From this risk aversion measure three dummy variables are created. The first

(second) {third} one has the value one when a participant makes less than three (two) {one}

25

However, the exogenous variables age, squared age and the male dummy variable remain significant at the 10% significance level using this subsample. 26

But the exogenous variables are now also not significant anymore using the 10% significance level. 27

At a 5% significance level in contrast to the 1% significance level in the full sample.

Subsample Real Real Real Real no job status excl. Real no job status excl. Real no job status excl.

Risk aversion measure NUMSAFE ARE RRP NUMSAFE ARE RRP

Coefficient risk aversion measure -0,070 -4,752 -0,236 -0,057 -3,711 -0,205

p value risk aversion measure 0,341 0,369 0,306 0,453 0,495 0,391

Mc Fadden's R squared 0,049 0,049 0,050 0,046 0,046 0,047

Result in line with results of the full sample yes yes yes yes yes yes

Subsample Hypothetical Hypothetical Hypothetical Hypothetical no job status excl. Hypothetical no job status excl. Hypothetical no job status excl.


Coefficient risk aversion measure 0,010 0,612 0,036 0,006 1,318 0,021



Result in line with results of the full sample no no no no no no

28

safe choice(s), because a participant can to a certain extent be considered as risk loving in

that case. Unfortunately, unreported results show that all these three dummy variables are

also insignificant in explaining self-employment status regardless which control variables

from table 1 are included.

The last thing which is tried to improve the post estimation performance of the

exogenous model is using a different definition of self-employment. In all previous models an

individual was characterized as self-employed when working as a self-employed, a

freelancer or when owning a family business. Now two new self-employment variables are

created. In the first one the freelancers from the original group are eliminated in order to

ensure homogeneity of the investigated group, namely only self-employed individuals with

staff. In the second one, independent professionals28 are added to the original group of self-

employed individuals to see whether including them alters the results. A third one could

exclude family business owners from the group of self-employed. These individuals might

have inherited the family business and therefore their self-employment status is not the result

of a low degree of risk aversion. Because only three family business owners are present in

the sample, this definition is not put to the test.

Unreported sample statistics show that there are only extremely small differences

between the original group and the two new created groups of self-employed individuals.

Table 9 shows the results of the logit regression using the exogenous model with the

different operationalizations of self-employment. The signs of the risk aversion measures

when independent professionals are included are similar to those of the original

operationalization. However, when the freelancers are left out, all risk aversion measures are

predicted with the wrong sign as shown in table 11. This last result is exactly the opposite of

the result when the original definition of self-employment is used. This implies that the results

are extremely sensitive to the definition of self-employment. Please note that still all risk

aversion measures appear insignificant.

Table 11

Robustness checks for the results of the final model for different operationalization of self-

employment

28

A clear description of this group lacks in current literature.

Operationalization of self-employment Minus freelancers Plus independent professionals


Coefficient risk aversion measure 0,038 1,525 0,128 -0,032 -2,196 -0,103



Result in line with results of the original definition no no no yes yes yes

29

4.5 Detecting influential observations

The unsatisfactory results of paragraph 4.4 may be caused by outliers and influential

observations, because logit models are very sensitive to both. Whether these are present in

the full sample is checked using the exogenous model with the absolute risk aversion

measure in this section29.

Looking to observations which are more far away from other observations may gain

insight in whether outliers are present30. Pearson residuals are displayed in figure 3,

deviance residuals are displayed in figure 4 and the observations’ leverages are displayed in

figure 5, all against their id number. From these graphs can be concluded that there are

indeed some observations with high residual values, but that their influence on the estimates

is quite small as can be read from figure 5 (leverage < 0.03).

Figure 3 Figure 4

Pearson residuals against id number31 Deviance residuals against id number31

Some observations may be outliers in the sense that they have big impact on the

goodness of fit of the model. To detect them, an approximation of the difference in the

Pearson χ2-statistic for each observation is computed. In figure 6 each dot is an observation,

and the belonging y-value represents the (approximation of the) reduction of the value of the

Pearson χ2-statistic if that observation is eliminated. As a rule of thumb is used that an

observation is regarded as an outlier if its influence on the χ2-statistic is twice as big as the

mean influence. Unreported results show that leaving out these observations slightly

improves the goodness of fit of the exogenous model.

29

Unreported results show that the results of this paragraph are invariant to the used degree of risk aversion. 30

The more common method of looking to observations which are far away from their predicted probability is not used because of the bad post estimation performance of the exogenous model. 31

A one (zero) next to an observation indicates that an individual is (not) self-employed.

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-2-1

01

23

devia

nce r

esid

ual


30

But before eliminating these observations, it may as well be interesting to see what is

special about them. They all turn out to be self-employed individuals with a low or high age32.

This is indeed not what is expected from the theory, but these observations cannot be

considered as outliers in the sense that they must be data entry errors and hence these

observations are not eliminated.

Figure 5 Figure 6

Pregibon leverage against id number31 Δχ2-statistic against id number31

Another possibility is that there are some observations with big impact on the

estimated coefficients. This is investigated by looking to an observation’s Pregibon’s dbeta,

which measures the influence of a covariate pattern on a coefficient estimate. A rule of

thumb for this statistic is that an observation can be considered as influential if it has a

Pregibon’s beta larger than 0.2. In figure 6 can be seen that according to this rule eight

observations have influential impact on the estimates. Further inspection of these

observations reveals that those observations are all 17 year-old males with 3 safe choices in

the lottery experiment and a certainty equivalent of 27.5. There is nothing suspicious about

this covariate pattern so there is no reason to eliminate these individuals.

32

Observation number 848934 is a male aged 19 who is self-employed, but can be considered as risk averse. Observation number 863528 is a female aged 69 who is self-employed and risk loving. Observation number 891308 is a 24 year old male who is self-employed and risk averse.

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31

Figure 7

Pregibon's dbeta against id number24

All in all can be concluded that there are no real outliers present with respect to the

combination of the exogenous covariates and the derived degrees of risk aversion. There are

some influential observations in terms of influence on the estimated coefficients or influence

on goodness of fit statistics but further inspection of these observations shows that there is

no reason to exclude them from the analysis.

4.6 Heteroskedasticity and its possible solutions

The bad post estimation performance of the exogenous model can also have another cause:

heteroskedasticity. By inspecting the estimation results for heteroskedastic residuals, a

severe problem is encountered: in a misspecified logit model, which the used exogenous

model clearly is, it is impossible to distinguish between heteroskedastic residuals due to this

misspecification and non-constant residuals due to different variances between groups in the

sample. Because no variables to solve the misspecification problem are available, as is

discussed in paragraph 4.3, it is tried to solve the heteroskedasticity problem with the

available variables.

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.2.4

.6

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32

Figure 8 Figure 9

Pearson residuals against level of education33 Pearson residuals against the degree of urbanization34

Previous research indicates that the level of education has a different effect on the

decision to become self-employed for individuals belonging to different educational

categories (see e.g. Le, 1991). Self-employed individuals are most present at both ends of

the level of education distribution (Simoes et al., 2013). Therefore it can be expected that the

variance for individuals belonging to the highest and lowest educational categories is

different from the variance of individuals belonging to the other categories. Moreover, it can

be argued that other variables which are not included in the model but influential on self-

employment status, e.g. available wealth and entrepreneurial ability, could differ between

individuals with different educational degrees as well. Figure 7 provides some very weak

support that the variance differs between the levels of education. However, unreported

results show no noteworthy differences between regression results when the variance is

allowed to differ between educational categories35.

Furthermore previous studies include regional dummies in their reduced form

equation for self-employment (see for example, Brown et al., 2011), because labor markets

tend to vary between regions. Unfortunately, the region of the participants of the LISS panel

is not available. However, a classification in the categories extremely urban to not urban is

available. The probability to become self-employed might be higher in an extremely urban

region because there is a larger market for services offered by self-employed individuals.

However, the probability of self-employment might also be lower in extremely urban regions

because more jobs are available and hence there is less need to become self-employed.

Both explanations state that variances differ between individuals belonging to regions with

33

Level of education in categories maintained by Statistics Netherlands, ranging from 1 (primary school) to 6 (university degree). 34

1 means extremely urban, 5 means not urban at all 35

This result is invariant to whether the educational degree dummies are included in the model or not.

-20

24

6

sta

nda

rdiz

ed

Pe

ars

on r

esid

ual

1 2 3 4 5 6Level of education in CBS (Statistics Netherlands) categories

-20

24

6

sta

nda

rdiz

ed

Pe

ars

on r

esid

ual

1 2 3 4 5Urban character of place of residence

33

different degrees of urbanization. However, figure 8 shows only very weak support for this

reasoning and unreported results show no noteworthy differences between regression

results when the variance is allowed to differ between regions with a different degree of

urbanization36.

5. Conclusion

Summarizing, the derived degrees of risk aversion turned out not to be significant

explanatory variables for self-employment status, as was also found in Tucker (1988), Parker

(2008) and Dohmen et al. (2011) and therefore the first hypothesis of this paper is rejected. A

negative sign for all risk aversion measures is found, so the second hypothesis is not

rejected. Moreover, the consistency of the negative signs for the different used measures of

risk aversion implies that there might be at least some relationship between risk aversion and

self-employment. However, it appeared impossible to find a non-misspecified model to

explain the relationship between self-employment status and risk aversion, probably because

the main determinant is missing in the available data. The exogenous model fits the data the

best, but still has bad predictive quality. This is not caused by outliers in the data or

extremely influential observations. From a theoretical point of view it seems plausible that the

error terms in the exogenous model are heteroskedastic, but because of miss specification it

is impossible to detect its source. The results are invariantly insignificant to the used

measure of risk aversion, only considering participants in the real or hypothetical payoff

condition and whether individuals with unknown job status are left out of the sample. In fact,

the results are even invariant to all different possible combinations of these factors.

Moreover, maintaining a different definition of self-employment does not generate results

which are significant and even shows that the signs of the risk aversion measures are

extremely sensitive to this defintion.

6. Discussion

From the results in chapter four follows that a theoretically underbuilt model works worse

than a model with only exogenous variables, using the data of the LISS panel. In this section

is discussed what probably causes this and how these flaws can be prevented in future

research within this field.

One part of the answer lies within the used model: the logit binary choice model is

very sensitive to misspecification because the estimates become biased, inefficient and

inconsistent in that case. This may be one of the reasons that the risk aversion measures are

36

This result is invariant to whether the different degree of urbanization dummies are included in the model or not.

34

insignificant in the exogenous model. This is tested by using the less sensitive linear

regression technique in a model based on the reverse relationship between self-employment

and risk aversion, i.e. in which way self-employment status influences risk attitude37, as is

discussed in paragraph 2.3.2. If the coefficient of the self-employment dummy variable is

significant with the right sign in this reverse model, this could be a not-waterproof38 signal

that insignificance of the risk aversion measures is caused by the sensitivity to

misspecification of the logit model. However, table 12 shows that the self-employment

dummy variables are still insignificant in the reverse relationship estimated using linear

regression. This result weakly indicates that the sensitivity of the logit model cannot be fully

blamed for the found results.

Table 12

Results of applying linear regression on a model based on the reverse relationship between

risk aversion and self-employment

Another possible explanation for the insignificant results could be that the derived

degrees of risk aversion are not a good proxy for risk taking behavior in real life, as Dohmen

et al. (2011) mention. This constructional invalidity can be examined by the combining the

results of the used lottery experiment with the results of another experiment of the LISS

panel, in which participants had to answer a self-assessment risk question39, as is discussed

in paragraph 2.2. 84 LISS panel members participated in both experiments and from them

both risk aversion measures are available. As can be seen in table 13, the correlation

between the answer on the self-assessment risk question and the from the experiment

derived degrees of risk aversion is in the right direction, albeit modest in magnitude. This

may be a sign that the used lottery experiment is not the best way to approximate real life

risk taking behavior. Another sign for this is the found difference in risk aversion between

participants in the real payoff condition and the hypothetical payoff condition: employing both

payoff conditions in the same experiment might have resulted in inconsistent degrees of risk

aversion between the two payoff conditions. Hence, a tentative conclusion of the present

37

Among the regular exogenous control variables age, squared age and a male dummy. 38

Assumptions necessary for reliable OLS estimates are highly violated, for example because the dependent variable is not continuous etc. 39

This question is: “how do you see yourself: are you generally a person who is fully prepared to take risks or do you try to avoid taking risks”. Answers are given on a 10-point Likert scale: 0 means ‘Not at all willing to take risks’ and 10 means ‘Very willing to take risks’.

Dependent variable NUMSAFE ARE RRP

Coefficient of the self-employment dummy variable -0,125 -0,001 -0,042

p value self-employment dummy variable 0,429 0,671 0,405

Sign corresponds to sign of the risk aversion measure in the exogenous model Yes Yes Yes

35

study is that a human’s risk taking behavior is too complicated to capture in a partly incentive

lottery experiment with just five choices, as the one used in the present study. In future

research the design of the lottery experiment should be revised: it is interesting to see

whether adding larger and smaller sure payoffs and an indifference option to the experiment

alters the found degrees of risk aversion.

Table 13

Correlation between the general risk measure and the derived degrees of risk aversion

A last explanation for the insignificant results is the lack of a main determinant of self-

employment status, as suggested by a logit regression of self-employment status on ŷ and

ŷ2, as is discussed in paragraph 4.4. The theoretical model of Praag and Cramer (2001)

states that this missing determinant of the decision to become self-employed might be

entrepreneurial ability, but none of the available variables is a good proxy for this.

Moreover, another potential missing determinant of self-employment status might be

the ability to overcome the financial constraints associated with setting up an own business.

Perhaps an individual’s accumulated wealth is a better proxy for this, than whether the

individual has an own dwelling, as is included in the model from paragraph 4.3. An

accumulated wealth variable was not used in the analysis because firstly previous research

found that this variable is prone to severe measurement errors, secondly it is hard to

distinguish between high wealth as a cause of self-employment and high wealth as a

consequence of self-employment and thirdly wealth variables were only available for 1541

participants of the lottery experiment. Deleting the observations without available wealth

status would have decreased the sample size with roughly 40% and could have created a

biased main sample because there might be a link between risk aversion and willingness or

ability to complete the questions in a financial assets survey40. Table 14 shows what

happens if logged accumulated wealth41 is added to the analysis. Again all risk aversion

measures are predicted with the insignificant right sign, regardless whether mortgages and

financial assets are included in the logged wealth variable. It is noteworthy that the logged

wealth variable appears insignificant, but increases the significance of the simple and relative

40

Self-employed individuals may have more financial literacy for example, other explanations are also possible. 41

Operationalized as the total value of total assets (money, investments, real estate, expensive valuables, loans, life insurance) minus outstanding debts.

Correlation with the answer of the general risk measure

Number of safe choices -0,334

Absolute risk aversion -0,198

Relative risk aversion -0,330

36

risk aversion measure as compared to the exogenous model, as can be seen by comparing

table 14 with table 7. This may indicate that the ability to overcome the financial constraints is

indeed an important omitted variable in the exogenous model, but that the operationalization

of this variable is not right yet or that measurement errors disturb the model improvement of

including this variable.

Table 14

Results of the exogenous model when a logged wealth variable is added

Other shortcomings of this research are the big amount of irrational participants in the

experiment potentially creating bias in the sample. Of course, an individual may display

irrational behavior in both real life and experimental settings. However, possibly some

participants made mistakes in the experiment because they did not understand the

questions: 46.5% of the participants reported that the questions were difficult or very difficult

to answer and 28.3% addressed that the questions were unclear or very unclear. Irrationality

caused by unclearness of the questions should be minimized in a future experiment42. This

can probably be reached by reformulating the questions, explanations by a real person,

different graphics and control questions whether the participant understood the experiment.

Furthermore, the lack of family background characteristics, as used in other research

about this topic, makes it hard to compare the found results of the present study with those of

other studies. Moreover, the sample appears not to be representative with respect to the

percentage of self-employed individuals it contains: 7.0% of the sample’s labor force43 is self-

employed, compared to 14% of the Dutch labor force in 2009 (Centraal Bureau voor de

Statistiek [CBS], 2014). In addition, because the signs of the risk aversion measure appear

sensitive to the definition of self-employment, it may be interesting to examine the differences

among self-employed individuals in different categories of self-employment more thoroughly,

e.g. “Do freelancers have different characteristics than owners of family businesses?”.

42

For example by reformulating the questions, explanations by a real person, different graphics and control questions whether the participant understood the experiment. 43

It seems more logical to exclude the individuals whose job status is missing from the sample’s labor force, but this might not be appropriate for all those individuals: some of them might actually be looking for a job or did just not fill in the answer on this question and are therefore part of the labor force according to the standard definition of labor force. Therefore 7% is an underestimation of the real experimental fraction.

Logged wealth variable Total wealth Minus mortgages Minus mortgages and assets

Measure of risk aversion NUMSAFE ARE RRP NUMSAFE ARE RRP NUMSAFE ARE RRP

Coefficient risk aversion measure -0,726 -1,747 -0,236 -0,073 -1,762 -0,238 -0,073 -1,752 -0,024

P-value risk aversion measure 0,262 0,726 0,245 0,259 0,724 0,243 0,258 0,726 0,242

Mc Fadden's R squared 0,024 0,0222 0,0241 0,0237 0,0218 0,0238 0,0237 0,0219 0,0239

Result in line with results without logged wealth included Yes Yes Yes Yes Yes Yes Yes Yes Yes

37

Finally, replicating this research with another dataset is interesting because this makes it

possible to determine whether insignificance of most control variables in the full model is

based on random factors or not.

Due to these flaws and the insignificant results there is no basis for extending the

findings of this study in general. Future research which takes into account the

aforementioned recommendations is necessary to investigate whether the effect of risk

aversion on self-employment status remains insignificant.

38

References Burke, A.E., Fitzroy, F. R., & Nolan, M. A. (2002). Self-employment wealth and job creation: the roles of gender, non-pecuniary motivation and entrepreneurial ability. Small Business Economics, 19, 255–270. Caliendo, M., Frank, F., & Kritikos, A. (2009). Risk attitudes of nascent

entrepreneurs: new evidence from an experimentally-validated survey. Small Business Economics, 32, 153–167.

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Appendix I

Table 2

Differences in characteristics between subsamples

Pay-off condition Both

Included individuals All Only employed Only known job status

N 2651

1958

1832 Mean Std. Err. Mean Std. Err. Mean Std. Err.

% Male 48,8% 50,0% 50,4% 50,0% 51,3% 50,0%

Age 49,002 17,068 43,554 14,681 43,746 13,823

% Married 59,5% 49,1% 55,6% 49,7% 56,8% 49,6%

% Partnered 76,4% 42,5% 77,2% 42,0% 77,7% 41,7%

% With children 39,1% 48,8% 47,9% 50,0% 47,8% 50,0%

Number of children 0,798 1,138 0,977 1,181 0,962 1,162

Education level 3,526 1,516 3,723 1,477 3,810 1,446

% Own dwelling 75,1% 43,3% 77,8% 41,5% 78,4% 41,2%

% Self-employed 4,9% 21,5% 6,6% 24,8% 7,0% 25,6% Number of safe choices 3,517 1,762 3,500 1,738 3,475 1,737

Absolute risk aversion 0,019 0,000 0,018 0,001 0,018 0,001

Relative risk aversion 0,579 0,011 0,576 0,012 0,568 0,013

Pay-off condition Real

Included individuals All Only employed Only known job status

N 1043

771


% Male 49,6% 50,0% 52,3% 50,0% 53,5% 49,9%

Age 49,384 16,820 44,128 14,640 44,148 13,786

% Married 59,9% 49,0% 56,4% 49,6% 57,6% 49,5%

% Partnered 75,6% 42,9% 77,0% 42,1% 77,8% 41,6%

% With children 40,7% 49,2% 49,7% 50,0% 49,8% 50,0%


Education level 3,472 1,542 3,669 1,510 3,772 1,474

% Own dwelling 73,3% 44,3% 76,7% 42,3% 77,4% 41,9%




i

ii

Pay-off condition Hypothetical

Included individuals All Only employed Only known Jobstatus

N 1608

1187


% Male 48,3% 50,0% 49,1% 50,0% 49,9% 50,0%

Age 48,753 17,228 43,181 14,702 43,485 13,847

% Married 59,3% 49,1% 55,0% 49,8% 56,3% 49,6%

% Partnered 76,9% 42,2% 77,3% 41,9% 77,6% 41,7%

% With children 38,0% 48,6% 46,8% 49,9% 46,4% 49,9%


Education level 3,562 1,498 3,758 1,455 3,834 1,427

% Own dwelling 76,2% 42,6% 78,6% 41,0% 79,0% 40,7%




the effect of risk aversion on self- employment status

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