Investigate the influence of political parties on individual risk attitude : using personal wealth as connection variable

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Master’s Thesis

Title of the thesis

Investigate the Influence of Political Parties

on Individual Risk Attitude

Using Personal Wealth as Connection Variable

Xi Li

Student number: 10824243

Date of final version: August 26, 2015 Master’s programme: Econometrics

Specialisation: Free Track Supervisor: Zhenxing Huang Second reader: Zhenzhen Fan

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Introduction

Util now, a lot of research has found strong relationships between political participation and economic behavior including contextual field and individual field. From prospective of reality, political affiliations affect almost everyone’s life, and compared to those countries with single-party system, those countries with multi-single-party system are coped with more affairs as every party has its own characteristics. Personally, whether is party member, to some degree, influ-ence choices on job type and career path which leave further effects on personal wealth such as income, investment and so on.

Moreover, personal wealth play a very important role in decision making which is highly closed to risk attitude. Jr. and Chow (1992) analyzed the relationship between asset allocation and individual risk aversion, and they found that individuals’ risk aversion decreased, remained constant or increased with increasing wealth. And other foundings also supported the strong relationship between personal wealth and risk aversion.

However, in fact, there are few paper discussing a direct relation lying in political parties and risk aversion, even though whether a person belongs to certain political party is also one of his social attributes. Hence, for the sake of verifying this latent relation, the following chapters will cope with problem via two methods, one of which prefer a ”Bridge Variable” — one aspect of personal wealth, and the other of which relies on a straightforward relation between political parties and risk aversion. And then in the final conclusion, we can check whether the results from these two methods are consistent. If they are not consistent, either results are note reli-able; if they are consistent, our previous conjecture that there exist a relation between political parties and risk aversion is bolstered.

The datum used to survey are from LISS panel, an organization affiliated with Tilburg Uni-versity. And in following study, we picked up data in the time period 2009-2010 and extracted variables from different datasets and hence combined them into one dataset. Two differences approaches to measure risk attitude, exponential utility function with Arrow-Pratt relative risk

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CHAPTER 1. INTRODUCTION 2 aversion and power utility function with Arrow-Pratt absolute risk aversion.

In this paper, considering the number of political party, we divided all parties into four groups—Liberal, Confessional, Socialist and Other, based on criterions from H. Pellikaan and Otjes (2007). And deriving individuals’ ideal parties which are graded with highest score is regarded as a supplement to political party and at the same time a implication of people’s atti-tude towards parties. As for personal wealth, since it’s very hard and unreasonable to integrate all the aspects of personal wealth, we listed four sectors, housing status, monthly net income, personal property and investment, to represent personal wealth.

All the regressive models in this paper starts with linear model setup and ordinary least square (OLS). When revising models, restricted by our data, the most general problem coming up is heteroskedascity and then instead of switching linear model to non-linear model, OLS will be optimized by using other estimated methods, weighted least square (WLS) or feasible general least square (FGLS).

The remainder of this thesis is organized as follows. Chapter 2 describes the existing litera-tures about the previous foundings and researches. Chapter 3 describes the general specification of those models that will be used in this thesis. Chapter 4 describes the database. Chapter 4 describes all the different specifications used to get more accurate models. Chapter 5 presents results in details. Chapter 6 concludes.

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Chapter 2

Literature Review

Connecting religion, one of personal social attributes, to risk aversion and reporting new evi-dence for this relationship are the main topics of Charles N. Noussair (2013). In this paper, they first provide a evidence for supporting the link between an incentivized risk aversion and church member personally and then they stepped further to an extensive information affiliated to religious background and practice. In their empirical investigation, they found risk aversion has positive correlation with religiosity and the attendance rates of religious gatherings. This paper has stimulated us to study other personal social attributes instead of religiosity, since political parties are kind of similar to religion.

The first problem needs to be dealt with is how to measure risk attitude. Pratt (1964) gave a summary via considering utility functions for money and regarding risk as a proportion of total wealth. And Zuhair et al. (1992) studied the effect of utility form on classification of risk preferences by comparing predictive results of different utility function forms, where they concluded that exponential function performed better. Based on those researches, we assumed utility function exponential form while power utility function are also chosen to make compar-ison.

In terms of political affiliations and wealth, ALBERTO ALESINA (1996) drew a conclusion that political instability reduces growth and furthermore this link also depends on executive changes and the ideological composition. Nevertheless in Simpson (1990), he investigated if political rights would influence income inequality by using cross-national data to verify. And H. Pellikaan and Otjes (2007) supplied a good way to classify parties into different groups by evaluating those parties in European political system. This classification system is used in our own data.

Finally, many previous studies show that there is a strong relation between personal wealth and risk aversion, Jr. and Chow (1992) that confirmed there is a negative relationship between asset allocation and relative risk aversion, Richard A. Cohn (1990) studied the interrelation

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CHAPTER 2. LITERATURE REVIEW 4 between investment and risk aversion.

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Chapter 3

The Model

3.1 Model Setup

In the following sections, three models are going to be presented, the first one for measuring the personal risk attitude, the second one for investigating the relationship lying in political parties and personal wealth and the final one for exploring the link between personal wealth and risk attitude.

3.2 Measurement of Risk Attitudes

In application of risk attitude estimation, every analyst will deal with a choice among several utility functional forms such as polynomial utility function, exponential utility function, power utility function and etc., since researchers have found that the choice of functional form has influence on the classification of risk attitude. Zuhair et al. (1992) compared the accuracies of predicting harvesting strategy by applying the three utility functional forms(polynomial util-ity function, exponential utilutil-ity function, power utilutil-ity function) separately and thence they concluded that the exponential utility function was the best predictor. Moreeover, Kirkwood (1997) showed that the estimation of constant risk aversion using exponential utility function are accurate.

Considering the previous conclusions and assuming constant risk aversion which can hold based on the theoretical basis, ”whenever all possible outcomes of any uncertain alternative are changed by the same specified amount the decision makers certainty equivalent for the alternative also changed by that same amount” from Kirkwood (1997), I choose exponential utility function as following:

U = k − θe−λx (3.1)

Where k and θ are parameters and e is the base of natural logarithms and x is the monetary measure. And λ refers to Arrow-Pratt relative risk aversion coefficient (RRA), an investor’s

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CHAPTER 3. THE MODEL 6 tolerance for risk measured relative to his wealth level, which is positive and normalized with wealth. The Arrow-Pratt relative risk aversion of exponential utility function is expressed in (3.2) :

RRA = −x ∗ λ (3.2)

Although in (3.1) there exists three parameters to be specified, only the risk aversion coef-ficient will be taken into account as (3.1) can be simplified via the simulate equality, namely:

e−λx = pe−λa+ (1 − p)e−λb (3.3)

where a and b denotes the related sure payoffs, having probability p and 1 − p respectively.

In order to investigate whether utility function form will influence the results or not, I should include at least one more utility function form to compare the results, then power utility function (3.4) are chosen and Arrow-Pratt absolute risk aversion (ARA(3.5) which varies with wealth are considered.

U = x

1−γ

1 − γ (3.4)

ARA = γ

x (3.5)

where x is the monetary measure and γ is the ARA of power utility function.

The estimation equality for searching γ boils down to (3.6):

x1−γ = p ∗ a1−γ+ (1 − p) ∗ b1−γ (3.6) where a and b denotes the related sure payoffs, having probability p and 1 − p respectively.

3.3 Linear Model between Political Parties and Personal Wealth

The evidence lying in the analysis of date from Chapter 4: Data suggests that whether a person is a party member and which party he belongs to, to some extent, shows differences in his personal wealth no matter to all parts or to just one. So here propose two linear multiregressive models simultaneously:

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CHAPTER 3. THE MODEL 7

SP W = α + β1X1+ β2X2+ β3X3+ β5D1+ β6D2+ β7D3+ β8D4 (3.8)

Where

SP W = Housing Status, Logarithmic Net Monthly Income, Standardized Personal Property, Standardized Investment,

α= intercept, X1= age,

X2= gender,

X3= Schooling (discrete variables, the lowest level is primary school and the highest level is

university),

P1= dummy variable for denoting whether subject is a party member: 0 if non–party member

and 1 if party member,

D1= dummy variable for Liberal, one category of all political parties: 0 if not in Liberal and 1

if in Liberal,

D2= dummy variable for Confessional, one category of all political parties: 0 if not in

Confes-sional and 1 if in ConfesConfes-sional,

D3=dummy variable for Socialist, one category of all political parties: 0 if not in Socialist and

1 if in Socialist,

D4=dummy variable for Other Parties, one category of all political parties: 0 if not in Other

and 1 if in Other Parties,

Here in the statistical analyses, dummy variable represent the absence or presence of a factor.

Considering the sub-question whether individual ideal party will give different conclusions, then replacing the Party and Party Groups with Ideal Party and Ideal Party Groups, the two models have changed a little in the independent variables, shown in Model (3.9) and Model (3.10).

SP W = α + β1X1+ β2X2+ β3X3+ β4IP1 (3.9)

SP W = α + β1X1+ β2X2+ β3X3+ β4D1+ β5D2+ β6D3 (3.10)

Where

SP W = Housing Status, Logarithmic Net Monthly Income, Standardized Personal Property, Standardized Investment,

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CHAPTER 3. THE MODEL 8 α= intercept,

X1= age,

X2= gender,

X3= Schooling (discrete variables, the lowest level is primary school and the highest level is

university),

IP1= discrete variable of ideal party groups, 1 for Liberal, 2 for Confessional, 3 for Socialist

and 4 for Other parties,

D1= dummy variable for Liberal, one category of all political parties: 0 if not in Liberal and 1

if in Liberal,

D2= dummy variable for Confessional, one category of all political parties: 0 if not in

Confes-sional and 1 if in ConfesConfes-sional,

D3=dummy variable for Socialist, one category of all political parties: 0 if not in Socialist and

1 if in Socialist,

3.4 The Linear Regressive Model of Personal Wealth on Risk

Aversion Coefficients

To investigate the relationship between the Personal Wealth and Risk Aversion Coefficients, the Constrained Linear Regression is in the first place, because firstly there are already a lot of and secondly with restricted data and the manipulation of risk aversion measurement we need to take the limited values of risk aversion into account and hence add a constraint to the constant term will, to some extent, present more reasonable results. And the related Constrained Linear Model is as follows:

RA = α + β1X1+ β2X2+ β3X3+ β4Housing + β5Income + β6T otalW ealth (3.11)

Where

RA=RRA of exponential utility function or ARA of power utility function, α= constant term,

X1= age,

X2= gender,

X3= schooling (discrete variables, the lowest level is primary school and the highest level is

university),

Housing= housing status, indicating the different type of housing subjects have, Income=logarithmic net monthly income,

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CHAPTER 3. THE MODEL 9

3.5 The Linear Regressive Model involving Political Group and

Risk Aversion Coefficients

model (3.7), (3.8) and (3.11) are set for hunting the intermediate variable for political parties and risk aversion. What’s more, based on the above models, in this section, the core is connect all the three main variables together via another linear regressive model (3.12) :

RA = α + β1X1+ β2X2+ β3X3+ β4P ersonalW ealth + β5P oliticayP arties (3.12)

where

P ersonalW ealth = four categories of personal wealth, and note that we use at least one and at most all of them;

P oliticalP arties = Dummy variables denoting all the political parties either with true political parties or with ideal political parties.

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Chapter 4

Data

4.1 Data for Measuring Risk Attitude

I use data from a subsurvey questionnaire, naming ”Measuring Higher Order Risk Attitudes of the General Population” and collected on December 2009, belonging to LISS panel managed by CentERdata, an organization affiliated with Tilburg University. In this dataset, several experi-ments were carried out and among those experiexperi-ments I choose the one which has a lottery paid e 5 and e 65 with equal possibility 1

2 and a sure payoff differing by trial in a ascending sequence

frome 20 to e 40 or in a descending sequence from e 40 to e 20.Furthermore, statistically, 5788 persons took part in the experiments, but the complete responses are 3425.

Since the measurement of risk attitude is rooted in an assumption that the participants are rational, indicating that the participants, those playing in an ascending sequence, cannot switch from a safe choice (with sure payment) to the lottery as long as they ever choose safe choice in-stead of the lottery, but the participants, those playing in a descending sequence, cannot switch from lottery to a safe choice as long as they ever choose the lottery instead of the corresponding safe choice, I develop a new concept named critical choice, an average of two serial numbers, which manifests the relevant two trials where our subjects changed their option from safe choice to the lottery and vice versa.

Hence we find to a way to represent the value of x by calculating the corresponding payment of a critical choice. Meanwhile, I supplement two latent trials, one with a sure payment e 15 and the other with a sure payment e 45, in order to calculate the critical value x when certain subjects focus on safe options or the lottery in all the five trials.

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CHAPTER 4. DATA 11

4.2 Analysis of the Data for Political Parties and Personal Wealth

Data on the investments of a selected sample of the LISS panel are used to derive personal wealth and gain information of political parties. In order to present the two parts, I combine four datasets—Political and Values, Assets, Housing and Basic Information.

With regard to political parties, there are two variables to be addressed, and one, true po-litical party, indicates the real responses collected via the question ”of which popo-litical party are you a member?” and the other, ideal political party, is collected by searching the party which has the highest evaluated score for each subject. Summarizing the number of each political party of the two variables as Table 4.1.

Table 4.1: The number of Each Political Party

Real Political Party Ideal Political Party Christian Democrat Party(CDA) 82

(26.98%) 565 (9.52%) Labor Party(PvdA) 56 (17.95%) 484 (8.15%) Liberal Party(VVD) 21 (6.73%) 520 (8.76%) Socialist Party(SP) 47 (15.06%) 465 (7.83%) Green Party 18 (5.77%) 540 (9.10%) Fortuyn Party(LPF) 0 / Social-liberal Party 12 (3.85%) 1209 (20.37%)

Chrisian Union Party 39

(12.5%)

360 (6.06%) Christian Reformed Party(SGP) 17

(5.45%)

183 (3.08%)

Verdonk’s Dutch Pride Party 0 102

(1.72%) Wilders’ Freedom Party 4

(1.28%)

721 (12.15%)

Animal Welfare Party 7

(2.24%) 787 (13.26%) Other Party 9 (2.88%) / Total 312 5936

Note: the ”/” denotes that there is no such option in the evaluated system on political parties.

Based on Table 4.1 and the fact that the sample consists of 6327 complete responses, only about 300 persons gave actual political parties where they belong to, however if considering the ideal political party,5936 persons having made their choices. In other words, ideal political

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CHAPTER 4. DATA 12 party as an additional variable not only reveals individual propensity towards political parties but also expands the dataset compared to the true political party.

Concerning how to measure personal wealth, here first of all, I split personal wealth into three big parts, the housing status—categorical variable, net monthly income and the personal property—the total value of movable belongings, and the investment including two ingredients— the value of risky assets and bonds. The data analyzed are a merged pattern by incorporating Housing, Assets and Basic Information. Table 4.2 reports the samples the demographic char-acteristics corresponding to wealth.

Table 4.2: The Distribution of Personal Wealth

Housing Status Freq. Percent Net Monthly Income Freq. Percent

tenant 909 27.82% <=500 4,493 38.65% subtenant 25 0.76% 500-1000 1,541 13.26% (co-)owner 2,255 69.00% 1000-2000 3,744 32.21% other 79 2.42% 2000-3000 1,351 11.62% Total 3,268 100.00% 3000-4000 334 2.87% 4000-5000 83 0.71%

Personal Property Freq. Percent >5000 78 0.67%

<=0 122 3.39% Total 11,624 100.00

0-10000 1,477 41.03% 10000-20000 654 18.17%

The Total Value of Investment Freq. Percent 30000-40000 269 7.47% 40000-50000 152 4.22% <=50000 413 78.22% 50000-60000 108 3.00% 50000-100000 44 8.33% 60000-70000 58 1.61% 100000-200000 34 6.44% 70000-80000 54 1.50% 200000-300000 11 2.08% 80000-90000 53 1.47% 300000-400000 4 0.76% 90000-100000 40 1.11% 400000-500000 6 1.14% >100000 242 6.72% >500000 16 3.03% Total 3,600 100.00% Total 528 100.00%

In order to investigate the relationship between political parties and personal wealth, I step further, reducing the scales of Net Monthly Income with logarithmic transformation as no neg-ative value exists and standardizing Personal Property and Investment as there are negneg-ative observations. The related information of these new variables separated by Political Categories can be seen from Figure 4.2.

And for political party, H. Pellikaan and Otjes (2007) proposed a model of political space based on the criteria that whether a political party can get a seat in the European Parliament and hence I classify all the party political parties considered into four categories, Liberal (includ-ing Liberal Party and Social-liberal Party), Confessional (includ(includ-ing Christian Democrat Party, ChristenUnie and Christian Reformed Party), Socialist (including Labor Party, Socialistische

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CHAPTER 4. DATA 13 Partij and GroenLinks) and Other (including Groep Wilders, Partij voor de Dieren, Lijst vijf Fortuyn and other parties). The new groups of political parties are unfolded before our eyes with Figure 4.1 showing the specific ratios of each group, which indicates the Confessional and the Socialist take big shares with 44.23% and 38.78% respectively, and however the Liberal and Other account for just over 16% in sum.

Figure 4.1: The Ratios of the Four Political Groups

4.3 Data Analyze on Personal Wealth and Risk Aversion

Coef-ficient

Since we have two methods to measure risk attitude, RRA of exponential utility and ARA of power utility function, the two-way line graphs shown in the Figure 4.3 and Figure 4.4 are relevant to values of Risk Aversion Coefficient and Critical Value, where the two figures are apart from each other, RRA of exponential utility increasing with critical value while ARA of power utility decreasing with critical value.

And moreover it’s very interesting to notice that based on both utility functions, the ratio of risk aversion on the leftmost and the ratio of risk aversion on the rightmost take up a big part of the total quantity, instuitional to be seen from the Figure 4.5 and Figure 4.6.

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CHAPTER 4. DATA 14

4.4 Ideal Parties

As said in previous section, a lot of people are either not willing to disclose their political rele-vant information or not in any parties, leading to the small size of parties member which may influences the outcomes of the regression of political parties and personal wealth. Yet in our LISS Panel data, it’s very useful to have those parties graded with 1 to 10 scale, a way to show individual sympathy towards those parties. Then I extract a new variable from those evaluated questions named Ideal Parties, a way to represent the party or the parties with highest scores.

Table 4.3 enlarged the size of parties and the Social Liberal Party went down well with in the public, accounting for over 20%, yet the Verdonk’s Dutch Pride Party is not well accepted by people, accounting just for 1.72%. Compared to the number of people of true political parties which is less than 400, the number of people who has a ideal party are near 6000,a huge data size increase.

Next like what I have dealt with true political parties, for ideal parties, it can be classified into four party groups, namely Liberal, Confessional, Socialist and Other, the statistics of clas-sification showed in Figure 4.7. In comparison to Figure 4.1, instead of having Socialist and Confessional as the main components, Other Parties which may not in the mainstream of polit-ical parties earn more fame and supports, however the group Confessional which has the largest number of members in the real situation just account for 5.56% in the classification of Ideal Parties. It’s very surprising to see people prefer giving higher scores to those rarefied parties, directing a different way to see how people regard those political parties, in other words, this is also why it’s important to add Ideal Parties in the study. Hence linking to personal wealth, the statistics are presented in Figure 4.8.

Table 4.3: The Description of Ideal Parties

Parties Name Freq. Percent(%)

Social Liberal Party — 1,209 20.37 Animal Welfare Party — 787 13.26 Wilders’ Freedom Party — 721 12.15 Christian Democrat Party — 565 9.52

Green Party — 540 9.10

Liberal Party — 520 8.76

Labor Party — 484 8.15

Socialist Party — 465 7.83

Christian Union Party — 360 6.06 Christian Reformed Party — 183 3.08 Verdonk’s Dutch Pride Party — 102 1.72

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CHAPTER 4. DATA 15

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CHAPTER 4. DATA 16

Figure 4.3: RRA with Critical Value

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CHAPTER 4. DATA 17

Figure 4.5: RRA Frequency

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CHAPTER 4. DATA 18

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CHAPTER 4. DATA 19

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Chapter 5

Results

5.1 The Outcomes of Risk Taking Coefficient

First of all, let’s describe statistical characteristics of several important variables and showing the results below:

As showed in Table 5.1, it’s straightforward to see that the statistics of critical choices from both sequence are compatible, especially the means and the standard deviations, however on the part of critical values, the mean from the sequence 1 is just over 20, much smaller comparing the mean 39 from the sequence 1, interpreting an interesting fact that participants in sequence 1 are much more risk averse then those in sequence 2. A convincing explanation is that people have propensity to choose a safe choice and even stick to safe choice if they are picked to play in an increasing sure payment system.

Table 5.1: Summaries of Critical Choices and Critical Values Variables Critical Choice

(Sequence 1) Critical Choice (Sequence 2) Critical Values (Sequence 1) Critical Values (Sequence 2) observations 1738 1719 1738 1719 mean 1.567894 1.553229 20.33947 39.73386 Std. Dev. 1.084376 1.055194 5.42188 5.275969 min 1 1 17.5 22.5 max 5 5 37.5 42.5

First of all, for exponential utility function, recalling (3.3), where x denote the critical val-ues and the possibility p is known as 1₂, I estimate λ by restricting its start interval to [0.2, 1], because when the start points in the vicinity of 0 or over 1 the optimal solutions found are not convinced. We can draw this conclusion from Figure 5.1. Based on restrictions and the values for x obtained, risk aversion coefficients can be gained via the process searching for the optimal λ of every subject and the result is shown in Figure 5.2, noting that actually because of utilizing Arrow-Pratt relative risk aversion coefficient (RRA), there is a functional link lying in the two variables, namely:

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CHAPTER 5. RESULTS 21

RRA = −x ∗U

00_(λ)

U0_(λ) (5.1)

where U refers to the utility function (3.1).

Figure 5.1: The Optimal Lamda Found

Then as for power utility function, the same logic was exploited and estimation method is found on the equality (??), hence the Arrow-Pratt absolute risk aversion (ARA) is definited:

ARA = γ

x (5.2)

5.2 The Regression of Parties on Personal Wealth

In fact, before any regression exploited, Correlation Test need to be done among the independent variables—Age, Gender, Schooling, Marital Status and Party, to assure the regressive results are reliable. Table 5.2 illustrates that rooted on the value of correlate coefficient around -0.5385, Marital Status has a close negative relationship with Age, which in practice is an actual reflection as the fact that marriage links with age on behalf of some laws and certain general concepts on Matrimony. Here we prefer Age to Marital Status, because Age as a variable is more complete and is more convinient to obtain.

Based on the Models (3.7) and (3.8) present in Chapter 3, Multivariate Regression, as our main method, is applied and the outcome of the regression including the four dependent

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vari-CHAPTER 5. RESULTS 22

Figure 5.2: The Relationship Between Critical Values and Risk Aversion Coefficients

Table 5.2: Correlation Test on Independent Variables

VARIABLES Age Gender Schooling Marital Status Party

Age 1.0000

Gender -0.0717 1.0000

Schooling -0.0501 -0.0681 1.0000

Marital Status -0.5385 0.0175 0.0203 1.0000

Party 0.1235 -0.0530 0.0590 -0.0394 1.0000

ables is presented in the Figure 5.3. Although Party seems to have no effect in any section of personal wealth, it’s tempting to speculate that the regressive result of Personal Property is remarkably similar to that of Investment, and because of the similarity a reasonable conjecture is that Personal Property and Investment are correlated, which can be inspected by Correlation Test in Table 5.3. It’s pretty apparent that Personal Property is highly correlated with Invest-ment with corresponding coefficient 0.64, which proved my prior conjecture.

Table 5.3: The Correlation Test on Four Sections of Personal Wealth Housing Monthly Income Property Investment Housing 1.0000

Monthly Income 0.0256 1.0000

Property 0.0395 0.1563 1.0000

Investment 0.0618 0.1644 0.6423 1.0000

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Figure 5.3: The Outcomes of Multivariate Regression With All Variables

derived variable Standardized Total Wealth calculated by summing up Personal Property and Investment, and the Correlation Test is shown in Table 5.4. Now it’s clear that the three de-pendent variables (Housing, Monthly Income and Total Wealth) are not correlated to the other.

Table 5.4: The Correlation Test on Three Sections of Personal Wealth Housing Monthly Income Total Wealth Housing 1.0000

Monthly Income -0.0045 1.0000

Total Wealth 0.0696 0.0675 1.0000

After done with this barrier, Multivariate Regression consisting of three dependent variables is applied again. Figure 5.4 shows several valuable clues that firstly Schooling and Constant Term are significant at level 0.01 through this Multivariate Regression, and Gender has negative relationship with Monthly Income and Total Wealth, While on the contract Age are positively related to Monthly Income and Total Wealth, both significant at level 0.01. Party which we really focus on is merely negatively related with Monthly Income at level 0.05, indicating that being a party member will decrease individual monthly income. Howbeit Party, in view of the regressive results, does not delivery messages that the political parties will not influence Housing and Total Wealth, and at the same time all the political parties are playing an important role in Monthly Income, since we haven’t taken political groups into account.

Hence instead of using Party to check whether being a party member has an effect on Per-sonal Wealth, I refine the model from (3.3) to (??) in order to verify that even though from the global perspective being party members matter little to personal wealth, belonging to which party group sometimes takes seat, whose regressive results can be seen from Figure 5.5. From this new outcome, the properties of Age, Gender, Schooling and Constant are rarely changed, while the significant levels of the groups of the political parties are dramatically different from each other, Confessional having negative coefficient in Monthly Income at level 0.01 and Social-ist negatively related to Housing at level 0.01 and the Liberal and Other parties didn’t show

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Figure 5.4: The Outcomes of Multivariate Regression With Three Dependent Variables

any significance.

5.3 Replacing True Political Parties with Ideal Political Parties

First one change, the dummy variable for denoting Other Parties dropped in model (3.10), need to be clarified, since in the categories of ideal parties either the quantity of the total data or that of each group has experienced data volume expansion, which add the probability of cor-relation and in fact from Table 5.5, it’s apparent that the Other Parties are highly correlated with the other three groups, especially the correlated value 0.5316 between Socialist and Other. So dropping dummy variable of Other Parties can efficiently avoid colinearity.

Hence running the Multivariate Regression found in Model (3.9), the corresponding result are in Figure 5.6 and Model in (5.3), where Age are negatively related to Housing, while posi-tively related with Monthly Income and Total Wealth, all at level 0.01; Gender, 1 denoting male and 2 denoting female, indicates that in general women are more likely to earn less and have less wealth as the coefficients on both Monthly Income and Total Wealth are negative; Schooling is good impetus to personal wealth; as for Ideal Group, expect insignificance in Total Wealth, it has a negative relationship with Housing, however, a positive relationship with Monthly Income both at level 0.01.

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Figure 5.5: The Outcomes of Multivariate Regression with Party Groups

Housing = 1.916 − 0.00308 ∗ Age − 0.00807 ∗ Gender+ 0.0320 ∗ Schooling − 0.0330 ∗ IdealGroup M onthlyIncome = 6.576 + 0.0115 ∗ Age − 1.062 ∗ Gender+ 0.225 ∗ Schooling − 0.141 ∗ IdealGroup T otalW ealth = −0.0384 + 0.000382 ∗ Age − 0.00738 ∗ Gender+ 0.00423 ∗ Schooling − 0.00169 ∗ IdealGroup

(5.3)

As shown in previous section, a negative relationship at level 0.05 have been found between Party and Monthly Income and if we combine this result with the new founding, it’s very inter-esting to see that being a real party member are completely not the same thing as supporting a party with high evaluated score. The Ideal Group, nevertheless, are still meaningful to be studied, since it reveals people’s another prospective towards political parties.

Table 5.5: Correlation Table of Ideal Political Parties Liberal Confessional Socialist Other Liberal 1.0000

Confessional -0.1706 1.0000

Socialist -0.2414 -0.2366 1.0000

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Figure 5.6: Multivariate Regression of Ideal Groups on Personal Wealth

Futher survey on separate political parties, from Figure 5.7, Liberal, Confessional and So-cialist are all significant in Housing and Monthly Income below level 0.1; however, like the conclusion drawn from the true parties groups, no party group showed any significance in Total Wealth. Moreover, compared to previous case that even for Housing and Monthly Income there are merely one or at most two political groups significant, this time all of the three political parties are significant both in Housing and Monthly Income.

Housing = 1.797 − 0.00313 ∗ Age + 0.000739 ∗ Gender + 0.0327 ∗ Schooling+ 0.0968 ∗ Liberal + 0.0710 ∗ Conf essinal − 0.0835 ∗ Socialist M onthlyIncome = 7.155 + 0.0115 ∗ Age − 1.055 ∗ Gender + 0.226 ∗ Schooling− 0.417 ∗ Liberal − 0.296 ∗ Conf essinal − 0.246 ∗ Socialist T otalW ealth = −0.0446 + 0.000378 ∗ Age − 0.00702 ∗ Gender + 0.00426 ∗ Schooling+ 0.00438 ∗ Liberal + 0.00472 ∗ Conf essinal − 0.00274 ∗ Socialist

(5.4)

5.4 The Regression of Personal Wealth on Risk Aversion

Coef-ficients

Since considered two kinds of measurements of risk aversion, I present the results first on RRA. Based on the model (??),starting the model with the basic linear regression, which is always a priority in econometric analytic steps. Although the results shown in Figure 5.8 indicates the

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Figure 5.7: Multivariate Regression of Three Ideal Political Groups on Personal Wealth

model itself didn’t pass the test, the significant variables are merely Standardized Total Wealth and Constant Term, which the rest explanatory variables are ineffective.

In other words, if heteroscedasticity exists in this model, OLS in this framework will not be supported as Gauss-Markov theory fails, which can lead to the low explanation of independents variables. To figure out whether heteroscedasticity affects or not, by checking residual plots to get general idea and meanwhile White Test for heteroscedasticity is another convinced way to draw conclusion. As those residual plots cannot clearly shed light on heteroscedasticity, from the view of the White Test which are more intuitive in the Figure 5.9, wtih the probability 0.0810, we cannot accept the null hypothesis—Homoskedasticity.

Inasmuch as the probability is small, it’s very worthy of further investigation on those big gap among variances of different variables. First of all, show the descriptive statistics of the corresponding variables in Table 5.6, where Age and Schooling, especially Age, have Standard-ized Deviation 20.8 and 2.4 respectively. This recalls the function of WLS, adding weights to independent variables based on quantity of information that they offered. Classically, WLS assume that data with big variance provides less information than data with small variance, and after this transformation is applied to the data, the regression method are still OLS.

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CHAPTER 5. RESULTS 28 more significant and has more significant explanatory variables below level 0.1 including School-ing, Monthly Income, Total Wealth and Constant, especially Monthly Income and Schooling switching from insignificant variables of the simple OLS regressive results to significant variables of WLS regressive results. As far as meliorations are introduced by WLS, the current model un-folded and delivered more inquisitive and believable and the corresponding linear model is (5.5).

RRI =53.34406 − 0.0535794 ∗ Age − 0.1987046 ∗ Gender + 0.5609036 ∗ Schooling− 0.9826382 ∗ Housing − 0.9142903 ∗ M onthlyInomce − 21.42485 ∗ T otalW ealth

(5.5)

Figure 5.8: Simple Linear Regression of Personal Wealth on RRA

Table 5.6: Describtion of Some Explanatory Variables

Variable Obs Mean Std. Dev.

Age 12211 36.65171 20.84936

Gender 12211 1.506429 .4999791

Schooling 12211 4.409549 2.385406

Housing 3268 1.770196 .5675699

Std.Monthly Income 11624 -1.27e-09 1

People with higher Schooling have larger RRA. Meanwhile, the Monthly Income and Total Wealth both have negative relationship with RRA, which reflects that, to some extent, poor people hold conservative opinions on risk.

Secondly, we consider power utility function accompanied by ARA. The linear regressive results can be obtained from 5.11, where the model passed test at level 0.1 while similar to the result from the regression on RRA, only Total Wealth and Constant term are significant, leading

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Figure 5.9: White Test for Heteroscedasticity

to White Test in Figure 5.12 with possibility 0.1530. As the possibility is too small, it’s tempting to apply WLS to revise the previous method, the regressive result shown in Figure 5.13. Except schooling negatively related to ARA, Age, Income and Total Wealth are all positively related to ARA, which are dramatically different from that of RRA.

5.5 The Regression of Political Groups on Risk Aversion

In this section, Party Group and Ideal Party Group are involved and are discussed separately. Two correlation tests are done before starting models in Table 5.7 and Table 5.8. In Table 5.7, all independent variables are not highly correlated to each other; however, in Table 5.8, the ideal party group Other are correlated with the remained three ideal party groups, especially Socialist with corraletion -0.5123. Then in case of colinearilty, Ideal Other will not be used in the regressive model.

Regressing party group on RRA and ARA supplied corresponding results in Figure 5.14 and in Figure 5.15 with White test following. OLS method are not suitable to these linear models as both have heteroskedasticity. Hence, FGLS is used for estimating weighting matrix and add different weights to explanatory variables, revising previous OLS and making estimators consistent. Figure 5.18 and Figure 5.19 make clear that either for RRA or for ARA, Schooling, Income, Total Wealth and Other party are significant below level 0.05, while except that Other party is negatively related to both risk aversions, the rest Schooling has positive relation with RRA but negative relation with ARA, and moreover Income and Total Wealth have negative

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Figure 5.10: Weighted Regression of Personal Wealth on RRA

Figure 5.11: Linear Regression of Personal Wealth on ARA

signs in RRA but positive signs in ARA. Furthermore, the Liberal party is significant in RRA as well.

Then, replace true political party groups with ideal political party groups, instead of start-ing from OLS, for ideal political groups, both linear regression take FGLS into account directly, results shown in Figure 5.20 and Figure 5.21. For both cases, Ideal Liberal group is significant below level 0.01, but totally opposite signs, positive sign for RRA and yet negative sign for ARA.

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Figure 5.12: White Test for Heteroscedasticity

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Table 5.7: Correlation Test with Party Group

age gender schooling housing income total wealth liberal confessional socialist other

age 1.0000 gender -0.1477 1.0000 schooling -0.1612 -0.1075 1.0000 housing -0.0984 -0.0123 0.1026 1.0000 income 0.0572 -0.0917 0.0599 0.0117 1.0000 total wealth 0.1073 -0.1104 0.1229 0.0708 0.1165 1.0000 liberal 0.0199 -0.0094 0.0480 0.0265 0.0199 0.0111 1.0000 confessional 0.0578 0.0050 -0.0098 0.0290 -0.0128 0.0042 -0.0128 1.0000 socialist 0.0800 -0.0526 0.0652 -0.0548 0.0040 0.0006 -0.0156 -0.0246 1.0000 other 0.0208 -0.0127 -0.0234 0.0452 -0.0019 -0.0139 -0.0050 -0.0079 -0.0096 1.0000

Table 5.8: Correlation Test with Ideal Party Group

age gender schooling housing income total wealth ideal liberal ideal confessional ideal socialist idealother age 1.0000 gender -0.1429 1.0000 schooling -0.1697 -0.1080 1.0000 housing -0.0971 -0.0054 0.1092 1.0000 income 0.0542 -0.0875 0.0571 0.0113 1.0000 total wealth 0.1052 -0.1067 0.1241 0.0700 0.1150 1.0000 ideal liberal 0.0020 -0.0094 0.0139 0.0730 -0.0099 0.0343 1.0000 ideal confessional 0.0807 -0.0358 -0.0204 0.0432 -0.0034 0.0438 -0.1799 1.0000 ideal socialist -0.0288 0.0875 0.0144 -0.0892 0.0338 -0.0474 -0.2348 -0.2377 1.0000 ideal other -0.0353 -0.0420 -0.0075 -0.0076 -0.0193 -0.0160 -0.3877 -0.3925 -0.5123 1.0000

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Figure 5.15: Linear Regression of Party Group on ARA

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Figure 5.17: White Test with ARA

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Figure 5.19: Linear Regression on ARA with Method FGLS

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Chapter 6

Conclusion

The results of all the model runs can be summarized as follows:

1. Estimated equalities measured risk attitude by giving optimal value of each simulation, where the utility functions were assumed to be exponential and power, but starting value had to be restricted to make sure optimals values can be found efficiently.

2. Monthly Net Income, as one part of personal wealth, worked as a ”Bridge Variable” be-tween political party and RRA of exponential utility function or ARA of power utility function, connect political groups with risk aversion coefficients. However, Housing showed no signifi-cance in both RRA and ARA, and Total Wealth played an important role in RRA and RAR but political groups no matter true or ideal didn’t have any relations with Total Wealth.

3. By analyzing the ingredients of true political party groups and ideal party groups, it’s very interesting to see big differences lying in the distributions of party groups. Confessional party group account for 44.23% ranking the first in true political groups, while in ideal political groups it just take up 5.56%. The contradictory situation occurred to Other group which jump from the smallest part(6.41%) of true political groups to the biggest part (71.09%) of ideal political groups, indicating that a party where a participant belongs to, to some extent, doesn’t concur with a party in his heart.

4. After regressing political party directly on RRA and ARA, If considering RRA, the Lib-eral party group from true parties are negatively related to RRA and that from ideal parties are positively related to RRA; nevertheless, if referring to ARA, only Other party group from true parties has negative relation with ARA and Ideal Liberal from ideal parties also has negative relation with ARA, these inconsistences stating that there is no such party group found to inte-grate true political parties and ideal political parties. Two potential reasons, one is because of fundamental difference between true and ideal political parties, the other can be seen from the unequal distribution of party groups in which certain group has very large and on the contrary

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CHAPTER 6. CONCLUSION 38 certain group has considerably small size.

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Appendix A

Programs

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APPENDIX A. PROGRAMS 40 % The program used to find risk aversion coefficients

%clear all; %clc; %file=xlsread(’critical_option picking’); %id=file(:,1);sequence=file(:,2);s1=file(:,3);s2=file(:,4);s3=file(:,5);s4=file(:,6);s5=file(:,7); %global n %n=size(id,1); %cri=ones(n,1); %for i=1:n % s=file(i,3:7); %if sequence(i)==1 % [r,c]=find(s==2); % if size(c)~=0 % cri(i)=c(1); % else cri(i)=1; % end %elseif sequence(i)==2; % [r,c]=find(s==1); % if size(c)~=0 % cri(i)=c(1); % else cri(i)=1; % end %end %end

%% define the parameter of the utility function %global cri_x

%cri_x=zeros(n,1); %for i=1:n

% cri_x(i)=payment(cri(i),sequence(i)); %end

%% find the optimal risky coefficients of exponential utility function %iter=9; %xvalue=zeros(iter,1); %fvalue=ones(iter,1); %lamda=zeros(n,1); %for j=1:n % i=1; % for x0=0.2:0.1:1 % F=@(x) abs(2*exp(-x*cri_x(j))-exp(-65*x)-exp(-5*x)); % [xval,fval]=fsolve(F,x0); % xvalue(i)=xval; % fvalue(i)=fval; % i=i+1; % end; % row=find(fvalue==min(fvalue)); % lamda(j)=xvalue(row(1)); %end

%% draw figure to confirm that the start value matters %xval=zeros(301,1); %yval=zeros(301,1); %i=1; %for x=0:0.01:3 % F=@(x) abs(2*exp(-x*30)-exp(-65*x)-exp(-5*x)); % [xx,yy]=fsolve(F,x); % xval(i)=xx; % yval(i)=yy; % i=i+1; %end %x = 0:0.01:3; %y = myfunction(x,30); %figure %plot(x,xval)

%title(’the optimal lamda based different start values’) %xlabel(’the value of lamda’)

%ylabel(’the optimal value of lamda’) %figure

%plot(x,y)

%% simple measurement of risk aversion %count=zeros(n,1); %for i=1:n % s=file(:,3:7); % for j=1:5 % if s(i,j)==2 % count(i,1)=count(i,1)+1; % else % end % end %end

%% power utility function %iter=11; %xvalue=zeros(iter,1); %fvalue=ones(iter,1); %gamavalue=zeros(n,1); %for j=1:n % i=1; % for x0=2:0.1:5 % G=@(x) abs(2*power(cri_x(j),1-x)-power(65,1-x)-power(5,1-x)); % [xval,fval]=fsolve(G,x0); % xvalue(i)=xval; % fvalue(i)=fval; % i=i+1; % end; % row=find(fvalue==min(fvalue)); % gamavalue(j)=xvalue(row(1)); %end %xval=zeros(301,1); %yval=zeros(301,1); %i=1; %for x=0:0.01:3 % G=@(x) abs(2*power(42.5,1-x)-power(65,1-x)-power(5,1-x)); % [xx,yy]=fsolve(F,x); % xval(i)=xx; % yval(i)=yy; % i=i+1; %end %x = 0:0.01:3; %y = myfunctionpower(x,30); %figure %plot(x,xval)

%title(’the optimal lamda based different start values’) %xlabel(’the value of lamda’)

%ylabel(’the optimal value of lamda’) %figure %plot(x,y) %function pay=payment(x,y) %if y==1 % if x>=2 % pay1=15+5*x; % pay2=15+5*(x-1); % pay=0.5*pay1+0.5*pay2; % else % pay=17.5; % end %elseif y==2 % if x>=2 % pay1=45-5*x; % pay2=45-5*(x-1); % pay=0.5*pay1+0.5*pay2; % else % pay=42.5; % end %end %function F=myfunction(x,cri_x) %F=abs(2*exp(-x*cri_x)-(exp(-x*65)+exp(-x*5))); %end %function G=myfunctionpower(x,cri_x) %G=abs(2*power(30,1-x)-power(65,1-x)-power(5,1-x)); %end

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Bibliography

ALBERTO ALESINA, SULE OZLER, N. R. P. S. (1996). Political instability and economic growth. Journal of Economic Growth, 1:189–211.

Charles N. Noussair, tefan T. Trautmann, G. v. d. K. N. V. (2013). Risk aversion and religion. J Risk Uncertain, 47:165183.

H. Pellikaan, H. V. and Otjes, S. (2007). Europe in the netherlands:political parties.

Jr., W. B. R. and Chow, K. V. (1992). Asset allocation and individual risk aversion. Financial Analysts Journal, 48:32–37.

Kirkwood, C. W. (1997). Notes on attitude toward risk taking and the exponential utility function.

Pratt, J. W. (1964). Risk Aversion in the small and in the large, volume 32.

Richard A. Cohn, Wilbur G. Lewellen, R. C. L. G. G. S. (1990). Individual Investor Risk Aversion and Investment Portfolio Composition, volume 50.

Simpson, M. (1990). Political Rights and Income Inequality: A Cross-National Test, volume 55. Zuhair, S. M., Taylora, D. B., and Kramer, R. A. (1992). Choice of utility function form: its effect on classification of risk preferences and the prediction of farmer decisions. Agricultural Economeics, 6:333–444.

Investigate the influence of political parties on individual risk attitude : using personal wealth as connection variable

Master’s Thesis

Title of the thesis