The Impact of Social Mobility and Within-Family Learning on

Voter Preferences

Harry Krashinsky

University of Toronto

Abstract

Income-maximizing consumers should vote in predictable ways: support for liberal,

redistributive governments should fall as income rises. But weak empirical evidence for these

voting patterns might suggest that voters are influenced by perceptions of social mobility

from within-family learning, or expectations regarding future income dynamics. To examine

these effects, this paper uses two different data sources, including new information from a

data set of twins. Little evidence is found to suggest that expectations of future upward

mobility alter voting preferences, but a new econometric approach shows that within-family

learning and family-specific effects are quite important determinants of voting preferences.

(D31, D63, H20, C10)

1 Introduction

The analysis of voter preferences has traditionally assumed that voters are economic agents

who cast their votes to maximize current income.1 This has given rise to models which asserted

that poor voters prefer more liberal governments that would enact redistributive taxation

policies, and rich voters would prefer more conservative governments that would not use as

much redistributive taxation. But recently, different theories have been proposed to account

for the weak empirical relationship between social status and voting preferences, since many

have wondered why some lower-income individuals tend to be conservative voters. One popular

theory (Benabou and Ok, 2001; Alesina and La Ferrara, 2001) asserts that the poor anticipate

upward mobility in the future, so they would rationally want lower tax rates to maximize

the gain from this potential windfall. Another view (Piketty, 1995) is that family background

matters a great deal to one’s political beliefs, and this influence can occur through within-family

learning; a voter updates her political beliefs depending upon how other family members have

fared in the economy.

To consider the effect of the potential of upward mobility (POUM) on preferences,

this paper will consider the relationship between income and voting preferences by analyzing

two data sets: the American National Election Survey (ANES) and a new source of political

information from a data set of twins. Benabou and Ok’s POUM hypothesis predicts that

some lower-class voters will vote for a conservative government if their income exceeds an

unknown income threshold, but all other voters below this threshold will prefer a more liberal

government. Due to the importance of this threshold in the POUM hypothesis, this paper will

rely upon established methods for detecting unobserved break points in data (Quandt (1960),

Andrews (1993), Piehl et.al. (2004)). But, contrary to the theory’s predictions, the results will

confirm that for both data sets, there is no significant change in voter preferences as income

increases. To examine the impact of family background and within-family learning on voting1There are many papers in the literature that make such an assumption. Some of these papers include

Corneo and Gruner (2000), Alesina and Rodrik (1994), Roberts (1977), Durlauf (1996), Turrini (1998).

1

patterns, this paper will use a new econometric technique on the new politics supplement from

a data set of twins. First, it will be demonstrated that there are large correlations in political

beliefs between siblings, which implies that family effects are quite important in determining

political beliefs. Second, since the measurement of voting preferences tends to use rank-

order variables, a new econometric methodology will be used to incorporate a family-specific

fixed effect in an ordered-response model. The new estimator is developed using the work

of Chamberlain (1980) and McFadden (1974), and results from this approach find that fixed

effects do alter the parameter estimates in this study, but even after controlling for the effects of

family background, within-family learning is a significant determinant of political preferences.

The remainder of the paper is structured as follows: section two provides a literature

review on voter preferences, section three describes the data used in this study, section four

presents the econometric frameworks for the analysis and results from the data, and section

five concludes the paper.

2 Literature Review and Theoretical Frameworks

A large literature exists on the determination of voting preferences and preferences for

redistribution, and most of the literature is concerned with the effect of differences in income

on voting attitudes. One group of articles asserts that as a voter’s income increases, he

should prefer less redistribution. For instance, studies by Roberts (1977), Meltzer and Richard

(1981), Alesina and Rodrik (1994) and Corneo and Gruner (2000) use a model that relies

on a median voter framework where individual utility is dependent upon personal income.

Richer voters are less likely to favour redistribution because it decreases their income, while

poorer voters are inclined to vote for redistribution to obtain more income. In a similar

vein, some authors have also argued that educational attainment can affect voting preferences

because it can serve to segment the economy into different income classes, and maintain (or

increase) these income differentials over time. Durlauf (1996) and Turrini (1998) both present

models that demonstrate how differences in education could lead to larger income differentials

2

in the economy. The basic premise of these models is that productivity shocks cause income

segregation (either across neighborhoods or across educational groups), so that the economy

is sorted into high- and low-income groups. The high-income groups tend to invest more

in their children’s education than the low-income groups, and this can lead to sustained or

even increasing income inequality. In this case, larger investments in education would cause

an individual to become more conservative; for example, a highly-educated (and thus high-

income) person would be less inclined to vote for redistributive tax policies, since this would

make it less likely that the high-income status would be passed on to his children.2

Alternatively, other authors have diverged from these ideas in an attempt to explain

the relatively small empirical correlation between income and preference for redistribution, and

two popular models have arisen in the literature. One model, by Benabou and Ok, suggests

that the prospect of upward mobility (POUM) leads some poor voters to actually prefer lower

tax rates — if there is potential that they (or their children) will not be poor in the future, then

they could rationally be expected to prefer lower tax rates so that when their upward mobility

occurs, it would not be diminished by large tax payments. Using estimates from the PSID,

Alesina and La Ferrara construct a measure of potential upward mobility and find that there

is indeed a significant relationship between preferences for redistribution and these measures.

In the simplest version of the model developed by Benabou and Ok, pre-tax incomes

evolve over time according to a deterministic transition function, f , so that if an individual’s

income in the current period is y, then his income in period t is f t(y). For further simplicity,

suppose that an individual only cares about next period’s income, and has the option to vote

for one of two tax rates which will be applied to next period’s income: r0 and r1, such that

r0 < r1. If the current period’s income distribution is represented by F0, and next period’s

income distribution is represented by F1, then an individual will vote for r1 if her next period’s2Durlauf, for instance, assumes that there is an income threshhold, above which certain neighborhoods

are no longer prone to negative productivity shocks. One reason for this is that the high-level of human

capital investment that takes place in this neighborhood is a kind of insurance against such a negative shock.

Redistributive income policies would do nothing except bring this neighborhood closer to (or below) this critical

threshhold.

3

earnings will be below the average earnings for all consumers:

f(y) <

ZfdF0 = µF1

Suppose further that the income transition function is concave but not affine. In this case,

Benabou and Ok use Jensen’s inequality to demonstrate that an agent with average income in

the current period (µF0) will have a higher-than-average income in the next period:

f(µF0) = f(

ZydF0) >

ZfdF0 = µF1

As a result, it is possible that individuals with less-than-average income in the current period

will have higher-than-average income next period, and thus prefer lower tax rates to higher tax

rates because of this prospect of upward mobility. In particular, Benabou and Ok demonstrate

that there will exist a unique income level in the current period, y∗0, such that all individuals

whose income is below this unique income level will prefer r1 to r0, and all individuals with an

income above this level will prefer r1 to r0.3 The overall advantage of the POUM hypothesis is

that it can account for the empirically weak relationship between income and voting preferences,

because it can rationalize why lower-income voters may opt for less-redistributive, or more

conservative governments.

As an alternative explanation for the weak relationship between income and redistrib-

utive preference, Piketty argues that an individual’s perceptions regarding inequality can be

influenced by his or her family. A voter who grew up in a poor family could develop beliefs

about income disparities which were affected by this background and persist into adulthood,

regardless of what adult income the individual earns. Specifically, Piketty asserts that the

main factors in determining mobility are effort (e), social origins and luck. For simplicity, he

constructs a two-period model where the effort supplied in the first period and family back-

ground (or luck) determines income in the second period. In this model, it is possible to obtain

one of two incomes: y1 and y0, where y1 > y0. Furthermore, the probability that one obtains3As the transition function f becomes more concave, y∗0 will become smaller. Benabou and Ok also demon-

strate that y∗0 will become smaller in a multi-period framework when either voters become more far-sighted, or

the duration of the tax scheme is increased.

4

a high income is defined as follows:

P (yit = y1|eit = e, yit−1 = y0) = π0 + θe

P (yit = y1|eit = e, yit−1 = y1) = π1 + θe

where yit represents an individual’s income, and yit−1 represents parental income. To recognize

the fact that children from higher-income families have better opportunities than children from

lower-income families, it is assumed that π0 < π1. Effort is assumed to have a positive effect

on the probability of obtaining a high income, so that θ > 0. Income is taxed in this model at

rate τ ∈ [0, 1], so that the after tax income for someone with pre-tax income of y0 is defined as

y0τ = τy0 + (1− τ)Y , where Y is aggregate income for all consumers.

If the parameters (π0,π1, θ) are known with certainty, then all agents adopt a given

level of effort and every agent has the same preferred tax rate:

τ =A(π1 − π0)

θ2

where A is a function of the percentage of high-income individuals in the model, as well as other

factors.4 Clearly, the preferred tax rate is positively related to (π1−π0), and negatively related

to the parameter θ. Thus, if luck or family background plays a large role in the determination

of income, then (π1 − π0) will be large, and the preferred tax rate will be high to address this

imbalance. However, if effort is relatively important, then θ will be large, which will cause the

preferred tax rate to be low.

But Piketty’s model also addresses the case when all consumers don’t know the parame-

ters (π0,π1, θ) with certainty. In this case, individuals make inferences about these parameters

from their families’ experiences to update their beliefs about (π1 − π0) and θ based upon the

impact of effort and luck on income.5 If an individual observes that high effort has caused

an income realization of y1, then she will place a greater weight on the importance of the4A is equal to H

a(y1−y0) , where H is the proportion of high-income voters, and a is drawn from the individual’s

utility function. Please refer to Piketty (1995) for further details.5Piketty assumes that learning about the effects of effort is accomplished only through private information

(from the family), and that families don’t perturb e very much because it is costly.

5

parameter θ, and thus prefer lower tax rates. However, if high effort does not result in a high

income realization, then the individual will attribute this to bad luck, and put more weight

upon (π1 − π0), which will cause her to prefer higher tax rates.

An interesting feature of this model is that it allows agents to begin at the same income

but then diverge into low- and high-income groups, with moderate amounts of upward and

downward mobility between these two groups. In the long run, the model implies that there

will be more left-wing voters (who favour more redistributive tax policies) in the lower-class,

and more right-wing voters in the upper class, but the upper class will not consist exclusively

of conservative voters and the lower class will not exclusively consist of liberal voters. This

fact arises from the strong impacts of family experiences on voting patterns. Some empirical

evidence in favour of this theory is assembled by Fong (2001), who compiles evidence about the

beliefs of rich and poor voters in regard to their preferred levels of taxation, and she finds that

wealthier voters favour greater redistribution because they believe that circumstances beyond

an individual’s control cause him to be wealthy or poor, and voters with less income feel that

an individual is in greater control of his destiny, and as such tend not to favour redistribution.

This is also consistent with some separate evidence assembled by Alesina and La Ferrara, who

also find that voters tend to be more conservative if they believe that all individuals have equal

opportunities, and that effort and hard work determine one’s income. Conversely, more liberal

voters tend to believe that not all people have equal opportunities, and that luck or family

connections are important determinants of personal income.

These papers demonstrate that an analysis of voting preferences must account for two

different problems. First, to properly consider the potential for upward mobility on voting

preferences, it is necessary to have microdata with information on voting beliefs and personal

characteristics such as income. Second, Piketty’s theory and Fong’s evidence demonstrate

that family background effects must be incorporated into any analysis of voting preferences.

To account for this, both standard and new econometric techniques will be used to include a

fixed-effect for family background in an empirical model that measures the impact of various

6

personal characteristics (such as education, income, and other variables) on political beliefs,

and such a technique must be applied to data with information on a respondent’s family, or

data on multiple family members. As such, in addition to a standard data set which surveys

individuals on the voting preferences as well as income and demographic variables, new data

will be used in this project which involves respondents who are twins. This data set has

been employed in other studies to examine the effects of different observable characteristics on

wages,6 but its information on political beliefs has never before been used. The fact that the

twins are from the same family allows for the incorporation of a familial fixed effect into the

estimation technique, but first, the specifics of the data are described in the next section.

3 Data

The data sets used in this analysis are the 1994 wave of the American National Election

Study (ANES) and the 1995 wave of a data set composed of identical twins which was collected

at the Twinsburg Twins Festival in Twinsburg, Ohio.7 The interview questions in the data set

of twins were modeled after those in the Census and CPS instruments, and some additional

questions were specifically designed for interviewing twins, such as the twin’s report of his or her

sibling’s educational attainment, which will be used in the empirical work for this study.8 Some

of the data from the first three waves of this survey were used in studies by Ashenfelter and

Krueger (1994) and Ashenfelter and Rouse (1998), who provide a discussion of the procedures

used to collect these data. Several political questions were included in the 1995 wave of the

survey, and were patterned after those asked by the ANES. To analyze the political preferences

of the twins, data used in this study are drawn from the sub-sample of identical white twins9

6See Ashenfelter and Krueger (1994), Ashenfelter and Rouse (1998), Krashinsky (2004).7 It was not possible to use data collected in the same years for both surveys, since the ANES is only collected

every two years, and the politics survey was only give to the twins once, in 1995.8This report has been used as an instrumental variable to account for the effect of measurement error on the

return to education.9The sample of white twins was selected to avoid convoluting the analysis with the anomolous sub-sample

of black twins. Ashenfelter and Rouse (1998) document the fact that the coefficient on a indicator variable for

black twins is positive in a regression on the pooled sample of twins, suggesting that the black sub-sample of

twins may not be representative of the general population.

7

interviewed in the 1995 wave of the survey, both of whom have worked within two years prior

to the interview and are living in the United States.

An important preliminary concern about the Twins data is whether or not it is roughly

comparable to the general population in the United States. This issue is addressed in Table

1, which displays the characteristics of the Twins sample and compares them to respondents

from the 1994 supplement of the ANES. The ANES conducts national surveys of the American

electorate in presidential and midterm election years and carries out research and development

work through pilot studies in odd-numbered years. Overall, the survey is designed to elicit

political preferences and beliefs of a representative sample of the American voting public.

Politically-based questions in the 1995 wave of the Twins survey were intentionally patterned

after those in the ANES to determine the representativeness of the Twins data, and Table 1

displays the means and standard errors of certain variables common to both data sets. In

general, the two samples seem similar. Respondents from both surveys are quite close in

average age, education and earnings, with some differences evident in characteristics such as

the percentage of married or female respondents.

To determine if these differences cause a significant difference in political attitudes be-

tween the two samples, Table 2 reports the distribution of political preferences for respondents

from both surveys. These preferences were measured by asking both sets of respondents to

list their general political beliefs on a seven-point scale: 1 represented “most liberal”, while

7 denoted “most conservative”. The results in Table 2 suggest that the distribution of the

respondents’ preferences is quite similar for both surveys, and this is formally demonstrated

by the fact that a chi-squared test of the similarity of the two distributions is not rejected at

the 5% level of significance.10 Since the political views in each survey are quite similar, this

implies that the sample of twins is not an unrepresentative subsample of the overall population

of voters. As complementary evidence to this, Table 3 reports results of ordered logit models

using the identical twins data set and the ANES to consider if the two samples are roughly10The Pearson test statistic of 6.79 has a p-value of 0.340, which implies that we cannot reject the hypothesis

at the 5% level of significance that the two distributions are the same.

8

similar in a multivariate analysis. In these models, the seven-point scales were used as the

dependent variable in an ordered logit model, and the independent variables for the model

included income, educational attainment, and other individual and job-related characteristics.

The results in this table demonstrate that the coefficient estimates for the identical twins sam-

ple are generally close to those from the ANES. In both samples, the coefficients on age,

education and hourly wages are positive, and the coefficients for education and hourly wage

are not statistically significant. This is generally consistent with results from other studies

which find that the relationship between conservative voting tendencies and income is not as

strong as might be expected. It is also seen that female voters in both samples are significantly

more liberal than their male counterparts, although being a married female does not have a

strong effect on voting behavior. The only difference between the two data sets is evident with

the marital dummy. However, this coefficient is not significant in either data set, and when a

test of the similarity of the two sets of coefficients are run with these data, the hypothesis that

all of the coefficients are the same cannot be rejected at the 5% level of significance.11 Also,

later results were estimated with and without the married male sub-sample, and it did not

alter the main results. In general, this suggests that the two data sets provide similar basic

information.

Since the results in Tables 1 through 3 demonstrate that the sample of twins is generally

similar to the ANES sample, these data sources will be useful to consider different determinants

of political preferences. The data sets will first be used to consider whether significant changes

in preferences exist at some income threshold, as Benabou and Ok’s POUM hypothesis would

predict. Also, since the twins come from the same family, this allows for a consideration of how

familial influences enter into this analysis, which is important for Piketty’s theory. However,

to incorporate these family effects into a standard econometric analysis which uses an ordered-

response model, it is necessary to construct a new estimator. The econometric approaches for

studying both theories, and the main empirical results are described in the next section.11The test of the similarity of all six coefficients has a test statistic of 11.21 with a p-value of 0.082.

9

4 Econometric Framework and Results

As previously discussed, both the data set of identical twins and the ANES gauge political

attitudes using a seven-point ordinal measure. In the case of the POUM hypothesis, it is

necessary to consider whether or not respondents are significantly more conservative above

some critical, unknown income value, y∗0. This can be accomplished by implementing tests

designed by Quandt (1960) and Andrews (1993), which consider the maximum test statistic for

the null hypothesis of no significant change in political attitudes over all possible break points

in the data. Specifically, suppose that the following ordered response model is estimated:

y = β ∗ income+ γZ + ε

where y represents an individual’s ranking on the seven-point political scale, income represents

an individual’s hourly wage rate, Z represents other covariates, and ε is an error term. The

basic approach to consider whether or not there is a break point in the data is to test the

following hypothesis:

HO : β = β0 for all levels of income

H1 : β = β1 if income < y∗, and β = β2 if income > y

∗

The analysis requires that a Wald statistic be computed for all possible break points in the

data, and if the maximum Wald statistic exceeds an appropriate critical value, then the null

hypothesis of parameter constancy for the income coefficient is rejected. In this context, the

test of the POUM hypothesis would require that at least one break point exist in the data so

that the null hypothesis of no change in political preferences across income be rejected.

The presence of a break in political preferences was tested in two ways for both data

sets: first, a logit framework was used to analyze a binary dependent variable for y equal to

one if the respondent’s political preference ranked at 4 or higher on the political scale, and zero

otherwise. The second framework used an ordered logit to analyze the presence of break points

for the seven-point political scale as the dependent variable, y. The test was straightforward

10

— it considered the significance of δ in the following regression:

y = β ∗ income+ δ ∗ income ∗ threshold+ γZ + ε

where threshold is an indicator variable equal to one if the respondent’s hourly wage exceeded

some critical value, which was initially set at $7 per hour, and was increased in 25-cent incre-

ments as the model was re-estimated, until the critical income value was $30 per hour.12 Table

4 presents estimates of the maximum Wald statistics from this test for the ANES and data set

of twins, and Figures 1 and 2 graph the values of all the test statistics calculated for both data

sets, with a horizontal line imposed on the graph whose vertical intercept is 8.85, the critical

value for these test statistics.

For both the simple logit and ordered logit estimation approaches, the maximum test

statistics were found to be below the average hourly wage rate for both the ANES and data set

of twins, as the POUM would suggest, but the maximum test statistics were much lower than

the 8.85 critical value at the 5% level of significance for such a statistic.13 This suggests that

there are no significant breaks in political preferences across different levels of income the data,

which runs counter to the POUM hypothesis. As stated earlier, Alesina and La Ferrara find

some empirical evidence in favor of the POUM hypothesis, but their findings and the results

in this paper can be reconciled by the fact that their test of the POUM hypothesis relates

political attitudes to estimated future income, given year-to-year income dynamics observed in

the data at each income percentile. The test presented here is much different, and would seem

to be a more direct test of the POUM hypothesis.

To consider if there is better empirical support for an alternative hypothesis which12The values of $7/hour and $30/hour were chosen according to Andrews (1993) suggestion that the search

process take place over a range of income values between the fifteenth and eighty-fifth percentiles of the income

distribution. This ensures that for every possible break point considered by the test, at least 15% of the

respondents lie below the break point, and at least 15% of the respondents lie above the break point.13Andrews (1993) derives the critical values for these maximum test statistics, and the 8.85 critical value is

relevant when the search region trims 15% of the lowest income values and 15% of the highest income values.

Piehl et. al. (2003) perform a similar type of test in their work, and mention that the reason for such a large

critical value (instead of 3.84 for a standard test statistic) is that this process searches for a break point across

all possible values of the indepedent variable.

11

relies on familial influences to account for atypical voting patterns, a simple exploration of

family effects using the data set of twins is important. This will determine if there are any

first-order facts in favour of hypotheses like Piketty’s theory of within-family learning. The first

fact to suggest that family effects are important for the analysis is that there is a correlation

of 0.34 between the two siblings political preferences, as measured by the seven-point political

scale in the data set of twins, suggesting that there is positive relationship between two family

member’s political beliefs. Table 5 investigates this within-family relationship more formally

in a regression context by including a variable representing the sibling’s political beliefs, and

the results from the first row of this Table demonstrate that there is a significant effect of a

sibling’s political beliefs on the respondent’s political beliefs, even after controlling for other

covariates. This analysis uses two different approaches: the first three columns consider an

indicator variable for the respondent that is equal to one if the respondent’s political beliefs

rank at 4 or higher on the seven point-scale and zero otherwise, and a similar variable is

created for the respondent’s sibling. Using a linear probability model in columns one and

two, it is clear that the sibling’s political preference variable is highly significant, with a t-

value of approximately 3, even after controlling for other covariates. The third column of

this table demonstrates that these results are unchanged if a logit estimation approach is used.

The fourth through sixth columns of Table 5 compare the seven point political scale for the

respondent and the sibling, and the results are similar to those in the first three columns.

Columns 4 and 5 demonstrate that there is a highly significant relationship between these two

variables in the linear probability model; the t-statistic on the sibling’s political views is roughly

4 in this case. Column 6 shows that the results are the same in an ordered logit model.

The results in Table 5 suggest two things that are relevant to the analysis: first, that

family-specific effects are an important determinant of individual political preferences, because

of the strong within-twin correlations in voting preferences. Thus, it is important to incorporate

a family-specific effect into the econometric analysis of a respondent’s political beliefs. Second,

the findings in Table 5 suggest that there may be credence to Piketty’s hypothesis, which

12

suggests that within-family learning helps to shape one’s political preferences. A test of

Piketty’s theory will be proposed in an outline of the relevant econometric issues for including

a fixed effect in an analysis of the data set of twins.

To incorporate a family-specific fixed-effect into the analysis, consider a framework for

both twins where one would be interested in determining the effect of a series of variables, X,

on an individual’s political preferences, y. Econometrically, we are interested in the following

model:

y1j = β0X1j + α0Zj +Aj + ε1j (1)

y2j = β0X2j + α0Zj +Aj + ε2j

whereXij represents a vector of individual characteristics for twin i from family j, Zj represents

common characteristics for family j, Aj is a family-specific fixed effect and εij is an individual-

specific error term.14 In the simplest version of this model, suppose that yij is equal to one if the

respondent has a political belief that ranks at 4 or higher on the seven-point political scale, and

zero otherwise. In this case, eliminating the family-specific fixed effect can be accomplished

by estimating an ordered logit15 using the within-twin difference of all the variables in the

model, or by using Chamberlain’s (1980) conditional logit approach, which is also tantamount

to estimating a logit model using within-twin differences of all the variables in the model for

twin pairs with different values of y1j and y2j :16

(y1j − y2j) = β0(X1j −X2j) + (ε1j − ε2j) (2)

To test Piketty’s model, which asserts that political beliefs are determined by within-

family learning about luck and effort, two key variables need to be included in the above model.

First, let Iij represent twin i’s income, and let ∆E1j =¯̄̄E1j −E∗2j

¯̄̄, where E1j represents the

14The identifying assumption of this model is that the returns to individual characteristics Xij are the same

for both twins, and that familial influences are correlated between twins.15An ordered logit is necessary because the within-twin difference in the dependent variables, (y1j − y2j),

can take on three different values: -1, 0 or 1. But this approach is somewhat lacking, and its deficiencies are

discussed in more detailed when the ordered-logit model is analysed.16See Chamberlain (1980) and McFadden (1974).

13

twin one’s own-reported level of education, and E∗2j represents his report of his sibling’s level

of education,17 a variable that is unique to this particular data set, and will be important for

this analysis. If these two variables are included in a conditional logit approach, then the

within-twin differencing would result in the following model:

(y1j − y2j) = γ1(∆E1j −∆E2j) + γ2(I1j − I2j) + β0(X1j −X2j) + (ε1j − ε2j) (3)

where ∆E2j is twin 2’s analogue of ∆E1j . In this model, ∆E1j − ∆E2j is equal to zero

only if both twins have an accurate report of each other’s education. However, a key aspect

to this approach is that if one twin has an incorrect report of his sibling’s education, then

Piketty’s theory suggests that this will cause the two twins to draw different conclusions about

the preferred tax rate, and have different political preferences. This occurs because, assuming

that education is a function of effort,18 γ1 represents the effect of an increase (∆E1j −∆E2j),

twin one’s perceived effort relative to his sibling, holding constant the within-twin difference

in income. As an example of a case where (∆E1j − ∆E2j) is not zero, suppose that sibling

1 has sixteen years of education and sibling two has 12 years of education. Suppose further17Ashenfelter and Krueger (1994) show that the correlation between a twin’s education and his sibling’s report

of this educational attainment is less than 1. In this paper’s sample, there are 114 pairs of twins; only 60 pairs

of twins have consistent reports of each others’ educational attainment.18There is a large literature on optimal schooling choice that builds on the work of Becker (1967). For

example, Card (2001) derives the optimal schooling choice S for an individual with an infinite planning horizon

by modelling life cycle utility in year t as being dependent upon consumption c(t) and the relative disutility of

school versus work φ(t). If the discount rate is ρ, then the consumer maximizes the following lifecycle utility

function V :

V (S, c(t)) =

Z S

0

(u(c(t)− φ(t))e−ρtdt+Z ∞

S

u(c(t))e−ρtdt

Solving this expression for S results in a level of schooling that is negatively related to φ(t).

Typically, it is assumed that φ(t) is related to the unobserved component of a consumer’s ability, such as her

proficiency in learning new ideas and her inherent willingness to exert effort through study. Since the twins are

assumed to have an equal proficiency at learning, then (assuming that the marginal benefit is the same for both

twins) the only reason for a within-twin difference in the optimal schooling choice would arise from differences

in effort. Indeed, this is quite consistent with Ashenfelter and Rouse’s finding that twins with different levels

of education reported that the reason for this difference was an exogenous shock that required a greater level of

effort. For instance, many female twins reported that divorce or marriage that made them respectively more or

less willing to get more education. Similarly, the modal response among male twins was that different career

interests made them more or less willing to obtain education.

14

that sibling two accurately reports both her own and her sibling’s educational attainment, but

suppose that sibling one underestimates her twin’s level of education by one year. In that

case, (∆E1j − ∆E2j) = |16− 11| − |12− 16| = 1; twin 1 will believe that there is a greater

within-twin educational difference than twin 2, but both twins will observe the same within-

twin difference in income. As such, twin 1 should place a greater emphasis on the effect of

luck than twin 2, because twin 1 believes that effort (or education) has a smaller impact on

income. In this context, twin 1 will be more liberal than twin 2, and thus (y1j − y2j) < 0,

since lower values of y reflect more liberal views. Similarly, if twin one overestimates her

sibling’s educational attainment by one year, then (∆E1j − ∆E2j) = −1. This reflects the

fact that twin two believes there is a greater difference in effort between the two twins (but a

constant difference in income), and will cause twin two to be more liberal than twin one, and

thus (y1j − y2j) < 0. Therefore, since there is a negative relationship between (∆E1j −∆E2j)

and (y1j − y2j) in this process, then γ1 should be negative if Piketty’s theory is correct. In

this sense, a unique test is available for Piketty’s theory, given the availability of one twin’s

estimate of his sibling’s education.

The results in Table 6 explore this specification. The first two columns of the Table

estimate simple logit models, without any within-twin differencing of the variables. The

results in the first column demonstrate that the only variable that is significant is age, and

the findings in column two show that the inclusion of the perceived difference in educational

attainment between twins, ∆E1j , is not significant, and does not alter the impact of the

other variables in the model. Columns three and four perform an ordered logit estimation

of the within-twin differenced variables, and column three shows that the net difference in

perceived educational attainment, controlling for difference in income, is negatively significant.

As previously discussed, this means that if one twin overestimates his sibling’s educational

attainment, then he will be more liberal. This is strongly supportive of Piketty’s hypothesis,

because a significantly negative estimate of γ1 suggests that if one twin overestimates his

sibling’s education, then for a given within-twin difference in income, this will lead him to

15

believe that the income-generating process is more arbitrary and dependent upon luck than

effort. As a result, he will favour more liberal, redistributive governments.

One potential concern with this approach is that using a twin’s estimate of his sib-

ling’s education has typically been used to account for measurement error in the educational

variable.19 If the difference (∆E1j −∆E2j) is only representative of measurement error, and

not a true signal, then the negative estimate of γ1 could be due to some non-learning process.

For instance, the correlation between the net difference in the perceived difference in education

(∆E1j −∆E2j) and the self-reported difference in education (E1j −E2j) is quite high,20 so the

significance of γ1 could be caused by the simple difference in self-reported education between

the two twins if, for instance, a more unequally-educated sibling simply dislikes inequality

more. Column four accounts for this possibility by including the difference in self-reported

education in the regression, and the main results are unchanged. The within-twin difference

in perceived educational differences still has a significantly negative effect on political beliefs,

and the within-twin difference in education does not have a significant effect. Columns 5 and

6 perform a similar exercise, but rely upon the conditional logit approach to account for a

family-specific fixed effect, and show basically the same results as in columns 3 and 4: the

within-twin difference in perceived educational differences has a significantly negative effect,

even if the self-reported difference in education is included in the regression.

The results in Table 6 relied upon a dependent variable that only took two different

values. A more detailed analysis of the impact of within-twin differences in perceived edu-

cational differentials on political beliefs would use a more detailed dependent variable — the

respondent’s score on the seven-point political scale. This would require using an ordered logit

approach, but prior work has demonstrated that it is not possible to include a family-specific

fixed effect into this framework, because it can not be identified using standard estimation ap-

proaches.21 As with the case where a binary dependent variable was used in the analysis, it is19See Ashenfelter and Krueger (1994), Ashenfelter and Rouse (1998), and Krashinsky (2004).20The correlation between these two variables is approximately 0.4.21Specifically, there is no way to identify the estimated break points between the different categories for the

unobserved, latent dependent variable separately from the fixed effect, so the estimation strategy is defeated.

16

possible to estimate an ordered logit model on transformed data; using within-twin contrasts,

the ordered logit could be estimated using standard methods. That is, we would assume a

latent variable model with the transformed data:

(y1j − y2j)∗ = β0(X1j −X2j) + uj (4)

where (y1j − y2j)∗ is the latent variable, and uj is distributed logistically, such that:

(y1j − y2j) = −6 if (y1j − y2j)∗ < γ1

(y1j − y2j) = −5 if γ1 ≤ (y1j − y2j)∗ < γ2

(y1j − y2j) = −4 if γ2 ≤ (y1j − y2j)∗ < γ3 (5)

...

(y1j − y2j) = +5 if γ11 ≤ (y1j − y2j)∗ < γ12

(y1j − y2j) = +6 if γ12 ≤ (y1j − y2j)∗

The limitation of this model is that it doesn’t provide the same information as the ordered

logit model estimated with untransformed data. Specifically, the dependent variable can range

from -6 to +6, and the ordered logit measures the effect of the within-twin-differenced variables

on moving from one category to another. This approach is advantageous because it controls

for family fixed effects, and loosely captures the effect of the independent variables on moving

between the categories of the ordered logit. But the weakness of this strategy is that it is

not necessarily measuring the appropriate effect; for instance, a value of 1 in the dependent

variable could be created if one twin had a political belief of 7 while the other had a belief of

6, or if one had a 3 while the other had a 2 (and so on). This ordered logit approach restricts

the effect of the independent variable on moving from one category to the next (say, from 2 to

3) to be identical. But the fact that there may be different effects of a particular variable on

moving from one category to the next is a possibility that should be considered, so this version

of the ordered logit model may be too restrictive for this exercise.

See Maddala (1983).

17

To properly capture the family-specific fixed effect in the ordered logit framework,

a new approach is necessary.22 This approach works closely with the analysis conducted

by Chamberlain (1980), who determined how to incorporate a fixed effect into a multinomial

logit, using a conditional likelihood approach. His model is not ideal for this problem, however,

because although it would provide consistent estimates of β, a multinomial logit is inefficient

in comparison with an ordered logit (since it ignores the covariances between the different

responses the dependent variable). A potential improvement to the multinomial logit is to

use Chamberlain’s (1980) fixed-effect logit model to obtain consistent estimates of the ordered

logit model, and then to use optimal minimum distance to determine the best estimate of β.

Specifically, six dummy variables, denoted as A1 to A6, are created and defined in terms of the

individual’s political preferences (which range from 1 to 7), y, as follows:

A1ij = 1 if 2 ≤ yij ≤ 7

= 0 otherwise

A2ij = 1 if 3 ≤ yij ≤ 7 (6)

= 0 otherwise

...

A6ij = 1 if yij = 7

= 0 otherwise

Each variable is then used in a fixed-effect logit model to determine the effect of different

covariates on the dummy variable. The adaptation of Chamberlain’s (1980) approach in this

case is to condition on the sum of the dependent variables for each set of twins — specifically,

on the condition that the sum of both twins’ dependent variables is 1.23 In this case, the22As far as I know, no one has considered how to include a fixed-effect into an ordered-response model.23The probability that this sum is two or zero is, obviously, 1 (if the sum is zero, then it must be the case that

both twins have a dependent variable of zero; the same argument can be made for the case where this sum is 2).

18

probability that a twin’s response is equal to one is:

P (A1ij = 1) =eαj+X1jβ

1 + eαj+X1jβ(7)

where αj is the family-specific fixed effect. The conditional probability has been shown by

Chamberlain and McFadden (1974) to be:

P [A11j = 1|(A11j +A12j = 1)] = e(X1j−X2j)β

1 + e(X1j−X2j)β(8)

which is no longer prone to the incidental parameters problem.24 Estimating this model with

the six different dummy variables A1 −A6 (constructed from the original dependent variable)

provides six consistent25 estimates of β that can be calculated while incorporating the family-

specific fixed effect. Furthermore, unlike the case where (y1j − y2j) was used as the model’s

dependent variable, this approach allows for a finer analysis of the difference in each twin’s

political beliefs. With these six moment conditions that provide consistent estimates of β, an

optimal minimum distance approach can be used to find an optimal estimate of this parameter.

Another advantage of using this model lies in the incorporation of individual-specific

threshold points for the ordered logit model. Since a fixed effect can be incorporated into the

model, the underlying ordered logit model becomes less restrictive. With a fixed effect, the

model is specified as:

yi = 1 if αi +X0ijβ + εij < γ1

= 2 if γ1 < αi +X0ijβ + εij < γ2

... (9)

= 7 if γ6 < αi +X0ijβ + εij

Since the fixed effect itself may be moved to either side of the inequality, then the threshold24The incidental parameters problem is solved because αj is no longer part of the expression for the conditional

probability.25See the appendix to this paper for a brief discussion of the consistency of this estimator.

19

levels themselves, γ1 and γ2, may be indexed to the individual, so that:

yi = 1 if eαi +X 0ijβ + εij < λ1i

= 2 if λ1i < eαi +X 0ijβ + εij < λ2i

... (10)

= 7 if λ6i < eαi +X 0ijβ + εij

where eαi = cαi, λji = γj − (1 − c)αi, and 0 < c < 1. Because it was already demonstrated

that this model can be estimated with a series of fixed-effect logit models, then the estimator

presented in this paper not only produces a consistent estimate of β in an ordered response

model with a fixed effect, it also provides a consistent estimate with family-specific thresholds.

This is advantageous because it does not restrict the thresholds of all respondents to be the

same, and is consistent with Piketty’s model which explicitly accounts for families updating

their preferences in different ways. Specifically, there may be different probabilities that

individuals in different families will move between certain thresholds on the seven-point political

scale as they use family-specific learning to update their political beliefs based on effect of effort,

luck or family background on social mobility. As a result, the flexibility to have family-specific

fixed effects as well as family-specific threshold levels in the ordered response model is quite

necessary for this analysis.

As with Table 6, Table 7 first considers an ordered logit model estimated both with

and without the perceived within-twin difference in education. As with the first two columns

of Table 6, the first two columns of Table 7 show that age is the only significant variable, but

only in column two. Performing a within-twin ordered logit in column three demonstrates that

the perceived within-twin difference in education is again negatively significant, and remains

significant in column four, after the inclusion of the self-reported within-twin difference in

education (which itself is not significant). As was discussed, though, this estimation strategy is

somewhat lacking, and a superior approach can be taken by using an optimal minimum distance

approach with estimates from a fixed-effect logit model. These estimates are displayed in the

Table’s fifth and sixth columns, and are substantively similar to the findings in columns three

20

and four: the perceived within-twin difference in education is negatively significant, and this

remains true even after the inclusion of the within-twin difference in self-reported education.

The findings in Table 7 are strongly significant, and highly supportive of Piketty’s theory of

within-family learning.

To benchmark these results against a more established approach, the seventh column

shows estimates from Chamberlain’s conditional fixed effect in the multinomial logit model.

The multinomial logit model is also a consistent estimator of the parameter of interest, but is,

in general, much less efficient than the ordered logit, and this is reflected in the standard errors

seen in this column.26 All of the reported standard errors are larger for the multinomial logit

results than for the ordered logit, and this is especially true with the coefficient of interest,

education. For this variable, the multinomial logit approach yields standard errors which are

roughly two-and-a-half times as large as the ordered logit, demonstrating another attractive

component of this model — an improvement in the efficiency of an estimator for a fixed-effect

in the ordered response model.

One potential criticism of this estimation approach is that it applies a large-sample

estimator to a relatively small sample of data. In Table 1, it was reported that the sample

size of the data set of identical twins is only 228, and since the estimation procedure relies

upon within-twin differences, the effective sample size for the ordered logit model with a family

fixed effect is only 114. As such, the distribution of the estimator may not have the assumed

asymptotic properties of a large-sample estimator. To deal with this, Table 8 displays the

bootstrapped estimates of the confidence intervals for the coefficients estimated with an ordered

logit model that includes a family fixed-effect. As the results demonstrate, the bootstrapped

confidence intervals are generally supportive of the findings in Table 7, particularly about26 In addition to this, Chamberlain’s suggested approach for incorporating a fixed effect into the multinomial

logit framework involves conditioning on only two of the dependent variable’s values. For instance, in the

data set of twins, the multinomial logit approach would condition on only two of the possible seven responses,

throwing away large amounts of variation in the data. The multiple dummy variables (A1 to A6) used in this

paper’s ordered response model capture much more information provided by the data, allowing for more precise

estimates.

21

the effect of perceived differences in education on political beliefs, since the upper-bound of

the 95% confidence interval on the education coefficient is less than zero. The bootstrapped

results suggest that the other variables in the model are not significant, but more importantly

imply that the findings on perceived educational differences are not weakened by potential

small-sample biases affecting the estimator.

In general, the results in Tables 6 through 8 suggest that the theories proposing atypical

voting patterns by lower-class and upper-class voters have some empirical support. The cross-

sectional results show no strong relationship between income or education with conservative or

liberal voting preferences, which is consistent with Benabou and Ok’s POUM hypothesis, and

Piketty’s theory of within-family learning, both of which suggest reasons why some lower-class

voters prefer more conservative governments. However, the results are most strongly supportive

of Piketty’s theory which proposes that the effect of family background is important and will

obscure the cross-sectional analysis of the effect of different variables on political beliefs. Also,

the within-family updating of voting attitudes given the effects of effort and luck should be seen

once family-specific effects are accounted for in the analysis. The findings in Tables 6 and 7

do indeed show that accounting for family influences will alter the estimation results, and that

this actually makes the effect of perceived within-twin differences education more significant.

The increase in significance of this variable suggests that within-family updating does occur,

based upon the impact of family background and effort.

5 Conclusion

There is a long literature on the determination of political preferences and the preference

for redistribution. Many papers have approached this issue by asserting that lower-class voters

should prefer more redistribution and upper-class voters less redistribution, but recently, others

have considered cases where liberal or conservative political preferences are not as neatly divided

across the social spectrum. Two popular theories in this new literature were considered in this

paper: the POUM hypothesis, and Piketty’s theory of within-family learning. The POUM

22

hypothesis dictates that there should be some critical income level, below which all voters prefer

more redistribution, and above which all voters prefer less redistribution. The strength of this

theory is that the critical income level can be below the average income level in the economy,

which can confound overall relationships between income and voting patterns, because some

poorer voters will actually prefer more conservative governments. However, tests in this paper

could not find a significant break point in two different data sets on voting preferences, which

did not support the POUM hypothesis.

Conversely, Piketty’s hypothesis about within-family learning was well-supported by

the data. Piketty asserts that familial influences can affect voter preferences, as can within-

family learning about the effects of effort and luck. To properly consider this hypothesis, it was

necessary to use a new data set composed of twins, and a new estimation technique to account

for family influences on voting preferences. A simple cross-sectional estimate of the impact

of different variables on either a binary dependent variable or a seven-point scale representing

political attitudes showed only a mildly positive correlation between education and income

with conservative voting preferences, suggesting that factors such as family influences may be

confounding the analysis. Using both standard and new econometric techniques for including

a family-specific fixed-effect into the analysis, it was demonstrated that perceived differences

in within-twin education had a significantly negative impact on preferences, suggesting that

this variable makes voters more liberal, controlling for family effects. This finding was quite

supportive of Piketty’s model in two ways: first, it showed that the concern about family effects

on voting habits is well-founded, and second, it showed that voters engage in updating based

upon the relative effects of effort and luck that they observe within their families.

23

6 Appendix

To prove that using a conditional logit function with the transformed dependent variable Ai

(discussed in the econometric framework) will provide a consistent estimate of the fixed-effect

ordered response model, consider the case of an ordered logit model for an individual i in family

j whose dependent variable yij has three values: 1, 2, and 3. If there is a fixed-effect in this

model, then the probabilities that each value is assumed as as follows:

P (yij = 1) = P (αi +Xijβ + εij < µ1)

P (yij = 2) = P (µ1 ≤ αi +Xijβ + εij < µ2)

P (yij = 3) = P (µ2 ≤ αi +Xijβ + εij)

Conditioning on whether or not one of the dependent variables for the two people in family

j are greater than or equal to 2, the conditional probability that y1j ≥ 2 is:

P (y1j ≥ 2|(either y1j ≥ 2 or y2j ≥ 2))

=P (y1j ≥ 2)

P (y1j ≥ 2) ∗ P (y2j < 2) + P (y1j < 2) ∗ P (y2j ≥ 2)

In the case where εij is distributed logistically, then the right hand side of this expression can

be simplified to:

P (y1j ≥ 2|(either y1j ≥ 2 or y2j ≥ 2)) = e(X1j−X2j)β

1 + e(X1j−X2j)β

which does not depend on αi and also provides a consistent estimate of β through a maximum

likelihood approach if this expression is incorporated into a standard likelihood function.

24

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27

Table 1: Sample Means For Twins and ANES Samples

Twins ANES

Age 37.89 (11.49)

38.76 (10.49)

Education 14.34

(2.00) 14.03

(2.07)

Married 0.44 (0.50)

0.57 (0.50)

Female 0.49

(0.50) 0.40

(0.49)

Married Female 0.25 (0.43)

0.19 (0.40)

Hourly Wage 15.43

(9.36) 15.29

(8.45)

N 228 489

Standard deviations are listed in brackets beneath the sample means. The samples are composed of white voters who are at least 18 years of age, who earn at least $5/hour and no more than $100/hour.

Table 2: Political Preferences For Twins and ANES Respondents

Seven-Point Scale Twins ANES

1 5 (0.022)

10 (0.020)

2 21 (0.092)

45 (0.092)

3 33 (0.145)

52 (0.106)

4 74 (0.325)

133 (0.272)

5 41 (0.180)

98 (0.200)

6 47 (0.206)

135 (0.276)

7 7 (0.031)

16 (0.033)

Pearson Chi-Squared Statistic: 6.79 (p-value = 0.340)

Column percentages are listed in brackets beneath the number of respondents in each cell. The samples are composed of white voters who are at least 18 years of age, and earn at

least $5/hour and no more than $100/hour. The Pearson statistic tests the null hypothesis that the distributions of political preferences from the two samples are the same.

Table 3: Estimated Logit and Ordered Logit Coefficients For Twins and ANES Respondents

Logit Ordered Logit Twins ANES Twins ANES

Education -0.094 (0.082)

-0.045 (0.120)

0.041 (0.066)

0.063 (0.043)

Age 0.041 (0.017)

0.058 (0.024)

0.021 (0.011)

0.017 (0.008)

Married -0.725 (0.513)

-0.136 (0.633)

-0.497 (0.369)

0.415 (0.219)

Female -0.590 (0.431)

-0.816 (0.631)

-0.561 (0.323)

-0.864 (0.246)

Married*Female 0.522 (0.653)

0.657 (0.863)

0.813 (0.502)

0.114 (0.333)

Hourly wage -0.009 (0.018)

0.023 (0.029)

0.018 (0.015)

0.007 (0.011)

Standard errors are listed in parentheses beneath the coefficient estimates. The estimates from the first two columns are derived from estimates of logit models which use a dependent variable equal to one if the respondent’s political preferences ranked four or higher on the seven-point scale, and zero otherwise. The last two columns display estimates from an ordered logit model which uses the seven point scale itself as the dependent variable. The samples from both data sets are composed of white voters who are at least 18 years of age, and earn at least $5/hour and no more than $100/hour.

Table 4: Values of the Maximum Wald Statistics Testing for a Structural Break in Voting Preferences Across Income

Binary Dependent

Variable Seven-Point Scale

ANES Twins ANES Twins

Maximum Wald Statistic 3.996 2.219 2.624 4.216

Hourly Wage for Maximum Wald Statistic

$14.25 $12.00 $14.50 $12.00

The test for the maximum Wald statistic used logit models to analyze voter preferences. The results in the first two columns use a simple logit framework with a binary dependent variable equal to one if the individual’s political preferences are 4 or higher on the seven-point scale, and zero otherwise, and independent variables including hourly wages, education, age, union status, marital status, gender and the interaction between these two variables. To consider whether or not there is a structural break in voting preferences as income rises, the model also includes the interaction between hourly wage and an indicator variable equal to one if income exceeds a given level. This level was allowed to vary; it started at $7/hour and increased in 25 cent increments up to $30/hour, and maximum Wald statistic represents the test statistic for this variable. The first column of the table uses data from the ANES, and the second column uses the data set of identical twins. The last two columns perform an ordered logit analysis using the seven-point political scale as the dependent variable, and the same independent variables as in the first two columns. Using a similar practice as with the logit case, tests for breaks in voting preferences across income began at $7/hour and the break point was increased in 25 cent increments up to $30/hour. The choice of $7/hour and $30/hour as the income range to consider was based upon Andrews (1993) suggestion of trimming the search area so that at least 15% of the data was below the lowest level of income and 15% of the data was above the highest level of income.

Table 5: Effect of Sibling Preferences on Own Preferences for Respondents from the Sample of Twins

Binary Dependent Variable Seven-Point Scale OLS Logit OLS Ordered

Logit

Sibling’s Political Preference

0.245 (0.072)

0.219 (0.074)

1.087 (0.344)

0.829 (0.209)

0.817 (0.222)

0.444 (0.100)

Education -0.015 (0.015)

-0.085 (0.086)

0.024 (0.047)

0.004 (0.073)

Age 0.006 (0.003)

0.038 (0.017)

0.012 (0.008)

0.013 (0.015)

Married -0.134 (0.080)

-0.866 (0.497)

-0.477 (0.267)

-0.575 (0.391)

Female -0.094 (0.073)

-0.568 (0.423)

-0.367 (0.237)

-0.445 (0.305)

Married Female 0.101 (0.117)

0.644 (0.654)

0.657 (0.382)

0.894 (0.539)

Hourly wage -0.001 (0.003)

-0.009 (0.019)

0.014 (0.013)

0.016 (0.017)

Union Member -0.069 (0.075)

-0.421 (0.404)

0.041 (0.249)

0.097 (0.375)

Standard errors are listed in parentheses. The results in the first three columns use a binary dependent variable equal to one if the individual’s political preferences are 4 or higher on the seven-point scale, and zero otherwise, and the variable “Sibling’s Political Preference” is a binary dependent variable equal to one if the sibling’s political preferences are 4 or higher on the seven-point scale, and zero otherwise. The first two columns of the table present OLS estimates of a linear probability model with heteroskedasticity-robust standard errors, and the third column presents estimates from a logit model. The final three columns of the table uses a dependent variable that is a seven-point political preference scale, and for these three columns, the variable “Sibling’s Political Preference” is the respondent’s sibling’s opinion on the seven-point scale. The fourth and fifth columns present OLS estimates of a linear probability model with heteroskedasticity-robust standard errors, and the sixth column presents estimates from an ordered logit model.

Table 6: Logit Estimates of Voting Preferences for Respondents from the Sample of Twins

Logit Within-Twin Ordered Logit Logit With Fixed Effect

Perceived Within-Twin Difference in Education

-0.205 (0.145)

-0.176 (0.152)

-0.589 (0.236)

-0.531 (0.269)

-2.195 (1.122)

2.180 (1.193)

Education -0.054 (0.090)

-0.091 (0.206)

-0.948 (0.704)

Age 0.046 (0.017)

0.044 (0.018)

Married -0.762 (0.467)

-0.772 (0.470)

-1.081 (0.647)

-1.134 (0.657)

-0.535 (0.513)

-0.510 (0.506)

Female -0.611 (0.423)

-0.607 (0.420)

Married Female 0.599 (0.642)

0.600 (0.644)

0.942 (0.888)

1.033 (0.908)

1.185 (0.701)

1.164 (0.690)

Hourly wage -0.014 (0.017)

-0.011 (0.018)

-0.026 (0.023)

-0.023 (0.024)

0.070 (0.082)

0.158 (0.123)

Union Member -0.530 (0.388)

-0.530 (0.391)

0.026 (0.523)

0.066 (0.529)

-0.082 (0.935)

-0.099 (1.009)

Standard errors are listed in parentheses. The results in the first two columns are from a logit model which uses a binary dependent variable equal to one if the individual’s political preferences are 4 or higher on the seven-point scale, and zero otherwise. In columns one and two, the variable “Perceived Within-Twin Difference in Education” is equal to ∆Ei , the absolute value of the difference between the twin i’s education and his/her report of his/her sibling’s education. In columns three and four, an ordered logit is used to estimate the model using within-twin differences of the variables. In this case, the dependent variable is the within-twin difference in the binary dependent variable representing voting preferences, and the “Perceived Within-Twin Difference in Education” is equal to ∆E1 - ∆E2. Columns five and six present estimates from a fixed-effect logit model.

Table 7: Ordered Logit Results for the Sample of Twins

Ordered Logit Within-Twin Ordered

Logit Ordered Logit With Fixed Effect

Multinomial Logit with

Fixed Effect

Perceived Within-Twin Difference in Education

-0.159 (0.098)

-0.202 (0.104) -0.604

(0.212) -0.461 (0.233) -0.880

(0.357) -0.984 (0.398) -1.190

(0.812)

Education 0.088 (0.079)

-0.248 (0.173)

-0.319 (0.294)

Age 0.019 (0.010)

0.023 (0.011)

Married -0.491 (0.353)

-0.471 (0.352)

-0.945 (0.610)

-1.077 (0.612)

-0.566 (0.823)

-0.947 (0.845)

-0.385 (1.298)

Female -0.564 (0.315)

-0.557 (0.322)

Married Female 0.835 (0.505)

0.827 (0.506)

1.487 (0.780)

1.664 (0.780)

0.649 (1.307)

1.256 (1.284)

-0.175 (3.756)

Hourly wage 0.023 (0.016)

0.018 (0.017)

-0.010 (0.018)

0.001 (0.020)

-0.038 (0.027)

-0.028 (0.028)

0.037 (0.052)

Union Member -0.090 (0.370)

-0.080 (0.359)

0.215 (0.394)

0.334 (0.404)

0.073 (0.653)

0.653 (0.768)

3.616 (7.270)

Standard errors are listed in parentheses. The results in the first two columns are from an ordered logit model which uses the seven-point political preference scale as the dependent variable. In columns one and two, the variable “Perceived Within-Twin Difference in Education” is equal to ∆Ei , the absolute value of the difference between the twin i’s education and his/her report of his/her sibling’s education. In columns three and four, an ordered logit is used to estimate the model using within-twin differences of the variables. In this case, the dependent variable is the within-twin difference in the binary dependent variable representing voting preferences, and the “Perceived Within-Twin Difference in Education” is equal to ∆E1 - ∆E2. The results in columns five and six use an optimal minimum distance approach to include a fixed-effect in the ordered logit model, and the results in column seven also use an optimal minimum distance strategy to include a fixed effect in the multinomial logit model.

Table 8: Bootstrapped Estimates of Ordered Logit with Fixed Effects

100 Replications 95% Confidence Interval

1,000 Replications 95% Confidence Interval

10,000 Replications 95% Confidence Interval

Perceived Within-Twin Difference in

Education

(-1.332, -0.090) (-1.206, -0.086) (-1.272, -0.086)

Education (-0.105, 0.253) (-0.098, 0.257) (-0.102, 0.244)

Hourly wage (-0.095, 0.075) (-0.114, 0.093) (-0.116, 0.104)

Union Status (-0.023, 2.273) (-0.449, 2.550) (-0.485, 2.548)

Marital Status (-2.490, 0.093) (-2.389, 0.551) (-2.700, 0.489)

Married Female (-0.588, 4.260) (-0.821, 3.450) (-1.044, 3.348)

The table reports bootstrapped estimates of the 95% confidence intervals for each of the coefficients in the ordered logit model that includes a fixed

effect. For each replication, the optimal minimum distance estimates of the coefficients were calculated, and this distribution of coefficient values was used to obtain the upper and lower bounds of the confidence intervals displayed in the table.

02

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810

5 10 15 20 25 30Hourly Wages

Logit Tests Ordered Logit Tests

Sup Wald Tests of Structural Breaks in Voting Preferences Using Twin Data

Figure 10

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68

10

5 10 15 20 25 30Hourly Wage

Logit Tests Ordered Logit Tests

Sup Wald Tests of Structural Breaks in Voting Preferences Using ANES Data

Figure 2

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