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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
46
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
24
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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