Explaining social policy preferences: The effects
of cognitive and noncognitive skills
Daniel Stegmueller
Department of Government, University of Essex
[email protected]
Abstract
What explains individuals’ social policy preferences? This paper argues for the relevance of
basic cognitive and noncognitive skills, which so far have not received much attention in
empirical political economy models. It provides empirical evidence on how innate cognitive
abilities and noncognitive skills, such as self-confidence and motivation, affect individuals’
preferences. They do so by shaping labor market outcomes, such as educational choices,
permanent incomes, and experiences of unemployment spells. This mechanism is tested
explicitly by building on recent advances in the statistical analysis of causal mechanisms
using high-quality data from the German Socio-Economic Household Panel. In contrast to
recent claims made by psychologists, I find that higher cognitive and noncognitive abilities
lead to more conservative social policy preferences. My results also confirm that this effect
is due to the causal link between skills, labor market outcomes, and preferences.
1. Introduction
A recent wave of research in political economy moves beyond country-level analyses and
tries to understand the social policy preferences of individual citizens (e.g., Iversen and
Soskice 2001; Alesina and La Ferrara 2005; Cusack et al. 2006; Scheve and Stasavage
2006; Shayo 2009; Rehm 2011; Rehm et al. 2012; Margalit 2013). However, individual
traits like intelligence and self-confidence are ignored in this literature. In this paper
I show empirically that an individual’s basic set of skills – cognitive abilities as well as
noncognitive capacities, such as self-confidence and motivation – systematically shapes
social policy preferences. I provide direct evidence for the mechanism linking skills and
policy preferences. Building on recent advances in causal mediation analysis (Imai et al.
2010a, 2011), I show that an individual’s labor-market characteristics, i.e., education,
permanent income, and unemployment experiences, mediate the effect of both cognitive
and noncognitive skills on social policy preferences.
This extends the vast majority of the literature, which focuses on socio-economic factors,
such as social class (Svallfors 2006), current and future income (Benabou and Ok 2001),
welfare attitudes and beliefs (Alesina and Angeletos 2005), or on ‘cultural’ factors such as
religion (Scheve and Stasavage 2006). Recent research has stressed the insurance aspect of
social policy and focuses on risks due to holding specific skills or occupational unemployment
patterns (Iversen and Soskice 2001; Cusack et al. 2006; Rehm et al. 2012). What all these
approaches have in common is that they use variables which are not exogenously determined,
but the result of individual choices and behavior. For example, skill specificity is a function
of one’s choice of education; income is determined by one’s ability and motivation, which
also influence the probability of becoming unemployed. I argue that these factors are
endogenous to an individual’s cognitive and non-cognitive skills, which should be included
in models of social policy preferences and examined as their distal causes.
The papers’ main contribution is empirical and methodological. I develop a mixed outcome measurement model for cognitive and noncognitive skills, which explains observed
ability test scores, psychological test items, and observed labor market status variables.
Furthermore, I distinguish between true (latent) preferences and observed survey responses,
and use an ordinal ideal point model to measure individuals’ policy preferences. Jointly
estimating these components allows me to examine the effects of cognitive and noncognitive
skills on preferences, while controlling for measurement error in each component. Using a
2
causal mediation modeling strategy allows me to disentangle effects of skills on preferences
that operate via labor market variables from unspecified alternative explanations.
2. Cognitive skills, noncognitive skills, and social policy preferences
Cognitive skills.
My claim regarding the importance of skills is supported by a wave of
recent research, which demonstrates the importance of cognitive abilities for labor market
outcomes (e.g., Cameron and Heckman 1993; Cawley et al. 2001; Green and Riddell 2003;
Bronars and Oettinger 2006; Heckman et al. 2006; Strenze 2007; Anger and Heineck 2010).
Cognitive skills (or ‘intelligence’) represents the general ability of efficient “highly general
information processing” (Gottfredson 1997: 81), which determines individuals’ performance
in education and the labor market (Jensen 1998). Higher cognitive abilities are not just
relevant for academic pursuits. Personell psychologists generally agree on the fact that they
are relevant for a wide range of jobs, since they affect job performance and trainability.
Thus, if cognitive abilities determine individuals’ choices and failures or successes in the
labor market, they can be expected to exert systematic effects on policy preferences. More
precisely, since previous research shows that advantageous labor market positions tends to
lower demand for redistributive policies, I expect to find that individuals with high levels of
cognitive skills hold more conservative social policy preferences, and that this effect operates
predominantly through labor market variables.
In contrast, (political) psychologists, who have examined effects of intelligence on ideology
and preferences, generally claim that cognitive ability leads to more liberal social policy
preferences (e.g., Deary et al. 2008; Kanazawa 2009, 2010; Schoon et al. 2010). These
claims stand in direct contrast to findings in economics and the literature on the political
economy of redistribution. In this paper, I will re-examine these claims, using a population
survey instead of more limited (student) samples and explicitly defined measurement
models.1
Noncognitive skills. Focussing only on cognitive abilities is too one-sided. Recent research
in labor economics argues for, and provides evidence of, the importance of noncognitive
skills – such as motivation and self-confidence – for a range of economic and social outcomes
1
For a recent critique of this research see Morton et al. 2011. The dependent variable in the studies
mentioned above is often not clearly specified and different studies use differing attitudinal or general
left-right measures.
3
(Bowles et al. 2001; Carneiro et al. 2003; Cunha et al. 2005; Heckman et al. 2006; Lindqvist
and Vestman 2011). Similarly, political scientists have begun to study the role of personality
on preferences and ideologies (see Gerber et al. 2010 for an extensive overview).
An especially relevant noncognitive skill is self-confidence, which is related to the psychological concept of locus of control (Rotter 1966). Individuals with a strong internal locus
of control are characterized by the belief that outcomes are mainly shaped by their own
skills and choices. Thus having high confidence in one’s own abilities can compensate
for lower levels of cognitive ability in the labor market (Benabou and Tirole 2002; Drago
2011). Indeed, Groves (2005) shows that a higher locus of control is positively related to
female earnings in the US, while Cebi (2007) shows that higher locus of control of men and
women is rewarded positively in the US labor market. This finding is supported by Heckman
et al. (2006) who show that cognitive and noncognitive skills are determinants of economic
success. Consequently, I expect to find that noncognitive skills exert a negative effect on social
policy preferences, and that this effect operates mainly through labor market variables.
3. Explaining social policy preferences
In the following I outline my analytical strategy and describe a causal mediation framework
(e.g., Imai et al. 2011), which explicates how skills affect policy preferences via labor
market outcomes.2 Imagine a simplified scenario where individual i (i = 1, . . . , N ) possesses
a preferred level of social policy θi , which is a function of a set of skills Ω. Different
(counterfactual) skill bundles are denoted by ωi and ω0i , respectively. Realized values of
confounding factors Xi are denoted by xi . A straightforward estimate of the total effect of
skills on preferences is
T E = E(θi (ω0i |xi ) − θi (ωi |xi )),
(1)
i.e., the expected (counterfactual) difference in social policy preferences for, say, high and
low skill holding other confounding variables constant.
To understand how skills shape preferences, one needs to move beyond estimating total
effects. In testing the argument that labor market outcomes are the primary mechanism
linking skills to policy preferences, I separate the effect of skills mediated via labor market
outcomes from the vast number of alternative mechanisms that could link skills and prefer-
2
General identification results for this setup are discussed in Imai et al. (2010b).
4
ences. More precisely, denote by Mi (Ωi = ωi |Zi = zi ) an individual’s labor market position
as function of skills, Ωi , and other background factors, Zi . The (average) effect of skills on
social policy preferences that is due to labor market outcomes – the mediated effect – is given
by
M E = E(θi (ωi , Mi (ω0i |zi )|xi ) − θi (ωi , Mi (ωi |zi )|xi )),
(2)
i.e., the change in preferences caused by a change in labor market outcomes resulting from
a change in skill levels from ω to ω0 while holding other confounding factors zi constant.
The remaining (or: direct) effect is calculated by holding labor market outcomes at a constant
skill level
DE = E(θi (ω0i , M (ωi |zi )|xi ) − θi (ωi , M (ωi |zi )|xi ))
(3)
and represents all mechanisms other than labor market outcomes linking skills to preferences.
In section 5 I present the statistical model used to estimate these effects in detail. Before
doing so I describe the unique data set that enables my analyses.
4. Data
I use individual-level panel data from the German Socio-economic Panel (GSOEP), a longitudinal representative survey of German households conducted since 1984.3 It provides
high quality data on individuals’ labor market activities, such as income, work experience,
and unemployment spells. In addition to a core set of questions, additional modules related
to specific topics are fielded. Relevant to my question are modules on personality measures
fielded in 1999, a battery of welfare preference items contained in the 2002 wave, and, for
the first time, a test of cognitive abilities administered to a subset of individuals in 2006.4 In
the following I describe the data on cognitive and noncognitive skills and preferences. More
detailed information on covariates used in the analysis is given in [online] Appendix A.1.
The number of individuals who participated in all necessary waves and which are inter3
For details see /www.diw.de/en/soep. The original version of the data were assembled while I was
ECASS visitor at the Institute of Socio-Economic Research, University of Essex.
4
The obvious downside is that cognitive skills are measured after preferences. However, evidence suggests
that fluid intelligence (as used in this paper) represents essentially innate abilities and is stable after
childhood, independent of one’s environment (e.g., Hopkins and Bracht 1975; Schuerger and Witt 1989).
Furthermore, I also conducted a robustness test where cognitive skills are age standardized, which produced
identical results.
5
viewed using CAPI in 2006 (and thus eligible for participating in the cognitive test) is 1,816.
In order to create a homogeneous sample, I focus on males with completed education.5 This
yields a sample of 827 male adults. Of those 202 refused to participate in the cognitive
ability test. I treat missing responses as part of my measurement models, thus my final
sample size 827.6
Cognitive skills are of course hard to measure, especially in the context of a large household
survey. The GSOEP uses an adapted version of a standard psychological symbol-digits
correspondence test (Lang et al. 2007; Schupp et al. 2008). It measures the concept of ‘fluid
intelligence’, which represents general analytical performance, such as pattern recognition,
perceptual speed, and problem solving skills, which are ‘fluid’ in the sense that they can
be applied to almost any problem (Cattell 1987: 97). After pre-testing, this test was
administered in 2006 to the subset of individuals surveyed via CAPI. In the implemented
symbol-digit test (SDT), individuals have to match numbers to symbols. Nine symbols
corresponding to nine numbers are displayed permanently on the screen, and individuals
have to match numbers to a stream of displayed symbols as quickly as possible.7 The
frequency of correct matches is assessed in three 30 second intervals, yielding an “ultrashort” 90 second test (Lang et al. 2007; Schupp et al. 2008). While such a short test cannot
provide the same level of detail as longer test batteries (such as the widely used AFQT),
it is well suited for application in a general survey, where participation is voluntary and
question time limited. Pre-tests have shown that scores obtained from this ultra-short test
correlate highly with established long-form psychological ability tests (Lang et al. 2007;
von Rosenbladt and Stocker 2005). Its shortness will result in less precise measurements of
individual ability. In my latent variable setup, described below, this uncertainty is taken into
account in all parts of the model.8
Noncognitive skills have been represented by an individual’s self-confidence or locus of
control in a range of previous studies (e.g., Drago 2011; Flossman et al. 2007). Similarly,
I use a set of items measuring locus of control, originally introduced by Rotter (1966),
and fielded in the GSOEP in 1999. Individuals responded to a number of statements
5
A proper analysis including women would have to solve the selection problem of female labor market
participation, or present separate analyses for men and women (which would increase the paper’s length
and complexity). But note that simply including all women does not change my core results.
6
In models estimated as robustness checks using listwise deletion of missing values, sample size is 625.
Results are indistinguishable between both data sets.
7
Classical psychological tests usually require individuals to choose symbols. This procedure is reversed in the
GSOEP to enable data entry using standard CAPI tools.
8
See Jackman (2008: section 4) for a discussion of the biases when ignoring measurement uncertainty.
6
regarding self-efficacy, self-confidence and achievement of success using agree-disagree
scales. Initial exploratory analyses suggest that a subset of the full 10 item scale is sufficient
to represent a one-dimensional measure of noncognitive skills. Flossman et al. (2007) arrive
at a similar result using the same data; Heckman et al. (2006) discuss the preference for a
one dimensional representation of noncognitive skills using US data. Thus, I use five items
to measure the extent to which an individual thinks he is in control of his life and success
depends on his own actions. Using an ordinal item response theory model (described below),
I create a one-dimensional measure of noncognitive skills. Online appendix A.2 lists items
and provides more details of my initial analyses.
To capture Social policy preferences, I use the 2002 wave of the GSOEP, which provides
a set of items tapping if individuals prefer the private market or the state as provider of
financial security for people of old age, for families, for individuals needing care, in case
of illness, or in case unemployment.9 I argue that responses to these items are driven
by individuals’ underlying social policy preferences: individuals who prefer a more active
welfare state, which spends more on social services, will respond positively to those items.
This underlying policy preference should be captured using an appropriate measurement
model (e.g., Ansolabehere et al. 2008; Jackman 2008), as described in the following section.
5. Model
I estimate the effect of skills (cognitive and noncognitive) on policy preferences θi of
individual i via the following equation:
θi = γ0 xi + ζ0 mi + η1 ωci + η2 ωni + εi , εi ∼ N (0, σε2 )
(4)
where xi are control variables capturing heterogeneity between individuals; mi is a vector
of endogenous labor market outcomes, mi = ( yil , yie , yiu )0 , shaped by skills (detailed below);
and ωci and ωni are cognitive and noncognitive skills. Both preferences and skills are not
directly observable, but have to be captured by appropriate measurements described below.
9
Response categories range from ‘only the private market’ to ‘only the state’. For more details see appendix A.2.
These items have been used previously (e.g., Alesina and Fuchs-Schündeln 2007), however no measurement
model for them has been proposed.
7
5.1. Measuring social policy preferences
The majority of studies on individual policy preferences uses a single survey item. Often born
out of limitations of survey design or coverage, this widespread practice has some drawbacks.
Preferences are captured only imperfectly when using a single survey item as dependent
variable. Using multiple items is preferable since it leads to an improved measurement of
social policy preferences (cf. Ansolabehere et al. 2008; Jackman 2008). Furthermore, jointly
estimating measurement model equations together with substantive model equations takes
measurement error into account and yields more conservative standard errors (Skrondal and
Laake 2001). Following recent research (e.g., Treier and Jackman 2008; Stegmueller 2011),
I employ an ordinal probit item response theory model, which expresses preferences as an
unobserved (latent) variable, θ , which generates observed categorical survey responses to
policy questions (for an introduction to Bayesian IRT models, see Jackman 2009: ch.9). I
model response ysis of individual i to each question s (s = 1, . . . , S), which has Ts categories,
as a function of a threshold and a discrimination parameter:10
ysis = Φ(τsst − λss θi )
(5)
To ensure that the model reflects the ordinal nature of survey items, τss is a vector of
thresholds for item s with length Ts − 1 with a strictly monotonous ordering constraint, such
that τsa < τs b , ∀a < b, ∀s. The latent variable θ represents individuals’ social policy ideal
points. Its location and scale are identified by specifying its distribution as normal with
fixed variance, θ ∼ N (0, 1). This latent variable strategy is preferable over using simple
sum-scores as it includes measurement uncertainty in the model.
A further advantage of a latent variable model, is that response bias can be captured in
the model. The sample used in my analyses includes individuals who lived in the former
German Democratic Republic, and experienced a period of socialist socialization (Alesina and
Fuchs-Schündeln 2007; Svallfors 2010). It is possible that those individuals will instinctively
respond more positively to any question involving state activity. This response bias (often
10
To avoid a proliferation of variables and coefficients in the remainder of the paper, I opt for a slight abuse of
notation and use superscripts to denote the equation they belong to (e.g. ‘s’ for social policy preference
equations, ‘l’ for labor income, etc.)
8
termed differential item functioning in the psychometric literature) can be captured by
including a parameter in the measurement model which captures distinct response behavior.
yssj = Φ(τsst − λss θi − δ1 w i )
(6)
Here w i is an indicator variable equal to one if someone grew up under East German
socialism; and δ1 captures the extend to which responses are biased up- or downwards. For
more details on this strategy see Perez (2011) and Stegmueller (2011).
5.2. Measuring cognitive and non-cognitive skills
I model skills via a two-dimensional model with two orthogonal factors for cognitive and
noncognitive skills, following recent work in economics by Heckman and colleagues (e.g.,
Carneiro et al. 2003; Heckman et al. 2006; Cunha et al. 2010). Since my measures of
cognitive abilities are continuous while my noncognitive skill items are categorical, I employ
a mixed measurement model for joint continuous and discrete variables (Heckman 2001;
Quinn 2004).11
In the measurement equation for cognitive ability, I assume that measurements made using
the Symbol-Digit-Test are generated by latent continuous cognitive skills. In the equation for
locus of control items, I stipulate that categorical item responses are driven by an underlying
latent continuous variable representing noncognitive skills. More precisely, let ycic be the
number of correct number-symbols pairs in each 30 second block c (c = 1, . . . , C) achieved
by individual i; and let ynin be his response to non-cognitive test item n (n = 1, . . . , N ) with
Tn categories. Then, responses are modeled as a function of an individual’s latent cognitive
ωci and non-cognitive ωni abilities:
11
ycic = µc + λcc ωci + ψc ,
ωc ∼ N (0, 1)
(7)
ynin = Φ(τnnt − λnn ωni ),
ωn ∼ N (0, 1)
(8)
In a more complex measurement model setup Heckman et al. (2006) allow for reverse causality between
schooling and cognitive and non-cognitive skills, since many of their subjects were still at school when
completing the tests. In my case all individuals still in school are excluded from the analysis, and I therefore
do not extend my model in that direction. I do, however, allow for endogenous schooling, i.e. I model the
fact that schooling is a choice influenced by latent cognitive and non-cognitive ability.
9
with ωci ⊥ ωni .12 Here, λn and λc are discrimination or loading parameters indicating how
latent skills are transferred into observed responses. Equation (7) describes a classical
linear measurement equation with means µc and residual variances ψc . In the following
application I restrict µc = 0 since I use standardized values from the cognitive abilities test.
Equation (8) describes an IRT model for categorical noncognitive skill items with thresholds
or difficulties τnnt . Since responses are given on an ordinal scale, I enforce monotonically
ordered thresholds such that τna < τnb , ∀a < b, ∀n. Location and scale of both latent skill
variables are fixed by using a standard-normal prior distribution.13
5.3. Endogenous schooling, income, and unemployment experience
When analyzing social policy preferences, economic outcomes such as (permanent) income,
unemployment experiences and choice of education are not exogenous. Rather, they are
shaped by cognitive and noncognitive skills. Heckman et al. (2006) demonstrate how a
variety of economic and social outcomes are determined by cognitive as well as noncognitive
skills, using US panel data. Thus, I model economic outcomes relevant to policy preferences
as functions of cognitive and noncognitive skills.14
Education
I model an individual’s educational choice as the highest level of education
achieved. For each individual i, I record ysie , where s = 1, . . . , S denotes the school certificate,
such as vocational or high school education. Adopting the perspective that certificates
can be (roughly) ordered on a continuum, I model education choice via an ordered probit
specification:
ysie = Φ(τse + αe0 zei + β1e ωci + β2e ωni ).
(9)
Here τse are ordered thresholds distinguishing between different educational certificates, zei
is a vector of control variables such as immigration status and parental background with
12
The orthogonality restriction between cognitive and noncognitive skills allows for a parsimonious model
setup, where individual skills can vary independently on both dimensions. Nonetheless, the data provide
enough information to identify a model with correlated factors (Carneiro et al. 2003). This yields only a
negligible correlation of 0.056 ± 0.036.
13
Alternatively, one could fix one of the λs in each equation and freely estimate the variance of both skill
measures. I prefer this approach since it normalizes the distribution of both latent variables and makes
easier the visual comparisons in plots presented below. Furthermore, one might question the normality
assumption for both latent skill factors. In online appendix A.5 I show that a model that allows for
non-normal factors (using a finite mixture of normals) leads to quite similar latent skill estimates.
14
As an “added bonus” including behavioral outcomes in skill measurement equations (in addition to psychological survey items) improves measurements of cognitive and noncognitive skills (e.g. Heckman et al.
2006; Cunha et al. 2010), and makes the two factor model rotation invariant (cf. Carneiro et al. 2003).
10
coefficients αe . Finally, β1e and β2e capture effects of cognitive and noncognitive skills on
education choice.
Income As argued before both cognitive and noncognitive abilities determine and individual’s productivity and performance and are thus important parts of his earning function
(Griffin and Ganderton 1996). I concentrate on long-term or ‘permanent’ labor income,
abstracting from transitory income shocks in the current cross-section, since previous work
suggests that permanent income is the more important factor shaping policy (or redistribution) preferences (Idema and Rueda 2011; Ansell 2013; Stegmueller forthcoming). I
model an individual’s permanent labor income yil (calculated from longitudinal income
information for each individual) as function of standard variables such as work experience
and immigration status collected in zli and of cognitive (ωci ) and noncognitive (ωni ) skills:
yil = αl0 zli + β1l ωci + β2l ωni + εli , εl ∼ N (0, σε2l ).
Unemployment
(10)
Researchers modeling unemployment dynamics often rely on random
effects specifications to capture effects of unobserved factors such as ability and motivation.
Having measures of cognitive and noncognitive allows me to model these previously unobserved effects directly. Instead of focusing on which individuals are unemployed in the
current cross-section of data, I use information in the panel to construct a variable indicating
if a respondent has experienced spells of unemployment in its work history. I model the
propensity of experiencing unemployment yiu via a probit equation:
yiu = Φ(τu + αu0 zui + β1u ωci + β2u ωni ),
(11)
where τu is a threshold or intercept, zui is a vector of control variables, such as immigration
status and age, with associated coefficients αu . The effect of an individual’s cognitive skills,
ωci , and his noncognitive skills, ωni are captured by β1u and β2u , respectively.
This completes the specification of the skills measurement model. The model setup implies
that conditional on control variables in zi , the dependence across all measurements, choices,
and outcomes is due to ωc and ωn . Controlling for this dependence in equations (7) – (11)
means controlling for endogeneity in the model (Heckman et al. 2006: 424).
11
5.4. Priors and estimation
I specify and estimate this system of equations in a Bayesian framework (for introductions see
Gill 2008a or Jackman 2009). I assign appropriate (hyper-) priors to all model parameters.
Priors for coefficients of latent variables in measurement equations are elicited by choosing
parametrization of a half-normal distribution such that parameters are expected to have
mean 0.5 and values greater than 10 occur with a low probability of p = 0.1: λc , λn , λ r ∼
N+ (0.5, 7.413). This represents an a priori expectation of a non-zero relationship between
latent skills and their observable manifestations, and orients the latent variables (e.g.,
such that higher test scores are related to higher latent cognitive skills).15 For threshold
parameters in probit equations, I choose parameters for the normal distribution such
that values lie in the interval [−10, 10] with probability p = 0.9: τ r , τn , τu ∼ N (0, 6.08).
Residuals in equations with continuous left hand side variables are drawn from an inverse
Gamma distribution εl , ε r ∼ Γ−1 (1, 2). A zero-centered normal prior with large variance
ensures regression type estimates for all control variables in my policy preferences equation,
γ v ∼ N (0, 100). The same prior is used for controls in skill outcome measurement equations
αu , αl , αe ∼ N (0, 100). Finally, priors for coefficients for effects of cognitive and noncognitive
skills in economic outcomes and choice equations and in the policy preferences equation are
normally distributed with prior mean zero and a large variance β l , β e , β u , η ∼ N (0, 100).
Given the relatively large sample size of several hundred cases, the data dominate these
priors, and results are insensitive to prior perturbations.16
I estimate the model using MCMC sampling using a standard Gibbs sampler with Metropolis
steps for updating the probit threshold vectors. I run two chains for 200,000 iterations,
discarding the first half as burn-in. To reduce memory usage, I thin each chain by a factor of
20. Visual inspection as well as diagnostics of the resulting 2 × 10, 000 samples suggested by
Gelman and Rubin (1992) and Geweke (1992) show no signs for absence of convergence.
Furthermore, I conducted an “insurance run” (Gill 2008b) running the sampler for 500,000
iterations – yielding identical results.
15
Note that this restriction does in no way influence my results (since the latent factors are rotation invariant
through their relation to the outcome equations).
16
I conducted robustness tests using a different Gamma prior specifications for residuals (shape and scale =
0.001); priors for coefficients with variances 10 times larger; and lambda priors with mean 0. Results are
indistinguishable from the ones presented here.
12
Table 1: Ordinal IRT measurement equations for social policy preferences. Posterior means
with highest posterior density regions.
Discrimination
parameters λir
Thresholds τirt
Sick
λ1r
1.470
[1.292, 1.652]
Unemployed
λ2r
0.867
[0.772, 0.966]
Care
λ3r
1.384
[1.223, 1.546]
Old
λ4r
1.590
[1.394, 1.797]
Families
λ5r
0.543
[0.480, 0.616]
τ11
τ12
τ21
τ22
τ31
τ32
τ41
τ42
τ51
τ52
τ53
0.180
1.756
−0.504
0.736
0.097
1.789
0.329
1.990
−1.300
0.464
1.388
[0.072, 0.293]
[1.582, 1.936]
[−0.588, −0.419]
[0.654, 0.829]
[−0.009, 0.202]
[1.632, 1.963]
[0.210, 0.448]
[1.782, 2.197]
[−1.388, −1.208]
[0.389, 0.534]
[1.291, 1.481]
Note: Estimated East bias parameter δ1 =0.414 with 95% HPD interval from 0.218 to 0.606.
6. Results
In this section, I start by describing results from the measurement equations of my model
in the next two subsections. Readers only interested in core results are welcome to skip
ahead to subsection 6.3, which describes the total effect of skills on social policy preferences
followed by subsection 6.4, which details the mediating effects of labor market outcomes.
6.1. Social policy preferences measurement
Table 1 shows estimates for the ordinal IRT model of social policy preferences. I find that
latent preferences are most strongly related to statements regarding state responsibility for
financial security for the sick, the old, and those needing care. Their relationship to state
responsibility for financial security of families is somewhat weaker, but still unequivocally
non-zero.
Estimates of thresholds for each item are located at different points of θ , thus providing
information over a wide range of latent policy preferences. Besides providing an explicit
model of observed survey responses, the ordinal IRT model used here allows me to include
possible response bias due East German socialist socialization. The posterior mean of this
bias parameter, δ1 , is 0.41 with a highest posterior density interval that does not include
13
zero (ranging from 0.22 to 0.61). This suggests the existence of systematically different
response tendencies of respondents who grew up under socialism. Capturing this tendency
as part of the measurement model yields an unbiased individual preference estimate θi ,
irrespective of the side of the wall an individual grew up.
6.2. Cognitive and noncognitive skills measurement
Estimates for measurement equations for cognitive and noncognitive skills are given in
Table 2. Not surprisingly latent cognitive skills and observed test scores are highly correlated,
as shown in Panel (A). A one-dimensional latent skill factor explains the majority of the variance in observed scores. Similarly, latent noncognitive skills and observed categorical survey
responses are strongly related, as high discrimination parameters show. The relationship is
somewhat weaker for the last item, but the HPD region of its discrimination is still bound
n
n
away from zero. Furthermore, its threshold estimates τ51
and τ52
show that it provides
valuable information at the lower end of the latent noncognitive skill spectrum. Estimates
displayed in Panel (B), show a strong relationship between latent skills and individuals’
observed education choice and labor market outcomes (more details in subsection 6.4).
I plot the marginal distributions of cognitive and noncognitive skills in Figure 1. For three
eduction levels (those with less than high school, high school, and more than high school
education), I plot kernel density estimates of the posterior means of ωc in panel A and
ωn in panel B. Figure 1 shows considerable individual variation in both cognitive and
noncognitive skills. A substantial portion of the sample has low levels of cognitive skills of
two standard deviations below the (normalized) mean, especially among those with no high
school education. At the other end of the distribution are individuals with high cognitive
skills, found predominantly among the higher educated. A similar picture emerges with
regard to noncognitive skills, which exhibits similar spread with considerable proportions
of the sample more than one standard deviation below or above the mean. One should
note the existence of lower educated individuals with high skills and (especially) of highly
educated individuals with lower cognitive skills. This suggests that using education as proxy
for ability or productivity in models explaining policy preferences is bound to produce rather
unreliable results.
Panel (C) of Figure 1 shows the joint distribution of cognitive and non-cognitive skills. I plot
the posterior mean of [ωc , ωn ] for each individual. A contour plot of the two-dimensional
density estimate is superimposed to visualize the distribution of skills. It again emphasizes
14
Table 2: Measurement equations for cognitive and noncognitive skills. Posterior means and 95%
highest posterior density regions.
(A) Skill indicators
Thresholds τnit
Residual variances ψc
Loading/Discrimination
parameters λi
SDT 1−30 sec.
SDT 31−60 sec.
SDT 61−90 sec.
λ1c
λ2c
λ3c
0.876
0.948
0.865
[0.827, 0.921]
[0.904, 0.990]
[0.818, 0.910]
ψ1c
ψ2c
ψ3c
0.255
0.115
0.269
LoC 1
λ1n
0.916
[0.797, 1.030]
LoC 2
λ2n
0.714
[0.617, 0.808]
LoC 3
λ3n
1.030
[0.886, 1.157]
LoC 4
λ4n
0.768
[0.664, 0.869]
LoC 5
λ5n
0.429
[0.353, 0.501]
n
τ11
n
τ12
n
τ21
n
τ22
n
τ31
n
τ32
n
τ41
n
τ42
n
τ51
n
τ52
n
τ53
−1.072
0.432
−0.535
0.679
−1.323
0.338
−0.999
0.451
−1.333
−0.251
0.878
[0.229, 0.280]
[0.097, 0.134]
[0.244, 0.297]
[−1.177, −0.973]
[0.351, 0.519]
[−0.612, −0.455]
[0.597, 0.763]
[−1.444, −1.200]
[0.249, 0.423]
[−1.092, −0.909]
[0.376, 0.532]
[−1.422, −1.245]
[−0.319, −0.185]
[0.800, 0.953]
(B) Skill outcomes
Cognitive skills ωC
Education
Perm. Income
Unemployment
β1e
β1l
β1u
0.223
0.265
−0.251
[0.159, 0.291]
[0.201, 0.327]
[−0.331, −0.165]
Noncognitive skills ωN
β2e
β2l
β2u
0.220
0.293
−0.184
[0.148, 0.291]
[0.225, 0.352]
[−0.264, −0.106]
Note: Foreign bias in cognitive test (SDT items) δ2 = −0.416 with 95% HPD interval from −0.511 to −0.318. Estimates α of
controls in skill outcome equations not shown (see appendix A.3 for full table).
the wide variety of existing cognitive–non-cognitive skill combinations. It is not uncommon
for individuals with below average cognitive abilities to have higher noncognitive skills and
vice versa. Inasmuch as both cognitive and noncognitive skills are factors determining labor
market success (as argued above), this stresses that both latent skills need to be included in
a complete model of redistribution preferences.
6.3. Total Effect of skills on social policy preferences
Table 3 shows estimates (posterior means and standard deviations) of the total effect (eq. 1)
of cognitive and noncognitive skills. Besides latent skills I include a number of socio-
15
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0.08
0.16
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0.2
0.5
less than HS
high school
more than HS
0.4
−1
0.3
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0.1
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−1
0.0
−3
−2
−1
0
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1
2
0
ωc
1
2
3
Figure 1: Distribution of latent cognitive (panel A) and non-cognitive (panel B) skill factors by
education level (kernel density estimates of posterior means, bandwidth 0.35 evaluated over 200
point grid). Panel C plots the position of each individual in two-dimensional cognitive–noncognitive
skill space (contour plot of 2-dimensional density estimate superimposed).
economic controls to capture heterogeneity between individuals and households. These
include an individual’s age, immigration status, household size, house ownership, whether
he is divorced, a union member, self-employed, or currently living in the eastern part of
Germany. Estimates of controls are available in online appendix A.4.
Specifications (1) and (2) show that both cognitive and noncognitive skills exert a strong
negative effect on social policy preferences. This conclusion remains virtually unchanged
when including both latent skills simultaneously in specification (3). When adding a range
of individual and household controls in (4), I find a slight increase in the posterior standard
deviation of the cognitive skill effect, as well as a slight reduction of the estimated magnitude
of noncognitive skills. However, the conclusion remains the same: the higher someones
cognitive and noncognitive skills the lower his preferences for extensive social policy.
To illustrate the substantive magnitude of these effects, I conduct a series of simulations
displayed in Figure 2, which shows expected values of latent social policy preferences for
deciles of cognitive and noncognitive skills. Panel (A) shows posterior means and HPD
intervals for the effect of cognitive skills on preferences, holding all other covariates as
well as noncognitive skills at their sample means. Panel (B) repeats the same calculation
16
Table 3: Estimated total effects of cognitive and noncognitive skills on social
policy preferences. Posterior means and standard deviations.
(1)
Skills
Cognitive [η1 ]
(2)
−0.153
(0.034)
Noncognitive [η2 ]
Controls [γ]
−0.198
(0.036)
no
no
(3)
−0.148
(0.034)
−0.198
(0.037)
(4)
−0.141
(0.037)
−0.192
(0.037)
no
yes
Note: Total effects calculated from preference equation (eq. 4) estimated jointly with system of measurement equations (eq. 6 to 11). Controls included in (4) are age, house ownership, household size,
immigration status, being divorced, union member, self-employed, currently living in East Germany.
For estimates see table A.4.
using noncognitive skills. Both figures show the substantive relevance of skills. For example,
moving four deciles around the mean of the cognitive or noncognitive skill distribution
reduces social policy preferences by 0.4 and 0.5 standard deviations, respectively.
In panel (C) I simulate changes in social policy preferences when simultaneously raising
or lowering cognitive and cognitive skills. Shown is again the posterior expectation of
social policy preferences for all possible combinations of latent skill deciles. This makes the
substantial effect of skills even more apparent. Holding all else equal and moving from a
moderately low combination of skills (such as third deciles) to a high combination (such as
sixth deciles) lowers preferences by almost one standard deviation. These conclusions are
robust under a wide variety of alternative specifications (cf. section 6.5).
6.4. Mediated skill effects via labor market outcomes
I now turn to the mediated effect of skills. In other words: is the effect of skills on social
policy preferences due to individuals’ labor market outcomes, as argued above, or is it simply
a result of a myriad of other (substantively irrelevant) factors? To answer this question, I
proceed in two steps.
First, I demonstrate how latent skills determine commonly used labor market variables by
conducting several simulations displayed in Figure 3. Panels (A) show effects of cognitive
(A1) and noncognitive (A2) skills on the probability of choosing higher education, for each
latent skill decile. The probability of obtaining a higher education certificate increases
17
A
0.6
E(θ)
0.4
0.2
0.0
−0.2
−0.4
−0.6
1
2
3
4
5
1
2
3
4
5
ωc
6
7
8
9
10
6
7
8
9
10
0.6
B
E(θ)
0.4
0.2
0.0
−0.2
−0.4
−0.6
ωn
C
0.6
E(θ)
0.4
0.6
0.0
−0.2
0.4
0.6
−0.4
0.2
0.4
−0.6
0.0
1
3 0.2
0.0
2
E(θ)
E(θ)
0.2
−0.2
4
5
ωc
6
7
8
9
10
−0.2
−0.4
−0.4
−0.6
1
2
3
4
5
ωc
6 −0.6 7
1
8
9
3
2
10
4
5
ωn
6
7
8
9
10
Figure 2: Simulated effect of cognitive and noncognitive skills on social policy preferences holding
all else equal. Panels A and B show separate effect of cognitive and noncognitive skills, panel C shows
the effect of cognitive and noncognitive skills varied simultaneously. Based on 10,000 simulated
values, evaluated over a 100 point grid.
monotonically with latent noncognitive and (especially) cognitive skills. Similarly, an
individual’s permanent income depends strongly on latent skills. Panels (B) show that an
increase in either cognitive or noncognitive skills by one decile increases permanent income
by roughly 200 Euros, holding all else equal. Finally, panels (C) show the relationship
between unemployment and latent skills. It shows a remarkably strong effect of latent
cognitive skills: an increase in cognitive skills of one decile lowers the probability of
18
A2
0.4
0.3
Pr(ys = 4)
Pr(ys = 4)
A1
0.2
0.1
0.0
0.4
0.3
0.2
0.1
0.0
1
2
3
4
5
c
6
7
8
9
10
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
ω
B1
2
3
4
5
ωc
6
7
8
9
C2
8
9
10
ωn
6
7
8
9
10
6
7
8
9
10
0.7
0.6
Pr(yu = 1)
Pr(yu = 1)
0.6
7
28
26
24
22
20
18
16
14
10
0.7
6
x100
E(yL)
E(yL)
1
C1
B2
x100
28
26
24
22
20
18
16
14
ωn
0.5
0.4
0.3
0.2
0.5
0.4
0.3
0.2
0.1
0.1
1
2
3
4
5
c
6
7
8
9
10
ω
ωn
Figure 3: Simulations showing how labor market outcomes are determined by deciles of cognitive
skills (1) and noncognitive skills (2) holding other covariates at means. Panels A shows probability
of choosing college education, panels B shows expected permanent income, and panels C shows
probability of experiencing spells of unemployment. Based on 10,000 simulated values, evaluated
over a 100 point grid. Simulation posterior means and 95% HPD intervals.
experiencing spells of unemployment by roughly 5 percentage points. Moving from the
second to the ninth cognitive decile reduces this probability by over 30 percentage points,
ceteris paribus. The effect of noncognitive skills is somewhat less marked, but still highly
relevant. These results clearly indicate that labor market outcomes are dependent on latent
cognitive and noncognitive skills.
Second, I calculate (i) the mediated effect of skills on social policy preferences (cf. eq. 2),
which represents the theoretically relevant link between skills, labor market outcomes,
and preferences, as well as (ii) the remaining direct effect (cf. eq. 3), which represent a
19
Table 4: Mediated effects of cognitive and noncognitive skills on social policy preferences.
Posterior means and standard deviations.
(1)
Cognitive
skills
Total effect
– mediated effect
– remaining direct effect
Controls
(2)
Noncognitive
skills
−0.148
(0.034)
−0.079
(0.015)
−0.069
(0.035)
−0.198
(0.037)
−0.075
(0.014)
−0.123
(0.039)
no
Cognitive
skills
Noncognitive
skills
−0.141
(0.037)
−0.062
(0.016)
−0.079
(0.040)
−0.192
(0.037)
−0.060
(0.015)
−0.132
(0.040)
yes
Note: Calculated from equation (4). Controls included in (2) are age, house ownership, household size, immigration status,
being divorced, union member, self-employed, currently living in East Germany. Table 3.
(possibly large) number of other channels of influence.17 Estimates displayed in Table 4
show the total effect of skills decomposed into the mediated effect and the remaining direct
effect for specifications excluding (1) and including (2) the set of individual controls xi . I
find clear mediating effects of labor market outcomes for cognitive skills. The estimated
mediation effect of labor market outcomes is −0.062 ± 0.016, while the remaining effect is
−0.079 ± 0.04. This indicated that a range of other, unspecified channels might link skills
to social policy preferences, but their effect is uncertain (or “not significant”) compared
to the clear-cut systematic effect of labor market outcomes. For noncognitive skills, I
find a relevant remaining effect, −0.132 ± 0.04, indicating the significant presence of
mechanisms other than labor market outcomes. But the mediating effect of labor market
outcomes for noncognitive skills is as clear-cut as for their cognitive counter-part, estimated
as −0.06 ± 0.015. In other words, an individual’s three basic labor market variables –
education, permanent income, unemployment experience, go a long way in explaining why
cognitive and noncognitive skills systematically shape his social policy preferences.
Furthermore, the highly relevant link between latent cognitive and noncognitive skills, labor
market outcomes, and preferences suggests that excluding basic skills from empirical models
17
One cannot rule out the possibility that an unobserved variable influences both mediator and outcome
conditional on controls and treatments (although I argue that many possible unobserved socio-economic
confounders will simply be functions of latent skills). This creates correlated residuals between mediation
and outcome equations which can not be estimated as part of the model. Thus Imai et al. (2010b) propose
to conduct sensitivity analyses by simulating over a range of possible correlations. My simulations show
stable substantive effects up to error correlations of ≈ 0.5.
20
Table 5: Difference in estimated labor market effects when ignoring latent skills
Education
Unemployment
Permanent income
Diff.
in %
0.037
0.023
0.042
46.1
47.0
34.1
of social policy preferences will overstate the effects of labor market variables. To illustrate
this point, I re-estimate my model given in equation (4) and constrain all latent skill effects
to zero. Table 5 shows the difference in estimates for three labor market variables on
social policy preferences. I find that all estimates are inflated. The estimate of income on
preferences is more than 30 percent larger; while the effect attributed to unemployment
experiences is increased by almost 50 percent. While these findings do not, of course,
replace results from a full-fledged Monte Carlo study, they do indicate that researchers
ignoring cognitive and noncognitive skills might to so at their own peril.
6.5. Robustness checks
Before moving on the concluding section, I conduct a number of robustness checks. Table 6
shows estimates of total cognitive and noncognitive skill effects on social policy preferences
under several alternative specifications. Since several scholars have emphasized distinct
preferences of the religious (e.g., Scheve and Stasavage 2006), specification (1) includes
an individual’s religious identification as Catholic, Protestant, or other. To capture possibly
distinct preferences of individuals outside the labor market, specification (2) adds a dummy
for retired individuals. Using years of schooling instead of educational certificates constitutes
specification (3). In (4) I allow for differences in preferences between individuals with
differing levels of skill specificity (e.g., Iversen and Soskice 2001). To control for differences
between industries and local labor market conditions, specifications (5) and (6) include 7
industry and 15 state fixed effects, respectively. Instead of imputing missing information
of (mainly) cognitive test items and other covariates, specification (7) is estimated on a
subsample of observed responses only, reducing the sample size by 23 percent. While
psychometric research has shown that cognitive skills are largely stable after age eight and
thus independent of age, noncognitive skills might change over the life-cycle (Borghans
et al. 2008: 976). Thus, specification (8) allows for linear and quadratic age effects in
21
Table 6: Robustness checks. Estimates of cognitive and
noncognitive skill effects under nine alternative specifications. Posterior means and standard deviations.
cognitive
−0.149
(0.037)
−0.147
(0.037)
−0.140
(0.037)
−0.151
(0.040)
−0.142
(0.038)
−0.169
(0.039)
−0.132
(0.039)
−0.142
(0.038)
−0.146
(0.046)
(1) Religion
(2) Retirement
(3) Years of schooling
(4) Skill specificity
(5) Industry fixed effects
(6) State fixed effects
(7) Listwise deletion
(8) ωn age effects
(9) 5 66% subsamples
noncognitive
−0.192
(0.036)
−0.191
(0.037)
−0.192
(0.037)
−0.198
(0.040)
−0.187
(0.037)
−0.224
(0.038)
−0.160
(0.042)
−0.189
(0.036)
−0.192
(0.045)
Note: Coefficients for cognitive and noncognitive skill effects in social policy
preferences equation; estimated jointly with all measurement equations.
Sample size is 625 in (7); 551 in (9).
noncognitive skills. Finally, in order to check robustness against the presence of unobserved
heterogeneity, specification (9) creates 5 datasets with one third of all observations deleted
at random and re-estimates the model 5 times on these random subsets. The final estimate
is the average of these 5 models with ‘standard errors’ penalized proportional to the variance
between each set of estimates (Rubin 1987). Under each and every specification I find
clear negative effects of cognitive and noncognitive skills, comparable in size to my main
specification.
7. Conclusion
In this paper I have set out to empirically demonstrate the relevance of cognitive and
noncognitive skills for individuals’ social policy preferences, and how their effect operates
22
via basic labor market outcomes. To do so rigorously, I have created measurement models for
social policy preferences and for cognitive as well as noncognitive skills. Similar to results of
economic research on skills, I establish that an individual’s set of skills can be summarized
by a two-dimensional vector of cognitive and noncognitive skills. These two skill factors
drive observed survey responses, performance in aptitude tests, and labor market choices
and outcomes. Thus, variables such as income, education, or unemployment risk, which are
commonly taken as exogenous in individual level models of preference formation, are all
driven by unobserved skill factors.
By measuring these previously unobserved skill factors, and by using an explicit mediation
model, I am able to show that they shape social policy preferences in a systematic fashion.
Individuals with higher cognitive skills are more likely to hold an advantageous position
in the labor market, and consequently prefer a less active government in matters of social
policy. The same holds for individuals with high noncognitive skills. In fact, those two
effects are almost fully linearly additive, which has two important consequences. First,
noncognitive skills can compensate for lack of cognitive ability in the labor market and vice
versa. This can explain why individuals with low ability – often proxied by low education
in previous research – might still prefer limited social policies. Second, individuals who
command both high cognitive and noncognitive skills are strongly opposed to social policy,
even when controlling for a range of socio-economic characteristics and events. I conducted
a wide variety of robustness checks, which confirmed these basic findings.
My results suggest that commonly unobserved characteristics, such as ability, motivation,
and self-confidence, should be taken seriously in models for individual preferences. They cast
doubt on popular claims of a relationship between ‘intelligence’ and left-wing preferences
based on simplistic models (e.g., Kanazawa 2010, 2009), and thus add a further voice to
existing criticisms (Morton et al. 2011). In line with what we would expect from a basic
political economy perspective, I find that individuals with high cognitive and/or noncognitive
skills succeed in the labor market: They complete higher levels of education, have higher
life-time incomes, and are far less likely to experience unemployment. Consequently, they
prefer a less – and not more – extensive welfare state.
23
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27
A. [Online] Appendix
A.1. Sample descriptives, test participation
Table A.1 gives means (and standard errors) for covariates in my estimation sample, and for
individuals who did and did not participate in cognitive testing. The final column provides a
logit model for test refusal.
28
Table A.1: Means of full sample, test-participants and non-participants. Logit model for probability
of cognitive test refusal. Estimates and standard errors.
Estimation
sample
Age
Permanent Income
Education
Elementary
General vocational
Vocational + degree
Higher education
Work experience
Grown up East
Living East
HH size
House owner
Foreigner
Divorced
Unemployment exp.
Union member
Self-employed
N
a
b
44.8
(0.4)
1753
(33)
Test
participants
44.2
(0.5)
1766
(35)
Test
refusers
46.6
(1.1)
1705
(79)
0.17
(0.01)
0.15
(0.02)
0.25
(0.04)
0.57
(0.02)
0.13
(0.01)
0.13
(0.01)
21.5
(0.5)
0.13
(0.01)
0.12
(0.01)
2.83
(0.05)
0.45
(0.02)
0.14
(0.01)
0.08
(0.01)
0.44
(0.02)
0.28
(0.02)
0.09
(0.01)
0.59
(0.02)
0.13
(0.02)
0.13
(0.02)
21.3
(0.5)
0.14
(0.02)
0.13
(0.01)
2.86
(0.06)
0.44
(0.02)
0.12
(0.01)
0.07
(0.01)
0.44
(0.02)
0.28
(0.02)
0.08
(0.01)
0.52
(0.04)
0.11
(0.03)
0.11
(0.03)
22.3
(1.1)
0.09
(0.02)
0.09
(0.02)
2.71
(0.12)
0.46
(0.04)
0.21
(0.03)
0.11
(0.03)
0.44
(0.04)
0.26
(0.04)
0.13
(0.03)
827
625
Logit model for test refusal. Correctly classified cases: 77.9%.
Reference category
29
202
Refusal
Probabilitya
0.076
(0.022)
0.000
(0.000)
0.688
(0.258)
–b
−0.172
(0.324)
−0.406
(0.387)
−0.066
(0.022)
−0.733
(0.784)
0.453
(0.788)
−0.091
(0.084)
0.392
(0.227)
0.797
(0.281)
0.517
(0.356)
0.042
(0.222)
−0.043
(0.233)
0.746
(0.333)
827
3.0
●
2.5
●
●
Eigenvalue
●
Full item set
Reduced item set
2.0
●
1.5
●
1.0
●
●
●
0.5
●
●
●
0.0
1
2
3
4
5
Component
Figure A.1: Eigenvalues of noncognitive skill measurement items. Full item set (10 items) and
reduced set (5 items) used in analysis.
A.2. Exploratory analysis of measurement items
Noncognitive skills
Eigenvalues of the correlation matrix of the original 10 set of items
are given in Figure A.1. This suggest that three factors should be used. However, three and
two factor solutions yield non-parsimonious solutions characterized by high cross loadings
of items on different factors. A more straightforward model is achieved with a reduced set
of five items; Eigenvalues of the correlation matrix suggest that one factor suffices.
Panel (A) of Table A.2 lists items used in the noncognitive skill measurement model. Items
are originally recorded on five point agree–disagree scales, but since outer categories are
very sparsely populated I collapsed responses to three or four categories (this does not
influence the distribution of the latent noncognitive skill variable or my final results). As
can be seen from the last column, few individuals refused to respond to these items. I deal
with missing responses as part of my measurement model.
Redistribution
Exact wording and details of items used in the redistribution measurement
model are given in panel (C) of Table A.2. Items are originally recorded on five point agree–
disagree scales, but since outer categories are very sparsely populated I collapsed responses
to three or four categories (this does not influence my final results, but removes thresholds
to be estimated from the IRT model). Nonresponse is low for all items. Eigenvalues of
the correlation matrix of redistribution items are given in Figure A.2. They suggest that a
one-factor model provides a good summary of the data.
30
Table A.2: Items used in measurement models
Item
categories
Missing %
3
3
4
3
3
1.2
1.7
1.0
0.6
1.1
–
–
–
24.4
24.4
24.4
3
3
3
3
4
0.7
0.7
0.9
0.9
1.0
(A) Locus of control items
I doubt my abilities when problems arise
I haven’t achieved what I deserve
What you achieve depends on luck
Others make the crucial decisions in my life
I have little control over my life
(B) Symbol correspondence test
SCT correct 1-30 sec.
SCT correct 31-60 sec.
SCT correct 61-90 sec.
(C ) State responsibility for financial security
When Sick
In Old-Age
When unemployed
When Requiring Care
For Family
4
●
Eigenvalue
3
2
1
●
●
●
●
4
5
0
1
2
3
Component
Figure A.2: Eigenvalues of redistribution measurement items.
31
3.0
Eigenvalue
2.5
●
2.0
1.5
1.0
0.5
●
●
0.0
1
2
3
Component
Figure A.3: Eigenvalues of cognitive skill measurement items.
Cognitive skills
Figure A.3 shows (not surprisingly) that the three cognitive ability mea-
surements should be summarized by one factor. Eigenvalues are correlated based on the
correlation matrix of observed values. This excludes 24% of respondents who refused to
participate in the cognitive test (cf. panel (B) of Table A.2). I deal with missing responses as
part of my measurement model, and I conducted robustness tests of my final results using
both imputed and listwise-deleted data.
32
A.3. Estimates of controls used in skill outcome equations
Table A.3: Full table of skill outcome equations. Posterior means and 95% HPD regions.
Cognitive skills
Non-cognitive skills
Foreign
East
Age
Income
School choice
Unemployment
0.265
[0.201 0.327]
0.293
[0.225 0.352]
−0.306
[−0.445 −0.154]
−0.823
[−0.979 −0.680]
0.001
[−0.146 0.149]
0.223
[0.159 0.291]
0.22
[0.148 0.291]
−0.348
[−0.516 −0.174]
−0.251
[−0.333 −0.165]
−0.184
[−0.264 −0.106]
0.583
[0.393 0.770]
0.571
[0.387 0.760]
−0.3
[−0.373 −0.231]
Parental education
Work experience
0.322
[0.261 0.381]
0.219
[0.090 0.350]
Note: Based on 10,000 MCMC samples.
A.4. Full table of social policy preference equation including controls
33
Table A.4: Estimated effects of cognitive and noncognitive skills on redistribution preferences. Posterior means and standard deviations.
(1)
Skills
Cognitive
Noncognitive
(2)
−0.146
(0.033)
−0.227
(0.035)
Controls
Age
(3)
−0.139
(0.033)
−0.222
(0.036)
(4)
−0.149
(0.037)
−0.206
(0.036)
−0.061
(0.032)
−0.022
(0.033)
−0.174
(0.061)
0.204
(0.089)
0.288
(0.117)
0.079
(0.065)
−0.355
(0.119)
0.145
(0.114)
HH size
House owner
Foreigner
Divorced
Union member
Self-employed
Living east
Note: Shown are coefficients from redistribution equation estimated jointly with system of
measurement equations. Based on 10,000 MCMC samples.
34
A
0.6
less than HS
high school
more than HS
0.5
0.4
0.3
0.2
0.1
0.0
−3
B
−2
−1
0
ωc
1
0.5
2
3
less than HS
high school
more than HS
0.4
0.3
0.2
0.1
0.0
−3
y cic
n
y ni
ωc
ωn
µ�c
c
c c
2
y−2
+ ψ c y c =0n λ c ω c + ψ1c
ci = λ c ω i −1
c i
ci
n y c = λncc ω c +nψ cn ω
y ni =ciΦ(τ nt −i λ n ωyin) = Φ(τ n − λ n ω n )
nt
n i
ni
y n = Φ(τ n c− λ nncω ni )
cω c c∼niN K (µ c , nt
c
c
�
)
= λ c ω i + ψ c k k ω ∼ N K (µ k , � k )
ω cN∼K (µ
N n(µ cn, � c ) �, . . . ,nK n
n∼
ω n nt
= Φ(τ
− λ nn ωKkni,)�kk ),ωk nk ∼= N
K (µ k , � k ), k = �, . . . , K
n
n
n
c ωc ∼
n cN K (µ kc , � k ),
n k = �, . . . , K
c
n
µ
=
µ
=
�,
λ
=
λ
=
�
� )
�
∼ N K�(µ k , �
µc �� = µn � = �, λ�c = λ�n = �
c k n
µ = nµ� = �, λ� = λ� = �
∼ N KK(µ∼kn�Multinomial(π)
, � k ), k = �, K
. . .∼, Multinomial(π)
K
K
∼
Multinomial(π)
= µ�n = �, λ�c = λ�n = �
3
K = � ∶ π̂ = [�.��, �.��]K = � ∶ π̂ = []
K ∼ Multinomial(π)
K = � ∶ π̂ = []
Figure A.4: Distribution of non-normal latent skill factors
K = � ∶ π̂ = []
A.5. Non-normal latent skill factors
Figure A.4 shows the distribution of posterior means of cognitive and noncognitive latent
skills factors using a more flexible distributional specification. Specifically I use a finite
mixture of normals distribution (details are given at the bottom of Figure Figure A.4). The
resulting distribution is substantively similar to the one used in the main text of the paper.
35