Parallel session IARIW 2014

1. Has the attitude of US citizens towards
redistribution changed over time?
Maria Grazia Pittau and Roberto Zelli
Sapienza University of Rome
Fifth ECINEQ Meeeting
Bari, July 2013
Maria Grazia Pittau and Roberto Zelli Fifth ECINEQ Meeeting
Has the attitude of US citizens towards redistribution changed over time?

2. Perceptions have always shaped reality, and understanding
how beliefs evolve has been a central focus of
intellectual history".
Joseph Stiglitz, The price of inequality, 2012, p.148
Maria Grazia Pittau and Roberto Zelli Fifth ECINEQ Meeeting
Has the attitude of US citizens towards redistribution changed over time?

3. Importance of predictors
Preferences for redistribution I
An extensive literature has investigated individual and contextual
factors that can help explain citizens' attitudes towards the role
of the government in redistributive policies.
Predictors based on economic self interest: current personal
income; prospects of economic mobility (in both directions)
(Ravallion and Lokshin, 2000; Benabou and Ok, 2001; Alesina and
La Ferrara, 2005); uncertainty about future incomes due to insecurity
in the labor market (Iversen and Soskice, 2001; Cusack et al., 2006),
Rehm, 2009).
Predictors based on beliefs: beliefs in regards to the causes of
inequality, concern for fairness, religious convictions, forms of
altruism, as well as social norms about what is acceptable or not in
terms of inequality and poverty (Feong, 2001; Alesina and La
Ferrara, 2005; Benabou and Tirole, 2006,..).
Maria Grazia Pittau and Roberto Zelli Fifth ECINEQ Meeeting
Has the attitude of US citizens towards redistribution changed over time?

4. Importance of predictors
Preferences for redistribution II
Gender, ethnicity, as well as party identi

5. cation, social class and
religious aliation, are thought to be relevant for mapping such
beliefs and thus identifying people's preferences.
Maria Grazia Pittau and Roberto Zelli Fifth ECINEQ Meeeting
Has the attitude of US citizens towards redistribution changed over time?

6. Importance over time
Empirical analyses of determinants of preferences are mostly
concerned with a static period of time and create the perception of
stationary association between determinants and preferences.
We remove the assumption of invariance of such eects over
time, and for the United States we want to address the following
empirical questions:
Has overall propensity towards redistribution increased or decreased
in the U.S. over the past few decades? Is it possible to identify trend
patterns?
To what extent have associations between individual determinants
(such as income, education, race, gender,..) and attitudes towards
redistribution varied over time?
Do temporal patterns actually re
ect cultural and economic changes
in the country aecting individuals of all ages (period eects) or are
they due to the strati

7. cation of dierent generations in the sample
(cohort eects)?
Maria Grazia Pittau and Roberto Zelli Fifth ECINEQ Meeeting
Has the attitude of US citizens towards redistribution changed over time?

8. Time series cross section
Repeated cross-sectional (TSCS) data from the General Social
Survey (GSS) over the period from 1978 to 2010.
Support for redistribution from question EQWLTH:
Some people think that the government in Washington ought to reduce the income
dierences between the rich and the poor, perhaps by raising the taxes of wealthy
families or by giving income assistance to the poor. Others think that the government
should not concern itself with reducing this income dierence between the rich and the
poor.
Card on a 1 to 7 scale from 1 =Should to 7 =Should not
govt reduce di no govt action
1 2 3 4 5 6 7
Yi=1 Yi=0
Overall the number of respondents to the question is 23,765.
Respondents can be nested within cells created by the
cross-classi

9. cation of two types of social context: birth cohorts and
survey years.
Maria Grazia Pittau and Roberto Zelli Fifth ECINEQ Meeeting
Has the attitude of US citizens towards redistribution changed over time?

10. Time series cross section
Pattern of propensity towards redistribution in the U.S.: 1978{2010.
30 40 50 60 70
Years
Propensity toward redistribution
1978 1983 1986 1989 1993 1996 2000 2004 2008
The solid line represents national average.
The dotted line represents the estimated linear trend.
Dierent symbols represent dierent cohorts in each year of the interview.
Maria Grazia Pittau and Roberto Zelli Fifth ECINEQ Meeeting
Has the attitude of US citizens towards redistribution changed over time?

11. Time series cross section
No clear evidence of a changing-time pattern but rather a near
at
trend for the whole period.
What about the role of individual predictors? We are able to capture
temporal patterns of predictors' eects (

12. t), net of age and cohort
eects, by estimating a time-varying slope multilevel model.
Maria Grazia Pittau and Roberto Zelli Fifth ECINEQ Meeeting
Has the attitude of US citizens towards redistribution changed over time?

13. Multilevel model
Why multilevel models?
Pooling data regression including time-dummies
Increase the number of observations ) improvement of estimates precision
No investigation on dynamics
Multilevel models with time as level of variation
Considered as partial pooling models
They provide more accurate estimates of time-series eects than un-pooled
models
They are able to capture temporal patterns net of cohort eects
Separate regressions - no pooling model
It allows a meta-analysis of estimated coecients over time
Insucient observations and sparseness of data ) uncertainty of estimates
Overstate the variation across years
Maria Grazia Pittau and Roberto Zelli Fifth ECINEQ Meeeting
Has the attitude of US citizens towards redistribution changed over time?

14. Multilevel model
Why multilevel models?
Pooling data regression including time-dummies
Increase the number of observations ) improvement of estimates precision
No investigation on dynamics
Multilevel models with time as level of variation
Considered as partial pooling models
They provide more accurate estimates of time-series eects than un-pooled
models
They are able to capture temporal patterns net of cohort eects
Separate regressions - no pooling model
It allows a meta-analysis of estimated coecients over time
Insucient observations and sparseness of data ) uncertainty of estimates
Overstate the variation across years
Maria Grazia Pittau and Roberto Zelli Fifth ECINEQ Meeeting
Has the attitude of US citizens towards redistribution changed over time?

15. Multilevel model
Why multilevel models?
Pooling data regression including time-dummies
Increase the number of observations ) improvement of estimates precision
No investigation on dynamics
Multilevel models with time as level of variation
Considered as partial pooling models
They provide more accurate estimates of time-series eects than un-pooled
models
They are able to capture temporal patterns net of cohort eects
Separate regressions - no pooling model
It allows a meta-analysis of estimated coecients over time
Insucient observations and sparseness of data ) uncertainty of estimates
Overstate the variation across years
Maria Grazia Pittau and Roberto Zelli Fifth ECINEQ Meeeting
Has the attitude of US citizens towards redistribution changed over time?

16. Multilevel model
Logistic model - one predictor
i = logit1(t[i];k[i] +

17. t[i];k[i]xi); for i = 1; : : : ; n: (1)
where
logit1(z) = 1
1+ez is the inverse-logistic function
x is an individual-level predictor, e.g. personal income
t[i];k[i] and

18. t[i];k[i] are the varying coecients of the model
subscript t[i] and k[i] indexing, respectively, the year t of the interview and the
cohort k of the respondent i.
Assuming no interactions:

19. t;k =

20. 0 +

21. t +

22. k
The year and cohort coecients are assigned a multi-normal (MN) probability
distribution with mean vector and covariance matrix to be estimated from the
data
Maria Grazia Pittau and Roberto Zelli Fifth ECINEQ Meeeting
Has the attitude of US citizens towards redistribution changed over time?

23. Multilevel model
Logistic model - multiple predictors, some '

24. xed', some varying
i logit1(X0
i B0 + XiBt[i];k[i]); for i = 1; : : : ; n
Bt;k = B0 + Bt + Bk
Bt MN(UtG; ) for t = 1; : : : ; T
Bk MN(0;
); for k = 1; : : : ;K;
where
X0 is the matrix of individual predictors, B0 the R-vector of their un-modeled
regression coecients;
X is the matrix of individual predictors that have coecients varying by groups;
Bt[i];k[i] is the vector of the modeled regression coecients for the groups that
include unit i.
Ut is the t-th row of the matrix of group-level predictors and G is the associated
matrix of group-level regression coecients.
and
are the covariance matrices for the random coecients.
Maria Grazia Pittau and Roberto Zelli Fifth ECINEQ Meeeting
Has the attitude of US citizens towards redistribution changed over time?

25. Maximum penalized likelihood
Estimation strategy? Not so simple I
Three levels of variations (

26. rst level coecients that vary by time and
cohort), implying complex covariance structures
Marginal likelihood estimates (where random eects are treated as
nuisance parameters by integrating them out).
Methods for approximating the integral in the likelihood (PQL, Laplace,
adaptive Gaussian quadrature) suer from very slow convergence and
unexpected features that can occur due to regularization problems of the
covariance matrices.
We adopted the maximum penalized likelihood (MPL) approach recently
suggested by Chung et al. (2012) to regularize the covariance matrix, say
, away from its boundary j j = 0.
In multivariate cases, Chung et al. recommend adding as penalty term in
the penalized log-likelihood function the log-Wishart on the covariance
matrix , which is equivalent to the sum of log-gamma penalties on the
eigenvalues of 1=2.
Maria Grazia Pittau and Roberto Zelli Fifth ECINEQ Meeeting
Has the attitude of US citizens towards redistribution changed over time?

27. Maximum penalized likelihood
Estimation strategy? Not so simple II
With a certain choice of parameters, the use of a Wishart distribution
shifts the estimate of each eigeinvalue away from zero, that is, it keeps
the variances away from zero and the correlation matrix positive de

28. nite.
The exponential of the penalty term can be regarded as a bayesian prior
density for and the MPL estimates can be viewed as posterior modal
estimates. The Wishart prior is weakly informative, in the sense that
the log-likelihood at the maximum penalized likelihood estimates tends to
be not much lower than the maximum since the priors supply some
directions but still allow inference to be driven by the data.
Maria Grazia Pittau and Roberto Zelli Fifth ECINEQ Meeeting
Has the attitude of US citizens towards redistribution changed over time?

29. Unmodeled and population average modeled coecients
Unmodeled and modeled coecients
The coecients of some predictors did not show variability over time and
for this reason they have been left unmodeled.
We left unmodeled those coecients whose size was small and their
pattern over time (and over birth cohort) was almost stable.
Unmodeled coecients includes marital status, gender, religion, religion
functions attendance, employment status and previous spells of
unemployment.
Maria Grazia Pittau and Roberto Zelli Fifth ECINEQ Meeeting
Has the attitude of US citizens towards redistribution changed over time?

30. Unmodeled and population average modeled coecients
−1.0 −0.5 0.0 0.5 1.0
income
not married
married
age30
age30−65
age65
educ12
educ12−16
educ16
white
black
other
male
female
secular
catholic
protestant
other
not attend. rel
attend. rel
never unempl
unempl
not self−empl
self−empl
democrats
independent
republican
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
Maria Grazia Pittau and Roberto Zelli Fifth ECINEQ Meeeting
Has the attitude of US citizens towards redistribution changed over time?

31. Income
All things being equal, richer people in the U.S. are more adverse to
redistribution. The estimated income slope is on average

32. income = 0:50, meaning that a movement along the equivalent income
scale of two times the standard deviation, roughly corresponding to an
increase of 74.000 dollars, reduces the probability of supporting
redistribution by approximately 13%.
What about rich and poor individuals over time and across cohorts? Our
evidence shows that income eect varies over time but is not in
uenced
by birth cohort.
A strong temporal pattern occurs when we examine the predictive power
of income over the last thirty years. Income matters more at the end of
the period than in the 1970s.
Maria Grazia Pittau and Roberto Zelli Fifth ECINEQ Meeeting
Has the attitude of US citizens towards redistribution changed over time?

33. Income
−0.65 −0.60 −0.55 −0.50 −0.45 −0.40 −0.35
Regression slopes 1978 1980 1983 1986 1988 1990 1993 1996 1998 2000 2002 2004 2006 2008 2010
Year
l
l
l
l
l
l
l
l
l
l
l
l l
l
l
l
l
l
l
l
Maria Grazia Pittau and Roberto Zelli Fifth ECINEQ Meeeting
Has the attitude of US citizens towards redistribution changed over time?

34. Income
As an alternative perspective, we analyzed time dierences between poor
and rich on the probability scale.
Given that we have a high number of predictors (many of them
categorical), we opted computing an average predictive comparison, which
is the average of the predictive dierences in probability over the n
observations in the data (Gelman and Pardoe, 2007).
The predictive dierence of individual i for the input of interest u
evaluated at two dierent values, say ulo and uhi is de

35. ned as follows:
i =
logit1(yju(hi); vi; ) logit1(yju(lo); vi; )
u(hi) u(lo)
where y represents the response variable, vi the other observed inputs for
individual i and the vector of parameters.
Maria Grazia Pittau and Roberto Zelli Fifth ECINEQ Meeeting
Has the attitude of US citizens towards redistribution changed over time?

36. Income
0.25 0.30 0.35 0.40 0.45 0.50 0.55
probabilities
Avg pred difference = 0.17
predicted Averaged Year Avg pred difference = 0.27
Low income
High income
1978 1983 1986 1989 1993 1996 2000 2004 2008
Maria Grazia Pittau and Roberto Zelli Fifth ECINEQ Meeeting
Has the attitude of US citizens towards redistribution changed over time?

37. Education
Education has a traditional role in the economic literature on preferences:
the less educated an individual is, the more he (she) will tend to favor
redistribution.
On average, individuals with low level of education (less than 12 years) are
more in favor of redistribution by around 8% with respect to individuals
with an intermediate level of education (between 12 and 16 years), while
higher education (more than 16 years) does not imply a statistically
dierent response.
When we test for variation over time, two dierent time patterns: a
downward trend for less educated individuals and an upward trend for
more educated.
Maria Grazia Pittau and Roberto Zelli Fifth ECINEQ Meeeting
Has the attitude of US citizens towards redistribution changed over time?

38. Education
0.40 0.45 0.50 0.55
probabilities
predicted Averaged Avg pred difference = 0.06
Year Medium education
Low education
High education
Avg pred difference = −0.09
1978 1983 1986 1989 1993 1996 2000 2004 2008
Maria Grazia Pittau and Roberto Zelli Fifth ECINEQ Meeeting
Has the attitude of US citizens towards redistribution changed over time?

39. Political views
The self-declared position on the left-right scale works as a meaningful and
highly relevant instrument that people use to frame redistributive issues.
Coecients of political views are strongly signi

40. cant with the expected
signs: Democrats are expected to be more in favor of redistribution than
Republicans.
But what is more striking is how political redistributive issues have
become more strongly tied to political party identi

41. cation over the past
thirty years. From 1978 to 2010 Democrats and Republicans have moved
apart on individual preferences towards redistribution reaching the highest
level of political polarization on this issue in 2010.
Maria Grazia Pittau and Roberto Zelli Fifth ECINEQ Meeeting
Has the attitude of US citizens towards redistribution changed over time?

42. Political views
0.30 0.35 0.40 0.45 0.50 0.55
Democrats
probabilities
Independents
predicted Avg pred difference = 0.12
Averaged Republicans
Year Avg pred difference = 0.30
1978 1983 1986 1989 1993 1996 2000 2004 2008
Maria Grazia Pittau and Roberto Zelli Fifth ECINEQ Meeeting
Has the attitude of US citizens towards redistribution changed over time?

43. Ethnicity
After controlling for cohort, income, education, religion and especially
political orientation, black people and individuals belonging to non-white
ethnicities are, on average over the entire time span, more supportive of
redistribution than whites.
However, the impact of race over attitudes fades out over time
More variation characterizes the patterns of individuals who are neither
blacks nor whites (others): a decreasing time trend is statistically
signi

44. cant but estimates of the

45. 's are more spread out with relatively no
negligible standard errors.
This weakness is probably due to the aggregation of racial groups in the
GSS survey, which for every survey year identi

46. es only 3 groups, white/
black/ others.
Maria Grazia Pittau and Roberto Zelli Fifth ECINEQ Meeeting
Has the attitude of US citizens towards redistribution changed over time?

47. Ethnicity
0.45 0.50 0.55 0.60
Year Averaged predicted probabilities
Blacks
Others
Whites
Avg pred difference = 0.16
1978 1983 1986 1989 1993 1996 2000 2004 2008
Maria Grazia Pittau and Roberto Zelli Fifth ECINEQ Meeeting
Has the attitude of US citizens towards redistribution changed over time?

48. Ethnicity
Our analysis found unexplained variability among birth cohorts relevant
only for ethnic predictors.
There is very little unexplained variance in cohort eect for black
individuals.
Conversely, a moderately large variation characterizes individuals who are
neither blacks nor whites (others). The estimated standard deviation of
the slopes

49. k for this group is 0:08, which implies that cohort slopes vary
signi

50. cantly ranging from 0 to 0.39. Although our data does not allow us
to delve much further into this pattern, we believe that this unexplained
variation is large because it incorporates the eect due to the aggregation
of the racial groups in GSS.
A separate analysis at least for Asians and for Hispanics would presumably
lead to dierent results.
Maria Grazia Pittau and Roberto Zelli Fifth ECINEQ Meeeting
Has the attitude of US citizens towards redistribution changed over time?

51. Ethnicity
0.0 0.1 0.2 0.3 0.4 0.5 0.6
Regression slopes 1885 1895 1905 1915 1925 1935 1945 1955 1965 1975 1985
Cohort
l l l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l l l l l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
Blacks
Others
Maria Grazia Pittau and Roberto Zelli Fifth ECINEQ Meeeting
Has the attitude of US citizens towards redistribution changed over time?

52. Ethnicity
0.3 0.4 0.5 0.6 0.7
Year Averaged predicted probabilities
Democrat white
Democrat black
Republican white
Republican black
Avg pred difference = 0.14
Avg pred difference = −0.04
1978 1983 1986 1989 1993 1996 2000 2004 2008
Maria Grazia Pittau and Roberto Zelli Fifth ECINEQ Meeeting
Has the attitude of US citizens towards redistribution changed over time?

53. Age
Figure: Estimates and standard errors of time-varying beta coecients ^

54. t:
individuals aged 65 and over, along with the estimated multilevel regression line

55. age
t = b0 + b1t.
−0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0.0
l
Year
Regression slopes
l
l
l
l
l
l
l
l
l
l
l
l
l
l l
l
l
l
l
1978 1980 1983 1986 1988 1990 1993 1996 1998 2000 2002 2004 2006 2008 2010
Maria Grazia Pittau and Roberto Zelli Fifth ECINEQ Meeeting
Has the attitude of US citizens towards redistribution changed over time?

56. Age
Figure: Estimates and standard errors of birth cohort-varying beta coecients

57. ^k: individuals aged 65 and over.
−0.4 −0.3 −0.2
l
l
Cohort
Regression slopes
l
l
l
l
l
l
l
l
l
l
l l l l l l l l l l
1885 1895 1905 1915 1925 1935 1945 1955 1965 1975 1985
Maria Grazia Pittau and Roberto Zelli Fifth ECINEQ Meeeting
Has the attitude of US citizens towards redistribution changed over time?

58. Conclusions and further research
Despite a stable time trend in support for redistribution in the U.S., our
main

59. nding is that time eect is crucial for some predictors. On the
other hand, belonging to a speci

60. c cohort, to the extent that we can
disentangle its eect, has a much less pronounced eect on the attitude
towards redistribution.
In particular, we found the following patterns:
- Personal income has a strong performance as a predictor over the
whole period, but its eect increases constantly and steadily over
time.
- There are two dierent time patterns for education: a downward
trend for less-educated American citizens and an upward trend for
the highest education level. University or college graduates increase
their probability to be pro-redistribution constantly and signi

61. cantly
over time, while non-high school graduates reduce their likelihood
persistently.
- Systematic dierences between Democrats and Republicans have
enlarged in the past thirty years. Americans are much more polarized
on redistributive issues by self-declared party aliation than they
were in the past.
Maria Grazia Pittau and Roberto Zelli Fifth ECINEQ Meeeting
Has the attitude of US citizens towards redistribution changed over time?

62. Conclusions and further research
- Ethnicity matters at least until the 1990s but ethnic groups gradually
move closer over time and in the 2000s ethnic gaps seem to close.
This result holds only after having controlled for political views,
meaning that self-declared party identi

63. cation seems to overcome
ethnic group loyalty.
- In the late 1970s the racial gap was much more important than the
political gap in shaping preferences for redistribution. At the
beginning of the period, for black Americans being democrat or
republican did not in
uence their redistributive attitudes. Over time
we assist at a converge of trajectories: white or black Democrats
have same attitudes as well as white or black Republicans.
Multilevel models represent a powerful framework for understanding time
patterns and for modeling time-varying coecients. A step forward in the
analysis would be to include time series contextual variables, which could
help explaining the time variability of the slopes.
Maria Grazia Pittau and Roberto Zelli Fifth ECINEQ Meeeting
Has the attitude of US citizens towards redistribution changed over time?