Cross-Cutting Cleavages
and Government Spending∗
Erik Snowberg
Stanford GSB
snowberg@stanford.edu
www.stanford.edu/∼ esnowber
[Secondary Economics Job Market Paper ]
Abstract
When racial groups differ in terms of their political sensitivity—the propensity of
group members to change their vote based on changes in redistribution promised by a
candidate—the racial composition of a political jurisdiction affects redistributive policy even when preferences are correlated only with income. Furthermore, the extent
to which race and class are cross-cutting is important. Although the concept of crosscutting cleavages is well-known in political science and sociology, its implications have
yet to be analyzed formally. This paper formally defines, develops and tests a model of
cross-cutting cleavages to better understand the complex relationships between race,
class, preferences, political sensitivity and redistributive policy. I show that the effect of cross-cutting cleavages on redistributive policy depends critically on economic
parity—the ratio of average black income to average income. The cross-cutting cleavages model makes six predictions that are all supported by data from large U.S. cities
between 1942 and 1972.
∗
I thank Keith Krehbiel, David Baron, Gerard Padró-i-Miquel and Romain Wacziarg for their support
and insightful comments. This work was supported in part by the SIEPR Dissertation Fellowship through a
grant to the Stanford Institute for Economic Policy Research.
1
Introduction
How does the racial composition of a jurisdiction affect redistributive policy, such as the taxation and spending decisions of governments? Recent research rationalizes observed correlations between racial composition and redistributive policy by assuming that the preferences
of the median voter, and thus policy, change based on the racial composition of a jurisdiction
(Alesina, Baqir and Easterly, 1999; Lind, 2007).1 This is in contrast with canonical models
of the size of government which assume that preferences for redistribution are correlated
only with income (Romer, 1975; Roberts, 1977; Meltzer and Richard, 1981).
This paper focuses on how behavior affects the mapping from preferences to redistributive policies when racial and class cleavages are cross-cutting. Similar to canonical models
of the size of government, the theory does not assume any differences in preferences for
redistribution within a class: the poor like it and the rich dislike it regardless of race. In
the cross-cutting cleavages model, changes in racial composition, or the racial cleavage, of a
jurisdiction alter redistributive policies due to persistent differences between racial groups in
political sensitivity. Political sensitivity is broadly defined to include the propensity of citizens to vote, and if they do vote, their willingness to change their vote based on slight changes
in redistribution promised by a candidate. Political sensitivity is similar to an elasticity of
votes from a group with respect to changes in redistribution promised by a candidate.
The cross-cutting cleavages model is an extension of the redistributive politics framework
of Lindbeck and Weibull (1987) and Dixit and Londregan (1996) and is motivated by data on
political sensitivity in U.S. cities between 1942 and 1972. In this framework, redistributive
policy, specifically the equilibrium tax rate, is determined by the relative sizes and political
sensitivities of the rich and the poor. Political sensitivity has not been widely and consistently
1
Austen-Smith and Wallerstein (2006), in the only other formal study of redistribution involving both
race and class, study redistribution in the presence of affirmative action policies. Alesina, Baqir and Easterly
(1999) intend their model to describe only spending on productive public goods, although it could be applied
to more general redistributive policies.
Marxists believe that race is used by the capitalist class to create divisions among workers. See Wilson
(1978) for a summary. For a formal treatment of this theory see Roemer (1998) and Lee, Roemer and Van der
Straeten (2007).
1
measured. To address this measurement limitation and to generate testable predictions, the
cross-cutting cleavages model focuses on cities in the United States between 1942 and 1972,
years during which within each race the rich were more politically sensitive than the poor
and within each class whites were more politically sensitive than blacks.
There are two main contributions of the model. The first contribution is to formally
define and study the implications of cross-cutting cleavages in redistributive politics. Crosscutting cleavages is an old concept from political science that has not been formalized. A
cleavage is simply a trait that divides a society into a number of groups. In the extreme,
when two cleavages are reinforcing, both cleavages define the same groups. To the extent
that cleavages define different groups—for example if there are both rich and poor whites
and blacks—they cross-cut to some extent.
The degree of cross-cuttingness thus describes a pattern of groups in a jurisdiction. Specifically, I define the cross-cuttingness of the racial and class cleavage as the correlation between
race and income. That is, if knowing a citizen’s race does not increase the accuracy of a prediction of his or her class, then cleavages are said to be perfectly cross-cutting. In contrast,
if knowing a citizen’s race allows a perfect prediction of his or her class, then cleavages are
perfectly reinforcing.
Cross-cuttingness is parameterized here by a new variable, economic parity—the ratio of
average black income to average income. If economic parity is less than one, that is, blacks are
on average poorer than whites, then a rise in economic parity increases the cross-cuttingness
of the racial and class cleavages, holding constant the proportion of the city that is black
(the racial cleavage) and average income (the class cleavage). The theory predicts that this
change will lead to an increase in tax rates and government spending. This is true even
blacks are on average richer than whites, at which point the racial and class cleavage become
less cross-cutting with an increase in economic parity. Thus, the relationship between the
cross-cuttingness of the racial and class cleavages and redistributive policy is non-monotonic
and depends on specific parameters of the model.
2
Despite the fact that the concept of cross-cutting cleavages has not been formally studied,
it has been linked to many outcomes of interest. For example, (Lipset, 1960, pp. 88-89)
notes “[T]he chances for stable democracy are enhanced to the extent that groups and
individuals have a number of crosscutting, politically relevant affiliations.” Lowi (1964,
p. 697) summarizes the work of pluralists on cross-cutting cleavages: “Truman (1951), for
instance, stresses overlapping membership as a source of conflict ... In contrast, Bauer, Pool
and Dexter (1963) found that ... this very overlapping membership was a condition for
cohesion.” Underlying these conclusions of a monotonic effect of cross-cutting cleavages on
the outcomes of interest is an assertion about how cross-cutting cleavages affect the ability
of groups to overcome collective action problems. Here, in contrast, cross-cutting cleavages
affect outcomes in a non-monotonic way and have an effect without assertions about collective
action problems.
The second main contribution of the model is to show that when racial groups differ
in terms of their political sensitivity, the racial composition of a jurisdiction affects redistributive policy even when preferences are correlated only with income. Thus, observed
correlations between racial composition and redistributive policy can be rationalized without speculative assumptions about preferences. This is advantageous as the components of
political sensitivity, especially turnout, are much easier to document than the preferences of
large groups of individuals.
The model makes six predictions, all of which are supported by data from large U.S. cities
between 1942 and 1972. As discussed below, many of these predictions differ from those in
the existing literature. Moreover, when politicians can flexibly target spending to different
groups the predictions of the cross-cutting cleavages model continue to hold while previous
models, such as those of Meltzer and Richard (1981) and Alesina, Baqir and Easterly (1999),
which are based on the median voter framework, cannot make predictions.
3
2
The Model
This section describes and then formalizes the setup and equilibrium of the cross-cutting
cleavages model. It concludes with a subsection that justifies the ordering of political sensitivity between rich and poor blacks and whites. The explanations of the results in Section 3
depend on the lemma and terms defined in this section.
The model describes an election in a city in which citizens vote for one of two candidates
based on their policy platforms. Platforms are binding and consist of a tax rate and level
of government spending. Citizens are characterized by their economic class and their race.
These characteristics are associated with different levels of political sensitivity. A citizen’s
class also induces a particular tradeoff between preferences for taxes and government spending: the rich have a lower ideal tax rate than the poor as is common in probabilistic voting
models. The electoral model is symmetric, and in equilibrium the candidates propose the
same platform. That platform maximizes a sum of weighted citizens’ utilities, where the
weights are given by the political sensitivity of the citizen’s class-race group. The resulting
tax rate lies between the ideal tax rates of the rich and the poor, and an increase in the
political sensitivity of one class moves the tax rate closer to that class’s ideal tax rate.
More formally, there is a unit measure of infinitesimal citizens. A citizen’s class is either
rich or poor i ∈ {R, P }, and her race is either black or white j ∈ {B, W }. The rich here would
be more accurately described as middle-class—the label rich is used for congruence with the
literature. There are thus four class-race groups indexed by ij ∈ {RW, RB, P W, P B}. The
P
proportion of a city from each group is given by λij ∈ [0, 1] where ij λij = 1. The proportion
of the city from class i is λi = λiB + λiW , i ∈ {R, P }, and the proportion of a city from race
j is λj = λRj + λP j , j ∈ {B, W }. Groups also differ in terms of their political sensitivity.
The political sensitivity ψ ij ≥ 0 of a class-race group ij is defined to include the propensity
of citizens in that group to vote, and if they do vote, their willingness to change their vote
based in slight changes in a candidate’s redistributive platform. The demographics of a city
are illustrated in Figure 1.
4
Figure 1: A city is composed of rich and poor blacks and whites.
Poor citizens have exogenous pre-tax income y P regardless of race, and rich citizens
have exogenous income y R > y P regardless of race. The average income of race j is y j =
P
λRj y R +λP j y P
, and the average income of the city is y = ij λij y i . The utility U ij of a citizen
λj
from class i and race j is specified as
U ij (τ, g) = (1 − τ )y i + log(g),
(1)
where τ is a linear tax on income and g is per capita government spending.
A citizen’s ideal tax rate, when spending is constrained to equal tax revenue, depends
only on his or her own income, that is, preferences are solely class based as discussed in the
introduction. Rich and poor citizens have the same utility tradeoff between consumption
(1 − τ )y i and government spending g.2
2
The assumption that government spending is valued as the log of spending allows for a sharp prediction
about the effect of an increase in average income on the equilibrium tax rate in Propostion 1. If government
spending is valued according to some arbitrary strictly increasing, strictly concave function most results still
hold. Blacks may have a greater demand for government spending than whites (i.e. Bergstrom, Rubinfeld
and Shapiro (1982)), however, Rubinfield, Shapiro and Roberts (1987) show that this statistical pattern
5
There are two candidates, and each candidate chooses a platform to maximize his or
her vote share subject to the constraint that spending is less than tax revenue g ≤ τ y. As
candidates do not differ in any substantive way, in equilibrium both candidates propose the
same platform, as shown in Appendix A. As preferences in (1) do not depend on race, this
platform maximizes a sum of the weighted utilities of the rich and the poor. The weight for
i
class i is its political prominence ψ λi , the product of the class’s average political sensitivity
i
ψ =
λiB ψ iB +λiW ψ iW
λi
and size λi . Furthermore, in equilibrium the budget constraint binds
and per capita tax revenue τ y equals per capita spending g. These terms will be used
synonymously for spending.
Intuitively, for a fixed size, groups that are more likely to change their votes based
on changes in a candidate’s platform are more likely to swing the results of the election.
Candidates target these politically sensitive groups by moving their platform closer to the
group’s ideal policy to gain a greater vote share. For a fixed level of political sensitivity
larger groups can provide more votes, and hence greater swings in total vote share, which
enhances the group’s political prominence.
The equilibrium tax rate τ∗ and per capita tax revenue g∗ = τ∗ y are thus a function
of the vector of population proportions ~λ = {λRW , λRB , λP B , λP W }, the vector of political
~ = {ψ RW , ψ RB , ψ P B , ψ P W }, and the vector of incomes ~y = {y R , y P }. The results
sensitivity ψ
~ and examine demographic changes—that is, changes in ~λ, the
in Section 3 fix ~y and ψ
proportion of the population in each group. Section 4, which deals with robustness of the
theory, examines changes in the underlying income ~y of the rich and poor on the equilibrium.
Demographic changes effect the equilibrium tax rate τ∗ and per capita tax revenue g∗ =
P
τ∗ y through the relative political prominence of the poor
ψ λP
,
R
ψ λR
the ratio of the political
prominence of the poor to the political prominence of the rich.
Lemma 1 Changes in the equilibrium tax rate associated with any demographic change are
P
in the same direction as changes in the relative political prominence of the poor
ψ λP
R
ψ λR
asso-
arises due to a failure to account for the lower geographic mobility of blacks.
6
ciated with that demographic change.
P
If the relative political prominence of the poor
ψ λP
R
ψ λR
increases, so will the relative weight of
the poor in the candidate’s vote share maximization. Politicians respond by moving their
proposed tax rate closer to the ideal tax rate of the poor. Thus, the equilibrium tax rate
rises.
In contrast, consider a purely economic baseline—a social planner who maximizes total
social welfare. Since a social planner maximizes the unweighted sum of citizen’s utilities,
this is the same as the cross-cutting cleavages model when all class-race groups had the same
level of political sensitivity. The tax rate set by the social planner τs∗ =
1
y
depends only on
average income, whereas in the cross-cutting cleavages model the tax rate depends on the
relative political prominence of the poor. This highlights the role of politics in setting a tax
rate that differs from the economic baseline in the cross-cutting cleavages model.
2.1
Political Sensitivity
The relative political sensitivity of each class-race group ij is central to the predictions of the
model. Verba and Nie (1972), and Section 5.4, finds blacks are less likely to vote than whites,
and individuals with high socio-economic status are more likely to vote than individuals with
low socio-economic status. Verba, Schlozman and Brady (1995) finds similar patterns that
extend (often more strongly) to other political behavior such as participating in protests and
contributing to campaigns. Wilson (1960) and Dawson (1994) show that blacks are more
committed to one party or the other than whites. Wilson (1960) and Banfield and Wilson
(1963) find that blacks are more likely to be part of a local political machine, and hence
less politically sensitive than whites during the period under study. Pinderhughes (1987,
p. 113), in her study of Chicago politics, summarizes the difference in political sensitivity
between black and white voters as, “[B]lack voters ... consistently, almost uniformly, commit
themselves to the party, faction or individual candidate that is most supportive of racial
reform.”
7
As the above references make clear, a larger percentage of high-income than low-income
individuals vote, so the rich are more politically sensitive than the poor ψ Rj > ψ P j . Furthermore, a lower proportion of blacks than whites turnout to vote, and blacks are more likely
to be committed to one candidate or the other, so blacks are less politically sensitive than
~ where the
whites ψ iB < ψ iW . This establishes a partial ordering on political sensitivity ψ,
relationship between ψ RB and ψ P W is not determined. This ordering is sufficient to produce
the sharp predictions that are derived in the next section.3
3
Results
To generate predictions that can be tested with data available for the period under study, the
equilibrium tax rate can be re-written in terms of the variables of interest: average income y,
the proportion black λB and economic parity
yB
—the
y
ratio of average black income to average
B
income. Thus, the equilibrium tax rate will be written as τ∗ (y, λB , yy ) and the equilibrium
B
level of per capita tax revenue will be written as g∗ (y, λB , yy ). Taking a partial derivative of
the equilibrium tax rate with respect to one of the variables of interest implicitly keeps the
other two constant. This leads to straightforward tests of the model since the coefficient on
one of the variables of interest from a regression which includes all three variables of interest
is the estimated effect of changing that variable keeping the other two constant.
The variables of interest were chosen because a changes in these variables map into
changes in a particular aspect of the cleavage structure: a change in average income y alters
the class cleavage, a change in the proportion black λB alters the racial cleavage, and a
change in economic parity
yB
y
alters the cross-cuttingness of the racial and class cleavage,
or, given the definition of cross-cuttingness in Section 1, the statistical independence of race
3
The model does not take into account the potential endogeneity of political sensitivity. For example,
Washington (2006) finds that having black candidates on the ballot changes turnout patterns. This is not
be a particular concern, as in her study both white and black turnout increases at levels that are roughly
proportional to the overall turnout level of each group. In addition, Alesina and La Ferrara (2000) find that
other forms of engagement respond to the level of diversity in a community.
8
and class.4
The following three subsections examine how the equilibrium tax rate changes with an
increase in one of the variables of interest. Each subsection begins by describing the demographic change that increases one of the variables of interest keeping the other two constant.
This demographic change combined with Lemma 1 provides the intuition for how the equilibrium tax rate changes with the variable of interest. Each subsection concludes with a
brief discussion of the result and any associated corollaries. The final subsection considers
spending that may be targeted to different class-race groups and derives a testable prediction
about per capita welfare spending.
3.1
Changes in Class Composition
Consider a change in class composition, such as increasing the proportion rich and thus
average income, holding the other two variables of interest constant. This creates four
constraints that specify how the the proportions of the population ~λ change. An increase
in average income y, holding constant the proportion black λB and economic parity
yB
,
y
changes the underlying proportions of class-race groups as illustrated in Figure 2. Because
the proportion black is unchanged, there is no change in the racial cleavage. A greater
R
proportion of the city is rich, which increases their political prominence ψ λR . Because the
rich favor a lower tax rate τ politicians curry favor with this increasingly important group
by reducing the tax rate.
Proposition 1 An increase in average income, holding constant the proportion black and
B
economic parity, decreases the equilibrium tax rate:
∂τ∗ (y,λB , yy )
∂y
< 0.
4
Changes in average income, y, and the proportion black, λB , have effects on the statistical independence
of the race and class cleavages. However, these effects cannot be signed, whereas a change in economic parity,
yB
y , has unambiguous effects on the orthoganality of race and class. The definition of cross-cuttingness
here differs from Rae and Taylor (1970). Their measure of cross-cuttingness is based on the increase in
fractionalization introduced by adding another cleavage.
9
Figure 2: An increase in average income alters the class cleavage.
This prediction is in contrast to that of the median voter model of the size of government,
such as the two class version of the Meltzer and Richard (1981) model in Persson and Tabellini
(2000, Chapter 3.3). The median voter model predicts that an increase in the proportion
of the population that is rich generally raises the tax rate. This occurs because the median
voter, who is poor, votes for a higher tax rate because there is now more money in the city
to appropriate for his or her purposes. Because the median voter model makes predictions
about per capita tax revenue g = τ y the prediction that the tax rate will rise holds as
long as average income does not increase too much. If average income increases rapidly, the
predicted increase in per capita tax revenue may be accompanied by a decrease in the tax
rate.
The cross-cutting cleavages model considered here has the reverse indeterminacy—when
average income increases, the direction of the change in tax rates is well defined, but the diB
B
rection of the change in per capita tax revenue g∗ (y, λB , yy ) = τ∗ (y, λB , yy )y is indeterminate
B
because τ∗ (y, λB , yy ) decreases and y increases.
10
Figure 3: An increase in the proportion black alters the racial cleavage.
Corollary 1 An increase in average income, holding constant the proportion black and economic parity, has an indeterminate effect on equilibrium per capita tax revenue.
3.2
Changes in Racial Composition
A change in the proportion black λB , keeping average income y and economic parity
yB
y
fixed, maintains the proportion of the black population that is rich. Because average income
is kept constant, for every increase in the proportion of poor (rich) blacks, there must be
a corresponding decrease in the proportion of poor (rich) whites. If average black income
is less than average white income, y B < y, as illustrated in Figure 3, this implies that the
proportion of the white population that is rich must increase slightly.
11
Proposition 2 An increase in the proportion of the city that is black, holding constant
average income and economic parity, depends on the relative difference in political sensitivity
between races across classes,
ψ P W −ψ P B
.
ψ RW −ψ RB
In particular, the tax rate increases if and only if:
ψP W − ψP B
<Q
ψ RW − ψ RB
P
where Q =
ψ λP λRB
.
R
ψ λR λP B
The equilibrium tax rate increases with the proportion black if the difference in political
sensitivity between blacks and whites across the poor is smaller than the difference in political
sensitivity between blacks and whites across the rich. How much smaller depends on Q.
Intuitively, if the difference in political sensitivity is higher across the rich, an increase in
the proportion of the city that is black reduces the average political sensitivity of the rich
more than it reduces the average political sensitivity of the poor. This increases the relative
political prominence of the poor, so by Lemma 1, the equilibrium tax rate increases.
Alesina, Baqir and Easterly (1999) predict that if the proportion black is less than onehalf, an increase in the proportion black decreases spending on productive public goods.
If the logic of their model is extended to all government spending, then the prediction of
the cross-cutting cleavages model stands in contrast, as spending may increase with the
proportion black. Interestingly, this is not the result of blacks being on average poorer than
whites, as the average income of the population and of blacks are both held constant in the
proposition. Rather, the predictions are driven by differences in political sensitivity between
races that depend on class.
The theory here depends on an inequality, the direction of which is uncertain based on
previous research. In the empirical section, the limited data on turnout, a component of
political sensitivity, will be examined to see if the statistical patterns in that data match
those implied by the statistical patterns in taxation data and Proposition 2. Additionally,
the next two subsections derive testable predictions that depend on whether the tax rate
12
Figure 4: The cross-cuttingness of the race and class cleavage increase with economic parity.
increases or decreases with an increase in the proportion black.
3.3
The Effects of Cross-Cuttting Cleavages
The final variable of interest, economic parity
yB
,
y
is unique to this model.5 An increase in
economic parity, holding constant average income y and the proportion black λB , corresponds
to an increase in the proportion of blacks that are rich, and a corresponding increase in the
proportion of whites that are poor, as illustrated in Figure 4.
The proportion of the rich that are black and the proportion of the poor that are white
both increase with economic parity. This increases the average political sensitivity of the
poor and decreases the average political sensitivity of the rich as blacks are less politically
sensitive than whites. Because average income y is held constant, the proportion of the city
that is rich (or poor) does not change. Thus, the relative political prominence of the poor
5
The ratio of average black income to average white income is used in sociological studies as a measure of
economic deprivation of blacks rather than as a parameterization of the cross-cuttingness of racial and class
cleavages. See for example Spilerman (1970) and Olzak, Shanahan and McEneaney (1996).
13
P
ψ λP
R
ψ λR
rises, leading politicians to increase the tax rate.
Proposition 3 An increase in economic parity, holding constant the proportion black and
B
average income, increases the equilibrium tax rate:
∂τ∗ (y,λB , yy )
B
∂ yy
> 0.
If average black income is less than average income y B < y as in Figure 4, an increase in
economic parity
yB
y
brings the racial and class cleavages closer to statistical independence.
That is, the cleavages become more cross-cutting. However, if average black income is greater
than average income, then an increase in economic parity will decrease the cross-cuttingness
of the racial and class cleavages. Regardless of whether cross-cuttingness increases or deB
creases, an increase in economic parity increases the equilibrium tax rate, τ∗ (y, λB , yy ). This
shows the difficulty of making general predictions about the effects of cross-cutting cleavages.
To understand the effects of increasing or decreasing levels of cross-cuttingness, one must
be specific about which cleavages one is examining, and how the groups created by those
cleavages relate to one another through political and economic mechanisms.
Finally, the previous two propositions lead to a straightforward corollary.
Corollary 2 A change in the proportion black or in economic parity, keeping the other two
variables of interest fixed, leads to changes in the equilibrium level of per capita tax revenue
that are in the same direction as changes in the equilibrium tax rate.
A change in either the proportion black λB or economic parity
yB
y
keeps average income y
B
B
fixed. Thus, the change in per capita tax revenue g∗ (y, λB , yy ) = τ∗ (y, λB , yy )y will be in
the same direction as, and proportional to, the change in the tax rate.
3.4
Targeted Government Spending
The data analyzed in Section 5 provides information on aggregate local government spending
in several categories. Only one of these categories, spending on public welfare, can be thought
of as targeted to a particular group, in this case the poor. To utilize these data, an additional
14
prediction that depends on whether the equilibrium tax rate increases or decreases with an
increase in the proportion black (Proposition 2), is derived in this subsection when politicians
can target spending to different groups.
There are several reasons why a politician may be able to target spending to some groups
while excluding others. For example, there may be intrinsic differences in preferences for
different types of spending between groups. Additionally, to the extent that different groups
live in different areas of a city, politicians may be able to target spending to certain groups
that would be preferred equally by all groups: all citizens might like spending on parks, but
only if the park is located in their neighborhood.
Preferences are now specified as
i
j σ
σ
1
log
+ log
,
U (τ, ~σ ) = (1 − τ )y +
i
2
λ
λj
ij
i
(2)
where σ i is spending directed to class i ∈ {R, P } and σ j is spending directed to race j ∈
{B, W }. As shown in Subsection 4.1, all the previous results continue to hold with this
utility function. This utility function captures the intuition that, for example, rich and poor
blacks both have some similar preferences (σ j ) and some dissimilar preferences (σ i ) over
types of government spending.6 In addition, the value to a citizen of spending targeted to
race is independent of a citizen’s class, and each citizen values per capita spending directed
to race and class equally.7
6
Wilson (1978) argues that class is more important than race in black political identities. Other scholars,
such as Huckfeldt and Kohfeld (1989) disagree. This utility function takes the middle ground on this issue
by considering both.
7
The assumption that the rich might like increased government spending because it can be targeted
to them differs from the theoretical literature on this subject. However, it is clear that such targeting is
feasible. For example, in the period under study, Katzman (1968), Owen (1972) and Sexton (1961) all find
that education spending favors the rich in various municipalities. In other types of government expenditure,
Martin (1969) and Levy, Meltsner and Wildavsky (1974) both find that library expenditures primarily benefit
the rich, and Community Council of Greater New York (1963) finds that the rich benefit more from parks
than the poor do.
15
In equilibrium, the level of spending on race or class k ∈ {R, P, B, W }, σ∗k is:
k
σ∗k
ψ λk
=
,
2γ
R
P
ψ λR y R + ψ λP y P
where γ =
.
y
(3)
Holding γ constant, total spending on a race or class increases with the political prominence
of that group. Groups that are more sensitive and larger, thus more likely to be pivotal in
voting, are better provided for by politicians than small and politically insensitive groups.
Proposition 4 An increase in the proportion black, holding constant average income and
economic parity, will increase per capita spending on the poor if and only if the equilibrium
tax rate increases:
∂σ∗P
≥0
∂λB
B
⇐⇒
∂τ∗ (y, λB , yy )
∂λB
≥ 0.
In Proposition 2, whether tax rates rise or fall with an increase in the proportion black
depends on how that change affected the relative political prominence of the rich and poor.
When the relative political prominence of the poor increases, so does the tax rate - but as
can be seen from (3) this is also the condition that leads to an increase in per capita spending
on the poor.8
Changing racial composition has several well specified effects even though preferences
do not depend on race. Instead, the cross-cutting cleavages model makes sharp predictions
~ In sumwith only an empirically supported ordering on the vector of political sensitivities ψ.
mary, when the proportion black increases, holding constant average income and economic
parity, the equilibrium tax rate, per-capita tax revenue and per-capita spending on the poor
all increase or all decrease depending on the values of the vector of political sensitivities.
Specifically, all three of these variables will rise if and only if the difference in political sensitivity between blacks and whites across the poor is smaller than the difference in political
8
Per-capita spending on the poor may increase or decrease with an increase in average income or economic
parity. The intuition above does not apply in those cases because it ignores the effect of increasing the
political prominence of the poor on γ. In the case of an increase in the proportion black this omission is
inconsequential, but it is important when considering increases in average income or economic parity.
16
sensitivity between blacks and whites across the rich.
4
Robustness of the Theory
This section establishes that the above predictions are robust to relaxing two assumptions,
and makes no new testable predictions. First, it finds that all the main results hold when
politicians can very flexibly target spending to groups. Second, changes in the parameters
of interest driven by changes in the income of the rich and poor, rather than changes in the
population proportions of different groups, do not alter the main results.
4.1
Targeting
Suppose there are K different types of government spending, σ k , k ∈ {1, 2, 3, ..., K}. A
citizen in class i and race j then has utility given by:
U ij (τ, ~σ )
(1 − τ )y i +
=
K
X
k
αijk log
k=1
s.t.
K
X
k=1
where the condition
PK
k=1
αijk = 1 ,
X
βk
σ
ij
ij λ 1{αijk >0}
!
P
(4)
λij αijk > 0 , β k ∈ (0, 1]
ij
αijk = 1 ensures that each class-race group ij has the same
utility tradeoff between government spending and consumption. This maintains the earlier
assumption that preferences over tax rates depend only on a citizen’s class. Note that
some αijk s could be negative, allowing for types of government spending that bring positive
P
utility to one group and negative utility to another. The assumption that ij λij αijk > 0
ensures that in equilibrium all types of government spending are greater than zero.9 The
β k parameters capture how rival a particular form of government spending is. For a type
of spending k, β k = 1 means that the type of government spending is perfectly rival, and
9
If some type of government spending were zero then some groups would have infinite utility, and other
groups would have negative infinite utility, and equilibrium existence would no longer be guaranteed.
17
as β k → 0 that type of spending moves towards being perfectly nonrival. Finally, dividing
P
spending by ij λij 1{αijk >0} captures the idea that spending is shared among the groups
that gain positive utility from that form of government spending.10 The politicians’ budget
P
k
constraint is now K
k=1 σ ≤ τ y. Note that the single type of government spending in (1)
and the targeting in the previous section given by (2) are special cases of the utility function
in (4).
Even when politicians have the ability to flexibly target government spending, the main
results do not change.
Robustness Result 1 Propositions 1, 2 and 3 hold if citizen utility is given by (4).
Alesina, Baqir and Easterly (1999) show that racial diversity may lead to decreases in government spending due to diversity of preferences for different types of spending. In the
cross-cutting cleavages model adding preference diversity about spending does not affect the
results.11
4.2
Changes in Income Levels
All previous results attribute changes in the variables of interest—the proportion black λB ,
average income y and economic parity
yB
—to
y
changes in the population proportions of each
group ~λ = {λRW , λRB , λP B , λP W }. Changes in the last two variables of interest, however,
may be due to changes in the income of the rich and the poor ~y = {y R , y P }. Even if this is
the case, the relevant results still hold.
Robustness Result 2 An increase in average income through changes in ~y , holding economic parity constant, leads to a decrease in the equilibrium tax rate. An increase in economic parity through changes in ~y , holding average income constant, leads to an increase in
the equilibrium tax rate if and only if average black income is less than average income.
10
Note that I make no distinction between government spending for productive and consumptive purposes.
That is, adding preference diversity does not change the level of taxation and spending, or the comparative statics of the model.
11
18
5
Empirical Evidence
There are few established facts about the effect of race, class and the cross-cuttingness of
racial and class cleavages on tax rates. This section identifies some of these facts and assesses
the extent to which the predictions of the cross-cutting cleavages model are observed in
data from large U.S. cities between 1942 and 1972. It then examines turnout patterns to
determine whether the patterns in this limited data on political sensitivity are consistent
with the model.
The predictions of the cross-cutting cleavages model are straightforward to test as they
isolate the effect of increases in one of the three variables of interest—average income y, the
proportion black λB and economic parity
yB
—holding
y
the other two constant. Estimating
a specification of the form
x = α + βy y + βλB λB + β yB
y
yB
+
y
(5)
produces coefficients β that are the correlation of the dependent variable x with one of the
variables of interest, holding the other two constant. For example, if the dependent variable
is the tax rate τ , then βy is an estimate of the effect of increasing average income on the tax
rate holding constant the proportion black and economic parity.12
The predictions of the cross-cutting cleavages model are summarized in Table 1 in terms
of the coefficients in (5). When the proportion black increases, holding constant average
income and economic parity, the equilibrium tax rate, per-capita tax revenue and per-capita
spending on the poor all increase or all decrease depending on the values of the vector of
political sensitivities. That is, βy is predicted to be greater than zero or all less than zero
for all three dependent variables, depending on the condition in Proposition 2. When these
12
Related studies have measured ethnic diversity using the fractionalization or polarization measures (Easterly and Levine, 1997; Alesina, Baqir and Hoxby, 2004; Montalvo and Reynal-Querol, 2005), but when there
are two groups fractionalization= 2λB (1 − λB ) = 21 polarization, making the coefficient on proportion black
(λB ) both easier to interpret and theoretically motivated. For more on the measurement of polarization see
Esteban and Ray (1994).
19
Table 1: Summary of Theoretical Predictions
Dependent Variable
Independent
Variable
Tax Rate
(τ )
Per-Capita Spending
(g)
Per-Capita Spending
on the Poor (σ P )
βλB > 0
βλB > 0
βλB > 0
(λB )
βλB < 0
βλB < 0
βλB < 0
Average Income
(y)
βy > 0
no
prediction
no
prediction
Economic Parity
B
( yy )
β yB > 0
β yB > 0
no
prediction
Proportion Black
y
y
three coefficients are greater than zero, the cross-cutting cleavages model predicts that the
difference in political sensitivity between races across classes should be larger for the rich
than for the poor.
The following subsection briefly describes the taxation data; detailed information on the
data can be found in Appendix B. The middle subsections examine the data in a panel and
cross-sections of cities. The final subsections examine the limited data on political sensitivity
to make a final attempt at falsifying the cross-cutting cleavages model.
5.1
Taxation and Spending Data
The taxation and spending data are from U.S. cities with a population over 100,000 at
approximately five year intervals between 1942 and 1972. The population threshold is chosen
to select for cities with active political communities and to ensure data availability.13 The
time range is chosen because U.S. cities experienced large changes in ethnic makeup and
in the relative income of blacks during this period. The study ends in 1972 to avoid the
13
Banfield and Wilson (1963) find that small cities have distinct forms of political organization—usually
involving just a few individuals—from larger cities.
20
unmodeled effects of Asian and Hispanic immigration.14 Moreover, this period predates the
passage of Proposition 13 in California in 1978, which significantly altered the dynamics of
local taxation.
15
Income data is not easily available before 1940.
The main predictions of the theory are in terms of tax rates, however, tax rate data are
not available. The data do contain per capita tax revenue g = τ y and average income y for
each city. Dividing per capita tax revenue by average income gives a measure of the central
tendency of tax rates, τ̂ . Gramlich and Rubinfeld (1982) and others have found that the
income elasticity of property-tax payments is one, which supports the modeling assumption
that local tax rates can be approximated as a linear tax on income without the distortionary
effects of an income tax.16
5.2
Panel Data Analysis
Estimates from a cross-section of cities may reflect the selection of citizens into cities based
on tax rates rather than the selection of tax rates by politicians based on the demographics
of the city (Tiebout, 1956). Thus, a panel specification with city fixed effects is preferred as
it isolates the effects of demographic changes within a city over time. The empirical results
hold in cross-sectional data as well, as shown in the next subsection.
Table 2 estimates the linear, fixed-effects specification
xct = α +
βλB λB
ct
+ βy y ct + β yB
y
yB
ct
+ χ(controlsct ) + θt + µc + ct ,
y ct
(6)
where t indexes time and c indexes cities, using a panel of U.S. cities between 1942 and
1972. The city level dummy µc removes unobserved heterogeneity between cities, and the
14
It is possible that Hispanic populations may have had an effect before 1972. To control for this possibility
Table 7 drops observations from states that share a border with Mexico.
15
The next year where data is available is 1982. When examining expenditure data from the local level it
is common to conduct the analysis before Proposition 13 in California and Proposition 2 12 in Massachusetts.
For example, see Epple and Sieg (1999) and Epple, Romer and Sieg (2001).
16
Using this estimated tax rate as a proxy for a linear income tax is the same as using income as a proxy
for wealth. This specification also treats renters and homeowners similarly, which is common in the public
finance literature. For example see Epple, Romer and Sieg (2001).
21
year dummies θt control for any national shocks to the dependent variable.17
The controls are largely the same as those in Alesina, Baqir and Easterly (1999) and
attempt to capture other possible determinants of tax rates. Because the predictions of
the Meltzer and Richard (1981) model are in terms of the ratio of median to average income, adding this ratio as a control ensures that the cross-cutting cleavages model explains
variation in addition to that explained by Meltzer and Richard (1981). The population in
school controls for the spending needs of the city, as schools are an important component of
local government spending. This also controls for differences in preferences for government
spending and taxation that a more and less educated populace might have. The population
controls for any scale effects that might be present in larger communities. The number of
government employees controls for any propensity for patronage through city jobs a political
regime might have. Finally, the percent of the population over 65 controls for the effect of
seniors on spending found in Poterba (1997).
The results in Table 2 are supportive of the cross-cutting cleavages model. In accordance
with Proposition 1 the coefficient on average income y is negative and statistically significant.
When per capita tax revenue is the dependent variable the coefficient on average income
changes sign when controls are added and is not statistically significant in either column.
The coefficient on economic parity is positive and significant in all columns, conforming with
the prediction in Proposition 3 and Corollary 2. Finally, the coefficients on the proportion
black are positive when the tax rate τ̂ is the dependent variable. Corollary 2 then implies that
the coefficients on proportion black should be positive when per-capita tax revenue g is the
dependent variable, which is also the case. This has specific implications for the coefficient
on the proportion black when per-capita spending on the poor σ P is the dependent variable,
and specific implications for the pattern of political sensitivity across all four groups, both of
which will be tested. Finally, the standard deviation of the residuals from regressions of tax
rates and per capita tax revenue on the time and city fixed effects are 0.3 and 65 respectively.
17
Hausman (1978) tests reject the appropriateness of random-effects specifications in most of the specifications in Table 2.
22
Table 2: Panel Results
Dependent Variable:
Tax Rate
(τ̂ )
Per-capita Tax
Revenue (τ y)
Proportion Black
1.75∗∗∗
(0.47)
1.66∗∗∗
(0.48)
329∗∗∗
(106)
314∗∗∗
(104)
Average Income
-0.93∗∗∗
(0.30)
-0.55∗
(0.32)
-72.8
(65.1)
16.9
(69.1)
Economic Parity
0.33∗∗
(0.16)
0.31∗∗
(0.16)
81.4∗∗
(33.2)
61.8∗
(35.1)
Median to Average
Income Ratio
-0.85
(0.56)
-240∗∗
(107)
Population in School
-0.09
(0.07)
-12.6
(15.8)
-0.09∗∗∗
(0.03)
-21.3∗∗∗
(5.63)
City Employees
1.44∗∗
(0.58)
408∗∗∗
(135)
Senior
-5.44∗∗
(2.28)
-542∗∗∗
(426)
Population
Constant
R2
n (city × year)
9.08∗∗∗
(2.79)
7.02∗∗
(3.08)
651
(609)
158
(656)
0.897
828
0.910
806
0.853
828
0.882
806
Notes: ∗∗∗ ,∗∗ ,∗ denotes statistical significance at the 1%, 5% and
10% levels, respectively. All columns contain year and city
fixed effects. White (1980) heteroskedastictic-consistent
standard errors in parenthesis.
23
Thus, the explanatory variables can account for much of the remaining variation.
As discussed in Subsection 3.4 the data separates local government expenditures into
several categories, only one of which, spending on public welfare, is targeted to a specific
group—in this case the poor. Proposition 4 predicts that if tax rates increase with the
proportion black, so should per capita spending on the poor.
Table 3 estimates (6) with per capita public welfare expenditures as the dependent variable.18 The deficiency of this regression as a test of the proposed theory should be noted.
Public welfare spending is only one type of spending that may be preferred by the poor. Thus,
increases in public welfare spending may be accompanied by decreases in, for example, police protection for the poor, which the data does not measure. Regardless, per capita public
welfare spending increases with the proportion black, in accordance with Proposition 4.
5.3
Cross-Sectional Analysis
As a first check on the robustness of the panel results the linear specification
τ̂c = α + β1 λB
c + β2 y c + β3
yB
c
+ χ(controlsc ) + c
yc
(7)
is estimated in 1960, 1967 and 1972, where c denotes a city. The results are presented in
Table 4. These years are chosen because a control for education (the percent of the city with
at least four years of college) is available for these years. Analyses of other available cross
sections are substantively similar.19
The results of the cross-sectional analysis are once again supportive of the cross-cutting
cleavages model. In the cases where the coefficients on the variables of interest are statistically significant, a one-standard deviation in each of the independent variables is associated
18
The reduced sample size is due to the fact that local public welfare spending is not reported by the
Census Bureau for all years.
19
That is to say that two of the variables of interest have significant coefficients in the expected direction
while the coefficient on the third variable of interest is insignificant. The p-value on the coefficient for average
income βy in Column 2 of Table 4 is 0.13.
24
Table 3: Local Public Welfare Spending
Dependent Variable:
Per-Capita Public
Welfare Spending (σ P )
Proportion Black
376∗∗∗
(127)
300∗∗∗
(115)
Average Income
58.2
(37.3)
27.5
(34.1)
Economic Parity
-21.9
(20.4)
-25.0
(21.3)
Median to Average
Income Ratio
-95.8
(78.8)
Population in School
-14.8
(16.7)
Population
-4.22
(4.35)
City Employees
406∗∗∗
(113)
Senior
158
(261)
Constant
-568
(356)
-228
(343)
R2
n (city × year)
0.601
675
0.720
662
Notes: ∗∗∗ ,∗∗ ,∗ denotes statistical significance at the
1%, 5% and 10% levels, respectively. All columns
contain year and city fixed effects. White (1980)
heteroskedastictic-consistent standard errors in
parenthesis.
25
Table 4: Cross-sectional Results
Dependent Variable: Tax Rate (τ̂ )
1960
1967
1972
Proportion Black
0.64
(0.68)
0.50
(0.71)
2.39∗∗
(0.99)
2.23∗∗
(0.90)
2.21∗∗
(1.01)
1.86∗∗
(0.89)
Average Income
-1.55∗∗
(0.61)
-1.08
(0.70)
-0.24
(0.84)
0.47
(0.88)
-0.48
(0.87)
0.02
(0.83)
Economic Parity
2.50∗∗∗
(0.41)
2.50∗∗∗
(0.51)
3.72∗∗∗
(0.80)
4.13∗∗∗
(1.01)
2.54∗∗∗
(0.81)
2.62∗∗∗
(0.80)
Median to Average
Income Ratio
-1.92
(1.49)
-2.22
(1.83)
-1.06
(1.93)
Population in School
-0.57
(0.64)
-0.53
(1.08)
0.27
(1.03)
College
-1.27
(3.22)
0.09
(3.84)
0.47
(2.69)
Population
0.06
(0.12)
0.03
(0.25)
-0.20
(0.25)
City Employees
2.29∗∗
(0.96)
2.47∗∗
(1.21)
5.40∗∗∗
(1.70)
Proportion Senior
1.22
(2.44)
0.19
(2.74)
2.87
(3.65)
Constant
14.32∗∗∗
(6.02)
11.46∗
(6.35)
0.95
(8.39)
-4.29
(8.14)
4.28
(8.75)
-0.16
7.82
R2
n (cities)
0.328
122
0.468
122
0.267
131
0.431
131
0.174
141
0.403
141
Notes: ∗∗∗ ,∗∗ ,∗ denotes statistical significance at the 1%, 5% and 10% levels, respectively.
White (1980) heteroskedastictic-consistent standard errors in parenthesis.
26
with a one-third to one-half standard deviation change in the tax rate.
5.4
Turnout Patterns across Race and Class
The pattern of empirical findings and Proposition 2 imply an additional testable result of
the cross-cutting cleavages model. Specifically, tax rates rose with the proportion black, so
Propostion 2 predicts (since it is an if and only if statement) that the difference in political
sensitivity between races should be larger for the rich than for the poor. Turnout data can
thus be used to try to falsify the theory. The two separate analysis of turnout data in this
subsection fail to do so.
The American National Election Study (ANES) asks approximately 1,000 U.S. citizens
every other year whether or not they voted. The ANES also provides data on a respondent’s
race and rough data on where a respondent is in the country-wide income distribution. Panel
A of Table 5 classifies any respondent with income in the top third of the distribution as
rich.20 A respondent’s report of whether or not he or she voted is regressed on an indicator
for race, an indicator for whether the respondent was classified as rich, and the product of
these indicators. The condition in Propostion 2 requires the coefficient on the product of
the indicators, Black × Rich, to have a negative sign. While this is the case across all four
columns, in none of the columns is the coefficient statistically significant.
The first column of Panel A reports regression results for all urban respondents. Columns
2 and 4 restrict the sample to years with no presidential election. Columns 3 and 4 restrict
the sample to respondents in the top third or bottom third of the income distribution.
This later sample selection is made to draw a starker contrast between the rich and other
respondents. The data presented in the first panel do not falsify the theory, although there
are severe data limitations: in the first column only 219 black respondents are classified as
rich.21
20
Specifically, the data describes whether the respondent’s income was between the 0-16 percentile, 16-33
percentile, 33-66 percentile, 66-95 percentile or 95-99 percentile of the income distribution. Given the sparse
data, there is no flexibility in this cutoff.
21
It is well known that ANES respondents often report that they have voted when in fact they have not.
27
Table 5: Voter Turnout Patterns Match those required by Proposition 2
Panel A: ANES Turnout Data
Dependent Variable: Did Respondent Vote?
Rich and Very Poor
Respondents Only
offyear
only
offyear
only
Indicator for Black
−0.05∗∗
(0.02)
−0.09∗∗∗
(0.03)
-0.02
(0.03)
-0.06
(0.04)
Indicator for Rich
0.15∗∗∗
(0.02)
0.14∗∗∗
(0.02)
0.20∗∗∗
(0.02)
0.20∗∗∗
(0.03)
Black × Rich
-0.02
(0.04)
-0.00
(0.06)
-0.04
(0.04)
-0.02
(0.07)
R2
n (respondents)
0.135
6296
0.157
2879
0.195
3862
0.228
1743
Panel B: ROAD Turnout Data
Dependent Variable: MCD Group Turnout
Non-Homogenous
Areas Only
offyear
only
offyear
only
Proportion Black
-0.04
(0.03)
-0.06
(0.05)
0.01
(0.04)
0.03
(0.05)
Proportion Black ×
Average Black Income
0.68
(3.14)
1.61
(4.84)
0.22
(2.85)
-3.68
(4.15)
Proportion White ×
Average White Income
4.46∗∗∗
(0.26)
3.43∗∗∗
(0.38)
4.60∗∗∗
(0.58)
3.29∗∗∗
(0.87)
R2
n (MCD Group × year)
0.439
4257
0.186
2239
0.589
1177
0.357
582
Notes: ∗∗∗ ,∗∗ ,∗ denotes statistical significance at the 1%, 5% and 10% levels,
respectively. All regressions include state × year fixed effects.
White (1980) heteroskedastictic-consistent standard errors in parenthesis.
28
Panel B of Table 5 presents a second attempt to falsify the theory. Data from the Record
of American Democracy (ROAD) (King et al., 1997) is used in ecological regressions to
examine the effects of race and income on aggregate turnout in Minor Civil Division groups
(MCD Group - a level of data aggregation unique to this dataset) from 1986-1990.22
Turnout πmt is regressed on the proportion black λB the proportion black times average
black income λB y B and the proportion white times average white income λW y W . Panel B
estimates the specification
B B
W W
π mt = α + β1 λB
mt + β2 λmt y mt + β3 λmt y mt + θst + mt ,
(8)
where π is the observed turnout in MCD Group m at time t. θst is a state-year fixed effect,
introduced to control for turnout shocks due to particularly competitive statewide elections.
The partial derivative of the observed turnout with respect to the proportion of the city
B
that is black times average black income λB
mt y mt is β2 . In the cross-cutting cleavages model,
P
turnout is given by π = ij λij π ij . The derivative with respect to λB y B , keeping constant
λB and λW y W is given by:
dπ dλB y B λB ,
=
λW y W
π RB − π P B
yR − yP
thus
π RB − π P B
β2
=
RW
P
W
π
−π
β3
The point estimates of the coefficient on proportion black times average black income β2
are statistically indistinguishable from zero, so once again the condition in Proposition 2 is
satisfied. However, β2 is not statistically different from β3 , the coefficient on the proportion
white times average white income. Once again the analysis does not falsify the theory.
Sigelman (1982) finds that the tendency to over-report is stronger for blacks than for whites, and Hill and
Hurley (1984) finds that wealthier blacks are more likely to over-report than poor blacks or wealthier whites.
These patterns would strengthen the results of the analysis in Panel A of Table 5.
22
While it would be preferable to have data from the period under study, this data is the only easily
available dataset that is matched with demographic data at a level lower than congressional districts. For a
brief description of the data in ROAD see King and Palmquist (1997). It is important to note both that the
analysis of ROAD data uses OLS regressions and does not use the ecological inference techniques of King
(1997), and that ecological regressions generally suffer from aggregation bias which may bias results either
up or down.
29
Columns 3 and 4 of Panel B attempt to produce more precise estimates by eliminating MCD
Groups where less than five percent of the population is black or less than five percent of
the population is white, but this has little effect.23
Overall, the data are supportive of the cross-cutting cleavages model. The patterns in
taxation and spending data are consistent with the theory. Moreover, the taxation data
implies a specific prediction about the relative values of political sensitivity for each classrace group. Turnout data does not falsify this prediction.
5.5
Empirical Robustness
The large demographic changes in U.S. cities during the period under study were accompanied by large political and social changes, especially in the South. This subsection examines
two possible ways in which these changes may bias the results in Table 2.
In the cross-cutting cleavages model a decrease in the supression of black turnout increases
their political sensitivity, and leads to an increase in the equilibrium tax rate because blacks
are on average poorer than whites. If a decrease in the political repression of blacks were
correlated with one of the variables of interest, we might be observing the effects of this
decrease rather than the effects of demographic changes. For example, it might be easy to
suppress black voter turnout if blacks are a small proportion of the population, but impossible
when they are a large proportion of the population. This would bias the coefficient on the
proportion black upwards.24
Using data from the ANES, Table 6 examines the ratio of the average turnout of blacks
to average turnout
πB
π
across states and time. Because there are very few respondents in
each state for a given year, ten years worth of data from the ANES are used to estimate a
23
The exception is Column 3 where the p-value on a Wald (1943) test that β2 6= β3 is 0.14.
Oberholzer-Gee and Waldfogel (2005), in a study of political behavior in the late 1990s, find that
minority turnout increases with the size of the local minority population as the result of changes in media
structure. Leighley (2001), using ANES data, finds little evidence of rising black turnout with the proportion
of a community that is black. The racial threat hypothesis (Key, 1949) would predict that relative black
voter turnout decreases when the proportion black increases. If this hypothesis is correct, it would bias the
coefficient on proportion black downwards and hence is not of particular concern.
24
30
single state-decade observation of relative turnout. These estimates are then regressed on
demographic data from the decennial census.25 Panel A of Table 6 creates these state-decade
observations using all respondents in a state, whereas Panel B uses only urban respondents.
Table 6 shows that of the three variables of interest, only economic parity is robustly
correlated with relative black turnout. Because rich blacks are more politically sensitive than
poor blacks, an increase in economic parity is associated with an increase in the relative
political sensitivity of blacks in the cross-cutting cleavages model. Panel B confirms this
pattern for urban respondents, although the standard errors are somewhat larger because
the Census Bureau and the ANES, which supply the right and left-hand side variables
respectively, use different definitions of what constitutes an urban area.26
Even if relative black turnout were correlated with one of the variables of interest, if
black political sensitivity were increasing in a relatively uniform way across the country, the
effect of this increase would be controlled for by the year fixed effects in (6). However, it is
likely that that the relative political sensitivity of blacks increased at different rates in the
South as compared with the rest of the country. Year by south fixed effects are added to
the specification in (6) in Columns 1 and 4 of Table 2 to control for this possibility. The
inclusion of these fixed effects do not affect the results in Table 2. Columns 2 and 5 take this
approach one step further by including census division by year fixed effects.27 This reduces
the coefficient on economic parity by half as economic parity is highly correlated with the
fixed effects, but the other coefficients on the variables of interest are robust.
Finally, states that border Mexico have historically had larger Hispanic populations and
the different racial dynamics created by this population may affect the local tax rate. To
control for this Columns 3 and 6 drop data from the states that border Mexico: California, New Mexico, Arizona and Texas. Dropping these states does not affect the results in
25
The ANES does not identify a respondent’s location until 1956. The sample period is from 1956-1984
to increase the amount of data. Results are very similar if we omit data from 1976-1984.
26
The second panel has fewer observations because the U.S. Census dataset (PUMS) dataset does not
identify urban vs. rural respondents in states with less than 250,000 urban or rural residents.
27
There are nine census divisions in the U.S. each containing 4-6 states in close proximity to one another.
31
Table 6: Relative Voter Turnout of Blacks Increases as Relative Black Income Increases
Dependent Variable:
Ratio of Black Turnout to Overall Turnout
all
states
1960
and
1970
southern
states
nonsouthern
states
all
states
nonsouthern
states
Panel A: All Respondents
Economic Parity
1.46∗∗∗
(0.48)
1.37∗∗∗
(0.51)
2.24∗
(1.20)
2.29∗∗
(0.97)
2.66∗∗∗
(0.93)
3.51∗∗∗
(1.24)
Proportion Black
-0.03
(0.31)
-0.20
(0.41)
-0.91∗
(0.51)
1.56
(1.70)
-4.98∗∗∗
(1.64)
-4.64
(11.6)
Average Income
0.01
(0.08)
0.13
(0.15)
0.00
(0.16)
-0.07
(0.12)
-1.11
(1.29)
-2.22
(2.36)
State and Year
Fixed Effects
No
No
No
No
Yes
Yes
0.131
93
0.203
93
0.306
45
0.132
48
0.579
93
0.565
48
R2
n (state × decade)
Panel B: Urban Respondents Only
Economic Parity
1.06∗
(0.62)
1.08
(0.72)
1.99
(1.56)
2.55∗
(1.31)
2.68
(1.91)
4.45∗
(2.27)
Black
0.10
(0.34)
0.22
(0.52)
-0.54
(0.80)
0.73
(1.42)
-4.50∗∗
(1.76)
-4.82
(9.66)
Average Income
0.01
(0.07)
0.09
(0.20)
-0.08
(0.16)
-0.11
(0.12)
-1.31
(-2.29)
2.65
(3.30)
State and Year
Fixed Effects
No
No
No
No
Yes
Yes
0.083
71
0.088
49
0.115
34
0.156
37
0.499
71
0.541
37
R2
n (state × decade)
Notes: ∗∗∗ ,∗∗ ,∗ denotes statistical significance at the 1%, 5% and 10% levels, respectively.
White (1980) heteroskedastictic-consistent standard errors in parenthesis.
32
Table 7: Robustness Checks
Dependent Variable:
Tax Rate (τ̂ )
Tax Revenue
per capita (τ y)
Proportion Black
1.62∗∗∗
(0.54)
2.41∗∗∗
(0.62)
1.75∗∗∗
(0.52)
429∗∗∗
(121)
580∗∗∗
(138)
335∗∗∗
(117)
Average Income
-0.81∗∗∗
(0.29)
-0.86∗∗
(0.34)
-0.85∗∗∗
(0.35)
57.2
(60.8)
58.5
(75.1)
-48.7
(76.0)
Economic Parity
0.36∗∗∗
(0.17)
0.15
(0.18)
0.37∗∗
(0.17)
73.9∗∗
(31.7)
41.7
(30.9)
83.5∗∗
(36.6)
Constant
6.57∗∗
(2.45)
6.47∗∗
(3.19)
6.80∗∗∗
(3.39)
-680
(566)
-1010
(701)
156
(731)
North / South ×
Year Fixed Effects
Yes
No
No
Yes
No
No
Division ×
Year Fixed Effects
No
Yes
No
No
Yes
No
Year Fixed Effects
No
No
Yes
No
No
Yes
Border States
Omitted
No
No
Yes
No
No
Yes
R2
n (city × year)
0.902
828
0.920
828
0.894
682
0.871
828
0.895
828
0.852
682
Notes: ∗∗∗ ,∗∗ ,∗ denotes statistical significance at the 1%, 5% and 10% levels,
respectively. White (1980) heteroskedastictic-consistent standard errors in parenthesis.
All columns include city fixed effects.
Tabel 2 and shows that any potential bias introduced by the inability to control for Hispanic
population due to data limitations in the sample period is small.28
6
Conclusion
Canonical political economy models of government taxation and spending focus on the conflict between the rich and the poor over redistribution. This paper adds race to this equation.
However, it focuses on the consequences of the empirical fact that blacks and whites exhibit
28
Other robustness checks that do not substantively alter the results include splitting the sample around
the median population, dropping any year from the data, changing the units of measurement of many of the
control variables and splitting the sample into south/non-south samples.
33
different levels of political sensitivity, rather than the consequences of speculative differences
between races in preferences.
Considering race and class together allows me to formalize an old concept from political
science—that of cross-cutting cleavages—and examine its impact on the taxation and spending decisions of local governments. Specifically, the degree to which race and class cross-cut
each other exhibits a non-monotonic relationship with taxation and spending levels. This
non-monotonic relationship is mediated by economic parity—the degree to which different
races have similar distributions of income.
The model produces six predictions in total. All of these predictions are consistent with
correlations in the data from large U.S. cities between 1942 and 1972. In sum, adding
race and focusing on political sensitivity allows us to understand a richer set of patterns of
government taxation and spending decisions.
34
Appendix A
Theoretical Derivation and Proofs
There are two candidates c ∈ {1, 2} who seek to maximize their own vote share. Candidates
propose binding platforms that consist of a tax rate, τ c , and a level of government spending,
P
g c , subject to a budget balancing constraint: g c ≤ ij λij τ c y i = τ c y.
Following the terminology in Grossman and Helpman (2001, Chapter 3), in addition
to the positions candidates take on the pliable issue of spending, there are other issues,
such as charisma or a reputation for pursuing non-economic race related policies on which
candidates have fixed positions. A citizen from class-race group ij turns out to vote with
exogenously given probability π ij . Of the citizens who turn out to vote from class-race
group ij a proportion 1 − ξ ij is exogenously committed to voting for one candidate or the
other based on the fixed positions of the candidates. The remaining citizens that vote and
would consider voting for either candidate receive an extra utility for candidate 1 of x,
where x is the realization of a random variable drawn independently for each citizen from
a cumulative distribution function F (x).29 Each group varies in the relative prominence of
fixed versus pliable issues, with ζ ij indexing the prominence a member of class-race group
ij puts on pliable issues. A citizen in class-race group ij votes for candidate 1 if and only if
x + ζ ij U ij (τ 1 , g 1 ) ≥ ζ ij U ij (τ 2 , g 2 ), that is, if x ≤ ζ ij (U ij (τ 1 , g 1 ) − U ij (τ 2 , g 2 )).
The vote share S 1 for candidate 1 is given by
S1 =
X
λij π ij (1 − ξ ij )φij + ξ ij F (ζ ij (U ij (τ 1 , g 1 ) − U ij (τ 2 , g 2 ))) ,
(A.1)
ij
where φij is the proportion of exogenously committed voters in class-race group ij who vote
for candidate 1. The vote share of candidate 2 is given by an analogous expression so a Nash
Equilibrium in pure strategies where both candidates propose the same platform exists.
To ensure the existence of a symmetric equilibrium the probability density function, f (x) = F 0 (x), is
assumed to be symmetric about zero. For the necessary second-order conditions to hold F (x) cannot change
too quickly around zero. I follow the rest of the literature and assume that the second-order conditions hold.
For a discussion, see Acemoglu and Robinson (2006, Chapter 12).
29
Appendicies–1
In (A.1) the first term inside the brackets is constant, and in equilibrium candidate 1
takes the platform of candidate 2 as given. Thus the first-order conditions of each candidate’s
maximization problem are the same as the first-order conditions of the following problem:
max
τ,g
max
τ,g
X
λij ψ ij U ij (τ, g) s.t. g ≤ τ y
ij
X
i
ψ λi U i (τ, g) s.t. g = τ y
(A.2)
i∈{R,P }
i
where ψ ij = π ij ξ ij ζ ij > 0 is a class-race group’s political sensitivity, ψ =
λiB ψ iB +λiW ψ iW
λi
, and
i
ψ λi is a class’s political prominence. Each candidates’ Lagrangian L is given by:
L = (1 − τ )ŷ + ψ log(g) − γ (g − τ y) ,
R
P
R
(A.3)
P
where ŷ = ψ λR y R + ψ λP y P and ψ = ψ λR + ψ λP . The first order conditions yield
dL
= −ŷ + γy = 0
dτ
and
dL
ψ
= − γ = 0.
dg
g
taken together with the budget constraint, g∗ = τ∗ y, the equilibrium level of government
spending, g∗ , and tax rate, τ∗ , are given by:
g∗ =
ψy
ŷ
and
τ∗ =
ψ
ŷ
(A.4)
As noted in Section 2, the equilibrium tax rate and per capita tax revenue is re-written
P
B
in terms of ij λij , y, λB and yy , and partial derivatives are taken with respect to these last
~ and letting ~λ vary. This is equivalent to changing
three variables holding constant ~y and ψ
P
B
from the ~λ basis into another basis ~b = { ij λij , y, λB , yy } and taking partial derivatives
in this latter basis. Taking derivatives in the ~λ basis in the direction of a particular basis
vector in ~b makes the algebra more tractable. For the proofs, the equilibrium tax rate will
be written as τ∗ (~λ) and the equilibrium level of per-captia tax revenue will be written as
Appendicies–2
g∗ (~λ) = τ∗ (~λ)y to remind the reader that derivatives are being taken in the ~λ basis.
Formally, this is accomplished through the use of a directional derivative in the ~λ basis:
D~l τ∗ (~λ) = (∇τ∗ (~λ)) · ~l, where ~l is the demographic change—the direction of the derivative
in the ~λ basis.30 The function ~q(·) : ~b → R4 maps from the element of the basis b that is
changing and the demographic change in ~λ.
Lemma 1 For any arbitrary demographic change ~l, changes in the equilibrium tax rate are
P
in the same direction as changes in the relative political prominence of the poor
P
D~l τ∗ (~λ) ≥ 0
if and only if
D~l
ψ λP
R
ψ λP
R
ψ λR
!
≥0
ψ λR
Proof. Because ~l involves changes only to the proportions of the class-race groups ij:
P
D~l
ψ λP
R
!
=
ψ λR
1
R
(ψ λR )2
h R
i
P
P
R
ψ λR D~l (ψ λP ) − ψ λP D~l (ψ λR )
(A.5)
and
ψ
1 = 2 ŷD~l ψ − ψD~l ŷ
ŷ
ŷ
i
1 h R R R
P P P
R
P
R
P
R
P
= 2 (ψ λ y + ψ λ y ) D~l (ψ λR ) + D~l (ψ λP ) − (ψ λR + ψ λP ) D~l (ψ λR )y R + D~l (ψ λP )y P
ŷ
D~l τ∗ (~λ) = D~l
=
i
yR − yP h R R
P P
P P
R R
ψ
λ
D
λ
)
−
ψ
λ
D
λ
)
(ψ
(ψ
~l
~l
ŷ 2
(A.6)
the terms outside the brackets in (A.5) and (A.6) are positive, thus (A.5) is positive if and
only if (A.6) is.
Proposition 1 An increase in average income, holding constant the proportion black and
economic parity, decreases the equilibrium tax rate: Dq~(y) τ∗ (~λ) < 0.
30
Note that, for example,
∂τ∗ (~
λ)
∂λRW
= D~l τ∗ (λ) when ~l = {1, 0, 0, 0}.
Appendicies–3
yB
y
Proof. Holding λB and
constant while varying y gives four restrictions:
Dq~(y) λB = Dq~(y) λRB + Dq~(y) λP B = 0
Dq~(y y = Dq~(y) λRW + Dq~(y) λRB y R + Dq~(y) λP W + Dq~(y)
B
Dq~(y) yy
=
1
y
h
1
λB
RB R
Dq~(y) λ
y + Dq~(y) λ
PB P
y
−
i
B
y
y














PB
P

λ
y =1 



=0
Dq~(y) (~1 · ~λ) = Dq~(y) λRW + Dq~(y) λRB + Dq~(y) λP W + Dq~(y) λP B = 0
So ~q(y) =
n
B B
W yW
λB y B
λW y W
, λ y , − y(yλ R −y
P ) , − y(y R −y P )
y(y R −y P ) y(y R −y P )


















⇒

λW y W


Dq~(y) λRW = y(y
R −y P )











B B

y

Dq~(y) λRB = y(yλR −y

P)






λW y W

Dq~(y) λP W = − y(y

R −y P )










B B

y
PB
 D
= − y(yλR −y
P)
q
~(y) λ
o
. Substituting:
i
1 h R R W W PW
yB
P P
B B PB
W W RW
B B RB
Dq~(y) τ∗ (y, λ , ) = − 2 ψ λ (λ y ψ
+ λ y ψ ) + ψ λ (λ y ψ
+λ y ψ ) <0
y
ŷ y
B
Corollary 1 An increase in average income, holding constant the proportion black and economic parity, has an indeterminate effect on equilibrium per capita tax revenue.
Proof. Defining ∆W = ψ RW − ψ P W and ∆B = ψ RB − ψ P B then
Dq~(y)
i
1 h R R R RW W
P P P
RB B
PW W
PB B
g∗ = 2 ψ λ y (λ ∆ + λ ∆ ) − ψ λ y (λ ∆ + λ ∆ )
ŷ
Set y R = y P = y ≥ 1 and ∆W = ∆B = ∆ then the expression becomes:
i
d(τ y)
y∆ h R R 2
P P2
= 2 ψ λ −ψ λ
dy
ŷ
(A.7)
Now set λRW = 0.15, λRB = 0.05, λP W = 0.6, λP B = 0.2 and ψ RW = 1, ψ RB = ψ P W = 0.8,
ψ P B = 0.6. Then the term in brackets is equal to −0.034. Now, if ψ RW = 1, ψ RB = ψ P W =
0.6, ψ P B = 0.2, the term in brackets is equal to 0.02. Because the expression is continuous,
the sign of these examples would hold even if y R were slightly larger than y P .
Appendicies–4
Proposition 2 An increase in the proportion of the city that is black, holding constant
average income and economic parity, depends on the relative difference in political sensitivity
between races across classes,
ψ P W −ψ P B
.
ψ RW −ψ RB
In particular, the tax rate increases if and only if:
ψP W − ψP B
<Q
ψ RW − ψ RB
P
where Q =
ψ λP λRB
.
R
ψ λR λP B
Proof. Holding constant y and
B
RB
Dq~(λB ) λ = Dq~(λB ) λ
yB
y
PB
+ Dq~(λB ) λ
while varying λB gives four restrictions
=1
Dq~(λB ) y = Dq~(λB ) λRW + Dq~(λB ) λRB y R + Dq~(λB ) λP W + Dq~(λB )
Dq~(y)
yB
y
=
1
h
λB y
Dq~(y) λRB −
RB
λ
λB
y R + Dq~(y) λP B −
PB
λ
λB















λP B y P = 0 



i
yP = 0
Dq~(λB ) (~1 · ~λ) = Dq~(λB ) λRW + Dq~(λB ) λRB + Dq~(λB ) λP W + Dq~(λB ) λP B = 0


















⇒

RB


Dq~(λB ) λRW = − λλB











RB


D B λRB = λλB


 q~(λ )



PB


Dq~(λB ) λP W = − λλB












 D B λP B = λP B
q
~(λ )
λB
n RB RB
o
λ
λ
λP B λP B
So ~q(λ ) = − λB , λB , − λB , λB . Substituting:
B
Dq~(λB ) τ∗ (y, λB ,
i
y R − y P h P P RB RW
yB
R R PB
RB
PW
PB
)=
ψ
λ
λ
(ψ
−
ψ
)
−
ψ
λ
λ
(ψ
−
ψ
)
(A.8)
y
λB ŷ 2
This derivative is positive if the and only if the term in brackets is positive. This occurs if
and only if:
P
ψP W − ψP B
ψ λP λRB
<
R
ψ RW − ψ RB
ψ λR λP B
Proposition 3 An increase in economic parity, holding constant the proportion black and
average income, increases the equilibrium tax rate: Dq~“ yB ” τ∗ (~λ) > 0.
y
Appendicies–5
Proof. The three conditions Dq~“ yB ” λB = Dq~“ yB ” y = Dq~“ yB ” (~1·~λ) = 0 imply Dq~“ yB ” λRB =
y
y
y
y
−Dq~“ yB ” λRW = Dq~“ yB ” λP W = −Dq~“ yB ” λP B . Substituting:
y
y
Dq~“ yB ”
y
y
i
(y R − y P ) “ ” RB h R R P
yB
P P R
τ∗ (y, λ , ) =
Dq~ yB λ
ψ λ ∆ +ψ λ ∆
y
ŷ 2
y
B
To sign this expression use the constraint Dq~“ yB ”
y
Dq~“ yB ”
y
yB
y
Dq~“ yB ” λRB
y
yB
y
=1
1
RB R
PB P
“
”
“
”
=
Dq~ yB λ y + Dq~ yB λ y
=1
yλB
y
y
yλB
= R
>0
y − yP
B
so Dq~“ yB ” τ∗ (y, λB , yy ) > 0.
y
Corollary 2 A change in the proportion black or in economic parity, keeping the other two
variables of interest fixed, leads to changes in the equilibrium level of per capita tax revenue
that are in the same direction as changes in the equilibrium tax rate.
B
Proof. The equilibrium level of tax revenue per capita is equal to τ∗ (y, λB , yy )y. For
some demographic shift ~l, the change in tax revenue per capita is equal to D~l (τ∗ y) =
B
B
D~l τ∗ (y, λB , yy )y + τ∗ (y, λB , yy )D~l y. If y is constant than the second term is zero, and the
change in tax revenue is in the same direction as the change in the tax rate. Since changes
in λB and
yB
y
implicitly hold y constant, the change in per capita tax revenue with these
variables will be in the same direction as the change in the tax rate.
Proposition 4 An increase in the proportion black, holding constant average income and
economic parity, will increase per capita spending on the poor if and only if the equilibrium
Appendicies–6
tax rate increases:
Dq~(λB ) σ∗P ≥ 0
Dq~(λB ) τ∗ (y, λB ,
⇐⇒
yB
)≥0
y
Proof. Taking first order conditions of the candidate’s Lagrangian with citizen utility as
given by (2) yields σ∗P =
P
ψ λP y
.
ŷ
Thus:
i
yh
P
P
ŷ Dq~(λB ) (ψ λP ) − ψ λP Dq~(λB ) ŷ
ŷ
i
y R y h P P RB RW
R R PB
RB
PW
PB
=
ψ
λ
λ
(ψ
−
ψ
)
−
ψ
λ
λ
(ψ
−
ψ
)
λB ŷ 2
Dq~(λB ) σ∗P =
The term in brackets is the same as the term in brackets in (A.8), so per capita spending on
the poor increases with the proportion black if and only if the tax rate increases as well. Robustness Result 1 Propositions 1, 2 and 3 hold if citizen utility is given by (4).
Proof. Setting up and solving the candidate’s maximization problem yields:
k
σ =
from the budget constraint τ∗ y =
P
k
y
P
ij
λij ψ ij αijk
ŷ
σ k , that is:
K
1 X X ij ij ijk 1 X ij ij ψ
λ ψ α =
λ ψ =
τ∗ =
ŷ k=1 ij
ŷ ij
ŷ
where the first equality comes from the fact that each group has the same relative tradeoff
P
ijk
between consumption and government spending, K
= 1, and other equalities are by
k=1 α
definition. This is the same expression for the equilibrium tax rate as in (A.4), and thus all
previous results continue to hold.
Appendicies–7
B
For the next robustness result, define ~b0 = {y, yy } and the function q~0 : ~b0 → R2 as the
map between a change in the element of ~b0 and the changes in ~y . Since the robustness result
examines changes in income levels, denote the equilibrium tax rate here as τ∗ (~y ).
Robustness Result 2 An increase in average income through changes in ~y , holding economic parity constant, leads to a decrease in the equilibrium tax rate: Dq~0 (y) τ∗ (~y ) < 0. An
increase in economic parity through changes in ~y , holding average income constant, leads to
an increase in the equilibrium tax rate if and only if average black income is less than average
yB < y
⇐⇒
income: Dq~0 ( yB ) τ∗ (~y ) > 0
y
Proof. Start with a ceteris paribus change in y. There are two constraints:
R
R
P






P
Dq~0 (y) y = λ Dq~0 (y) y + λ Dq~0 (y) y = 1
B
Dq~0 (y) yy
Since
dτ∗
dy
=
1
λB y
h
λRB Dq~0 (y) y R + λP B Dq~0 (y) y P −
1
λB
= − ŷψ2 dŷ
and
dy
dŷ
dy
= ŷy ,
dτ∗
dy
Dq~0
”
B
y
y
R
y = λ Dq~0
B
Dq~0 “ yB ” yy
y
Once again
“
”
B
y
y
R
P
y + λ Dq~0
“
y
y
”
B
y
y
yB
.
y
dτ∗
dy
⇒




 D ~0 y P =
q (y)
yP
y
There are two constraints:







P
y =0
1
R
P
B
P
RB
= λB y λ Dq~0 “ yB ” y + λ Dq~0 “ yB ” y = 1
y




=0 
yR
y
= − τy∗ < 0.
Next consider a ceteris paribus change in
“
i
B



D ~0 y R =


 q (y)
y






⇒

B P


Dq~0 “ yB ” y R = − λR λPyλB −λλ P λRB



y






 Dq~0 “ yB ” y P =
y
yλB λR
λR λP B −λP λRB
dŷ
= − ŷψ2 dy
, and
P
Dq~0
“
”
B
y
y
R
yλR λP λB (ψ − ψ )
ŷ =
λR λP B − λP λRB
The numerator is negative, and the denominator is positive if and only if y > y B , so
if and only if y > y B .
dτ∗
dy
>0
Appendicies–8
Appendix B
Data
Tables B.1 and B.2 contain summaries of the data used in this paper.
Table B.1: Definitions of Variables
Variable
Symbol
Description
Dependent Variables
Tax Rate
τ̂
Tax rate in percent
Public Welfare
σ̂ P
Public welfare spending per capita
(in 1980 dollars)
Tax Revenue
per capita
τy
Tax revenue divided by population
(in 1980 dollars)
Independent Variables
Proportion Black
λB
Average Income
y
Log of average income of families and
unrelated individuals (in 1980 dollars)
Economic
Parity
yB
y
Ratio of average income of black
families and unrelated individuals to city average
Proportion of the city that is black
Median to Avg.
Income Ratio
Ratio of median income to average income for
families and unrelated individuals
Population in School
Population in city schools (in 100,000s)
College
Proportion of city population over 25 with at least
four years of college
Population
City population (in 100,000s)
City Employees
Number of city employees (in 100,000s)
Proportion Senior
Proportion of city residents over 65 years old
Data for the variables public welfare, tax revenue, black, population in school, college,
population, city employees and proportion senior variables are from the 1944, 1949, 1952,
1956, 1962, 1967, 1972, 1977 and 1983 County and City Databook (CCDB) published by
the U.S. Census Bureau. These data sources are converted to electronic format by Haines
(2005). Tax revenue is used rather than government expenditures because the later includes
government transfers that are not determined by local government decisions.31
31
For the early years tax revenue and government expenditures are closely connected, but they begin to
Appendicies–9
Table B.2: Summary Statistics of Variables
Variable
Mean
Std.
Dev.
Min.
No. of
Max. Obs.
Units
Dependent Variables
Tax Rate
1.42
0.92
0.27
7.28
860
percent
Public Welfare
18.3
58.5
0.00
736
763
1980 dollars
per capita
Tax Revenue
213
160
29
1461
975
1980 dollars
per capita
Independent Variables
Proportion Black
0.15
0.13
0.00
0.72
975
Proportion
Average Income
9.62
0.29
8.61
10.4
860
Log 1980 dollars
Avg. Black to
Avg. Income Ratio
0.67
0.13
0.25
1.08
828
Ratio
Median to Average
Income Ratio
0.85
0.06
0.59
1.01
860
Ratio
Population in School
0.73
1.39
0.12
15.2
945
Hundred-thousands
College
0.11
0.05
0.03
0.49
556
Proportion
Population
3.94
8.05
1.00
78.9
975
Hundred-thousands
City Employees
0.06
0.22
0.00
3.75
1182
Hundred-thousands
Percent Senior
0.09
0.03
0.03
0.30
924
Proportion
Appendicies–10
Demographic data is obtained for the years 1940, 1950, 1960, 1970 and 1980, while local
government data, specifically tax revenue per capita and public welfare spending, is obtained
for the years 1942, 1948, 1950, 1955, 1960, 1965, 1967 and 1972. To match these observations,
demographic data is linearly interpolated between the decennial years. When the variable
of interest is a proportion, such as the proportion of a city over 65, the population and
the population over 65 are interpolated separately. Other interpolation schemes, such as
interpolating the ratios themselves produced similar results.
Income data for 1960, 1970 and 1980 is from the U.S. Census Bureau’s Census of the
Population, Volume 2: Characteristics of the Population (COP). The Census Bureau summarizes income data at three levels: for families, families and unrelated individuals and for
all individuals over the age of 14. The family level contains all groups of 2 or more people
who are related and living together. Thus, single workers who live on their own are not
included in statistics at this level. Data at the level of families and unrelated individuals
correct for this deficiency; households of one are included in these data. The final category,
individuals over the age of 14 is self explanatory. Unfortunately, data at this level treats
an unemployed woman who is married to a man making $10,000 dollars a year the same as
an unemployed woman married to a man making $1,000 a year. It is likely that the former
woman would have a level of political sensitivity commensurate with her status as a member
of a rich household, while the later would exhibit similar political behavior to other members
of the poor. Thus, all data used in this analysis is for families and unrelated individuals.32
In all cases data is for the city itself rather than the city’s SMSA.
Data from the COP were entered by hand, and several checks were performed to ensure
accuracy. I entered some data, such as median family income, number of families and
population that are available in the CCDB and the COP and checked that the data from
both sources matched. When there was a mismatch in a variable for a given city and year,
diverge starting in the late 1960s. The results are substantively similar if any given year is left out of the
data.
32
Results using data at the family level are substantively similar to those presented below.
Appendicies–11
I re-entered all data for that city in that year and checked again. Finally, I entered data for
a random 10% of the sample twice. Almost all errors were due to entering the data for the
entire city from the city in the column next to it in the census tables.
For 1950, the COP contains separate income data for blacks only in southern states.
For 1940, the COP does not report income data for cities with populations below 250,000.
Income data appears not to have been collected at all by the Census Bureau before 1940.
To obtain estimates of income data for 1940 and 1950, I calculated income for these cities
using the 1% sample of U.S. households that the Census Bureau makes available through
the Public Use Microdata Sample (PUMS). In these data a respondent’s city is reported only
if the city has more than 100,000 residents. These data are made available electronically by
IPUMS (Ruggles et al., 2004). I also used this data to calculate the proportion of a city that
is over 65 in 1940.
To ascertain the accuracy of this data, I estimated several variables using PUMS data
that are available in the CCDB. The results of regressions of the estimated values on the
actual values are reported in Table B.3. The estimated values are statistically different from
the actual values only in the case of population in 1940. This indicates that there is some
oversampling in cities in 1940, which is not of particular concern since the variables of interest
deal with proportions and income, which are estimated with very high accuracy. As another
measure of the accuracy of these data, the correlation between predicted and actual values
is very high - above 0.8 in all cases, and for 0.89-0.99 in most cases.
Unfortunately PUMS data does not identify the city of residence in years after 1950.
However, it should be noted that the results remain substantively similar when any year is
dropped from the study.
One data point calculated from the PUMS data seemed unreasonable—economic parity
from Salt Lake City, UT in 1950 was 1.42. I dropped all observations for Salt Lake City
before 1960. Additionally, this variable for Gary, IN and Flint, MI in 1960 gave very high
values (1.25 and 1.15 respectively) that seemed out of line with the 1970 data. It seemed
Appendicies–12
Table B.3: Accuracy and Unbiasedness of PUMS Estimates of Variables
Dependent Variable: Estimate form PUMS
1940
1950
1.067∗∗∗
(0.009)
0.998
1.015
(0.014)
0.993
Population
coef.
s.e.
ρ
Proportion
Senior
coef.
s.e.
ρ
Proportion
Male
coef.
s.e.
ρ
1.052
(0.094)
0.8011
Proportion
Black
coef.
s.e.
ρ
coef.
s.e.
ρ
1.002
(0.011)
0.996
Median Family
Income
1.017
(0.084)
0.813
Proportion of
coef.
Families with
s.e.
Income <$2000 ρ
n
0.994
(0.009)
0.997
1.017
(0.058)
0.894
0.964
(0.058)
0.887
71
77
Notes: Coefficients and standard errors from a
regression of actual variables from the CCDB on
estimated variables from PUMS. ∗∗∗ denotes
statistically different from one at the 1% level.
ρ is the first order correlation between the
estimated and actual values.
Appendicies–13
safest to drop these observations, although including them does not alter the results.
All dollar amounts are converted to 1980 dollars using the inflation calculator found
online on the U.S. Bureau of Labor Statistics website at: http://www.bls.gov/cpi/.
Hawaii is the only state in the sample where a significant proportion of the non-white
population is not black. Hawaii is dropped from the sample. To keep the sample within the
continental United States, Alaska is dropped as well, although this has almost no impact on
the results as this eliminates only a single data point: Anchorage in 1972.
Appendicies–14
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