A Comparative Analysis of Inequality and Redistribution in Democracies

Research Note

Abstract: We compare the relationship between inequality and redistribution over time as well as among clusters of developed and less developed countries, using a number of statistical models to address the complexity of the relationship. Despite producing a voluminous literature on the topic, few scholars acknowledge heterogeneity in the relationship across space and time or use data on government redistribution and income inequality that is comparable cross-nationally. Our study uncovers a positive, short-term association between inequality and redistribution, controlling for endogeneity between redistribution and market income inequality. Long term, inequality also increases redistribution in developed democracies, but appears to decrease it in a number of developing nations.

José Alemán Dwayne Woods*Associate Professor ProfessorPolitical Science Department Political Science DepartmentFordham University Purdue University441 East Fordham Road Bearing Hall 2238Bronx, NY 10458 West Lafayette, Ind. 47907718.817.3955 (765) 494-4161aleman@fordham.edu dwoods2@purdue.edu

*We would like to thank Oscar Torres-Reyna and Michelle Dion for their collaboration with one of the authors in the early stages of this project. We also acknowledge the help provided by Meshri Ettolba, Cyrus Samii, Torben Iversen, Philip Shaw, Nate Silver, Mathew Lebo, Federico Podestà, Hrishikesh D. Vinod, Justin Esarey and Nathan Kelly with various technical questions, as well as feedback from Idalia Bastiaens, Vincent Mahler, and Matthew Lebo. The usual disclaimers apply.

Inequality has risen to the forefront of academic and policy concerns. Publications like

Thomas Piketty’s (2014) Capital in the Twenty-First Century and Anthony B. Atkinson’s (2015)

Inequality: What Can Be Done? have contributed significantly to broadening interest in the

subject. Scholars and pundits alike argue about whether inequality explains regime change and

stability, the onset and duration of conflict (Boix 2003), low levels of economic growth (Forbes

2000), pressure on the welfare state (Ha 2012), and the politics of redistribution (Morgan and

Kelly 2013).

Interest in inequality appears in foundational social science contributions by Tocqueville,

Smith, and Marx. Scholars, however, have reached somewhat of an impasse in studying the

effects of inequality on redistribution. While median-voter theorists hold that as pre-tax and pre-

transfer (or market) inequality increases in society, redistribution of this income by the

government increases (Meltzer and Richard 1981; Boix, 2003; Acemoglu and Robinson, 2006),

some studies reveal a relationship that is the opposite of the one Meltzer and Richard expected: a

‘Robin Hood paradox’ in which countries with the highest levels of inequality are the least

redistributive – and those with more egalitarian distributions redistribute the most (Bradley,

Huber, Moller, Nielsen, and Stephens 2003; Lindert 2004, 15; Iversen 2005, 6; de Mello and

Tiongson 2006).

We reengage this debate by comparing the relationship between inequality and

redistribution from 1990 to 2015 both within and among fifty-eight democracies.1 We uncover a

positive, short-term association between inequality and redistribution, controlling for

endogeneity between redistribution and market income inequality. Long term, inequality also

increases redistribution in developed democracies but appears to decrease it in a number of

developing nations.

1 Dates for the analysis reflect the available data.

INEQUALITY AND REDISTRIBUTION: WHAT SORT OF RELATIONSHIP?

In the last four decades, two bodies of work have emerged that posit opposite

relationships between inequality and redistribution: the median-voter theorem and the fiscal-

contract approach. The median-voter theory (Meltzer and Richard 1981) claims that as the level

of pre-tax, pre-transfer inequality increases in society, more citizens become relatively

impoverished, which causes them to demand higher transfers from the government (Boix 2003,

23). The model of the political process Meltzer and Richard (1981) constructed builds from the

notion that competition for votes drives legislators to enact into law the tax rate that is favored by

the median voter.2 This rate reflects the difference between median and mean incomes, or

inequality in the distribution of market income in society.3

The median-voter approach expects that increases in market inequality will lead to

increased demand for redistributive transfers. That is, when inequality in market income

increases within countries, demand for redistribution subsequently increases (Schmidt-Catran

2 Median-voter theorists assume that individuals care mainly about their post-tax, post-transfer

income, and “[v]oters with income below the decisive voter choose candidates who favor higher

taxes and more redistribution; voters with income above the decisive voter desire lower taxes and

less redistribution” (Meltzer and Richard 1981, 924). Although the model initially characterized

a majoritarian two-party system, “the median-voter theorem also applies to unidimensional

models of legislative politics in multiparty systems.” (Iversen 2010, 186).

3 More precisely, voters pay the government the same proportion of their income in taxes, while

receiving from the government a lump sum payment that is the same for all taxpayers. As

inequality increases, so too does the government’s tax take and the amount it redistributes to

voters.

2016, 119). But the cross-sectional relationship implied by the median-voter theorem, that higher

(lower) levels of inequality also cause a higher (lower) prevalence of redistributive desires, is not

borne out by the data (Schmidt-Catran 2016, 119).

Scholars also probe the direct effect of inequality on redistribution. As previously

mentioned, some studies reveal a ‘Robin Hood paradox’ in which countries with the highest

levels of inequality are the least redistributive – and those with more egalitarian distributions

redistribute the most. Discrepancies among the different theories arise in part from the focus of

many studies: variation in the share of government spending devoted to social transfers as

opposed to income redistribution (Houle 2017, 3). In addition, indicators of market income

inequality also vary greatly in the empirical literature.4

The median-voter theory neglects, on the one hand, the insurance role of welfare transfers

and, on the other, possible endogeneity between redistribution and market inequality.5

4 Examples include the ratio of the mean to median income (Meltzer and Richard 1983); the ratio

between the average income of the third quintile and the average income of the whole population

(Larcinese 2007, 14); the share of income of the bottom half and the bottom quintile of the

distribution (Milanovic 2000); the share of income accruing to the third quintile (Bassett et al.

1999); the income of the third and fourth quintiles (Perotti 1996); the distance between the upper

and middle thirds of the income distribution (Lupu and Pontusson 2011), and Gini coefficients of

post-tax, post-transfer inequality.

5 Meltzer and Richard (1981, 924) hint at an endogenous relationship between the two variables

when they write: “[i]n recent years, the proportion of voters receiving social security has

increased, raising the number of voters favoring taxes on wage and salary income to finance

redistribution,” although they are quick to clarify that those receiving these benefits would want

someone else to pay for them.

Consideration of the insurance role of transfers adds several complications to the simple median-

voter model. First, different short- and long-run relationships may operate between inequality

and redistribution, leading to multiple equilibria across countries (Benabou 2000, 97). Second,

inequality in market incomes may be endogenous to redistribution, leading to “history dependent

social contracts” (Glaeser 2006; Benabou 2000, 110). For example, market activities will tend to

reflect incentives to save, invest, consume, and work. These may result in a distribution of

market income different from what we would expect under an alternative combination of social

policies (Jesuit and Mahler 2010; Saunders 210, 526).

The most developed of these arguments, known as the “fiscal-contract” approach, moves

away completely from the idea that governments coerce voters to pay taxes (as per the median-

voter theory). Instead, it treats taxation as a credible commitment game in which taxpayers trade

tax burdens for government services (Timmons 2005, 2010). This approach is compatible with

the idea that various “equilibria” can exist between inequality and redistribution: a highly

inegalitarian, low redistributive equilibrium, and a more egalitarian, highly redistributive one.

Why? In societies with high tax burdens, most taxpayers also receive government

transfers. In societies with low tax burdens, conversely, taxpayers receive few benefits while

transfer recipients pay little in taxes. As Beramendi and Rehm (2016) imply, the mechanism

linking inequality and redistribution long term thus resides in the design of the tax-and-transfer

system. Proportional or regressive tax systems make publics more favorably disposed to a large

welfare state; progressive ones, publics that see redistribution as a zero-sum proposition. This

explains the apparent paradox of low inequality and high redistribution in Scandinavian and

continental European welfare states, but high inequality and low redistribution in Anglo-

American ones.

Benabou (2000) does not provide statistical tests of his formal models, and Timmons’

analyses of the effects of inequality on various measures of central government revenue are

“inconsistent across years and dependent variables” (Timmons 2005, 562). The fiscal contract

theory, moreover, expects a negative relationship between levels of inequality and levels of

redistribution, but is less clear about the effects of short-term changes in the distribution of

market incomes.

Existing theories elide important concerns involving the design of social policies. Meltzer

and Richard (1981) for example base their model on a proportional tax system while others

explicitly allow for progressivity in the tax code (Benabou 2000, 103). Median-voter theorists

also assume that taxes and transfers only distort the economy, and cannot increase economic

growth. However, income redistribution can take the form of public goods that increase the

economy’s total factor productivity. While we do not embrace any particular assumption, we

raise the possibility that these considerations complicate the relationship between inequality and

redistribution.

SOME DESCRIPTIVE EVIDENCE

In this section, we explore some descriptive patterns regarding inequality and

redistribution using data from the Standardized World Income Inequality Dataset or SWIID (Solt

2016). SWIID includes comparable estimates of market and overall inequality for the broadest

possible range of countries. All observations belong to countries with a Polity IV score of six or

more, a commonly used threshold that distinguishes partial democracies and non-democracies

from fully democratic regimes (Marshall, Gurr, and Jaggers 2016).

We represent inequality in a given country-year using the Gini coefficient of pre-tax and

transfer income.6 Some (for example, Kenworthy and Pontusson 2005, 463) recommend using a

measure of absolute redistribution, or the difference between market and net Gini, since a

measure of relative redistribution can be affected by short-term trends in market income

inequality (Mahler 2010, 532). Others counter, however, that an increase in pre-tax and transfer

inequality that results in automatic stabilization in taxes and transfers will result in increased

absolute redistribution without policies actually changing (assuming proportional taxation and

flat rate benefits) (Huber and Stephens 2014, 252; Swank 2015, 24). Consequently, they

recommend a measure of relative redistribution – the reduction in the Gini coefficient due to

taxes and transfers as a ratio of this coefficient.

We sidestep this debate by relying on the measure that best fits a particular analysis. For

now, we simply plot in Figure 1 levels of relative redistribution as a function of levels of

inequality (left panel) and changes in relative redistribution as a function of changes in inequality

(right panel).7

Figure 1: Relationship between Inequality and Redistribution in Democracies, 1975-2015.

6 Version 5.1 of the dataset allows users to incorporate uncertainty in the estimation of these

indices into their modeling, a step that Solt enthusiastically recommends. The code to use

multiply imputed estimates in regression equations, however, only works with one of the models

that we estimate. As a result, for each country-year observation, we average the hundred

multiply-imputed values of market inequality and redistribution and use those in our analyses.

7 The patterns do not change if we plot instead levels and changes in absolute redistribution.

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Levels and Changes in Market Inequality

Note: The plot on the right uses transformations of the variables that account, within a given country, for deviations in units of measurement from the cluster means on the left. We calculated these quantities using the method described in Bartels (2015).

From Figure 1, it does appear as if increases over time within countries in market

inequality lead to increases in redistribution (r=0.523; p<0.000). But countries that engage in

higher levels of redistribution are those with lower levels of inequality (r=-0.152; p<0.000).

Further analysis reveals, in line with the fiscal contract approach, that levels of redistribution in

Liberal democracies are the lowest of the three developed country groupings.8 But levels of

market inequality are high in Nordic and Continental welfare states as well.9

ADDITIONAL DETERMINANTS OF REDISTRIBUTION

8 For developed countries, we rely on the classification in Hicks and Kenworthy (2003, 54), with

a few adjustments: following Huber and Stephens (2014), we classify Finland as Nordic/social

democratic rather than conservative/Continental, Switzerland as conservative/Continental as

opposed to liberal/Anglo-American, and Italy as Mediterranean. For less developed countries, we

rely on Rudra’s (2007) classification, except for Greece, which we classify as Mediterranean

rather than Productive (Ferrera 2010). Finally, we follow Cook (2010) by grouping democracies

in Central/Eastern Europe (CEE) into a separate country category. When the classification of a

particular country is in dispute, we tend to follow the most recent one, since country and regional

experts usually update their categories using newly available information. We add Romania and

Slovakia to the CEE cluster based on similarities in inequality and redistribution with cluster

members.

9 Huber and Stephens (2012, 58) report a mean pre-tax and transfer Gini for the mid-1990s of 35

for both Nordic and Continental welfare states, versus a mean of 42.2 for the Liberal states.

These numbers are for the working age population (versus the entire population in the case of the

SWIID), and yet differences in market inequality between our respective numbers are not very

large. The discrepancy is not due to data sources since the Luxembourg Income Study (LIS) on

which scholars of developed countries rely for their data is employed as the standard for the

SWIID. Most likely, the generous public pensions provided in Nordic and Continental countries

explain the discrepancy, since they reduce incentives to save for retirement, biasing levels of

Scholars rely on additional variables to explain variation in redistribution across

democracies. According to power resources theory, union strength (mostly operationalized as

union density) and left governments increase redistributive spending (Bradley et al. 2003; Huber

and Stephens 2001, 2012). Recent applications of the theory also link these variables to equality

in the distribution of market income (Morgan and Kelly 2013; Volscho and Kelly 2012, 681).

Finally, scholars relate the institution of corporatism, which is associated with lower wage

differentials (Rueda 2008), to left governments and union strength. We include power resources

in our analysis10 and capture their effect on market inequality in the context of instrumental

variables estimation.

Veto players speak to the relationship between government cohesiveness and policy.

Both the number and the ideological distance among these actors matter for policy (Ha 2008;

Tsebelis 2002). As scholars have pointed out, both factors are inversely related to the capacity of

a political system to implement new policies. Since constitutional structures affect the number of

market inequality upwards (Kenworthy and Pontusson 2005, 463).

10 We downloaded these variables from Visser’s (2016) database on labor market outcomes.

Corporatism refers to the level of collective bargaining, which ranges from the company (1) to

the national level (5), and union density to “net union membership as a proportion of wage

earners in employment”. See the ICTWSS database codebook, page 3, available at

https://aias.s3-eu-central-1.amazonaws.com/website/uploads/1475058325774ICTWSS-

Codebook_Version-5.1_20160926.pdf . In the most recent version of the dataset, 99 observations

for union density that had positive values in prior versions are lacking information. Since this

accounts for only 5.85% of the observations for the variable, we fill in the missing observations

with a similar version of the variable derived from household surveys as opposed to union

reports. We thank Jelle Visser for pointing this alternative indicator out to us.

national parties and politicians and their ideological distances, the measure of veto players we

use, the political constraints index (polconiii) (Henisz 2017), is simultaneously a measure of

constitutional and partisan veto players.11 Polconiii considers three constitutional veto players,

the executive and (where they exist) both houses of parliament, and reflects heterogeneity in

party composition within the legislative and executive branches as well as congruence in party

control across branches. The index ranges from 0 to 1, 0 being the most cohesive, 1 the least.

While the theories we consider differ on the sources of variation in government

partisanship12, what constitutes “the government” – the kind of parliamentary support a cabinet

11 Note, however, that this index does not include subnational veto players such as federalism.

The dependent variable, redistribution, takes into account income redistributed regardless of

what level of government engages in this redistribution. Federalism is also indirectly reflected in

the polconiii index in two ways: federalist democracies tend to have more decentralized political

parties (Gerring and Thacker 2008), making national level parties less ideologically cohesive.

Secondly, federalism is usually reflected in the design of the legislature, in particular the upper

chamber.

12 The fiscal contract theory claims, for example, that parties tax their bases of support intensely

while also providing those groups with more services (Timmons 2005). Left governments, at

least in the OECD, thus rely more on consumption and labor taxes that are borne

disproportionately by the less well-off (see also Beramendi and Rehm 2016). This approach

explains variation across governments in income redistribution better than the median-voter

theorem. As many have observed, if politicians and parties compete for the median voter using

redistributive policies, parties would tack to the center in their platforms (Iversen 2010, 186).

Parties that differ very little in their redistributive platforms, however, is not what we observe in

the party systems of many democracies (Pontusson and Rueda 2010).

enjoys – means different things in different democracies (ranging from one-party majority rule in

first-past-the-post presidential systems to multi-party minority coalition government in PR-

parliamentary systems).13 Because polconiii is silent on the ideology of the government, we also

include a measure of the ideology of the chief executive’s party from the Database of Political

Institutions (Beck, Clarke, Groff, and Walsh 2001). Our variable takes a value of 1 if the party of

the chief executive can be construed as left of center and a 0 otherwise.

As originally formulated, the median-voter model presupposed that all eligible voters in a

polity actually vote (Larcinese 2007, 575; Mahler 2008, 162). More recently, some have argued

that the tax rate as well as the portion of government expenditures devoted to transfers increases

with electoral turnout (Boix 2003, 171-72; Mahler 2008; 2010). Others, however, have presented

evidence that poor people are much less likely to vote than the well-off (Blais 2000; Franzese

2002; Kenworthy and Pontusson 2005; Larcinese 2007; Mahler 2008, 167) and that political

participation is inversely related to economic inequality (Solt 2008). A recent careful analysis

using data on fourteen developed countries concluded that increases in turnout tend to increase

redistribution by reducing the income skew in turnout (Mahler, Jesuit, and Paradowski 2014). In

the statistical analysis, turnout is defined as the percentage of registered voters who cast votes in

the most recent parliamentary elections (IDEA 2017).14

13 Some scholars (for example, Iversen and Soskice 2006) have claimed that electoral systems,

proportional representation (PR) and single member plurality in particular, shape the

composition of government coalitions and hence redistribution. Since these institutions also

shape the ideology of political parties, we do not include information on institutional

characteristics in our models.

14 For the United States, we rely on Michael McDonald’s data

(http://www.electproject.org/national-1789-present) since voter registration is voluntary there,

We also control for a handful of economic and demographic factors, all of which are

routinely included in cross-national analyses of welfare spending. The variables were obtained

from the World Development Indicators database (World Bank 2014). Economic development

expands the tax base necessary for a government to redistribute income (Boix 2001). The level of

development is captured by GDP per capita (in thousands of inflation-adjusted 2011 international

dollars). Economic growth is likely to reduce the need for redistribution, while simultaneously

increasing its feasibility due to expanded tax collection.15 Unemployment (more precisely, the

unemployment rate) should have the opposite effects.

Scholars have found that female labor force participation, or the percentage of women

between 15 and 64 who are in the labor force; and a higher age dependency ratio, or the ratio of

the population over 64, increase demand for redistribution (Huber, Ragin, and Stephens 1993;

Huber and Stephens 2000; Haggard and Kaufman 2008, 40), although probably more so where

the welfare state incentivizes women’s social and economic emancipation as opposed to a “male

breadwinner” pattern of family relations (Huber and Stephens 2000).

Globalization may also shape popular and government commitments to redistribution

both by generating demands for compensation for economic risk (Garrett 1998; Rodrik 1998;

Mares 2005) and by constraining through competition the ability of governments to respond to

such demands (Bradley et al. 2003, 202; Rudra 2002), though the findings in this literature are

mixed (Ha 2012). We employ two indicators of economic globalization: exports and imports of

resulting in many voters being eligible but not actually registered to vote.

15 We exclude this variable from the first two series of models (see below) since we also include

the level of economic development in equations where dynamics are modeled with fixed effects.

In this context, economic growth (if expressed in real terms) is equivalent to the change in levels

of development from one year to the next.

goods, services and capital, expressed in current US international dollars, to capture the

possibility that the absolute volume of economic flows may create pressures for compensatory

government spending.

Further, we postulate that the duration of a country’s experience with democracy, or how

many years a country has remained continuously democratic since its last regime transition,

should affect income redistribution. Olson (1982) suggested that as the institutions and

procedures of a democratic regime consolidate, distributional coalitions tend to form, seeking

concentrated benefits for their members with diffuse costs for everybody else. Durability, from

the Polity IV dataset, is the measure of cumulative democratic experience we use (Marshall et al.

2016).

Finally, individuals usually see themselves (and are seen) as members of groups defined

by social characteristics that may overlap with their economic class (Shayo 2009; Lupu and

Pontusson 2011). Social policies in turn define and target categories of citizens, whether

individuals identify strongly with these categories or not. Some studies demonstrate a negative

association between ethnic fractionalization and welfare effort (Alesina and Wacziarg 1998;

Alesina and Glaeser 2004), a possibility that we control for in our analysis using the

fractionalization data created by Alesina, Devleeschauwer, Easterly, Kurlat, and Wacziarg

(2003).

STATISTICAL MODEL

A challenge all theories of redistributive politics face is that there are a number of

associations between inequality and redistribution that may manifest themselves differently

across countries and over time. To deal appropriately with this complexity, we decompose the

effects of changes in inequality from those of levels, explore the possibility of reciprocal

causation between inequality and redistribution, and model different temporal effects of

inequality for various democracies. Accordingly, we provide three sets of models of

redistribution: a random intercepts model distinguishing between the effects of levels of and

changes in inequality on levels of and changes in redistribution, two-stage least squares (2SLS)

and generalized method of moments (GMM) regressions modeling inequality endogenously, and

error correction models (ECM) capturing short-term and long-run determinants of redistribution

for various clusters of countries.

To separate cross-sectional from longitudinal effects, we adopt Bartels’ (2015) random

intercepts model for time series cross-sectional data. This model yields two kinds of estimates:

the effect of levels of covariates measured as cluster means (the between-cluster effects), and the

effect of deviations in units of measurement from these means (the within-cluster effects). By

including within- and between-cluster transformations of time-varying variables, the procedure

removes the correlation between country level variables and the random effects. Specifying

random intercepts also allows for the inclusion of time constant variables, since the latter would

not be correlated with the country indicators.

Since the variables corporatism and union density reduce the sample size considerably,

we estimate four different kinds of models. The first two exclude these variables, while two of

the models compute jackknife as opposed to cluster robust standard errors. The latter control for

any pattern of heteroskedasticity should error variances differ across clusters.16 Finally, we

standardize coefficients so as to make direct comparisons of their size possible. Appendix A

16 Transformations of the independent variables to account for cluster confounding should also

correct for other violations of regression assumptions (Bartels 2015).

provides a list of countries in the overall analysis; Appendix B lists the countries used in the

analysis with the reduced sample.

One drawback to this kind of modeling is that it allows us to estimate the effects of

inequality on redistribution, but not the reverse. Instrumental variables regression can account for

the effects of changes in covariates on changes in income redistribution, while controlling for

reciprocal effects. We pursue this analysis in three steps. In the first, we instrument market

inequality with lags of redistribution and imports in the context of 2SLS estimation.17 This

requires us to make the assumption – a very plausible one – that trade and capital inflows affect

redistribution primarily through their effects on market inequality. 18 As for the number of lags of

redistribution employed, we add as many lags as we can determine are significantly correlated

with the endogenous variable. Since lag number four is insignificantly related to market

inequality, we do not instrument with further lags. We only provide over time within country

estimates, not only because fixed effects control for any possible omitted variables, but also

because we are more interested in assessing any endogeneity occurring within countries over

time.

Our second specification only differs from the first in that we use feasible efficient two-

step GMM (Baum, Schaffer, and Stillman 2003, 7) as opposed to 2SLS estimation. Although the

first stage OLS estimates from feasible GMM do not differ from those of 2SLS, this approach, as

its name indicates, increases the efficiency of the second stage results. 2SLS estimates are thus

17 Because unemployment could also be to some extent endogenous to redistribution, we use the

first lags of unemployment in place of their contemporaneous values.

18 We are not able to include the variable exports in the first two instrumental variables

specifications as this makes the instruments invalid. Of the globalization variables, however, the

one we are most interested in because of its potential compensatory effects is imports.

efficient for homoscedasticity only, whereas GMM estimates are efficient for arbitrary

heteroskedasticity and autocorrelation. In both cases, standard errors are robust to

heteroskedasticity and autocorrelation within units.

As a final check on the suitability of instrumental variables estimation, we provide

estimates using two-step system GMM (Blundell and Bond 1998). Compared to feasible efficient

GMM estimation, system GMM uses all covariates in the model to generate a system of two

equations – one differenced and one in levels – for instrumenting the endogenous variable(s)

“internally” (Islam et al. 2017). With a greater number of instruments, the approach can

dramatically increase efficiency (Roodman 2009, 108). It also allows for inclusion of a lagged

dependent variable which, together with market inequality, is considered endogenous.19 The

method provides unbiased estimates of the effect of covariates on income redistribution,

controlling for redistribution in the previous year. To allow for the inclusion of time invariant

covariates (Roodman 2009, 115) and also because it is more efficient, we use the system (as

opposed to the difference) estimator with the Windmeijer correction for two-step estimation of

the standard errors.20 Since our panel has gaps, we maximize sample size by employing the

orthogonal deviation of the errors (Roodman 2009, 128).

A crucial difference between our two fixed effects models – 2SLS and feasible efficient

GMM – and our system GMM approach is that the first two exclude a lagged dependent

variable. As many have warned (for instance, Plümper, Troeger, and Manow 2005), a lagged

19 Endogeneity in the case of lagged redistribution does not imply reciprocal causation, but that

the variable is “correlated with past and possibly current realizations of the error”. (Roodman

2009, 86).

20 According to Bazzi and Clemens (2013, 166), because of concerns with weak instruments in

the difference estimator, practitioners now consider the system estimator the default.

dependent variable can severely bias parameter estimates in the context of fixed effects. In

system GMM, however, fixed effects are expunged, making it possible to include time invariant

variables (Roodman 2009, 115). One problem with this approach, however, is that because it

uses the lags of independent variables as instruments for the endogenous variables, the

instrument count tends to grow quickly in these analyses. For the results to be meaningful,

therefore, instruments should not exceed units in their number. Ideally, they should equal the

number of units, yielding a model that is exactly identified.

As a result, it is only possible to treat three variables as endogenous, lagged

redistribution, market inequality, and left executive.21 We also strive to maximize the number of

countries by pooling them in a single analysis, with the instrument matrix collapsed to minimize

the number of instruments. We use lags 2 to 9 of the regressors as instruments, which yields 39

instruments for 40 groups. One final caveat is that in system GMM, the first-differenced

instruments used for the variables in the levels equation should not be correlated with the

unobserved country effects. Of our excluded regressors, ethnic fractionalization is time invariant

and, as a result, it experiences no change in its value over time. We thus exclude this variable

(along with the remaining excluded regressors) from the levels equation.

While GMM modeling provides unbiased estimates of the determinants of redistributive

spending, these models only capture the effects of changes in covariates from the previous year

on the dependent variable. Some covariates could affect welfare generosity over several time

periods. As a result, we supplement the GMM analysis with single equation error correction

models (ECMs). The later assume that covariates have both transitory and lasting effects on the

21 Parties of the left tend to govern in DCs with generous welfare states (for example, Iversen

2005)

dependent variable and that there is a long run equilibrium between the dependent variable Y and

independent variables X.

ECMs relate the effect of first differences and first lags of independent variables on the

first difference of the dependent variable. Differences capture short-term dynamics, whereas lags

capture long-term effects. 22 We estimate these models using OLS with panel corrected standard

errors and the pairwise method for estimating the interpanel covariance matrix of the

disturbances. This technique ensures that in unbalanced panels, “elements of the variance-

covariance matrix are computed with all available pairs of panels.” (Swank 2015, 29). Although

these models require weak exogeneity of regressors, it is possible to address endogeneity by

entering exogenous variables with an additional lag. This time, in addition to market income

inequality and left executive, we also treat economic growth (Benabou 2000) as endogenous. As

a result, we use the first differences and first lags for these variables, and the difference of first

lags with second lags for the remaining exogenous covariates in the ECMs. This allows

exogenous variables to affect the dependent variable with some delay.23

ECMs allow one to ask whether different types of welfare states are unique in the way

they organize market-state relations. Since “a model able to capture long-run effects appears

indispensable” (Podestà 2006, 542), scholars have widely used error correction processes to

22 Lebo and Kraft (forthcoming) claim long-run-multipliers are unreliable and the coefficient on

the lagged dependent variable difficult to interpret in many error correction processes. Enns et al.

(2016, 10) defend, however, the general ECM used here (DeBoef and Keele 2008), concluding

that the model “is appropriate in a variety of data scenarios common to political science

research.”

23 Swank and Steinmo (2002) estimate their ECMs using a similar approach. We thank Luke

Keele for clarifying this point.

model the welfare state (Iversen and Cusack 2000; Iversen and Soskice 2006; Segura-Ubiergo

2007). If so, the long run association between inequality and redistribution could be different

depending on the type of welfare state. Consequently, we group countries into six clusters based

on the country classification we adopted in footnote 8 and present an ECM for each.24 Because

we confirmed the presence of auto correlation in the residuals, we follow standard practice and

add a lagged dependent variable to the right-hand side of the model (Podestà 2006, 542). For the

results to be valid, the coefficient on this variable should be between -1 and 0 and significant.

Standard practice also calls for the use of fixed effects for countries. Finally, because durability

captures the passage of time, it makes no sense to use it in ECMs and we thus exclude it from

this last set of analyses.

RESULTS AND DISCUSSION

We begin our substantive discussion with our random intercepts models in Table 1. As

the table indicates, no matter what specification or configuration of independent variables we

use, increases in inequality from the country baseline are always significantly and positively

24 Unfortunately, we could not include in this analysis the Productive and Protective clusters

along with observations not categorized by welfare state regime as the models we ran fitted

poorly. Although the SWIID has many advantages, data quality and availability for many

developing countries remains poor, resulting in estimates of inequality and redistribution for

these countries that may not be very accurate (Houle 2017). In many cases, moreover, the

SWIID’s data is not derived from information on both pre- and post-government income.

Instead, estimates are often based on only one source (either pre- or post-), the difference

between these figures in different years, and/or information from neighboring countries (Solt

2016, 1272).

associated with increases in absolute redistribution, net of other variables that also experience

changes within countries.25 In terms of substantive significance, no other time-varying covariate

is more significantly associated with changes in redistribution except for lagged redistribution,

which is simply referencing redistribution in the previous year.

Table 1. Random intercept models of the determinants of redistribution, 1991-2014

Independent variables

Cluster robust (full)

Jackknife (full)

Cluster robust

(reduced)

Jackknife (reduced)

Market inequality (b) 1.864*** 1.864** 2.921*** 2.921**Left executive (b) 0.315 0.315 0.302 0.302Political constraints (b) 1.871*** 1.871*** 2.436*** 2.436***Turnout (b) -0.154 -0.154 -0.771 -0.771GDP/pcp (b) 1.969*** 1.969** 2.008*** 2.008Unemployment (b) 0.435 0.435 -0.135 -0.135Exports (b) -0.171 -0.171 -1.331 -1.331Imports (b) 0.036 0.036 1.289 1.289Female labor force participation (b) 2.533*** 2.533*** 2.595*** 2.595**Age dependency ratio (b) 2.531*** 2.531** 2.491** 2.491Durability (b) -0.093 -0.093 -0.551 -0.551Ethnic fractionalization (b) -1.240** -1.240* -1.660** -1.660Lagged redistribution (w) 1.635*** 1.635*** 1.503*** 1.503***Market inequality (w) 0.625*** 0.625*** 0.987*** 0.987***Left executive (w) 0.068** 0.068** 0.064 0.064Political constraints (w) -0.035 -0.035 -0.017 -0.017Turnout (w) 0.011 0.011 -0.031 -0.031GDP/pcp (w) -0.148** -0.148* -0.135 -0.135Unemployment (w) 0.005 0.005 0.039 0.039Exports (w) -0.307* -0.307 -0.357* -0.357Imports (w) 0.298* 0.298 0.340* 0.340Female labor force participation (w) 0.056 0.056 0.237*** 0.237**Age dependency ratio (w) 0.119 0.119 0.037 0.037Durability (w) 0.020 0.020 -0.066 -0.066Corporatism (b) 0.167 0.167Corporatism (w) 0.049 0.049

25 Using relative redistribution as the dependent variable produces similar results although model

fit is slightly lower.

Union density (b) 0.393 0.393Union density (w) 0.076 0.076observations 1,126 1,126 666 666Number of countries 58 58 40 40R2 within 0.8805 0.8805 0.9034 0.9034R2 between 0.8516 0.8516 0.8314 0.8314R2 overall 0.871 0.871 0.8273 0.8273

Note: * p<0.05; ** p<0.01; *** p<0.001. (b) refers to between cluster effects, (w) to their within cluster counterparts. We report standardized coefficients but omit standard errors due to space constraints. The number of observations, coefficients of co-determination, and significance levels do not change if we use unstandardized coefficients instead.

As expected, ethnic fractionalization is significantly associated with lower levels of

redistribution while levels of dependent populations, female labor force participation and (to a

lesser degree) economic development emerge as strong guarantors of welfare generosity. Left

executive, although exhibiting the expected direction in its effect, is not significantly associated

with increases in redistribution when union density and corporatism are included in the analysis

(Rueda 2008). Market inequality (in levels) is significantly and positively associated with higher

levels of redistribution.26 On a final note, the models explain most of the variation in

redistribution – particularly within countries – judging by the three coefficients of

codetermination (or R2): within, between and overall.

Moving on to the IV-GMM estimation in Table 2, we discuss first results for the first

stage of the analysis, the model of market inequality. All three lags of redistribution affect

market inequality significantly, the first one positively so. The included exogenous variables

mostly affect market inequality in the way we would expect, with corporatism and female labor

26 Although this appears to contradict the relationship depicted in the first panel of Figure 1, a

lowess smother plot reveals that the relationship is negative for some countries and positive for

others. This indicates that important differences, which seem to be related to the type of welfare

state, exist among clusters of countries (Huber and Stephens 2014, 246).

force participation driving down gaps in market income, and lagged unemployment, economic

development, and the age dependency ratio significantly increasing those gaps.

Table 2. IV-GMM models of the determinants of redistribution, 1992-2013.

Independent variables Market inequality (OLS)

Absolute redistribution (2SLS)

Absolute redistribution (feasible efficient GMM)

Absolute redistribution (system GMM)

left executive -0.160 0.334** 0.206 0.165political constraints 0.836 -0.966 -1.031 -0.208turnout 0.023* -0.010 -0.023* -0.001GDP/pcp 0.000*** -0.000*** -0.000*** -0.000**lagged unemployment 0.129*** -0.108*** -0.095** -0.009female labor force participation -0.294*** 0.367*** 0.349*** 0.137***age dependency ratio 0.189*** -0.136** -0.183*** -0.072**durability 0.007 -0.002 0.024 0.008corporatism -0.274** 0.236* 0.196 0.200*Union density -0.010 0.022 0.048 0.010lagged redistribution 1.187*** 0.884***lag 2 of redistribution -0.337**lag 3 of redistribution -0.207**imports -0.000 0.000*market inequality 1.163*** 1.136*** 0.254**exports 0.000 -0.000*Ethnic fractionalization -1.556Observations 643 643 643 649R2 0.687 0.568 0.582Number of nations 40 40 40 40

Note: * p<0.1; ** p<0.05; *** p<0.01. Unstandardized coefficients reported. To save space, we do not report the intercept and standard errors.

Greater participation by women in the labor force tends to be associated with better

opportunities for them in the formal sector, which tends to compensate laborers better than the

informal sector of the economy. As a large literature has established, corporatism compresses

wage differentials between skilled and unskilled workers, reducing wage inequalities. We

surmise that unemployment increases gaps in market income precisely because it deprives some

of this income. The age dependency ratio also results in higher market inequality because it

implies a larger ratio of economically inactive citizens over those that are active in the labor

force. We expected economic development to be associated with decreases in market income

inequality, but the coefficient is positive. From visually inspecting the data, we cannot detect a

clear trend in either direction.

Regarding the suitability of the instrumentation strategy, our discussion pertains to both

the 2SLS and the feasible efficient GMM estimations, since the estimation strategy for the first

stage is the same for both. The Sanderson-Windmeijer (SW) chi-squared Wald statistic has a p-

value of 0, indicating a strong rejection of the null hypothesis that the endogenous regressor

(market inequality) is unidentified. The SW first-stage F statistic is 94.28, which is greater than

10, allowing us to reject the null hypothesis that our instruments are weak (Staiger and Stock

1997).27 The Kleibergen-Paap LM test rejects the null hypothesis that the equation as a whole is

under identified (p=0.000). The Anderson–Rubin Wald test and Stock–Wright LM test also

handily reject their null hypothesis that the endogenous regressors are irrelevant. The Hansen J

statistic readily accepts the null that that the instruments are valid (i.e., uncorrelated with the

error term), and that the excluded instruments are correctly excluded from the estimated equation

(p= 0.161). Finally, the endogeneity test strongly rejects the null hypothesis that we can actually

treat the endogenous regressor we specified as exogenous.

Turning now to the second stage of the 2SLS and feasible efficient GMM models, both

sets of results share strong similarities. Coefficients vary slightly in size between the two, but

both models indicate that increases in market inequality and female labor force participation are

positively and significantly related to increased redistribution; and that unemployment in the

previous year and the age dependency ratio are significantly related to decreased redistribution.

27 These test statistics, moreover, are heteroskedasticity and autocorrelation-robust.

These findings are expected except for the negative association between the age dependency

ratio and redistribution, and unemployment and redistribution. The latter relationship is driven

by countries with high unemployment rates such as Spain and South Africa. Regarding the age

dependency ratio, Huber and Stephens (2014, 259) find that a similar measure, employment as a

percentage of the working age population, significantly decreases income redistribution.

Regarding the system GMM estimation, the findings resemble the previous two models

with the exception of corporatism, whose positive and significant effect on redistribution is in

agreement with the results of the 2SLS but not the feasible efficient GMM specification. The

very significant coefficient on the lagged dependent variable indicates however that most

redistribution in a given country-year is primarily a function of redistribution in that country in

the previous year. For the purposes of comparison and using this model, we simulate the effects

on redistribution of an increase in lagged redistribution and inequality from the minimum to the

maximum values observed for these variables, respectively. The result is an 88.11 versus a 35.17

percentage point increase.28

Diagnostics also indicate that we have properly specified our models. Arellano-Bond

tests fail to find autocorrelation in the AR (2) residuals.29 The Hansen J statistic tests the null

hypothesis that we can regard the group of instruments as exogenous, which is indeed the case

when we notice that its p-value is above 0 but less than 1 (Roodman 2009, 98). Difference-in-

Hansen tests of exogeneity of instrument subsets also have p-values different from 0 but less

28 These simulations assume that all other variables are held at their sample means.

29 There is some autocorrelation in the AR (1) residuals, but the more important of the two tests is

the test for autocorrelation in the AR (2) residuals, since it involves the level in addition to the

differences equation (Mileva 2007, 7).

than 1. Finally, although the statistical software does not report a coefficient of codetermination,

plots of observed versus fitted values indicate the models fit the data very well.

As informative as these results are, they tell us very little about how countries came to

have such different levels of redistribution to begin with. Thus, an analysis of long-run dynamics

becomes pertinent. We turn our attention now to the ECMs, the results of which are displayed in

Table 3.

Table 3. ECMs of the determinants of redistribution, 1993-2015.

Independent Variables Nordic Continental Liberal Dual Mediterranean Central/Eastern Europe

redistributiont−1 -0.313*** -0.186*** -0.118* -0.094* -0.114*** -0.212***∆inequality 0.639*** 0.457*** 0.586*** 0.301*** 0.797*** 0.647***inequality t−1 0.153* 0.076* 0.222*** -0.214*** 0.143*** 0.116***∆left executive 0.267 -0.014 -0.008 0.294 0.110 0.222*¿t−1 -0.099 0.011 0.031 0.752*** 0.495*** 0.264**∆GDP growth -0.088*** -0.067*** -0.024 0.001 0.042 0.011GDP growtht−1 -0.241* 0.060 -0.140 -0.074 0.047 -0.041L∆Political constraints -24.263*** 0.429 -1.051 0.407* 0.770 0.554politicalconstraints t−2 -4.853 0.401 -2.323 0.280 1.492** 0.837L∆turnout 0.063 -0.017 -0.004 0.015** 0.010 -0.015turnout t−2 -0.010 0.028 -0.007 0.034*** 0.013 -0.010L∆GDP/pcp 0.000 -0.000*** 0.000 0.000 0.000 0.000GDP/ pcpt−2 -0.000* -0.000*** -0.000 -0.000*** 0.000 -0.000L∆unemployment -0.002 -0.047 0.017 0.004 -0.032 -0.014unemployment t−2 0.004 0.045 -0.077** 0.027 -0.052 -0.006L∆exports 0.000* 0.000 0.000 -0.000 0.000 -0.000exports t−2 0.000 0.000 -0.000 -0.000 0.000* -0.000**L∆imports -0.000* -0.000 -0.000 0.000 -0.000** 0.000importst−2 -0.000 -0.000 0.000 0.000 -0.000** 0.000**L∆female LFP 0.030 0.103 -0.204 0.357*** 0.063 0.113female LFPt−2 0.099 0.298*** -0.140 0.294*** -0.028 0.103L∆age dependency 0.824** -0.347* 0.788*** -0.296 0.342 0.317age dependencyt−2 -0.068 0.021 -0.054* -0.049 0.207*** 0.038L∆corporatism -0.097 -0.009 0.020 -0.228** 0.062corporatism t−2 -0.088 -0.298** 0.170 -0.341*** -0.022L∆Union density 0.077 0.111 0.009 0.025¿density t−2 0.035 0.085* -0.019 0.048R2 0.78 0.77 0.87 0.66 0.97 0.86N 86 96 109 82 68 158

Note: * p<0.1; ** p<0.05; *** p<0.01. “∆” indicates first differences, “L∆” difference of first lags, “t−1” first lags, and “t−2” second lags. To save space, we do not report standard errors, constants, and country fixed effects.

As expected, the coefficients on the lagged dependent variable are all between -1 and 0

and statistically significant. In line with the analysis in Table 1, Table 3 reveals that inequality

significantly increases redistribution short term across all clusters and long term in the developed

and CEE country clusters. Long term, however, inequality significantly decreases redistribution

in less developed countries. Left executives work to increase redistributive spending short term

in CEE countries as well as long term in the Dual, Mediterranean, and CEE clusters. The latter

finding is in line with Huber and Stephens’ (2012) recent claim that democratic governance has

allowed left parties to increase welfare spending in Latin America. Finally, measures of social

diversity (not reported) are mostly time invariant and as such, their effects insignificant and

indistinguishable from 0. The effects of other variables are somewhat more mixed.

CONCLUDING REMARKS

This note provided a systematic examination of the politics of income redistribution in

democracies. We began with the premise that inequality’s effects on redistribution are time-

sensitive, country specific, and mediated by other variables. We therefore depart from previous

studies in three important ways. First, we compare the effects of inequality over time as well as

among and within different country clusters. Second, we avoid pooling developed and less

developed countries together; in so doing, we assume that the effects of inequality and

redistribution likely differ across regimes and levels of development. Third, we use a number of

statistical models to address the complexity of the relationship between inequality and

redistribution. Our models tackle thorny issues of spatial and temporal differences in inequality’s

effect on redistribution as well as the problem of endogeneity. Other studies usually focus on one

or two of the issues identified, but never—at least to our knowledge—all three.

Focusing on theoretical and empirical puzzles in the literature, we have moved beyond

the ‘Robin Hood paradox’ and the positive short-term effect of inequality that is consistent with

the median-voter theory. As Table 3 demonstrates, the paradox arises because of differing long-

run effects of market inequality on redistribution. By tackling the problem of endogeneity, we

have also shown that redistribution affects inequality as much as inequality affects redistribution.

While we entertained the possibility that particular covariates vary in their effects by

cluster, the literature has not developed to the point where we are able to determine which

variables (if any) vary systematically in their effects, let alone when and why. We do capture

country-specific fixed effects in our equations, which accord with our two expectations: first,

that, even within clusters, important differences in the design and operation of the welfare state

remain; and, second, that while regime classifications do group countries according to important

historical and geographical legacies, they also mask important variation.

Still, we find that market inequality provides strong redistributive impetuses in developed

and Central/Eastern European countries, but it significantly reduces redistributive spending long-

term in a sample of developing democracies. Central and Eastern European welfare states thus

differ in important ways from their counterparts in less developed countries. These findings

illustrate why scholars should not make universal claims about the relationship between

inequality and redistribution.

Supplementary Information

Replication files are available at http://faculty.fordham.edu/aleman/ and the International

Studies Quarterly data archive.

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Appendix A. Countries in the overall analysis30

Continental Liberal Nordic MediterraneanAustria Australia Denmark GreeceBelgium Canada Finland ItalyFrance Ireland Norway PortugalGermany Japan Sweden SpainNetherlands United KingdomSwitzerland United StatesDual Productive Protective CEEArgentina Chile Dominican Republic Czech RepublicBrazil Colombia El Salvador EstoniaMexico Costa Rica India HungaryUruguay Israel Latvia

Korea (South) LithuaniaPanama PolandParaguay RomaniaSri Lanka SlovakiaThailand SloveniaCountries not part of a cluster

Bulgaria Honduras Moldova Russia VenezuelaGeorgia Kenya Peru South AfricaGuatemala Luxembourg Philippines Ukraine

Appendix B. Countries included in models with reduced sample

Argenti na Australi

30 We are willing to entertain alternative classifications of developing country welfare states.

After all, Rudra (2007, 388) derived her classification using only thirty-two observations. We

nevertheless opted for Rudra’s classification since it is inductively derived using the same set of

indicators for all countries.

aAustriaBelgiumBrazilBulgariaCanadaChileCzech RepublicDenmarkEstoniaFinlandFranceGermany

GreeceHungaryIndiaIrelandIsraelItalyJapanKorea (South)LatviaLithuaniaLuxembourgMexicoNetherlands

NorwayPhilippinesPolandPortugalRomaniaSlovakiaSloveniaSouth AfricaSpainSwedenSwitzerlandUnited Kingdom

United States