In the analyses below, we include all households, but show two sets of results. First, in our main specifications, we include pensions in market income, treating pensions as deferred wages. Market income that includes state pensions (specifically, state old age and survivors' benefits) is called _marketP_ income. This definition of market income _understates_ the extent of redistribution to the extent that pensions are progressive. Second, we report results that define market income to exclude pensions, and treat pensions as any other government transfer. This approach exaggerates the extent of redistribution if pension payouts are tightly linked to contributions.

# Noise and bias

For several reasons, estimates of redistribution and income inequality using household income surveys are likely to diverge from true levels of income distribution and redistribution. First, governments provide often substantial non-cash benefits, such as education and health services, that affect income distribution. Bourguignon and Verdier (2000), for example, argue that inequality operates on democratization through its effect on government incentives to subsidize education. The inability to observe non-pecuniary benefits does not reduce our ability to draw inferences from pecuniary transfers if the two types of transfers are correlated. If they are not – if, for example, education benefits increase with market income while income transfers decrease – then analyses based only on pecuniary transfers exaggerate the extent of redistribution.

This mis-measurement is unlikely to bias analyses of the effects of political conditions on redistribution. For approximately one-fourth of the sample, data on both gross school enrollment and income distribution are available. Controlling for income per capita and the share of the population that is young (school-aged), school enrollment is significantly associated with the log of income redistribution (measured as the difference between the ratio of the top and bottom quintile’s market income shares and the ratio of their post-transfer income shares). That is, like direct taxes, in those cases where school enrollment data are available, the provision of education appears to correlate with government redistribution.

Governments also tax indirectly, through value-added and sales taxes, while our evidence only identifies the effects of direct taxation. Since indirect taxes are generally regressive, our data could overstate the extent of tax-induced redistribution if countries that are least progressive with respect to income taxes rely less on indirect taxes than countries that are more progressive. Goñi, et al. (2011) find that this is not the case, however (for example, Latin America relies more on indirect taxes than Europe, but its income tax system is also much less progressive). In general, they conclude that indirect taxes have a small effect on income distribution (they are not progressive, but they are not sharply regressive, either). The omission of indirect taxes from our data is therefore unlikely to bias our results.

A second source of noise is that fiscal policies can influence market incomes as well as gross incomes. The prospect of receiving redistributive transfers influences the incentives of recipients to work. If transfers have large negative effects on the incentives of recipients to work, analyses based on LIS-style household surveys would therefore exaggerate the correlation between market income shares and redistribution, since the market incomes of those who receive the largest transfers have been driven down by the incentive effects of those same transfers.

However, for four reasons, this noise is unlikely to introduce bias into the analyses here and in previous research using household data. First, if taxes are paid disproportionately by richer market deciles and if they also discourage work effort, then incentive effects shift the market income shares of both high and low income groups in the same direction. Second, incentive effects are 9