E. Engel, A. Galetovic, C.E. Raddatz (1999). Taxes and Income Distribution in Chile: some Unpleasant Redistributive Arithmetic. Journal of Development Economics, vol. 59, 155-192.

Abstract
This paper quantifies the direct impact of taxes on income distribution at the household level in Chile and estimates the distributional effect of several changes in the tax structure. We find that income distributions before and after taxes are very similar (Gini coefficients of 0.488 and 0.496, respectively). Moreover, radical modifications of the tax structure, such as raising the value added tax from 18 to 25% or substituting a 20% flat tax for the present progressive income tax affect the after-tax distribution only slightly. We present some arithmetic showing that the scope for direct income redistribution through progressivity of the tax system is rather limited. By contrast, for parameter values observed in Chile, and possibly in most developing countries, the targeting of expenditures and the level of the average tax rate are far more important determinants of income distribution after government transfers. Thus, a high-yield proportional tax can have a far bigger equalizing impact than a low-yield progressive tax. Moreover, a simple model shows that the optimal tax system is biased against progressive taxes and towards proportional taxes, with a bias that grows with the degree of inequality of pre-tax incomes. Our results suggest that to reduce income inequality, the focus of discussion should be on the amount to be redistributed, the targeting of public spending, and the relative efficiency of alternative taxes, and not on the progressivity of the tax system.

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