here, the variation is due to both redistribution gains and efficiency costs.<sup>41</sup> There are two main take-aways from Figure 7. First, consistent with our model predictions, we find that over development, equity considerations tend to decrease the rate on food relative to non-food goods (thus increasing rate differentiation) but efficiency considerations tend to increase it. Equity effects dominate, so that optimal relative rates on food fall with development when both effects are taken into account. Second, comparing panels B and D, we see that once we take into account the fact that only formal varieties can be taxed, the optimal policy no longer subsidizes food relative to non-food in some poor countries (the ratio of food to non-food rates is higher than 1). Once the impossibility of taxing informal varieties is accounted for, taxing food less than nonfood goods cannot by justified on equity or on efficiency grounds in these countries. Appendix Figure A14 shows that both of these findings are robust to changing values of the cross-variety price elasticity.<sup>42</sup>

# **6.2 Effect of Consumption Tax Policy on Inequality**

Figure 8 presents the effects of different consumption tax scenarios on income inequality in the average country in our sample. In Panel A we use the calibrated optimal tax rates for each scenario (allowing efficiency costs to vary with development) and use these rates to calculate the net of tax income of each household in our data. Our redistribution metric is the percent change in Gini from the pre-tax income distribution to the netof-tax distribution. To benchmark our results against estimates in the literature, Panel B reports the inequality impacts of actual tax policies in place in a comparable sample of developing countries obtained by Lustig (2018). To calculate these effects, we use their Commitment to Equity (CEQ) database which contains information on income and estimates of taxes paid (consumption taxes, direct taxes and social security) for each income decile in 25 developing countries.<sup>43</sup> Importantly, their methodology does not systematically consider the possibility that some places of purchase may be informal,

> 41Formally, in the top panels we set the uncompensated price elasticities in expressions equal to -1 for all countries when calibrating expressions (6), (8) and (9). In the bottom panels we calibrate these elasticities using expression (4) and the parameter values detailed in Table 4.

> 42In Appendix Figure A13 we also show the calibrated optimal uniform rates on all formal varieties. Consistent with our theory, the optimal uniform rate falls over development for redistributive purposes. As predicted, allowing efficiency costs to vary with development lowers the optimal rates, especially in the poorest countries and more so the higher the cross-variety elasticity of substitution.

> 43In the first row of Panel B, we calculate the change in Gini from applying general consumption and excise taxes to disposable income plus indirect subsidies. In the second row of Panel B, we calculate the change in Gini from applying the direct tax and social security contributions to market income plus direct cash transfers. These exercises allow us to calculate the marginal Gini impacts of the indirect and direct tax systems, respectively.

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