The Optimal Earned Income Tax Credit (EITC) Schedule: A Trapezoid or a Triangle?

Appendix A Multi-Country Comparison of Wage Distribution Traits Among Low-Earners

Table A1 presents a multi-country comparison of relevant wage distribution traits among low earners in 44 countries. In the context of our analysis, the most relevant indicator in the table is the wage ratio between the 5th and 1st deciles. This metric closely resembles the ratio between income groups 4 and 1 in our analysis (as groups 1–4 account for about 50% of the working population).

Recall that in our simulations using Israel’s wage distribution and assuming extensive and intensive margin elasticities (η₁₋₄ = 1; ζ₁₋₄ = 0.05) – we obtained an optimal wage subsidy for the bottom wage group – followed by a net tax to the 2nd group (i.e. a triangle). Also recall that In order to obtain a trapezoid-like EITC scheme, we had to artificially tweak the wage distribution to a relatively even wage distribution for the bottom three groups, with a discrete jump in the wage rate of the fourth group so that their ratio with respect to the bottom wage group was 1, 1.21, 1.4, and 4. Note that this improbable distribution requires that the wage of the 50th percentile would be approximately 2.8 times higher than that of the 37th percentile. However, as evident from Appendix Table A1, in the 44 countries that were surveyed, such a high ratio does not exist even between Decile 5 and Decile 1 – nor did it exist during this century. The Highest Decile 5 to Decile 1 ratio that was recorded this century was 2.44, in Latvia, back in 2006. The current leader in this Metric is the US, with a Decile 5 to Decile 1 ratio of 2.06, followed by Estonia and Israel with 1.92. In contrast, when examining the Decile 9 to Decile 1 ratio one can see that it can be as high as 7.04 (in Colombia, 2007), yet the current leader is again the US with a ratio of 4.95, followed by Israel with 4.86. Furthermore, in some countries the Decile 9 to Decile 5 ratio can be as high as 3.85 (Turkey, 2006) and a ratio nearing three could be found not long ago in other countries (such as Colombia and Chile). In other words, empirically, high wage gaps are much more likely to be found within the top half of the wage distribution, and between the top and bottom deciles – than within the bottom five deciles. In the context of the optimal EITC this empirical observation is important because it shows that the conditions necessary for the optimal EITC scheme to be a trapezoid – do not occur empirically, nor did they occur this century, in any of the 44 surveyed countries.

Appendix B Optimal EITC Subsidies in Our Simulations

Recall Saez’s (2002) general equilibrium formula:

When ηi>0 ∀ i<5, and ηi=0 ∀ i>4, by moving from cumulative tax to average tax,

we obtain the following set of equations:

We then proceed to solve this set of equations by scanning through all possible values of t₄ (between 0 and 1), until a solution that satisfies all first order conditions is obtained. Note that, while this set of equations has multiple solutions there is always only one solution that satisfies the following conditions: 1) the marginal tax rate for each wage group must be smaller than 1; 2) the average tax rate must be increasing with wages.

Solving the system with endogenous social weights g_i and group size h_i using iteration.

We add to Saez’s solution the following iterative sequence:

1. The tax schedule is initially computed using the (exogenous) social weights and group sizes that correspond to pre-tax consumption levels; i.e. – the social weights and group sizes that persisted prior to redistribution via taxes and transfers.

2. Using the tax schedule that was computed in Equation (1), new social weights and group sizes are computed.

3. Those newly computed values of g_i and h_i are then used to compute a new tax schedule.

4. The new tax schedule is then used to compute new values of g_i and h_i, and so forth.

5. This iterative sequence is repeated until the tax schedule in iteration n perfectly matches the tax schedule in iteration n − 1.