Deduction in the Laffer curve and the elasticity of taxable income

In this paper, the authors use a simple dynamic general equilibrium model to study the relationship between deductions and three elasticities: the elasticity of the Laffer curve (the Laffer elasticity, hereafter), the elasticity of taxable income (ETI), and the income elasticity of tax revenue (the tax elasticity). the authors first show a decomposition of the Laffer elasticity, which consists of ETI and the tax elasticity. In the case with proportional income tax without deduction and lump-sum transfer, the tax elasticity is equal to unity, and we obtain a simple relationship between the Laffer elasticity and ETI. This decomposition suggests that earlier research that investigated these elasticities independently is related. The authors then calculate the analytical solutions of these elasticities with respect to labor and capital income under the steady state in the general equilibrium model with exogenous deduction and a social security tax. Since the solution in the model is too complex to analyze its features, the authors conduct a numerical simulation under plausible parameter values that are consistent with the results from Japanese data. The simulation shows that deduction can change these elasticities. Deduction shifts the Laffer curve and decreases the tax rate that maximizes the tax revenue. Further, deduction shifts ETI upward. The authors also check the robustness of the simulation with respect to the parameters. The result demonstrates that these elasticities largely depend upon the degree of relative risk aversion. Therefore, the authors conclude that the theoretical research on public finance, especially tax analyses, should consider deduction in the model.