Taxation under Learning-by-Doing: Supplementary Material

Section A in this supplement contains results for the Rawlsian-risk-neutral case. It provides a proof for Proposition 3 in the main text, relates wedges to marginal tax rates, and shows how optimal tax codes can also be derived using a perturbation approach in the spirit of Saez (2001) adapted to the dynamic economy with LBD under consideration. Section B contains numerical comparative statics results of relative wedges with respect to the agents’ degree of risk aversion, the Frisch elasticity of the agents’ labor supply, and the planner’s preferences for redistribution, for the case of the Pareto-lognormal distribution of productivity shocks discussed in Section 4 in the main body. Section C formally proves the equivalence between the 40-period economy used in the quantitative analysis in Section 5 in the main body and the 2-period economy used in Sections 2-4 in the main body. Section D describes the computational methods used in the main body and in Section B in the present supplement to establish all the numerical results. A Rawlsian-Risk-Neutral Benchmark This section has three parts. Section A.1 formally establishes the analytical results about the effects of LBD on the level, dynamics, and progressivity of the relative wedges, as reported in Proposition 3 in the main body. Section A.2 relates wedges to optimal tax rates. Finally, Section A.3 shows how optimal tax codes can also be derived using a perturbation approach in the spirit of Saez (2001) adapted to the dynamic economy with LBD under consideration. A.1 Proof of Proposition 3 in the main body From the analysis in the main text, we have that, when the disutility of labor is given by ψ(yt, θt) = 1 1 + φ ( yt θt )1+φ and period-2 productivity is given by θ2 = θ ρ 1y ζ 1ε2, in the absence of LBD, the period-t relative wedge is given by Ŵ t (θ ) = ρt−1 1 + φ θ1γ1(θ1) , (A.1)