Working Paper: NBER ID: w11029
Authors: Pierpaolo Benigno; Michael Woodford
Abstract: We reconsider the optimal taxation of income from labor and capital in the stochastic growth model analyzed by Chari et al. (1994, 1995), but using a linear-quadratic (LQ) approximation to derive a log-linear approximation to the optimal policy rules. The example illustrates how inaccurate "naive" LQ approximation --- in which the quadratic objective is obtained from a simple Taylor expansion of the utility function of the representative household --- can be, but also shows how a correct LQ approximation can be obtained, which will provide a correct local approximation to the optimal policy rules in the case of small enough shocks. We also consider the numerical accuracy of the LQ approximation in the case of shocks of the size assumed in the calibration of Chari et al. We find that the correct LQ approximation yields results that are quite accurate, and similar in most respects to the results obtained by Chari et al. using a more computationally intensive numerical method.
Keywords: Optimal Taxation; RBC Model; Linear-Quadratic Approach
JEL Codes: C63; H21
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| naive LQ approximations (C51) | inaccurate policy conclusions (J18) |
| correct LQ approximation (C51) | valid local approximation to optimal policy rules (C54) |
| correct LQ approach (C21) | results aligned with complex numerical methods (C60) |
| LQ approximation (C60) | adjustment of capital and labor taxes in response to real disturbances (H31) |
| LQ approach (C51) | accurate characterization of tax rate dynamics under optimal policy (H21) |
| optimal steady-state tax on capital (H21) | zero (Y70) |