Optimal Taxation in an RBC Model: A Linear-Quadratic Approach

We reconsider the optimal taxation of income from labour and capital in the stochastic growth model analysed 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 ‘naïve’ 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.