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

Abstract

We reconsider the optimal taxation of income from labor and capital in the stochastic growth model analyzed by Chari et al. (1994Chari et al. ( , 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. * Presented by the second author as a Plenary Lecture at

Toward a Taylor rule for fiscal policy

“…Thus, for different policy instruments, different feedback variables are important. This result is in line with Benigno and Woodford (2006a), who find that optimal rules for taxes on capital income and labor income should respond to different feedback variables in their model. Since the coefficient on hours worked in the rule for labor income taxes as well as the coefficient on investment in the rule for capital income taxes are clearly distinguishable from the other feedback variables, we choose them as candidates in our tax rules.…”

“…It also comprises two nominal rigidities, one for wages and one for prices, both following the adjustment process postulated by Calvo (1983). The fiscal policy sector is modeled following Benigno and Woodford (2006b) with wasteful government spending and distortionary taxes on capital and wages but also lump-sum taxation. The model presented here, as in the succession of Christiano, Eichenbaum, and Evans (2005), and Smets and Wouters (2007), is designed to capture the behavior of the private sector well and is widely acknowledged as one of the workhorses in dynamic macroeconomics.…”

“…One strand of the literature investigates fiscal policy from a welfare-maximizing perspective. Benigno and Woodford (2006a) determine the optimal feedback variables in policy feedback rules. As shown in Benigno and Woodford (2006b), this approach delivers complex rules depending on a number of variables.…”

“…Benigno and Woodford (2006a) determine the optimal feedback variables in policy feedback rules. As shown in Benigno and Woodford (2006b), this approach delivers complex rules depending on a number of variables. For the sake of empirical relevance, in this paper we are interested in simple feedback rules rather than in a description of complete optimal policy (e.g.…”

Using a projection method to analyze inflation bias in a micro-founded model

“…In most of the existing papers on the inflation bias, the one-period loss function assigned to the central bank is quadratic in inflation and the level of output relative to its target. It is well known that Rotemberg and Woodford (1997) and Benigno and Woodford (2006) have provided a microfoundation for the use of such a loss function by showing that this simple quadratic function can be derived as the second-order approximation to the non-linear social welfare function in a Calvo model.…”