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

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  • 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.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 11029.

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Date of creation: Jan 2005
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Handle: RePEc:nbr:nberwo:11029

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  1. Michael Woodford & Pierpaolo Benigno, 2004. "Inflation Stabilization and Welfare: The Case of a Distorted Steady State," 2004 Meeting Papers 481, Society for Economic Dynamics.
  2. Kim, Jinill & Kim, Sunghyun Henry, 2003. "Spurious welfare reversals in international business cycle models," Journal of International Economics, Elsevier, vol. 60(2), pages 471-500, August.
  3. Pierpaolo Benigno & Michael Woodford, 2008. "Linear-Quadratic Approximation of Optimal Policy Problems," Discussion Papers 0809-01, Columbia University, Department of Economics.
  4. V. V. Chari & Lawrence J. Christiano & Patrick J. Kehoe, 1993. "Optimal Fiscal Policy in a Business Cycle Model," NBER Working Papers 4490, National Bureau of Economic Research, Inc.
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