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

  • Benigno, Pierpaolo
  • Woodford, Michael

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.

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Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 4764.

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Date of creation: Nov 2004
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Handle: RePEc:cpr:ceprdp:4764
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  1. Hans M. Amman & David A. Kendrick, . "Computational Economics," Online economics textbooks, SUNY-Oswego, Department of Economics, number comp1, March.
  2. Stephanie Schmitt-Grohe & Martin Uribe, 2001. "Optimal Fiscal and Monetary Policy Under Sticky Prices," Departmental Working Papers 200105, Rutgers University, Department of Economics.
  3. Lars Peter Hansen & Thomas J. Sargent, 1993. "Recursive linear models of dynamic economies," Proceedings, Federal Reserve Bank of San Francisco, issue Mar.
  4. Pierpaolo Benigno & Michael Woodford, 2006. "Linear-Quadratic Approximation of Optimal Policy Problems," NBER Working Papers 12672, National Bureau of Economic Research, Inc.
  5. V.V. Chari & Lawrence J. Christiano & Patrick J. Kehoe, 1993. "Optimal fiscal policy in a business cycle model," Staff Report 160, Federal Reserve Bank of Minneapolis.
  6. Pierpaolo Benigno & Michael Woodford, 2005. "Inflation Stabilization And Welfare: The Case Of A Distorted Steady State," Journal of the European Economic Association, MIT Press, vol. 3(6), pages 1185-1236, December.
  7. Kim, Jinill & Henderson, Dale W., 2005. "Inflation targeting and nominal-income-growth targeting: When and why are they suboptimal?," Journal of Monetary Economics, Elsevier, vol. 52(8), pages 1463-1495, November.
  8. 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.
  9. Henry Kim & Jinill Kim & Ernst Schaumburg & Christopher A. Sims, 2005. "Calculating and Using Second Order Accurate Solutions of Discrete Time Dynamic Equilibrium Models," Discussion Papers Series, Department of Economics, Tufts University 0505, Department of Economics, Tufts University.
  10. Judd, Kenneth L., 1985. "Redistributive taxation in a simple perfect foresight model," Journal of Public Economics, Elsevier, vol. 28(1), pages 59-83, October.
  11. Schmitt-Grohé, Stephanie & Uribe, Martín, 2001. "Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function," CEPR Discussion Papers 2963, C.E.P.R. Discussion Papers.
  12. Michael Woodford, 2001. "Inflation Stabilization and Welfare," NBER Working Papers 8071, National Bureau of Economic Research, Inc.
  13. Judd, Kenneth L., 1996. "Approximation, perturbation, and projection methods in economic analysis," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 12, pages 509-585 Elsevier.
  14. Jinill Kim & Sunghyun Kim & Ernst Schaumburg & Christopher A. Sims, 2003. "Calculating and Using Second Order Accurate Solutions of Discrete Time," Levine's Bibliography 666156000000000284, UCLA Department of Economics.
  15. Chamley, Christophe, 1986. "Optimal Taxation of Capital Income in General Equilibrium with Infinite Lives," Econometrica, Econometric Society, vol. 54(3), pages 607-22, May.
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  17. Magill, Michael J. P., 1977. "A local analysis of N-sector capital accumulation under uncertainty," Journal of Economic Theory, Elsevier, vol. 15(1), pages 211-219, June.
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