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Optimal taxation in an RBC model: A linear-quadratic approach

  • Pierpaolo Benigno

    ()

    (New York University - Department of Economics)

  • Michael Woodford

    ()

    (Columbia University - Department of Economics)

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 - an 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 Columbia University, Department of Economics in its series Discussion Papers with number 0405-16.

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Length: 59 pages
Date of creation: 2004
Date of revision:
Handle: RePEc:clu:wpaper:0405-16
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  1. Lawrence J. Christiano & Martin Eichenbaum, 1990. "Current real business cycle theories and aggregate labor market fluctuations," Working Paper Series, Macroeconomic Issues 90, Federal Reserve Bank of Chicago.
  2. Jinill Kim & Dale Henderson, 2002. "Inflation Targeting and Nominal Income Growth Targeting: When and Why Are They Suboptimal?," Computing in Economics and Finance 2002 59, Society for Computational Economics.
  3. 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.
  4. Pierpaolo Benigno & Michael Woodford, 2006. "Linear-quadratic approximation of optimal policy problems," Discussion Papers 0607-02, Columbia University, Department of Economics.
  5. Woodford Michael, 2002. "Inflation Stabilization and Welfare," The B.E. Journal of Macroeconomics, De Gruyter, vol. 2(1), pages 1-53, February.
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  8. Schmitt-Grohe, Stephanie & Uribe, Martin, 2004. "Optimal fiscal and monetary policy under sticky prices," Journal of Economic Theory, Elsevier, vol. 114(2), pages 198-230, February.
  9. Hans M. Amman & David A. Kendrick, . "Computational Economics," Online economics textbooks, SUNY-Oswego, Department of Economics, number comp1.
  10. Pierpaolo Benigno & Michael Woodford, 2004. "Inflation stabilization and welfare: The case of a distorted steady state," Discussion Papers 0405-04, Columbia University, Department of Economics.
  11. 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.
  12. 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.
  13. Judd, Kenneth L., 1985. "Redistributive taxation in a simple perfect foresight model," Journal of Public Economics, Elsevier, vol. 28(1), pages 59-83, October.
  14. Jinill Kim & Sunghyun Henry Kim, 1999. "Spurious Welfare Reversals in International Business Cycle Models," Virginia Economics Online Papers 319, University of Virginia, 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.
  16. Lars Peter Hansen & Thomas J. Sargent, 1990. "Recursive Linear Models of Dynamic Economies," NBER Working Papers 3479, National Bureau of Economic Research, Inc.
  17. 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.
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