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Inflation Stabilization and Welfare: The Case of a Distorted Steady State

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  • Michael Woodford
  • Pierpaolo Benigno

Abstract

We consider the appropriate objective for monetary stabilization policy in a canonical “new Keynesian†model with staggered pricing of the kind proposed by Calvo (1983), but with a complete DSGE structure of the kind presented by Yun (1996) or Woodford (2003). It is shown that under certain conditions, a quadratic approximation to the expected utility of the representative household can be expressed as a discounted sum of a weighted average of the square of the inflation rate and the square of a particular measure of the “output gap. We also show that minimization of this quadratic loss function, subject to the linear constraints implied by a log-linearization of the model structural equations, allows optimal policy to be characterized to first order in the amplitude of exogenous disturbances. Our analysis thus provides foundations for the kind of linear-quadratic analysis of optimal monetary policy undertaken in studies such as Clarida et al. (1999). Both the relative weights on the two objectives and the proper definition of the output target with respect to which the output gap is measured depend on model parameters, in a way that we characterize analytically. We also consider the second-order conditions for welfare maximization and the conditions under which welfare cannot be increased (at least locally) by arbitrary randomization of policy. We characterize optimal policy, derive targeting rules that implement optimal policy, and show how the welfare consequences of simple (sub-optimal) policy rules can be evaluated. A quadratic welfare measure of a similar sort is derived by Rotemberg and Woodford (1997) and Woodford (2002) under the special assumption that an output or employment subsidy exists that offsets the distortion due to the market power of monopolistically competitive firms, so that the steady-state equilibrium level of output is efficient (in the case of stable prices). Here we generalize those results to the case of an arbitrary level of distorting taxes, so that the steady-state level of output may be inefficient (due to taxes as well as market power). While the quadratic loss function, and hence the form of an optimal targeting rule for policy, continues to have the same general form, the size of the steady-state distortions has important consequences both for the relative weights on the alternative stabilization objectives and for the way in which various disturbances should affect the target level of output. These findings have important consequences, in turn, for the degree to which optimal policy involves inflation stabilization in the face of real disturbances.

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Bibliographic Info

Paper provided by Society for Economic Dynamics in its series 2004 Meeting Papers with number 481.

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Date of creation: 2004
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Handle: RePEc:red:sed004:481

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Postal: Society for Economic Dynamics Christian Zimmermann Economic Research Federal Reserve Bank of St. Louis PO Box 442 St. Louis MO 63166-0442 USA
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Web page: http://www.EconomicDynamics.org/society.htm
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Keywords: Optimal Monetary Policy; LQ solution;

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References

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  1. Marc P. Giannoni & Michael Woodford, 2003. "Optimal Interest-Rate Rules: I. General Theory," NBER Working Papers 9419, National Bureau of Economic Research, Inc.
  2. P. Benigno & M. Woodford, 2003. "Optimal monetary and fiscal policy: a linear-quadratic approach," Proceedings, Board of Governors of the Federal Reserve System (U.S.).
  3. Benigno, Gianluca & Benigno, Pierpaolo, 2006. "Designing targeting rules for international monetary policy cooperation," Journal of Monetary Economics, Elsevier, vol. 53(3), pages 473-506, April.
  4. Gianluca Benigno & Pierpaolo Benigno, 2004. "Designing Target Rules for International Monetary Policy Cooperation," CEP Discussion Papers dp0666, Centre for Economic Performance, LSE.
  5. Christopher A. Sims & Jinill Kim & Sunghyun Kim, 2003. "Calculating and Using Second Order Accurate Solution of Discrete Time Dynamic Equilibrium Models," Computing in Economics and Finance 2003 162, Society for Computational Economics.
  6. Aubhik Khan & Robert King & Alexander L. Wolman, 2002. "Optimal monetary policy," Working Papers 02-19, Federal Reserve Bank of Philadelphia.
  7. Michael Woodford, 2001. "Fiscal Requirements for Price Stability," NBER Working Papers 8072, National Bureau of Economic Research, Inc.
  8. Marc P. Giannoni & Michael Woodford, 2003. "Optimal Inflation Targeting Rules," NBER Working Papers 9939, National Bureau of Economic Research, Inc.
  9. Pierpaolo Benigno & Michael Woodford, 2004. "Optimal stabilization policy when wages and prices are sticky: The case of a distorted steady state," Discussion Papers 0405-03, Columbia University, Department of Economics.
  10. Pierpaolo Benigno & Michael Woodford, 2004. "Inflation Stabilization and Welfare: The Case of a Distorted Steady State," NBER Working Papers 10838, National Bureau of Economic Research, Inc.
  11. Mark Gertler & Kenneth Rogoff, 2004. "NBER Macroeconomics Annual 2003, Volume 18," NBER Books, National Bureau of Economic Research, Inc, number gert04-1, October.
  12. Julio Rotemberg & Michael Woodford, 1997. "An Optimization-Based Econometric Framework for the Evaluation of Monetary Policy," NBER Chapters, in: NBER Macroeconomics Annual 1997, Volume 12, pages 297-361 National Bureau of Economic Research, Inc.
  13. Clarida, R. & Gali, J. & Gertler, M., 1999. "The Science of Monetary Policy: A New Keynesian Perspective," Working Papers 99-13, C.V. Starr Center for Applied Economics, New York University.
  14. Michael Woodford, 1999. "Commentary : how should monetary policy be conducted in an era of price stability?," Proceedings - Economic Policy Symposium - Jackson Hole, Federal Reserve Bank of Kansas City, pages 277-316.
  15. Robert King & Alexander L. Wolman, 1999. "What Should the Monetary Authority Do When Prices Are Sticky?," NBER Chapters, in: Monetary Policy Rules, pages 349-404 National Bureau of Economic Research, Inc.
  16. Marvin Goodfriend & Robert G. King, 1998. "The new neoclassical synthesis and the role of monetary policy," Working Paper 98-05, Federal Reserve Bank of Richmond.
  17. Sutherland, Alan, 2002. "A Simple Second-Order Solution Method For Dynamic General Equilibrium Models," CEPR Discussion Papers 3554, C.E.P.R. Discussion Papers.
  18. Dupor, Bill, 2003. "Optimal random monetary policy with nominal rigidity," Journal of Economic Theory, Elsevier, vol. 112(1), pages 66-78, September.
  19. V. V. Chari & Patrick J. Kehoe & Ellen R. McGrattan, 1996. "Sticky Price Models of the Business Cycle: Can the Contract Multiplier Solve the Persistence Problem?," NBER Working Papers 5809, National Bureau of Economic Research, Inc.
  20. 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.
  21. Christopher J. Erceg & Dale W. Henderson & Andrew T. Levin, 1999. "Optimal monetary policy with staggered wage and price contracts," International Finance Discussion Papers 640, Board of Governors of the Federal Reserve System (U.S.).
  22. Calvo, Guillermo A., 1983. "Staggered prices in a utility-maximizing framework," Journal of Monetary Economics, Elsevier, vol. 12(3), pages 383-398, September.
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