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COMPUTING MARKOV-PERFECT OPTIMAL POLICIES IN BUSINESS-CYCLE MODELS

Published online by Cambridge University Press:  28 September 2015

Richard Dennis  and
Tatiana Kirsanova
Richard Dennis*
Affiliation:
University of Glasgow
Tatiana Kirsanova
Affiliation:
University of Glasgow
*
Address correspondence to: Richard Dennis, Adam Smith Business School, University of Glasgow, Main Building, University Avenue, Glasgow G12 8QQ, United Kingdom; e-mail: richard.dennis@glasgow.ac.uk.
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Abstract

Time inconsistency is an essential feature of many policy problems. This paper presents and compares three methods for computing Markov-perfect optimal policies in stochastic nonlinear business cycle models. The methods considered include value function iteration, generalized Euler equations, and parameterized shadow prices. In the context of a business cycle model in which a fiscal authority chooses government spending and income taxation optimally, although lacking the ability to commit, we show that the solutions obtained using value function iteration and generalized Euler equations are somewhat more accurate than that obtained using parameterized shadow prices. Among these three methods, we show that value function iteration can be applied easily, even to environments that include a risk-sensitive fiscal authority and/or inequality constraints on government spending. We show that the risk-sensitive fiscal authority lowers government spending and income taxation, reducing the disincentive to accumulate wealth that households face.

Keywords

Markov-Perfect PolicyTime ConsistencyFiscal Policy
Type
Articles
Information
Macroeconomic Dynamics , Volume 20 , Issue 7 , October 2016 , pp. 1850 - 1872
Copyright
Copyright © Cambridge University Press 2015 

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References

REFERENCES

Adam, Klaus and Billi, Roberto (2007) Discretionary monetary policy and the zero-bound on nominal interest rates. Journal of Monetary Economics 54, 728–754.CrossRefGoogle Scholar
Ambler, Steve and Pelgrin, Florin (2010) Time-consistent control in nonlinear models. Journal of Economic Dynamics and Control 34, 2215–2228.Google Scholar
Anderson, Gary, Kim, Jinill, and Yun, Tack (2010) Using a projection method to analyze inflation bias in a micro-founded model. Journal of Economic Dynamics and Control 34, 1572–1581.Google Scholar
Backus, David and Driffill, John (1986) The Consistency of Optimal Policy in Stochastic Rational Expectations Models. Centre for Economic Policy Research discussion paper 124.Google Scholar
Benhabib, Jess and Rustichini, Aldo (1997) Optimal taxes without commitment. Journal of Economic Theory 77, 231–259.CrossRefGoogle Scholar
Benveniste, Lawrence and Scheinkman, Jose (1979) On the differentiability of the value function in dynamic models of economies. Econometrica 47, 727–732.Google Scholar
Christiano, Lawrence and Fisher, Jonus (2000) Algorithms for solving dynamic models with occasionally binding constraints. Journal of Economic Dynamics and Control 24, 1179–1232.Google Scholar
Clarida, Richard, Galí, Jordi, and Gertler, Mark (1999) The science of monetary policy: A New Keynesian perspective. Journal of Economic Literature 37, 1661–1707.Google Scholar
Cohen, Daniel and Michel, Philippe (1988) How should control theory be used to calculate a time-consistent government policy. Review of Economic Studies 55, 263–274.CrossRefGoogle Scholar
Currie, David and Levine, Paul (1985) Macroeconomic policy design in an interdependent world. In Buiter, Willem and Marston, Richard (eds.), International Economic Policy Coordination, pp. 228–273. Cambridge, UK: Cambridge University Press.Google Scholar
Currie, David and Levine, Paul (1993) Rules, Reputation and Macroeconomic Policy Coordination. Cambridge, UK: Cambridge University Press.CrossRefGoogle Scholar
Dennis, Richard (2007) Optimal policy in rational expectations models: New solution algorithms. Macroeconomic Dynamics 11, 31–55.Google Scholar
Domínguez, Begoña (2007) Public debt and optimal taxes without commitment. Journal of Economic Theory 135, 159–170.Google Scholar
Hansen, Lars and Sargent, Thomas (2008) Robustness. Princeton, NJ: Princeton University Press.Google Scholar
Inada, Ken-Ichi (1963) On a two-sector model of economic growth: Comments and a generalization. Review of Economic Studies 30, 119–127.CrossRefGoogle Scholar
Judd, Kenneth (1992) Projection methods for solving aggregate growth models. Journal of Economic Theory 58, 410–452.Google Scholar
Klein, Paul, Krusell, Per, and Rios-Rull, Jose-Victor (2008) Time-consistent public policy. Review of Economic Studies 75, 789–808.CrossRefGoogle Scholar
Klein, Paul and Rios-Rull, Jose-Victor (2003) Time-consistent optimal fiscal policy. International Economic Review 44, 1217–1245.Google Scholar
Kydland, Finn and Prescott, Edward (1977) Rules rather than discretion: The inconsistency of optimal plans. Journal of Political Economy 85, 473–491.CrossRefGoogle Scholar
Malin, Benjamin, Krueger, Dirk, and Kubler, Felix (2011) Solving the multi-country real business cycle model using a Smolyak-collocation method. Journal of Economic Dynamics and Control 35, 229–239.Google Scholar
Marcet, Albert and Lorenzoni, Guido (1999) The parameterized expectations approach: Some practical issues. In Marimon, Ramon and Scott, Andrew (eds.), Computational Methods for the Study of Dynamic Economies, pp. 143–171. Oxford, UK: Oxford University Press.Google Scholar
Martin, Fernando (in press) Policy and welfare effects of within-period commitment. Macroeconomic Dynamics.Google Scholar
Nakata, Taisuke (2013) Optimal Fiscal and Monetary Policy with Occasionally Binding Zero-bound Constraints. Finance and Economics Discussion Series 2013-40, Board of Governors of the Federal Reserve System.Google Scholar
Niemann, Stefan, Pichler, Paul, and Sorger, Gerhard (2008) Optimal Fiscal and Monetary Policy without Commitment. University of Essex Discussion Papers No. 654.Google Scholar
Niemann, Stefan, Pichler, Paul, and Sorger, Gerhard (2009) Inflation Dynamics under Optimal Discretionary Fiscal and Monetary Policies. University of Essex Discussion Papers No. 681.Google Scholar
Ortigueira, Salvador (2006) Markov-perfect optimal taxation. Review of Economic Dynamics 9, 153–178.Google Scholar
Ortigueira, Savador, Pereira, Joana, and Pichler, Paul (2012) Markov-Perfect Optimal Fiscal Policy: The Case of Unbalanced Budgets. Universidad Carlos III Economic Working Papers 1230.Google Scholar
Oudiz, Gilles, and Sachs, Jeffrey (1985) International policy coordination in dynamic macroeconomic models. In Buiter, Willem and Marston, Richard (eds.), International Economic Policy Coordination, pp. 274–330.Google Scholar
Pichler, Paul (2011) Solving the multi-country real business cycle model using a monomial rule Galerkin method. Journal of Economic Dynamics and Control 35, 240–251.Google Scholar
Smolyak, Sergey (1963) Quadrature and interpolation formulas for tensor products of certain classes of functions. Soviet Mathematics Doklady 4, 240–243.Google Scholar
Söderlind, Paul (1999) Solution and estimation of RE macromodels with optimal policy. European Economic Review 43, 813–823.Google Scholar
Stockman, David (2001) Balanced-budget rules: Welfare loss and optimal policies. Review of Economic Dynamics 4, 438–459.Google Scholar
Woodford, Michael (2003) Interest and Prices: Foundations of a Theory of Monetary Policy. Princeton, NJ: Princeton University Press.Google Scholar