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Alternative methods of solving state-dependent pricing models

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  • Edward S. Knotek
  • Stephen J. Terry

Abstract

We use simulation-based techniques to compare and contrast two methods for solving state-dependent pricing models: discretization, which solves and simulates the model on a grid; and collocation, which relies on Chebyshev polynomials. While both methods produce qualitatively similar results, statistically significant quantitative differences do arise. We present evidence favoring discretization over collocation in this context, given a lack of robustness in the latter.

Suggested Citation

  • Edward S. Knotek & Stephen J. Terry, 2008. "Alternative methods of solving state-dependent pricing models," Research Working Paper RWP 08-10, Federal Reserve Bank of Kansas City.
    • Handle: RePEc:fip:fedkrw:rwp08-10
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    File URL: https://www.kansascityfed.org/documents/5327/pdf-rwp08-10.pdf
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    1. Peter J. Klenow & Oleksiy Kryvtsov, 2008. "State-Dependent or Time-Dependent Pricing: Does it Matter for Recent U.S. Inflation?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 123(3), pages 863-904.
    2. Michael Dotsey & Robert G. King & Alexander L. Wolman, 1999. "State-Dependent Pricing and the General Equilibrium Dynamics of Money and Output," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(2), pages 655-690.
    3. Levy, Daniel & Bergen, Mark & Dutta, Shantanu & Venable, Robert, 1997. "The Magnitude of Menu Costs: Direct Evidence from Large U.S. Supermarket Chains," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 112(3), pages 791-824.
    4. Emi Nakamura & Jón Steinsson, 2010. "Monetary Non-neutrality in a Multisector Menu Cost Model," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 125(3), pages 961-1013.
    5. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
    6. N. Gregory Mankiw & Ricardo Reis, 2002. "Sticky Information versus Sticky Prices: A Proposal to Replace the New Keynesian Phillips Curve," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 117(4), pages 1295-1328.
    7. Mark J. Zbaracki & Mark Ritson & Daniel Levy & Shantanu Dutta & Mark Bergen, 2004. "Managerial and Customer Costs of Price Adjustment: Direct Evidence from Industrial Markets," The Review of Economics and Statistics, MIT Press, vol. 86(2), pages 514-533, May.
    8. Dotsey, Michael & King, Robert G., 2005. "Implications of state-dependent pricing for dynamic macroeconomic models," Journal of Monetary Economics, Elsevier, vol. 52(1), pages 213-242, January.
    9. Tauchen, George, 1986. "Finite state markov-chain approximations to univariate and vector autoregressions," Economics Letters, Elsevier, vol. 20(2), pages 177-181.
    10. Klenow, Peter J. & Willis, Jonathan L., 2007. "Sticky information and sticky prices," Journal of Monetary Economics, Elsevier, vol. 54(Supplemen), pages 79-99, September.
    11. Reiter, Michael, 2009. "Solving heterogeneous-agent models by projection and perturbation," Journal of Economic Dynamics and Control, Elsevier, vol. 33(3), pages 649-665, March.
    12. Mikhail Golosov & Robert E. Lucas Jr., 2007. "Menu Costs and Phillips Curves," Journal of Political Economy, University of Chicago Press, vol. 115(2), pages 171-199.
    13. Peter J. Klenow & Jonathan L. Willis, 2016. "Real Rigidities and Nominal Price Changes," Economica, London School of Economics and Political Science, vol. 83(331), pages 443-472, July.
    14. Terry, Stephen J. & Knotek II, Edward S., 2011. "Markov-chain approximations of vector autoregressions: Application of general multivariate-normal integration techniques," Economics Letters, Elsevier, vol. 110(1), pages 4-6, January.
    15. Virgiliu Midrigan, 2011. "Menu Costs, Multiproduct Firms, and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 79(4), pages 1139-1180, July.
    16. Juan Carlos Hatchondo & Leonardo Martinez & Horacio Sapriza, 2009. "On the cyclicality of the interest rate in emerging economy models: solution methods matter," Working Paper 09-13, Federal Reserve Bank of Richmond.
    17. Ricardo Reis, 2006. "Inattentive Producers," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 73(3), pages 793-821.
    18. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    19. Emi Nakamura & Jón Steinsson, 2008. "Five Facts about Prices: A Reevaluation of Menu Cost Models," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 123(4), pages 1415-1464.
    20. Koop, Gary & Pesaran, M. Hashem & Potter, Simon M., 1996. "Impulse response analysis in nonlinear multivariate models," Journal of Econometrics, Elsevier, vol. 74(1), pages 119-147, September.
    21. Aruoba, S. Boragan & Fernandez-Villaverde, Jesus & Rubio-Ramirez, Juan F., 2006. "Comparing solution methods for dynamic equilibrium economies," Journal of Economic Dynamics and Control, Elsevier, vol. 30(12), pages 2477-2508, December.
    22. Edward S. Knotek Ii, 2010. "A Tale of Two Rigidities: Sticky Prices in a Sticky-Information Environment," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 42(8), pages 1543-1564, December.
    23. Per Krusell & Anthony A. Smith & Jr., 1998. "Income and Wealth Heterogeneity in the Macroeconomy," Journal of Political Economy, University of Chicago Press, vol. 106(5), pages 867-896, October.
    24. Ricardo J. Caballero & Eduardo M. R. A. Engel, 1993. "Heterogeneity and Output Fluctuations in a Dynamic Menu-Cost Economy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(1), pages 95-119.
    25. Sims, Christopher A., 2003. "Implications of rational inattention," Journal of Monetary Economics, Elsevier, vol. 50(3), pages 665-690, April.
    26. Julio J. Rotemberg, 1987. "The New Keynesian Microfoundations," NBER Chapters, in: NBER Macroeconomics Annual 1987, Volume 2, pages 69-116, National Bureau of Economic Research, Inc.
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    Cited by:

    1. Hobijn, Bart & Nechio, Fernanda & Shapiro, Adam Hale, 2021. "Using Brexit to identify the nature of price rigidities," Journal of International Economics, Elsevier, vol. 130(C).
    2. Knotek, Edward S., 2024. "The roles of price points and menu costs in price rigidity," Journal of Monetary Economics, Elsevier, vol. 145(C).
    3. Stephen J. Terry, 2017. "Alternative Methods for Solving Heterogeneous Firm Models," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 49(6), pages 1081-1111, September.
    4. Matthew Klepacz, 2018. "Price Setting and Volatility: Evidence from Oil Price Volatility Shocks," 2018 Meeting Papers 145, Society for Economic Dynamics.
    5. Joseph Vavra, 2011. "Inflation Dynamics and Time-Varying Uncertainty: New Evidence and an Ss Interpretation," 2011 Meeting Papers 126, Society for Economic Dynamics.
    6. Matthew Klepacz, 2021. "Price Setting and Volatility: Evidence from Oil Price Volatility Shocks," International Finance Discussion Papers 1316, Board of Governors of the Federal Reserve System (U.S.).
    7. David Berger, 2012. "Countercyclical Restructuring and Jobless Recoveries," 2012 Meeting Papers 1179, Society for Economic Dynamics.
    8. Joseph Vavra, 2014. "Inflation Dynamics and Time-Varying Volatility: New Evidence and an Ss Interpretation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 129(1), pages 215-258.

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