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Logit price dynamics

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  • James Costain

    ()
    (Banco de España)

  • Anton Nakov

    ()
    (Banco de España)

Abstract

We propose a near-rational model of retail price adjustment consistent with microeconomic and macroeconomic evidence on price dynamics. Our framework is based on the idea that avoiding errors in decision making is costly. Given our assumed cost function for error avoidance, the timing of firms’ price adjustments is determined by a weighted binary logit, and the prices they choose are determined by a multinomial logit. We build this behavior into a DSGE model, estimate the decision cost function by matching microdata, and simulate aggregate dynamics using a tractable algorithm for heterogeneous-agent models. Both errors in the prices firms set, and errors in the timing of these adjustments, are relevant for our results. Errors of the first type help make our model consistent with some puzzling observations from microdata, such as the coexistence of large and small price changes, the behavior of adjustment hazards, and the relative variability of prices and costs. Errors of the second type increase the real effects of monetary shocks, by reducing the correlation between the value of price adjustment and the probability of adjustment, (i.e., by reducing the\selection effect»). Allowing for both types of errors also helps reproduce the effects of trend inflation on price adjustment behavior. Our model of error-prone pricing in many ways resembles a stochastic menu cost (SMC) model, but it has less free parameters than most SMC models have, and unlike those models, it does not require the implausible assumption of i.i.d. adjustment costs. Our derivation of a weighted logit from control costs oers an alternative justication for the adjustment hazard derived by Woodford (2008). Our assumption that costs are related to entropy is similar to the framework of Sims (2003) and the subsequent\rational inattention» literature. However, our setup has the major technical advantage that a firm’s idiosyncratic state variable is simply its price level and productivity, whereas under rational inattention a firm’s idiosyncratic state is its prior (which is generally an infinite-dimensional object).

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File URL: http://www.bde.es/f/webbde/SES/Secciones/Publicaciones/PublicacionesSeriadas/DocumentosTrabajo/13/Fich/dt1301e.pdf
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Bibliographic Info

Paper provided by Banco de Espa�a in its series Banco de Espa�a Working Papers with number 1301.

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Length: 55 pages
Date of creation: Feb 2013
Date of revision:
Handle: RePEc:bde:wpaper:1301

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Related research

Keywords: nominal rigidity; logit equilibrium; state-dependent pricing; near rationality; information-constrained pricing;

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References

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  1. Robert Lucas & Mike Golosov, 2004. "Menu Costs and Phillips Curves," 2004 Meeting Papers 144, Society for Economic Dynamics.
  2. Emi Nakamura & Jón Steinsson, 2008. "Five Facts about Prices: A Reevaluation of Menu Cost Models," The Quarterly Journal of Economics, MIT Press, vol. 123(4), pages 1415-1464, November.
  3. Filip Matejka, 2010. "Rationally Inattentive Seller: Sales and Discrete Pricing," CERGE-EI Working Papers wp408, The Center for Economic Research and Graduate Education - Economic Institute, Prague.
  4. Philip A. Haile & Ali Hortacsu & Grigory Kosenok, 0820. "On the Empirical Content of Quantal Response Equilibrium," Cowles Foundation Discussion Papers 1432R, Cowles Foundation for Research in Economics, Yale University, revised Jun 0820.
  5. Mark Zbaracki & Mark Ritson & Daniel Levy & Shantanu Dutta & Mark Bergen, 2004. "Managerial and Customer Costs of Price Adjustment: Direct Evidence from Industrial Markets," Macroeconomics 0402020, EconWPA.
  6. Caplin, Andrew S & Spulber, Daniel F, 1987. "Menu Costs and the Neutrality of Money," The Quarterly Journal of Economics, MIT Press, vol. 102(4), pages 703-25, November.
  7. Peter J. Klenow & Oleksiy Kryvtsov, 2005. "State-Dependent or Time-Dependent Pricing: Does it Matter for Recent U.S. Inflation?," NBER Working Papers 11043, National Bureau of Economic Research, Inc.
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  9. 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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  12. Mattsson, Lars-Goran & Weibull, Jorgen W., 2002. "Probabilistic choice and procedurally bounded rationality," Games and Economic Behavior, Elsevier, vol. 41(1), pages 61-78, October.
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  14. Marsili, Matteo, 1999. "On the multinomial logit model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 269(1), pages 9-15.
  15. Alisdair McKay & Filip Matejka, 2011. "Rational Inattention to Discrete Choices: A New Foundation for the Multinomial Logit Model," 2011 Meeting Papers 535, Society for Economic Dynamics.
  16. 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.
  17. Simon P. Anderson & Jacob K. Goeree & Charles A. Holt, 1999. "The Logit Equilibrium: A Perspective on Intuitive Behavioral Anomalies," Virginia Economics Online Papers 332, University of Virginia, Department of Economics.
  18. Patrick J. Kehoe & Virgiliu Midrigan, 2010. "Prices are Sticky After All," NBER Working Papers 16364, National Bureau of Economic Research, Inc.
  19. Barro, Robert J, 1972. "A Theory of Monopolistic Price Adjustment," Review of Economic Studies, Wiley Blackwell, vol. 39(1), pages 17-26, January.
  20. Richard Blundell & Steve Bond, 1999. "GMM estimation with persistent panel data: an application to production functions," IFS Working Papers W99/04, Institute for Fiscal Studies.
  21. Sims, Christopher A., 2003. "Implications of rational inattention," Journal of Monetary Economics, Elsevier, vol. 50(3), pages 665-690, April.
  22. James W. Bono & David H. Wolpert, 2009. "Statistical prediction of the outcome of a noncooperative game," Working Papers 2009-20, American University, Department of Economics.
  23. Martin Eichenbaum & Nir Jaimovich & Sergio Rebelo, 2011. "Reference Prices, Costs, and Nominal Rigidities," American Economic Review, American Economic Association, vol. 101(1), pages 234-62, February.
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