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Maćkowiak, B., Wiederholt, M. Optimal Sticky Prices Under Rational Inattention. Credit and Capital Markets – Kredit und Kapital, 52(4), 573-617. https://doi.org/10.3790/ccm.52.4.573
Maćkowiak, Bartosz and Wiederholt, Mirko "Optimal Sticky Prices Under Rational Inattention" Credit and Capital Markets – Kredit und Kapital 52.4, 2019, 573-617. https://doi.org/10.3790/ccm.52.4.573
Maćkowiak, Bartosz/Wiederholt, Mirko (2019): Optimal Sticky Prices Under Rational Inattention, in: Credit and Capital Markets – Kredit und Kapital, vol. 52, iss. 4, 573-617, [online] https://doi.org/10.3790/ccm.52.4.573
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Optimal Sticky Prices Under Rational Inattention

Maćkowiak, Bartosz | Wiederholt, Mirko

Credit and Capital Markets – Kredit und Kapital, Vol. 52 (2019), Iss. 4 : pp. 573–617

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Article Details

Publisher Name
Duncker & Humblot
DOI
https://doi.org/10.3790/ccm.52.4.573
Language
English
Pages
45
Keywords

Author Details

Prof. Dr. Bartosz Maćkowiak, European Central Bank, Monetary Policy Research, Kaiserstrasse 29, D-60311 Frankfurt am Main

Prof. Dr. Mirko Wiederholt, Northwestern University, Department of Economics, 2001 Sheridan Road, Evanston, IL 60208, USA

References

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  3. Angeletos, G.-M./Pavan, A. (2007): Efficient Use of Information and Social Value of Information, Econometrica, 75(4): pp. 1103–1142.  Google Scholar
  4. Ball, L./Romer, D. (1990): Real Rigidities and the Non-Neutrality of Money, Review of Economic studies, 57(2): pp. 183–203.  Google Scholar
  5. Bils M./Klenow, P. J. (2004): Some Evidence on the Importance of Sticky Prices, Journal of Political Economy, 112(5): pp. 947–985.  Google Scholar
  6. Boivin, J./Giannoni, M. P./Mihov, I. (2009): Sticky Prices and Monetary Policy: Evidence from Disaggregated US Data, American Economic Review, 99(1): pp. 350–384.  Google Scholar
  7. Boivin, J./Giannoni, M. P./Mihov, I. (1999): Monetary Policy Shocks: What Have We Learned and to What End? In Handbook of Macroeconomics. Vol. 1A, ed. John B. Taylor and Michael Woodford, pp. 65–148. Amsterdam: North-Holland.  Google Scholar
  8. Christiano, L. J./Eichenbaum, M./Evans, C. L. (2005): Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy, Journal of Political Economy, 113(1): pp. 1–45.  Google Scholar
  9. Cover, T. M./Thomas, J. A. (1991): Elements of Information Theory. New York: John Wiley and Sons.  Google Scholar
  10. Gabaix, X./Laibson, D. I. (2000): A Boundedly Rational Decision Algorithm, American Economic Review, 90(2): pp. 433–438.  Google Scholar
  11. Gertler, M./Leahy, J. (2006): A Phillips Curve with an Ss Foundation, National Bureau of Economic Research Working Paper 11971.  Google Scholar
  12. Goldberg, P. K. (1995): Product Differentiation and Oligopoly in International Markets: The Case of the U.S. Automobile Industry, Econometrica, 63(4): pp. 891–951.  Google Scholar
  13. Golosov, M./Lucas, R. E., Jr. (2007): Menu Costs and Phillips Curves, Journal of Political Economy, 115(2): pp. 171–199.  Google Scholar
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  16. Leeper, E. M./Sims, C. A./Zha, T. (1996): What Does Monetary Policy Do? Brookings Papers on Economic Activity, 1996(2): pp. 1–63.  Google Scholar
  17. Lucas, R. E. Jr. (1972): Expectations and the Neutrality of Money, Journal of Economic Theory, 4(2): pp. 103–124.  Google Scholar
  18. Lucas, R. E., Jr. (1973): Some International Evidence on Output-Inflation Tradeoffs, American Eco- nomic Review, 63(3): pp. 326–334.  Google Scholar
  19. Lucas, R. E., Jr. (1977): Understanding Business Cycles, Carnegie-Rochester Conference series on Public Policy, 5: pp. 7–29.  Google Scholar
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  21. Mankiw, N. G./Reis, R. (2002): Sticky Information versus Sticky Prices: A Proposal to Replace the New Keynesian Phillips Curve, Quarterly Journal of Economics, 117(4): pp. 1295–1328.  Google Scholar
  22. Midrigan, V. D. (2007): Menu Costs, Multi-Product Firms, and Aggregate Fluctuations, Center for Financial Studies Working Paper 2007/13.  Google Scholar
  23. Morris, S./Shin, H. S. (2002): Social Value of Public Information, American Economic Review, 92(5): pp. 1521–1534.  Google Scholar
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  28. Pischke, J. S. (1995): Individual Income, Incomplete Information, and Aggregate Consumption, Econometrica, 63(4): pp. 805–840.  Google Scholar
  29. Reis, Ri. (2006): Inattentive Producers, Review of Economic studies, 73(3): pp. 793–821.  Google Scholar
  30. Sims, C. A. (1998): Stickiness. Carnegie-Rochester Conference series on Public Policy, 49: pp. 317–356.  Google Scholar
  31. Sims, C. A. (2003): Implications of Rational Inattention, Journal of Monetary Economics, 50(3): pp. 665–690.  Google Scholar
  32. Sims, C. A. (2006): Rational Inattention: Beyond the Linear-Quadratic Case, American Economic Review, 96(2): 158–163.  Google Scholar
  33. Smets, F./Wouters, R. (2003): “An Estimated Dynamic Stochastic General Equilibrium Model of the Euro Area.” Journal of the European Economic Association, 1(5): pp. 1123–1175.  Google Scholar
  34. Taylor, J. B. (1980): Aggregate Dynamics and Staggered Contracts.” Journal of Political Economy, 88(1): pp. 1–23.  Google Scholar
  35. Townsend, R. M. (1983): Forecasting the Forecasts of Others, Journal of Political Economy, 91(4): pp. 546–588.  Google Scholar
  36. Uhlig, H. (1996): A Law of Large Numbers for Large Economies, Economic Theory, 8(1): pp. 41–50.  Google Scholar
  37. Uhlig, H. (2005): What Are the Effects of Monetary Policy on Output? Results from an Agnostic Identification Procedure, Journal of Monetary Economics, 52(2), pp. 381–419.  Google Scholar
  38. Woodford, M. (2003a): Identification Procedure. Journal of Monetary Economics, 52(2): pp. 381–419, Imperfect Common Knowledge and the Effects of Monetary Policy.  Google Scholar
  39. Woodford, M. (2003b): Interest and Prices: Foundations of a Theory of Monetary Policy, Princeton University Press.  Google Scholar
  40. Zbaracki, M. J./Ritson, M./Levy, D./Dutta, S./Bergen, M. (2004): Managerial and Customer Costs of Price Adjustment: Direct Evidence from Industrial Markets, Review of Economics and statistics, 86(2): pp. 514–533.  Google Scholar
  41. Aghion, P./Frydman, R./Stiglitz, J./Woodford, M.: Knowledge, Information, and Expectations in Modern Macroeconomics: In Honor of Edmund s. Phelps, Princeton University Press, ed., pp. 25–58.  Google Scholar
  42. Akerlof, G. A./Yellen, J. L. (1985): A Near-Rational Model of the Business Cycle, with Wage and Price Inertia, Quarterly Journal of Economics, 100(Supplement): pp. 823–838.  Google Scholar
  43. Angeletos, G.-M./Pavan, A. (2007): Efficient Use of Information and Social Value of Information, Econometrica, 75(4): pp. 1103–1142.  Google Scholar
  44. Ball, L./Romer, D. (1990): Real Rigidities and the Non-Neutrality of Money, Review of Economic studies, 57(2): pp. 183–203.  Google Scholar
  45. Bils M./Klenow, P. J. (2004): Some Evidence on the Importance of Sticky Prices, Journal of Political Economy, 112(5): pp. 947–985.  Google Scholar
  46. Boivin, J./Giannoni, M. P./Mihov, I. (2009): Sticky Prices and Monetary Policy: Evidence from Disaggregated US Data, American Economic Review, 99(1): pp. 350–384.  Google Scholar
  47. Boivin, J./Giannoni, M. P./Mihov, I. (1999): Monetary Policy Shocks: What Have We Learned and to What End? In Handbook of Macroeconomics. Vol. 1A, ed. John B. Taylor and Michael Woodford, pp. 65–148. Amsterdam: North-Holland.  Google Scholar
  48. Christiano, L. J./Eichenbaum, M./Evans, C. L. (2005): Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy, Journal of Political Economy, 113(1): pp. 1–45.  Google Scholar
  49. Cover, T. M./Thomas, J. A. (1991): Elements of Information Theory. New York: John Wiley and Sons.  Google Scholar
  50. Gabaix, X./Laibson, D. I. (2000): A Boundedly Rational Decision Algorithm, American Economic Review, 90(2): pp. 433–438.  Google Scholar
  51. Gertler, M./Leahy, J. (2006): A Phillips Curve with an Ss Foundation, National Bureau of Economic Research Working Paper 11971.  Google Scholar
  52. Goldberg, P. K. (1995): Product Differentiation and Oligopoly in International Markets: The Case of the U.S. Automobile Industry, Econometrica, 63(4): pp. 891–951.  Google Scholar
  53. Golosov, M./Lucas, R. E., Jr. (2007): Menu Costs and Phillips Curves, Journal of Political Economy, 115(2): pp. 171–199.  Google Scholar
  54. Hellwig, C./Veldkamp, L. (2009): Knowing What Others Know: Coordination Motives in Information Acquisition, Review of Economic studies, 76(1): pp. 223–251.  Google Scholar
  55. Klenow, P. J./Kryvtsov, O. (2008): State-Dependent or Time-Dependent Pricing: Does It Matter for Recent U.S. Inflation? Quarterly Journal of Economics, 123(3): pp. 863–904.  Google Scholar
  56. Leeper, E. M./Sims, C. A./Zha, T. (1996): What Does Monetary Policy Do? Brookings Papers on Economic Activity, 1996(2): pp. 1–63.  Google Scholar
  57. Lucas, R. E. Jr. (1972): Expectations and the Neutrality of Money, Journal of Economic Theory, 4(2): pp. 103–124.  Google Scholar
  58. Lucas, R. E., Jr. (1973): Some International Evidence on Output-Inflation Tradeoffs, American Eco- nomic Review, 63(3): pp. 326–334.  Google Scholar
  59. Lucas, R. E., Jr. (1977): Understanding Business Cycles, Carnegie-Rochester Conference series on Public Policy, 5: pp. 7–29.  Google Scholar
  60. Mackowiak, B. A./Wiederholt, M. (2007): Optimal Sticky Prices under Rational Inattention, Centre for Economic Policy Research Discussion Paper 6243.  Google Scholar
  61. Mankiw, N. G./Reis, R. (2002): Sticky Information versus Sticky Prices: A Proposal to Replace the New Keynesian Phillips Curve, Quarterly Journal of Economics, 117(4): pp. 1295–1328.  Google Scholar
  62. Midrigan, V. D. (2007): Menu Costs, Multi-Product Firms, and Aggregate Fluctuations, Center for Financial Studies Working Paper 2007/13.  Google Scholar
  63. Morris, S./Shin, H. S. (2002): Social Value of Public Information, American Economic Review, 92(5): pp. 1521–1534.  Google Scholar
  64. Morris, S./Shin, H.-S. (2003): Global Games: Theory and Applications, Advances in Economics and Econometrics, ed. Mathias Dewatripont, Lars Peter Hansen, and Steven J. Turnovsky, 56–114. Cambridge: Cambridge University Press.  Google Scholar
  65. Nakamura, E./Steinsson, J. (2008a): Facts about Prices: A Reevaluation of Menu Cost Models, Quarterly Journal of Economics, 123(4): pp. 1415–1464.  Google Scholar
  66. Nakamura, E./Steinsson, J. (2008b): Monetary Non-Neutrality in a Multi-Sector Menu Cost Model, National Bureau of Economic Research Working Paper 14001.  Google Scholar
  67. Phelps, E. S. (1970): Introduction: The New Microeconomics in Employment and Inflation Theory. In Microeconomic Foundations of Employment and Inflation Theory, by Edmund S. Phelps, pp. 1–23. New York: Norton.  Google Scholar
  68. Pischke, J. S. (1995): Individual Income, Incomplete Information, and Aggregate Consumption, Econometrica, 63(4): pp. 805–840.  Google Scholar
  69. Reis, Ri. (2006): Inattentive Producers, Review of Economic studies, 73(3): pp. 793–821.  Google Scholar
  70. Sims, C. A. (1998): Stickiness. Carnegie-Rochester Conference series on Public Policy, 49: pp. 317–356.  Google Scholar
  71. Sims, C. A. (2003): Implications of Rational Inattention, Journal of Monetary Economics, 50(3): pp. 665–690.  Google Scholar
  72. Sims, C. A. (2006): Rational Inattention: Beyond the Linear-Quadratic Case, American Economic Review, 96(2): 158–163.  Google Scholar
  73. Smets, F./Wouters, R. (2003): “An Estimated Dynamic Stochastic General Equilibrium Model of the Euro Area.” Journal of the European Economic Association, 1(5): pp. 1123–1175.  Google Scholar
  74. Taylor, J. B. (1980): Aggregate Dynamics and Staggered Contracts.” Journal of Political Economy, 88(1): pp. 1–23.  Google Scholar
  75. Townsend, R. M. (1983): Forecasting the Forecasts of Others, Journal of Political Economy, 91(4): pp. 546–588.  Google Scholar
  76. Uhlig, H. (1996): A Law of Large Numbers for Large Economies, Economic Theory, 8(1): pp. 41–50.  Google Scholar
  77. Uhlig, H. (2005): What Are the Effects of Monetary Policy on Output? Results from an Agnostic Identification Procedure, Journal of Monetary Economics, 52(2), pp. 381–419.  Google Scholar
  78. Woodford, M. (2003a): Identification Procedure. Journal of Monetary Economics, 52(2): pp. 381–419, Imperfect Common Knowledge and the Effects of Monetary Policy.  Google Scholar
  79. Woodford, M. (2003b): Interest and Prices: Foundations of a Theory of Monetary Policy, Princeton University Press.  Google Scholar
  80. Zbaracki, M. J./Ritson, M./Levy, D./Dutta, S./Bergen, M. (2004): Managerial and Customer Costs of Price Adjustment: Direct Evidence from Industrial Markets, Review of Economics and statistics, 86(2): pp. 514–533.  Google Scholar

Abstract

This paper presents a model in which price setting firms decide what to pay attention to, subject to a constraint on information flow. When idiosyncratic conditions are more variable or more important than aggregate conditions, firms pay more attention to idiosyncratic conditions than to aggregate conditions. When we calibrate the model to match the large average absolute size of price changes observed in micro data, prices react fast and by large amounts to idiosyncratic shocks, but only slowly and by small amounts to nominal shocks. Nominal shocks have strong and persistent real effects.

An optimizing trader will process those prices of most importance to his decision problem most frequently and carefully, those of less importance less so, and most prices not at all. Of the many sources of risk of importance to him, the business cycle and aggregate behavior generally is, for most agents, of no special importance, and there is no reason for traders to specialize their own information systems for diagnosing general movements correctly.

– Robert E. Lucas (1977, 21)

Table of Contents

Section Title Page Action Price
Bartosz Maćkowiak / Mirko Wiederholt: Optimal Sticky Prices Under Rational Inattention 573
Abstract 573
I. Quantifying Information Flow 577
II. Model 578
1. Description of the Economy 578
2. Equilibrium 573
III. Price Setting 573
IV. Analytical Solution when Exogenous Processes Are White Noise 573
V. The Firms’ Attention Problem 573
VI. Numerical Solutions 574
1. The Benchmark Economy 574
2. Varying Parameter Values 574
3. Optimal Signals 575
VII. Extensions and Shortcomings 575
1. The Gaussianity Assumption 575
2. The Independence Assumption 575
3. Reconsidering the Allocation of Attention 575
4. Shortcomings 575
VIII. Conclusion 575
Appendix A: Profit Loss 576
Appendix B: Information Flow Constraint in the White Noise Case 576
Appendix C: Proof of Lemma 1 576
Appendix D: Proof of Proportion 1 576
Appendix E: Proof of Proposition 2 576
References 576

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