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Asymmetric Price Adjustment in the Small

Author

Listed:
  • Levy, Daniel
  • Chen, Haipeng (Allan)
  • Ray, Sourav
  • Bergen, Mark
Abstract
Analyzing a large weekly retail transaction price dataset, we uncover a surprising regularity—small price increases occur more frequently than small price decreases for price changes of up to about 10 cents, while there is no such asymmetry for larger price changes. The asymmetry holds for the entire sample and for individual categories. We find that while inflation can explain some of the asymmetry, inflation is not the whole story as the asymmetry holds even after excluding inflationary periods from the data, and even for products whose price had not increased over the eight-year period. The findings hold for different measures of inflation and also after allowing for lagged price adjustments. We offer a consumer-based explanation for these findings.

Suggested Citation

  • Levy, Daniel & Chen, Haipeng (Allan) & Ray, Sourav & Bergen, Mark, 2006. "Asymmetric Price Adjustment in the Small," MPRA Paper 1097, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:1097
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    1. Reis, Ricardo, 2006. "Inattentive consumers," Journal of Monetary Economics, Elsevier, vol. 53(8), pages 1761-1800, November.
    2. Mark Bils & Peter J. Klenow, 2004. "Some Evidence on the Importance of Sticky Prices," Journal of Political Economy, University of Chicago Press, vol. 112(5), pages 947-985, October.
    3. Adam, Klaus, 2007. "Optimal monetary policy with imperfect common knowledge," Journal of Monetary Economics, Elsevier, vol. 54(2), pages 267-301, March.
    4. Besley, Timothy J. & Rosen, Harvey S., 1999. "Sales Taxes and Prices: An Empirical Analysis," National Tax Journal, National Tax Association;National Tax Journal, vol. 52(2), pages 157-178, June.
    5. Basu, Susanto, 1995. "Intermediate Goods and Business Cycles: Implications for Productivity and Welfare," American Economic Review, American Economic Association, vol. 85(3), pages 512-531, June.
    6. Dutta, Shantanu & Bergen, Mark & Levy, Daniel, 2002. "Price flexibility in channels of distribution: Evidence from scanner data," Journal of Economic Dynamics and Control, Elsevier, vol. 26(11), pages 1845-1900, September.
    7. Anil K Kashyap, 1995. "Sticky Prices: New Evidence from Retail Catalogs," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 110(1), pages 245-274.
    8. N. Gregory Mankiw, 1985. "Small Menu Costs and Large Business Cycles: A Macroeconomic Model of Monopoly," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 100(2), pages 529-538.
    9. Ricardo Reis, 2006. "Inattentive Producers," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 73(3), pages 793-821.
    10. Gordon, Robert J, 1990. "What Is New-Keynesian Economics?," Journal of Economic Literature, American Economic Association, vol. 28(3), pages 1115-1171, September.
    11. Julio J. Rotemberg, 2008. "Behavioral Aspects of Price Setting, and Their Policy Implications," NBER Working Papers 13754, National Bureau of Economic Research, Inc.
    12. 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.
    13. Baudry, L. & Le Bihan, H. & Sevestre, P. & Tarrieu, S., 2004. "Price Rigidity. Evidence from the French CPI Macro-Data," Working papers 113, Banque de France.
    14. 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.
    15. Ball, Laurence & Gregory Mankiw, N. & Reis, Ricardo, 2005. "Monetary policy for inattentive economies," Journal of Monetary Economics, Elsevier, vol. 52(4), pages 703-725, May.
    16. Dutta, Shantanu, et al, 1999. "Menu Costs, Posted Prices, and Multiproduct Retailers," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 31(4), pages 683-703, November.
    17. Coenen, Gunter & Levin, Andrew T. & Christoffel, Kai, 2007. "Identifying the influences of nominal and real rigidities in aggregate price-setting behavior," Journal of Monetary Economics, Elsevier, vol. 54(8), pages 2439-2466, November.
    18. Lach, Saul & Tsiddon, Daniel, 1996. "Staggering and Synchronization in Price-Setting: Evidence from Multiproduct Firms," American Economic Review, American Economic Association, vol. 86(5), pages 1175-1196, December.
    19. Tobin, James, 1982. "Money and Finance in the Macroeconomic Process," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 14(2), pages 171-204, May.
    20. Ray, Sourav & Chen, Haipeng (Allan) & Bergen, Mark & Levy, Daniel, 2006. "Asymmetric Wholesale Pricing: Theory and Evidence," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 25(2), pages 109-201.
    21. Ronald W. Ward, 1982. "Asymmetry in Retail, Wholesale, and Shipping Point Pricing for Fresh Vegetables," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 64(2), pages 205-212.
    22. Ball, Laurence & Romer, David, 2003. "Inflation and the Informativeness of Prices," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 35(2), pages 177-196, April.
    23. Milton S. Boyd & B. Wade Brorsen, 1988. "Price Asymmetry in the U.S. Pork Marketing Channel," Review of Agricultural Economics, Agricultural and Applied Economics Association, vol. 10(1), pages 103-109.
    24. Robert B. Barsky & Mark Bergen & Shantanu Dutta & Daniel Levy, 2003. "What Can the Price Gap between Branded and Private-Label Products Tell Us about Markups?," NBER Chapters, in: Scanner Data and Price Indexes, pages 165-225, National Bureau of Economic Research, Inc.
    25. Hernando, Ignacio & Álvarez, Luis J., 2004. "Price setting behaviour in Spain: stylised facts using consumer price micro data," Working Paper Series 416, European Central Bank.
    26. Samuelson, William & Zeckhauser, Richard, 1988. "Status Quo Bias in Decision Making," Journal of Risk and Uncertainty, Springer, vol. 1(1), pages 7-59, March.
    27. Levy, Daniel & Dutta, Shantanu & Bergen, Mark & Venable, Robert, 1998. "Price Adjustment at Multiproduct Retailers," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 19(2), pages 81-120.
    28. Leif Danziger, 1999. "A Dynamic Economy with Costly Price Adjustments," American Economic Review, American Economic Association, vol. 89(4), pages 878-901, September.
    29. Mark Bergen & Daniel Levy & Sourav Ray & Paul H. Rubin & Benjamin Zeliger, 2008. "When Little Things Mean a Lot: On the Inefficiency of Item-Pricing Laws," Journal of Law and Economics, University of Chicago Press, vol. 51(2), pages 209-250, May.
    30. Carlton, Dennis W, 1986. "The Rigidity of Prices," American Economic Review, American Economic Association, vol. 76(4), pages 637-658, September.
    31. Fisher, Timothy C. G. & Konieczny, Jerzy D., 2006. "Inflation and Costly Price Adjustment: A Study of Canadian Newspaper Prices," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 38(3), pages 615-633, April.
    32. Gupta, Sunil & Cooper, Lee G, 1992. "The Discounting of Discounts and Promotion Thresholds," Journal of Consumer Research, Journal of Consumer Research Inc., vol. 19(3), pages 401-411, December.
    33. 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.
    34. Frank, Murray & Jagannathan, Ravi, 1998. "Why do stock prices drop by less than the value of the dividend? Evidence from a country without taxes," Journal of Financial Economics, Elsevier, vol. 47(2), pages 161-188, February.
    35. David Neumark & Steven A. Sharpe, 1992. "Market Structure and the Nature of Price Rigidity: Evidence from the Market for Consumer Deposits," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 107(2), pages 657-680.
    36. Gadi Fibich & Arieh Gavious & Oded Lowengart, 2007. "Optimal price promotion in the presence of asymmetric reference-price effects," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 28(6), pages 569-577.
    37. Eytan Sheshinski & Yoram Weiss, 1992. "Staggered and Synchronized Price Policies Under Inflation: The Multiproduct Monopoly Case," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 59(2), pages 331-359.
    38. Levy, Daniel & Dutta, Shantanu & Bergen, Mark, 2002. "Heterogeneity in Price Rigidity: Evidence from a Case Study Using Microlevel Data," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 34(1), pages 197-220, February.
    39. Lach, Saul & Tsiddon, Daniel, 1992. "The Behavior of Prices and Inflation: An Empirical Analysis of Disaggregated Price Data," Journal of Political Economy, University of Chicago Press, vol. 100(2), pages 349-389, April.
    40. Eytan Sheshinski & Yoram Weiss, 1977. "Inflation and Costs of Price Adjustment," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 44(2), pages 287-303.
    41. Robert B. Barsky & Christopher L. House & Miles S. Kimball, 2007. "Sticky-Price Models and Durable Goods," American Economic Review, American Economic Association, vol. 97(3), pages 984-998, June.
    42. Ball, Laurence & Mankiw, N Gregory, 1994. "Asymmetric Price Adjustment and Economic Fluctuations," Economic Journal, Royal Economic Society, vol. 104(423), pages 247-261, March.
    43. Eichenbaum, Martin & Rebelo, Sérgio & Jaimovich, Nir, 2008. "Reference Prices and Nominal Rigidities," CEPR Discussion Papers 6709, C.E.P.R. Discussion Papers.
    44. Daniel Tsiddon, 1993. "The (Mis)Behaviour of the Aggregate Price Level," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(4), pages 889-902.
    45. Georg Müller & Sourav Ray, 2007. "Asymmetric price adjustment: evidence from weekly product-level scanner price data," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 28(7), pages 723-736.
    46. Levy, Daniel & Young, Andrew T., 2004. ""The Real Thing:" Nominal Price Rigidity of the Nickel Coke, 1886-1959," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 36(4 (Specia), pages 765-799.
    47. Konieczny, Jerzy D. & Skrzypacz, Andrzej, 2005. "Inflation and price setting in a natural experiment," Journal of Monetary Economics, Elsevier, vol. 52(3), pages 621-632, April.
    48. Daniel H. Pick & Jeffrey Karrenbrock & Hoy F. Carman, 1990. "Price asymmetry and marketing margin behavior: An example for California-Arizona citrus," Agribusiness, John Wiley & Sons, Ltd., vol. 6(1), pages 75-84.
    49. 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.
    50. Laurence Ball & N. Gregory Mankiw, 1995. "Relative-Price Changes as Aggregate Supply Shocks," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 110(1), pages 161-193.
    51. Klenow, Peter J. & Willis, Jonathan L., 2007. "Sticky information and sticky prices," Journal of Monetary Economics, Elsevier, vol. 54(Supplemen), pages 79-99, September.
    52. Davis, Michael C & Hamilton, James D, 2004. "Why Are Prices Sticky? The Dynamics of Wholesale Gasoline Prices," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 36(1), pages 17-37, February.
    53. Judith A. Chevalier & Anil K. Kashyap & Peter E. Rossi, 2003. "Why Don't Prices Rise During Periods of Peak Demand? Evidence from Scanner Data," American Economic Review, American Economic Association, vol. 93(1), pages 15-37, March.
    54. Sam Peltzman, 2000. "Prices Rise Faster than They Fall," Journal of Political Economy, University of Chicago Press, vol. 108(3), pages 466-502, June.
    55. Elizabeth J. Warner & Robert B. Barsky, 1995. "The Timing and Magnitude of Retail Store Markdowns: Evidence from Weekends and Holidays," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 110(2), pages 321-352.
    56. Rotemberg, Julio J., 2005. "Customer anger at price increases, changes in the frequency of price adjustment and monetary policy," Journal of Monetary Economics, Elsevier, vol. 52(4), pages 829-852, May.
    57. Sims, Christopher A., 2003. "Implications of rational inattention," Journal of Monetary Economics, Elsevier, vol. 50(3), pages 665-690, April.
    58. Leif Danziger, 2001. "Output and Welfare Effects of Inflation with Costly Price and Quantity Adjustments," American Economic Review, American Economic Association, vol. 91(5), pages 1608-1620, December.
    59. Anthony Downs, 1957. "An Economic Theory of Political Action in a Democracy," Journal of Political Economy, University of Chicago Press, vol. 65(2), pages 135-135.
    60. Bacon, Robert W., 1991. "Rockets and feathers: the asymmetric speed of adjustment of UK retail gasoline prices to cost changes," Energy Economics, Elsevier, vol. 13(3), pages 211-218, July.
    61. Saul Lach & Daniel Tsiddon, 2007. "Small price changes and menu costs," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 28(7), pages 649-656.
    62. Shugan, Steven M, 1980. "The Cost of Thinking," Journal of Consumer Research, Journal of Consumer Research Inc., vol. 7(2), pages 99-111, Se.
    63. 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.
    64. Cecchetti, Stephen G., 1986. "The frequency of price adjustment : A study of the newsstand prices of magazines," Journal of Econometrics, Elsevier, vol. 31(3), pages 255-274, April.
    65. Jeffrey D. Karrenbrock, 1991. "The behavior of retail gasoline prices: symmetric or not?," Review, Federal Reserve Bank of St. Louis, issue Jul, pages 19-29.
    66. Alan Kackmeister, 2007. "Yesterday's Bad Times Are Today's Good Old Times: Retail Price Changes Are More Frequent Today Than in the 1890s," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(8), pages 1987-2020, December.
    67. Kalyanaram, Gurumurthy & Little, John D C, 1994. "An Empirical Analysis of Latitude of Price Acceptance in Consumer Package Goods," Journal of Consumer Research, Journal of Consumer Research Inc., vol. 21(3), pages 408-418, December.
    68. Mark J. Zbaracki & Mark Bergen & Daniel Levy, 2006. "The Anatomy of a Price Cut: Discovering Organizational Sources of the Costs of Price Adjustment," Working Papers 2006-3, Bar-Ilan University, Department of Economics.
    69. Haipeng (Allan) Chen & Akshay R. Rao, 2002. "Close Encounters of Two Kinds: False Alarms and Dashed Hopes," Marketing Science, INFORMS, vol. 21(2), pages 178-196, August.
    70. Julio J. Rotemberg, 1982. "Monopolistic Price Adjustment and Aggregate Output," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 49(4), pages 517-531.
    71. Julio J. Rotemberg, 2002. "Customer Anger at Price Increases, Time Variation in the Frequency of Price Changes and Monetary Policy," NBER Working Papers 9320, National Bureau of Economic Research, Inc.
    72. Hannan, Timothy H & Berger, Allen N, 1991. "The Rigidity of Prices: Evidence from the Banking Industry," American Economic Review, American Economic Association, vol. 81(4), pages 938-945, September.
    73. Kahneman, Daniel & Knetsch, Jack L & Thaler, Richard, 1986. "Fairness as a Constraint on Profit Seeking: Entitlements in the Market," American Economic Review, American Economic Association, vol. 76(4), pages 728-741, September.
    74. Oliver Jean Blanchard, 1987. "Aggregate and Individual Price Adjustment," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 18(1), pages 57-122.
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    More about this item

    Keywords

    Asymmetric Price Adjustment; Price Rigidity; Rational Inattention; Rational Ignorance;
    All these keywords.

    JEL classification:

    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • M31 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Marketing and Advertising - - - Marketing
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • L16 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Industrial Organization and Macroeconomics; Macroeconomic Industrial Structure
    • L11 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Production, Pricing, and Market Structure; Size Distribution of Firms
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation

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