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Mixed Frequency Data in a Heterogenous Sticky Price Model

Author

Listed:
  • Jonas Andersson
  • Øivind Anti Nilsen
  • Hans J. Skaug

Abstract

We develop a model to estimate price-adjustment behavior when prices are observed more frequently than key explanatory variables such as wage costs. We propose a mixed-frequency stochastic (S, s)-model that accommodates infrequently observed costs and allows for plant-, product-, and season-specific heterogeneity. The model is estimated using a likelihood-based nonlinear state-space approach, enabling estimation as if all variables were observed at the same frequency. Applied to monthly price survey data matched with plant-level annual cost data for manufacturing producers, the model yields precise estimates of both cost pass-through and price-inaction thresholds, and reduces the blurring of intermittent price changes.

Suggested Citation

  • Jonas Andersson & Øivind Anti Nilsen & Hans J. Skaug, 2026. "Mixed Frequency Data in a Heterogenous Sticky Price Model," CESifo Working Paper Series 12379, CESifo.
  • Handle: RePEc:ces:ceswps:_12379
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    1. 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.
    2. Mikael Carlsson & Oskar Nordstrom Skans, 2012. "Evaluating Microfoundations for Aggregate Price Rigidities: Evidence from Matched Firm-Level Data on Product Prices and Unit Labor Cost," American Economic Review, American Economic Association, vol. 102(4), pages 1571-1595, June.
    3. Bo E. Honoré & Daniel Kaufmann & Sarah Lein, 2012. "Asymmetries in Price‐Setting Behavior: New Microeconometric Evidence from Switzerland," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 44(s2), pages 211-236, December.
    4. Wilko Letterie & Øivind A. Nilsen, 2022. "Pricing Behaviour and Menu Costs in Multi‐product Firms," Economica, London School of Economics and Political Science, vol. 89(355), pages 746-769, July.
    5. 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.
    6. Peter Karadi & Raphael Schoenle & Jesse Wursten, 2024. "Price Selection in the Microdata," Journal of Political Economy Macroeconomics, University of Chicago Press, vol. 2(2), pages 228-271.
    7. Dhyne, Emmanuel & Fuss, Catherine & Pesaran, M. Hashem & Sevestre, Patrick, 2011. "Lumpy Price Adjustments: A Microeconometric Analysis," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(4), pages 529-540.
    8. repec:fip:fedawp:99183 is not listed on IDEAS
    9. Foroni, Claudia & Guérin, Pierre & Marcellino, Massimiliano, 2018. "Using low frequency information for predicting high frequency variables," International Journal of Forecasting, Elsevier, vol. 34(4), pages 774-787.
    10. H. Baltagi, Badi & Heun Song, Seuck & Cheol Jung, Byoung, 2001. "The unbalanced nested error component regression model," Journal of Econometrics, Elsevier, vol. 101(2), pages 357-381, April.
    11. Bhattarai, Saroj & Schoenle, Raphael, 2014. "Multiproduct firms and price-setting: Theory and evidence from U.S. producer prices," Journal of Monetary Economics, Elsevier, vol. 66(C), pages 178-192.
    12. Zheng, Nan & Cadigan, Noel, 2021. "Frequentist delta-variance approximations with mixed-effects models and TMB," Computational Statistics & Data Analysis, Elsevier, vol. 160(C).
    13. Mary Amiti & Oleg Itskhoki & Jozef Konings, 2019. "International Shocks, Variable Markups, and Domestic Prices," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(6), pages 2356-2402.
    14. Mark Gertler & John Leahy, 2008. "A Phillips Curve with an Ss Foundation," Journal of Political Economy, University of Chicago Press, vol. 116(3), pages 533-572, June.
    15. Philip Vermeulen & Daniel A. Dias & Maarten Dossche & Erwan Gautier & Ignacio Hernando & Roberto Sabbatini & Harald Stahl, 2012. "Price Setting in the Euro Area: Some Stylized Facts from Individual Producer Price Data," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 44(8), pages 1631-1650, December.
    16. Caballero, Ricardo J. & Engel, Eduardo M.R.A., 2007. "Price stickiness in Ss models: New interpretations of old results," Journal of Monetary Economics, Elsevier, vol. 54(Supplemen), pages 100-121, September.
    17. Virgiliu Midrigan, 2010. "Is Firm Pricing State or Time Dependent? Evidence from U.S. Manufacturing," The Review of Economics and Statistics, MIT Press, vol. 92(3), pages 643-656, August.
    18. E. Glen Weyl & Michal Fabinger, 2013. "Pass-Through as an Economic Tool: Principles of Incidence under Imperfect Competition," Journal of Political Economy, University of Chicago Press, vol. 121(3), pages 528-583.
    19. Giovanni Olivei & Silvana Tenreyro, 2007. "The Timing of Monetary Policy Shocks," American Economic Review, American Economic Association, vol. 97(3), pages 636-663, June.
    20. Andres Blanco & Corina Boar & Callum J. Jones, 2024. "Nonlinear Dynamics in Menu Cost Economies? Evidence from U.S. Data," FRB Atlanta Working Paper 2024-11, Federal Reserve Bank of Atlanta.
    21. Daniel A. Dias & Carlos Robalo Marques & Fernando Martins, 2013. "Choosing between Time and State Dependence: Micro Evidence on Firms' Price-Reviewing Strategies," Scandinavian Journal of Economics, Wiley Blackwell, vol. 115(3), pages 756-780, July.
    22. Roberto S. Mariano & Yasutomo Murasawa, 2010. "A Coincident Index, Common Factors, and Monthly Real GDP," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 72(1), pages 27-46, February.
    23. 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.
    24. Andres Blanco & Corina Boar & Callum J. Jones & Virgiliu Midrigan, 2024. "Nonlinear Inflation Dynamics in Menu Cost Economies," FRB Atlanta Working Paper 10, Federal Reserve Bank of Atlanta.
    25. Fernando Alvarez & Francesco Lippi, 2014. "Price Setting With Menu Cost for Multiproduct Firms," Econometrica, Econometric Society, vol. 82(1), pages 89-135, January.
    26. Fernando Alvarez & Hervé Le Bihan & Francesco Lippi, 2016. "The Real Effects of Monetary Shocks in Sticky Price Models: A Sufficient Statistic Approach," American Economic Review, American Economic Association, vol. 106(10), pages 2817-2851, October.
    27. 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.
    28. Kristensen, Kasper & Nielsen, Anders & Berg, Casper W. & Skaug, Hans & Bell, Bradley M., 2016. "TMB: Automatic Differentiation and Laplace Approximation," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 70(i05).
    29. Virgiliu Midrigan, 2011. "Menu Costs, Multiproduct Firms, and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 79(4), pages 1139-1180, July.
    30. Kimball, Miles S, 1995. "The Quantitative Analytics of the Basic Neomonetarist Model," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 27(4), pages 1241-1277, November.
    31. Tor Jakob Klette, 1999. "Market Power, Scale Economies and Productivity: Estimates from a Panel of Establishment Data," Journal of Industrial Economics, Wiley Blackwell, vol. 47(4), pages 451-476, December.
    32. repec:fip:fedawp:99169 is not listed on IDEAS
    33. Dixon, Huw D. & Grimme, Christian, 2022. "State-dependent or time-dependent pricing? New evidence from a monthly firm-level survey: 1980–2017," European Economic Review, Elsevier, vol. 150(C).
    34. Klenow, Peter J. & Malin, Benjamin A., 2010. "Microeconomic Evidence on Price-Setting," Handbook of Monetary Economics, in: Benjamin M. Friedman & Michael Woodford (ed.), Handbook of Monetary Economics, edition 1, volume 3, chapter 6, pages 231-284, Elsevier.
    35. Gautier, Erwan & Le Bihan, Hervé, 2011. "Time-varying (S, s) band models: Properties and interpretation," Journal of Economic Dynamics and Control, Elsevier, vol. 35(3), pages 394-412, March.
    36. Buckle, Robert A. & Carlson, John A., 2000. "Menu costs, firm size and price rigidity," Economics Letters, Elsevier, vol. 66(1), pages 59-63, January.
    37. Denis Fougère & Erwan Gautier & Hervé Le Bihan, 2010. "Restaurant Prices and the Minimum Wage," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 42(7), pages 1199-1234, October.
    38. 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.
    39. Christos Genakos & Mario Pagliero, 2022. "Competition and Pass-Through: Evidence from Isolated Markets," American Economic Journal: Applied Economics, American Economic Association, vol. 14(4), pages 35-57, October.
    40. Giulietti, Monica & Otero, Jesús & Waterson, Michael, 2020. "Rigidities and adjustments of daily prices to costs: Evidence from supermarket data," Journal of Economic Dynamics and Control, Elsevier, vol. 116(C).
    41. Ghysels, Eric & Santa-Clara, Pedro & Valkanov, Rossen, 2004. "The MIDAS Touch: Mixed Data Sampling Regression Models," University of California at Los Angeles, Anderson Graduate School of Management qt9mf223rs, Anderson Graduate School of Management, UCLA.
    42. Jan De Loecker & Jan Eeckhout & Gabriel Unger, 2020. "The Rise of Market Power and the Macroeconomic Implications [“Econometric Tools for Analyzing Market Outcomes”]," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 135(2), pages 561-644.
    43. Frank Schorfheide & Dongho Song, 2015. "Real-Time Forecasting With a Mixed-Frequency VAR," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(3), pages 366-380, July.
    44. Aruoba, S. BoraÄŸan & Diebold, Francis X. & Scotti, Chiara, 2009. "Real-Time Measurement of Business Conditions," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(4), pages 417-427.
    45. Pierre Guérin & Massimiliano Marcellino, 2013. "Markov-Switching MIDAS Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(1), pages 45-56, January.
    46. Mikael Carlsson, 2017. "Microdata Evidence on the Empirical Importance of Selection Effects in Menu‐Cost Models," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 49(8), pages 1803-1830, December.
    47. Fernando E. Alvarez & Francesco Lippi & Luigi Paciello, 2011. "Optimal Price Setting With Observation and Menu Costs," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 126(4), pages 1909-1960.
    48. Rotemberg, Julio J. & Woodford, Michael, 1999. "The cyclical behavior of prices and costs," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 16, pages 1051-1135, Elsevier.
    49. Øivind A. Nilsen & Magne Vange, 2019. "Intermittent Price Changes in Production Plants: Empirical Evidence Using Monthly Data," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 81(1), pages 98-122, February.
    50. David Vincent, 2019. "Estimating (S,s) rule-regression models," London Stata Conference 2019 03, Stata Users Group.
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    More about this item

    Keywords

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    JEL classification:

    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • C34 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Truncated and Censored Models; Switching Regression Models
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications
    • L16 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Industrial Organization and Macroeconomics; Macroeconomic Industrial Structure

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