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A Multiple Break Panel Approach To Estimating United States Phillips Curves

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  • Bill Russell
  • Anindya Banerjee
  • Issam Malki
  • Natalia Ponomareva

Abstract

Phillips curves are often estimated without due attention being paid to the underlying time series properties of the data. In particular, the consequences of inflation having discrete breaks in mean have not been studied adequately. We show by means of simulations and a detailed empirical example based on United States data that not taking account of breaks may lead to biased, and therefore spurious, estimates of Phillips curves. We suggest a method to account for the breaks in mean inflation and obtain meaningful and unbiased estimates of the short- and long-run Phillips curves in the United States.

Suggested Citation

  • Bill Russell & Anindya Banerjee & Issam Malki & Natalia Ponomareva, 2011. "A Multiple Break Panel Approach To Estimating United States Phillips Curves," Dundee Discussion Papers in Economics 252, Economic Studies, University of Dundee.
    • Handle: RePEc:dun:dpaper:252
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    1. Russell, Bill, 2011. "Non-stationary inflation and panel estimates of United States short and long-run Phillips curves," Journal of Macroeconomics, Elsevier, vol. 33(3), pages 406-419, September.
    2. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    3. Peter N. Ireland, 2007. "Changes in the Federal Reserve's Inflation Target: Causes and Consequences," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(8), pages 1851-1882, December.
    4. Russell, Bill & Banerjee, Anindya, 2008. "The long-run Phillips curve and non-stationary inflation," Journal of Macroeconomics, Elsevier, vol. 30(4), pages 1792-1815, December.
    5. Pesaran, M. H., 1981. "Identification of rational expectations models," Journal of Econometrics, Elsevier, vol. 16(3), pages 375-398, August.
    6. Gali, Jordi & Gertler, Mark, 1999. "Inflation dynamics: A structural econometric analysis," Journal of Monetary Economics, Elsevier, vol. 44(2), pages 195-222, October.
    7. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
    8. Anindya Banerjee & Lynne Cockerell & Bill Russell, 2001. "An I(2) analysis of inflation and the markup," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(3), pages 221-240.
    9. Jean-Marie Dufour, 2003. "Identification, weak instruments, and statistical inference in econometrics," Canadian Journal of Economics, Canadian Economics Association, vol. 36(4), pages 767-808, November.
    10. Arellano, Manuel & Bover, Olympia, 1995. "Another look at the instrumental variable estimation of error-components models," Journal of Econometrics, Elsevier, vol. 68(1), pages 29-51, July.
    11. Rudd, Jeremy & Whelan, Karl, 2005. "New tests of the new-Keynesian Phillips curve," Journal of Monetary Economics, Elsevier, vol. 52(6), pages 1167-1181, September.
    12. Robert J. Gordon, 1997. "The Time-Varying NAIRU and Its Implications for Economic Policy," Journal of Economic Perspectives, American Economic Association, vol. 11(1), pages 11-32, Winter.
    13. Halunga, Andreea G. & Osborn, Denise R. & Sensier, Marianne, 2009. "Changes in the order of integration of US and UK inflation," Economics Letters, Elsevier, vol. 102(1), pages 30-32, January.
    14. George A. Akerlof & William T. Dickens & George L. Perry, 2000. "Near-Rational Wage and Price Setting and the Long-Run Phillips Curve," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 31(1), pages 1-60.
    15. McCallum, Bennett T, 1976. "Rational Expectations and the Natural Rate Hypothesis: Some Consistent Estimates," Econometrica, Econometric Society, vol. 44(1), pages 43-52, January.
    16. Gali, Jordi & Gertler, Mark & Lopez-Salido, J. David, 2001. "European inflation dynamics," European Economic Review, Elsevier, vol. 45(7), pages 1237-1270.
    17. A. W. Phillips, 1958. "The Relation Between Unemployment and the Rate of Change of Money Wage Rates in the United Kingdom, 1861–1957," Economica, London School of Economics and Political Science, vol. 25(100), pages 283-299, November.
    18. Michael T. Kiley, 2007. "A Quantitative Comparison of Sticky‐Price and Sticky‐Information Models of Price Setting," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(s1), pages 101-125, February.
    19. Argia M. Sbordone & Timothy Cogley, 2004. "A Search for a Structural Phillips Curve," Computing in Economics and Finance 2004 291, Society for Computational Economics.
    20. Mark Gertler & Jordi Gali & Richard Clarida, 1999. "The Science of Monetary Policy: A New Keynesian Perspective," Journal of Economic Literature, American Economic Association, vol. 37(4), pages 1661-1707, December.
    21. Bill Russell, 1998. "A Rules Based Model Of Disequilibrium Price Adjustment With Missing Information," Dundee Discussion Papers in Economics 091, Economic Studies, University of Dundee.
    22. Unknown, 2005. "Forward," 2005 Conference: Slovenia in the EU - Challenges for Agriculture, Food Science and Rural Affairs, November 10-11, 2005, Moravske Toplice, Slovenia 183804, Slovenian Association of Agricultural Economists (DAES).
    23. Robert J. Gordon, 1975. "The Impact of Aggregate Demand on Prices," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 6(3), pages 613-670.
    24. Timothy Cogley & Argia M. Sbordone, 2006. "Trend inflation and inflation persistence in the New Keynesian Phillips curve," Staff Reports 270, Federal Reserve Bank of New York.
    25. Gali, Jordi & Gertler, Mark & David Lopez-Salido, J., 2005. "Robustness of the estimates of the hybrid New Keynesian Phillips curve," Journal of Monetary Economics, Elsevier, vol. 52(6), pages 1107-1118, September.
    26. Anindya Banerjee, 2001. "Industry structure and the dynamics of price adjustment," Applied Economics, Taylor & Francis Journals, vol. 33(15), pages 1889-1901.
    27. Perron, Pierre, 1997. "Further evidence on breaking trend functions in macroeconomic variables," Journal of Econometrics, Elsevier, vol. 80(2), pages 355-385, October.
    28. S. G. B Henry & A. R. Pagan, 2004. "The Econometrics of the New Keynesian Policy Model: Introduction," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 66(s1), pages 581-607, September.
    29. Jeremy Rudd & Karl Whelan, 2007. "Modeling Inflation Dynamics: A Critical Review of Recent Research," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(s1), pages 155-170, February.
    30. Mark Gertler & Jordi Gali & Richard Clarida, 1999. "The Science of Monetary Policy: A New Keynesian Perspective," Journal of Economic Literature, American Economic Association, vol. 37(4), pages 1661-1707, December.
    31. James H. Stock & Mark W. Watson, 2007. "Why Has U.S. Inflation Become Harder to Forecast?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(s1), pages 3-33, February.
    32. Blundell, Richard & Bond, Stephen, 1998. "Initial conditions and moment restrictions in dynamic panel data models," Journal of Econometrics, Elsevier, vol. 87(1), pages 115-143, August.
    33. Nicoletta Batini & Brian Jackson & Stephen Nickell, 2000. "Inflation Dynamics and the Labour Share in the UK," Discussion Papers 02, Monetary Policy Committee Unit, Bank of England.
    34. Roberts, John M, 1995. "New Keynesian Economics and the Phillips Curve," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 27(4), pages 975-984, November.
    35. Galí, Jordi & Gertler, Mark, 1999. "Inflation Dynamics: A Structural Economic Analysis," CEPR Discussion Papers 2246, C.E.P.R. Discussion Papers.
    36. Stephen R. Bond, 2002. "Dynamic panel data models: a guide to micro data methods and practice," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 1(2), pages 141-162, August.
    37. Robert J. Gordon, 1970. "The Recent Acceleration of Inflation and Its Lessons for the Future," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 1(1), pages 8-47.
    38. Wayne Vroman, 1977. "Worker Upgrading and the Business Cycle," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 8(1), pages 229-252.
    39. Svensson, Lars E. O., 2000. "Open-economy inflation targeting," Journal of International Economics, Elsevier, vol. 50(1), pages 155-183, February.
    40. Stephen G. Cecchetti & Guy Debelle, 2006. "Has the inflation process changed? [‘Did the underlying behaviour of inflation change in the 1980s? A study of 22 countries,’]," Economic Policy, CEPR, CESifo, Sciences Po;CES;MSH, vol. 21(46), pages 312-352.
    41. Mavroeidis, Sophocles, 2005. "Identification Issues in Forward-Looking Models Estimated by GMM, with an Application to the Phillips Curve," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 37(3), pages 421-448, June.
    42. Bill Russell, 2006. "Non-Stationary Inflation and the Markup: an Overview of the Research and some Implications for Policy," Dundee Discussion Papers in Economics 191, Economic Studies, University of Dundee.
    43. Luca Benati, 2008. "Investigating Inflation Persistence Across Monetary Regimes," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 123(3), pages 1005-1060.
    44. Filippo Altissimo & Laurent Bilke & Andrew Levin & Thomas Mathä & Benoit Mojon, 2006. "Sectoral and Aggregate Inflation Dynamics in the Euro Area," Journal of the European Economic Association, MIT Press, vol. 4(2-3), pages 585-593, 04-05.
    45. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
    46. Jushan Bai & Pierre Perron, 2003. "Critical values for multiple structural change tests," Econometrics Journal, Royal Economic Society, vol. 6(1), pages 72-78, June.
    47. Batini, Nicoletta & Jackson, Brian & Nickell, Stephen, 2005. "An open-economy new Keynesian Phillips curve for the U.K," Journal of Monetary Economics, Elsevier, vol. 52(6), pages 1061-1071, September.
    48. James H. Stock & Mark W. Watson, 2007. "Erratum to "Why Has U.S. Inflation Become Harder to Forecast?"," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(7), pages 1849-1849, October.
    49. Perron, Pierre, 1990. "Testing for a Unit Root in a Time Series with a Changing Mean," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(2), pages 153-162, April.
    50. Jean‐Marie Dufour, 2003. "Identification, weak instruments, and statistical inference in econometrics," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 36(4), pages 767-808, November.
    51. Argia M. Sbordone & Timothy Cogley, 2004. "A Search for a Structural Phillips Curve," Computing in Economics and Finance 2004 291, Society for Computational Economics.
    52. Stock, James H & Wright, Jonathan H & Yogo, Motohiro, 2002. "A Survey of Weak Instruments and Weak Identification in Generalized Method of Moments," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 518-529, October.
    53. Schreiber, Sven & Wolters, Jurgen, 2007. "The long-run Phillips curve revisited: Is the NAIRU framework data-consistent?," Journal of Macroeconomics, Elsevier, vol. 29(2), pages 355-367, June.
    54. Yu-Fu CHEN & Bill RUSSELL, 2002. "An Optimising Model of Price Adjustment with Missing Information," Economics Working Papers ECO2002/03, European University Institute.
    55. Sumner, M T & Ward, R, 1983. "The Reappearing Phillips Curve," Oxford Economic Papers, Oxford University Press, vol. 35(0), pages 306-320, Supplemen.
    56. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
    57. Jushan Bai & Pierre Perron, 2003. "Computation and analysis of multiple structural change models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(1), pages 1-22.
    58. David Hendry & Jennifer L. Castle & Jurgen A. Doornik, 2010. "Testing the Invariance of Expectations Models of Inflation," Economics Series Working Papers 510, University of Oxford, Department of Economics.
    59. Anindya Banerjee & Bill Russell, 2006. "A markup model for forecasting inflation for the euro area," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(7), pages 495-511.
    60. George A. Akerlof & William R. Dickens & George L. Perry, 1996. "The Macroeconomics of Low Inflation," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 27(1), pages 1-76.
    61. Manuel Arellano & Stephen Bond, 1991. "Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(2), pages 277-297.
    62. Friedman, Milton, 1977. "Nobel Lecture: Inflation and Unemployment," Journal of Political Economy, University of Chicago Press, vol. 85(3), pages 451-472, June.
    63. Alogoskoufis, George S & Smith, Ron, 1991. "The Phillips Curve, the Persistence of Inflation, and the Lucas Critique: Evidence from Exchange-Rate Regimes," American Economic Review, American Economic Association, vol. 81(5), pages 1254-1275, December.
    64. King, Robert G. & Watson, Mark W., 1994. "The post-war U.S. phillips curve: a revisionist econometric history," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 41(1), pages 157-219, December.
    65. Banerjee, Anindya & Mizen, Paul & Russell, Bill, 2007. "Inflation, relative price variability and the markup: Evidence from the United States and the United Kingdom," Economic Modelling, Elsevier, vol. 24(1), pages 82-100, January.
    66. Sophocles Mavroeidis, 2004. "Weak Identification of Forward‐looking Models in Monetary Economics," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 66(s1), pages 609-635, September.
    67. Robert J. Gordon, 1977. "Can the Inflation of the 1970s be Explained?," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 8(1), pages 253-279.
    68. Bill Russell & Jonathan Evans & Bruce Preston, "undated". "The Impact Of Inflation and Uncertainty On The Optimum Price Set By Firms," Dundee Discussion Papers in Economics 084, Economic Studies, University of Dundee.
    69. Stephen Bond, 2002. "Dynamic panel data models: a guide to microdata methods and practice," CeMMAP working papers CWP09/02, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    70. Timothy Cogley & Argia M. Sbordone, 2008. "Trend Inflation, Indexation, and Inflation Persistence in the New Keynesian Phillips Curve," American Economic Review, American Economic Association, vol. 98(5), pages 2101-2126, December.
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    Cited by:

    1. David Norman & Anthony Richards, 2012. "The Forecasting Performance of Single Equation Models of Inflation," The Economic Record, The Economic Society of Australia, vol. 88(280), pages 64-78, March.
    2. Russell, Bill & Chowdhury, Rosen Azad, 2013. "Estimating United States Phillips curves with expectations consistent with the statistical process of inflation," Journal of Macroeconomics, Elsevier, vol. 35(C), pages 24-38.
    3. Jennifer L. Castle & Jurgen A. Doornik & David F. Hendry & Ragnar Nymoen, 2014. "Misspecification Testing: Non-Invariance of Expectations Models of Inflation," Econometric Reviews, Taylor & Francis Journals, vol. 33(5-6), pages 553-574, August.
    4. Nymoen, Ragnar & Swensen, Anders Rygh & Tveter, Eivind, 2012. "Interpreting the evidence for New Keynesian models of inflation dynamics," Journal of Macroeconomics, Elsevier, vol. 34(2), pages 253-263.
    5. Mariano Kulish & Adrian Pagan, 2016. "Issues in Estimating New Keynesian Phillips Curves in the Presence of Unknown Structural Change," Econometric Reviews, Taylor & Francis Journals, vol. 35(7), pages 1251-1270, August.
    6. Rao, B. Bhaskara & Paradiso, Antonio & Esposito, Piero, 2011. "Non-stationary inflation and panel estimates of the n ew Keynesian Phillips curve for Australia," MPRA Paper 29242, University Library of Munich, Germany.
    7. Aristidou, Chrystalleni, 2018. "The meta-Phillips Curve: Modelling U.S. inflation in the presence of regime change," Journal of Macroeconomics, Elsevier, vol. 57(C), pages 367-379.
    8. Russell, Bill, 2013. "Macroeconomics: Science or Faith Based Discipline?," SIRE Discussion Papers 2013-114, Scottish Institute for Research in Economics (SIRE).
    9. J. James Reade & Ulrich Volz, 2011. "From the General to the Specific," Discussion Papers 11-18, Department of Economics, University of Birmingham.

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    More about this item

    Keywords

    Phillips curve; inflation; panel data; non-stationary data; breaks;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation

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