Empirical Economics

, Volume 56, Issue 5, pp 1455–1475 | Cite as

Breaks and the statistical process of inflation: the case of estimating the ‘modern’ long-run Phillips curve

  • Bill RussellEmail author
  • Dooruj Rambaccussing


‘Modern’ theories of the Phillips curve inadvertently imply that inflation is an integrated or near-integrated process, but this implication is strongly rejected using US data. Alternatively, if we assume that inflation is a stationary process around a shifting mean (due to changes in monetary policy), then any estimate of long-run relationships in the data will suffer from a ‘small-sample’ problem as there are too few stationary inflation ‘regimes’. Using the extensive literature on identification of structural breaks, we identify inflation regimes which are used in turn to estimate with panel data techniques the US long-run Phillips curve.


Phillips curve Inflation Structural breaks Non-stationary data 

JEL Classification

C23 E31 


  1. Algama M, Keith JM (2014) Investigating genomic structure using changept: a Bayesian segmentation model. Comput Struct Biotechnol J 10:107–15CrossRefGoogle Scholar
  2. Almon S (1965) The distributed lag between capital appropriations and net expenditures. Econometrica 33:178–196CrossRefGoogle Scholar
  3. Andrews D (1993) Tests for parameter instability and structural change with unknown change point. Econometrica 61:821–856CrossRefGoogle Scholar
  4. Andrews D (2003) Tests for parameter instability and structural change with unknown change point: a corrigendum. Econometrica 71:395–397CrossRefGoogle Scholar
  5. Bai J (1994) Least squares estimation of a shift in linear processes. J Time Ser Anal 15:453–72CrossRefGoogle Scholar
  6. Bai J (1997) Estimation of a change point in multiple regression models. Rev Econ Stat 79:551–63CrossRefGoogle Scholar
  7. Bai J, Perron P (1998) Estimating and testing linear models with multiple structural changes. Econometrica 66:47–78CrossRefGoogle Scholar
  8. Bai J, Perron P (2003) Computation and analysis of multiple structural change models. J Appl Econ 18:1–22CrossRefGoogle Scholar
  9. Banerjee A, Lumsdaine R, Stock J (1992) Recursive and sequential tests of the unit-root and trend-break hypotheses: theory and international evidence. J Bus Econ Stat 10:271–87Google Scholar
  10. Banerjee A, Cockerell L, Russell B (2001) An I(2) analysis of inflation and the markup. J Appl Econ, Sargan Special Issue 16:221–240Google Scholar
  11. Banerjee A, Russell B (2001) The relationship between the markup and inflation in the G7 economies and Australia. Rev Econ Stat 83(2):377–87CrossRefGoogle Scholar
  12. Banerjee A, Russell B (2005) Inflation and measures of the markup. J Macroecon 27:289–306CrossRefGoogle Scholar
  13. Braun JV, Muller H-G (1998) Statistical methods for DNA sequence segmentation. Stat Sci 13:142–62CrossRefGoogle Scholar
  14. Cagan P (1956) The monetary dynamics of hyperinflation. In: Friedman M (ed) Studies in the quantity theory of money. Chicago University Press, Chicago, p 25.117Google Scholar
  15. Chen Y, Russell B (2002) An optimising model of price adjustment with missing information. European University Institute Working Papers, Eco No. 2002/3Google Scholar
  16. Chow GC (1960) Tests of equality between sets of coefficients in two linear regressions. Econometrica 28:591–605CrossRefGoogle Scholar
  17. Clarida R, Galí J, Gertler M (1999) The science of monetary policy: a new keynesian perspective. J Econ Lit 37:1661–1707CrossRefGoogle Scholar
  18. Enders W, Lee J (2012a) A unit root test using a Fourier series to approximate smooth breaks. Oxf Bull Econ Stat 74(4):574–99CrossRefGoogle Scholar
  19. Enders W, Lee J (2012b) The flexible Fourier form and Dickey–Fuller type unit root tests. Econ Lett 117(1):196–9CrossRefGoogle Scholar
  20. Friedman M (1968) The role of monetary policy. Am Econ Rev 58(1):1–17Google Scholar
  21. Frick K, Munk A, Sieling H (2014) Multiscale change point inference. J R Stat Soc Ser B (Stat Methodol) 76:495–580CrossRefGoogle Scholar
  22. Fryzlewicz P (2014) Wild binary segmentation for multiple change-point detection. Ann Stat 42:2243–2281CrossRefGoogle Scholar
  23. Fryzlewicz P, Sapatinas T, Subba Rao S (2006) A Haar–Fisz technique for locally stationary volatility estimation. Biometrika 93:687–704CrossRefGoogle Scholar
  24. Galí J, Gertler M (1999) Inflation dynamics: a structural econometric analysis. J Monet Econ 44:195–222CrossRefGoogle Scholar
  25. Galí J, Gertler M, Lopez-Salido JD (2001) European inflation dynamics. Eur Econ Rev 45:1237–1270CrossRefGoogle Scholar
  26. Gardner LA (1969) On detecting changes in the mean of normal variates. Ann Math Stat 40:116–26CrossRefGoogle Scholar
  27. Giraitis L, Kokoszka P, Leipus R (2003) Rescaled variance and related tests for long memory in volatility and levels. J Econ 112:265–94CrossRefGoogle Scholar
  28. Griliches Z (1967) Distributed lags: a survey. Econometrica 35(1):16–49CrossRefGoogle Scholar
  29. Harris D, McCabe B, Leybourne S (2008) Testing for long memory. Econ Theory 24:143–75CrossRefGoogle Scholar
  30. Hawkins DM (2001) Fitting multiple change-point models to data. Comput Stat Data Anal 37:323–41CrossRefGoogle Scholar
  31. Hendry D, Johansen S, Santos C (2008) Automatic selection of indicators in a fully saturated regression. Comput Stat 23:317–39CrossRefGoogle Scholar
  32. Jackson B, Sargle JD, Barnes D, Arabhi S, Alt A, Gioumousis P, Gwin E, Sangtrakulcharoen P, Tan L, Tsai TT (2005) An algorithm for optimal partitioning of data on an interval. IEEE Signal Process Lett 12:105–8CrossRefGoogle Scholar
  33. James B, James KL, Siegmund D (1987) Tests for a change-point. Biometrika 74:71–84CrossRefGoogle Scholar
  34. James NA, Matteson DS (2015) ecp: An R package for nonparametric multiple change point analysis of multivariate data. J Stat Softw 62:1–25Google Scholar
  35. Killick R, Eckleya IA, Ewans K, Jonathan P (2010) Detection of changes in variance of oceanographic time-series using change point analysis. Ocean Eng 37:1120–6CrossRefGoogle Scholar
  36. Killick R, Fearnhead P, Eckleya IA (2012) Optimal detection of changepoints with a linear computational cost. J Am Stat Assoc 107:1590–8CrossRefGoogle Scholar
  37. Koyck LM (1954) Distributed lags and investment analysis. North-Holland Publishing Co., AmsterdamGoogle Scholar
  38. Lee J, Strazicich MC (2003) Minimum lagrange multiplier unit root test with two structural breaks. Rev Econ Stat 85(4):1082–9CrossRefGoogle Scholar
  39. Lucas RE Jr, Rapping LA (1969) Price expectations and the Phillips curve. Am Econ Rev 59(3):342–350Google Scholar
  40. Lumsdaine RL, Papell DH (1997) Multiple trend breaks and the unit root hypothesis. Rev Econ Stat 79:212–8CrossRefGoogle Scholar
  41. MacNeill IB (1978) Properties of sequences of partial sums of polynomial regression residuals with applications to tests for change of regression at unknown times. Ann Stat 6:422–33CrossRefGoogle Scholar
  42. Mavroeidis S, Plagborg-Moller M, Stock JH (2014) Empirical evidence on inflation expectations in the new Keynesian Phillips curve. J Econ Lit 52:124–88CrossRefGoogle Scholar
  43. Nerlove M (1956) Estimates of the elasticities of supply of selected agricultural commodities. J Farm Econ 38(2):496–509CrossRefGoogle Scholar
  44. Page ES (1955) A test for a change in a parameter occurring at an unknown point. Biometrika 42:523–27CrossRefGoogle Scholar
  45. Page ES (1957) On problems in which a change in a parameter occurs at an unknown point. Biometrika 44:248–52CrossRefGoogle Scholar
  46. Perron P (1989) The great crash, the oil price shock, and the unit root hypothesis. Econometrica 57(6):1361–1401CrossRefGoogle Scholar
  47. Perron P (1990) Testing for a unit root in a time series with a changing mean. J Bus Econ Stat 8:153–62Google Scholar
  48. Perron P (2006) Dealing with structural breaks. In: Patterson K, Mills TC (eds) Palgrave handbook of econometrics: econometric theory, vol 1. Palgrave Macmillan, Basingstoke, pp 278–352Google Scholar
  49. Phelps ES (1967) Phillips curves, expectations of inflation, and optimal unemployment over time. Economica 34(3):254–81CrossRefGoogle Scholar
  50. Priyadarshana WJRM, Sofronov G (2015) Multiple break-point detection in array CGH data via the cross-entropy method. Trans Comput Biol Bioinform 12:487–98CrossRefGoogle Scholar
  51. Quant RE (1958) The estimation of the parameters of a linear regression system obeying two separate regimes. J Stat Assoc 53:873–80CrossRefGoogle Scholar
  52. Quant RE (1960) Tests of the hypothesis that a linear regression system obeys two separate regimes. J Stat Assoc 55:324–30CrossRefGoogle Scholar
  53. Rappoport P, Reichlin L (1989) Segmented trends and non-stationary time series. Econ J 99:168–77CrossRefGoogle Scholar
  54. Robinson P, Labato I (1998) A nonparametric test for I(0). Rev Econ Stud 65(3):475–495CrossRefGoogle Scholar
  55. Russell B (1998) A rules based model of disequilibrium price adjustment with missing information, Dundee discussion papers, Department of Economic Studies, University of Dundee, November, No. 91Google Scholar
  56. Russell B (2011) Non-stationary inflation and panel estimates of United States short and long-run Phillips curves. J Macroecon 33:406–19CrossRefGoogle Scholar
  57. Russell B (2014) ARCH and structural breaks in United States inflation. Appl Econ Lett 21(14):973–978CrossRefGoogle Scholar
  58. Russell B (2015) Modern’ Phillips curves and the implications for the statistical process of inflation, Dundee discussion papers, economic studies, University of Dundee, September, No. 289, forthcoming in Applied Economic LettersGoogle Scholar
  59. Russell B, Chowdhury RA (2013) Estimating United States Phillips curves with expectations consistent with the statistical process of inflation. J Macroecon 35:24–38CrossRefGoogle Scholar
  60. Russell B, Evans J, Preston B (2002) The impact of inflation and uncertainty on the optimum markup set by firms. European University Institute Working Papers, Eco No. 2002/2Google Scholar
  61. Scott AJ, Knott M (1974) A cluster analysis method for grouping means in the analysis of variance. Biometrics 30:507–12CrossRefGoogle Scholar
  62. Sen A, Srivastava MS (1975) On tests for detecting change in mean. Ann Stat 3:98–108CrossRefGoogle Scholar
  63. Starica C, Granger C (2005) Nonstationarities in stock returns. Rev Econ Stat 87:503–22CrossRefGoogle Scholar
  64. Stock JH, Watson MW (2007) Why has US inflation become harder to forecast? J Money Credit banking 39(s1):3–33Google Scholar
  65. Sullivan JH (2002) Estimating the locations of multiple change points in the mean. Comput Stat 17:289–96CrossRefGoogle Scholar
  66. Svennson LEO (2000) Open economy inflation targeting. J Int Econ 50:155–83CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University of DundeeDundeeUK

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