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

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Abstract

‘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.

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Notes

  1. For example, see among many others, Page (1955, 1957), Quant (1958, 1960), Chow (1960), Gardner (1969) and MacNeill (1978). See also the historical survey of break analysis in Perron (2006).

  2. Estimating breaks in time series data is closely related to the literature on testing whether data are stationary or persistent. This leads Perron (1989, 1990) and Rappoport and Reichlin (1989) to argue that highly persistent data may after allowing for breaks be stationary.

  3. The robustness of the outcomes from a single technique may be subjected to a small and limited number of changes to the assumptions of the estimating technique.

  4. The type of stationarity being discussed here is covariance stationarity once shifts in means have been accounted for. See Russell (2014) who finds that once the shifts in mean are accounted for in US inflation the data are homoscedastic.

  5. If the data are integrated, then the analysis proceeds within a cointegration framework. Within this framework, Banerjee et al. (2001) and Banerjee and Russell (2001, 2005) argue that while the ‘true’ statistical process for inflation is most likely stationary around a frequently shifting mean they proceed under the maintained assumption that this process can be approximated by an integrated process.

  6. We thank a referee for drawing our attention to the break-point estimation techniques of Frick et al. (2014), Fryzlewicz (2014) and James and Matteson (2015) from the statistics literature. These techniques generate similar break dates to those reported in this paper below. Further information and results from these techniques can be found at www.billrussell.info.

  7. An alternative approach to the one employed here is the unobserved components model of Stock and Watson (2007) that assumes the change in the mean rate of inflation evolves smoothly rather than abruptly across inflation regimes. However, the focus of this paper is to estimate the long-run relationship between the means of variables across inflation regimes rather than the transition between the means in successive inflation regimes.

  8. For a recent survey on the wide range of theoretical and empirical approaches to modelling inflation, see Mavroeidis and Stock, (2014).

  9. The SPC Phillips curve is ‘postmodern’ in the sense that it eschews the empirically invalid assumptions of full information and no missing markets as well as the logical implications of models incorporating identical representative agents. Instead, the knowledge set of agents contains elements that they can be reasonably expected to know and agents behave in ways consistent with the knowledge that agents are not identical.

  10. This argument is considered in more detail in Russell (2015).

  11. See also Nerlove (1956). Griliches (1967) provides an early survey of the econometrics of distributed lagged models.

  12. Other possible transformations leading to equation (4) include that of Almon (1965) and the rational distributed lag function of Lucas and Rapping (1969).

  13. See Perron (1989).

  14. Changes in monetary policy is used in the sense that the monetary policy instrument has either changed, or not changed, in such a way so that the mean rate of inflation does not remain constant.

  15. Inflation is measured as the quarterly change in the natural logarithm of the seasonally adjusted US gross domestic product implicit price deflator at factor cost. See “Data Appendix” for further details concerning the data.

  16. The flexible Fourier approach is thought to deal more effectively with the spurious rejection problems surrounding the approaches of Lumsdaine and Papell (1997) and Lee and Strazicich (2003).

  17. If the Volker deflation is a downward shift in the mean rate of inflation and the mean rates of inflation in the early 1960s and after 1990 are similar, then there must have been a similar upward shift in the mean either prior to or after the ‘Volker’ break in the early 1980s. Consequently, the ‘Volker’ break cannot exist on its own and there must be a minimum of two breaks in the data.

  18. If the long-run Phillips curve is not vertical and has a slope, then the curve must be nonlinear. If this is not the case, then as inflation increases to an infinite rate the forcing variable will exceed its conceptual boundaries.

  19. Personal correspondence between Bill Russell and Pierre Perron between March and June 2015 considers the issue of minimum trim size and the number of breaks when applying the Bai–Perron technique to inflation data. In this correspondence, Pierre Perron indicates that in his simulation work (based on 1 or 2 breaks in the data) he finds that BIC outperforms the other information criteria if persistence is low. He also acknowledges the importance of a practical approach to modelling breaks based on an understanding of the data when the number of breaks in the data may be large.

  20. The statistics literature refers to change-points and segmentation in the same manner as the econometrics literature refers to breaks in time series data.

  21. For example, see Braun and Muller (1998), Algama and Keith (2014) and Priyadarshana and Sofronov (2015).

  22. See also Killick et al. (2010).

  23. For sake of space, the estimation of the short-run Phillips curves assuming inflation is a stationary process around a shifting mean is not pursued here and readers are directed to Russell (2011).

  24. This proof by contradiction is another component of ‘postmodern’ theories of inflation in that agents cannot logically predict future breaks in mean inflation. Therefore, this information must logically be ‘missing’ and all optimisation behaviour of agents based on agents holding unbiased predictions of future relative prices is logically moot. See Russell and Chowdhury (2013).

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Authors and Affiliations

  1. University of Dundee, Dundee, DD1 4HN, UK

    Bill Russell & Dooruj Rambaccussing

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  1. Bill Russell
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  2. Dooruj Rambaccussing
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Correspondence to Bill Russell.

Additional information

We thank Tom Doan for generously making available the Bai–Perron programmes on the Estima website. All data are available at http://billrussell.info.

Appendix 1: Data appendix

Appendix 1: Data appendix

The US data are seasonally adjusted and quarterly for the period March 1960 to June 2015. The US national accounts data are from the National Income and Product Account (NIPA) tables from the USA, Bureau of Economic Analysis (BEA) and downloaded on 2 and 3 September 2015 except for Table 1.1.6 which was downloaded on 21 November. The database is available at www.BillRussell.info.

US data

Variable

Details

The price level

Defined as the gross domestic product implicit price deflator at factor cost (ipdfc) calculated from NIPA Table 1.10 as gross domestic income (line 1) less taxes on production and imports (line 7) plus subsidies (line 8) divided by real gross domestic product at constant prices (Billions of Chained 2009 Dollars) (NIPA Table 1.1.6 line 1). The price level is the natural logarithm of ipdfc (Database: lipdfc)

Inflation

Defined as the log change in the price level (Database dlipfc)

The markup (National Accounts Basis)

Defined as gross domestic income at factor cost divided by total compensation paid to employees (Database: mufc). Calculated from NIPA Table 1.10 as gross domestic income (line 1) less taxes on production and imports (line 7) plus subsidies (line 8) divided by compensations of employees paid (line 2). The markup is the natural logarithm of the markup (mufc) (Database: lmufc)

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Russell, B., Rambaccussing, D. Breaks and the statistical process of inflation: the case of estimating the ‘modern’ long-run Phillips curve. Empir Econ 56, 1455–1475 (2019). https://doi.org/10.1007/s00181-017-1404-5

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  • DOI: https://doi.org/10.1007/s00181-017-1404-5

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