The dynamics of inflation: a study of a large number of countries

Abstract

Over the last twenty years the statistical properties of inflation persistence has been the subject of intense investigation and debate without reaching a unanimous conclusion yet. In this article we attempt to shed further light to this debate using a battery of econometric techniques in order to provide robust evidence on the degree of inflation persistence and whether this has changed during the period in which several countries have followed inflation-targeting regimes or new monetary regimes. We consider the inflation rates of thirty developed and emerging economies using quarterly data for the period 1958 to 2007 which include alternative monetary policy regimes. The coefficient of the inflation parameter is estimated by Ordinary Least Squares (OLS), Autoregressive Moving Average (ARMA) and Autoregressive Fractionally Integrated Moving Average (ARFIMA) models. Furthermore, the grid-bootstrap Median Unbiased (MUB) estimator approach developed by Hansen (1999) is used to estimate the finite sample OLS estimates coupled with the 95% symmetric confidence interval. We also examine parameter stability of persistence coefficients by estimating a model with time-varying parameters.

Keywords:

• inflation dynamics
• persistence
• monetary policy
• time-varying coefficients
• recursive estimation
• rolling regression 

JEL Classification::

• C22
• E31

Acknowledgements

We thank participants at the EcoMod 2010 Conference, Istanbul Bigli University, Istanbul, 7–10 July 2010, at the 13th International Conference on Macroeconomic Analysis and International Finance, University of Crete, Rethymno, 28–30 May 2009 as well as at seminars at the Aristotle University of Thessaloniki, Athens University of Economics and Business, European University Institute and Hebrew University of Jerusalem for their helpful comments. Kouretas acknowledges financial support by a Marie Curie Transfer of Knowledge Fellowship of the European Community's Sixth Framework Programme under contract number MTKD-CT-014288, as well as by the Research Committee of the University of Crete under research grant no. 2257. We also thank without implicating, Michael Beenstock, Dimitris Georgoutsos, David Rapach and Joseph Zeira for many helpful comments and discussions on earlier drafts. Finally, we thank the editor Mark P. Taylor and two anonymous referees for valuable comments that improve the manuscript substantially. The usual disclaimer applies.

Notes

¹ One of the implications of the above analysis is that one can approximate the DGP of inflation as either a persistent or I(1) series or a stationary series around mean shifts. If one approximates inflation as stationary around level shifts in the mean then one cannot use inflation in tests of the fisher effect where an I(1) inflation series is required to be cointegrated, with cointegrating vector (1, −1), with an I(1) interest rate series.

² Nobay et al. (2010) note that the unit root feature of inflation is now reflected in theoretical models of the inflationary process. However, they argued that the assumption of a random walk in the inflation target implies a negative inflation target which is implausible given the zero lower bound on nominal interest. Recently, Buiter (2009) has challenged this notion and he demonstrated three ways to overcome the zero lower bound and therefore the possibility of negative nominal interest rates. In addition, Nobay et al. (2010) argue that inflation behaves as a near unit root process for rates near the inflation target but it is mean reverting for large deviations.

³ We chose to work with alternative univariate models for two reasons. First, in studying individual features of a time series, like persistence or volatility, using more sophisticated specifications such as Structure Vector Autoregression (SVAR) model or other type of structural models will not give us more information. Second, it may well be the case that the use of a more complicated model will most likely lead to the emergence of more questionable assumptions and therefore an increased risk associated with them. Therefore, we prefer to work with the minimum econometric framework.

⁴ The existence of regimes that are not explicitly taken into account may lead to spurious persistence (Perron, 1989).

⁵ Fractional integration can appear in inflation as a result of aggregating prices from heterogeneous firms in their price adjustment costs.

⁶ Fractionally integrated processes and I(0) process with structural breaks look very similar. Testing for the difference is difficult.

⁷ An ARIMA process assumes that a time series can be modelled in the time domain as a function of lagged values of itself and current and lagged values of the innovation or error to the process. An ARIMA(p, d, q) takes the general form where the AR lag polynomial is of order p, the order of integration is given by the differencing parameter d and the moving average polynomial if of order q.

⁸ Cook (2006) finds that the power of the tests in finite samples under alternative DGPs can be increased with alternative values for .

⁹ We used the Box–Jenkins procedure to identify several candidate models for each series and then chose the best fitting model based on residual serial correlation tests, significance of the parameter estimates and R ².

¹⁰ Perron and Qu (2007) suggest that small sample power can be improved if the parameters used to construct the estimate of the long-run variance are estimated from Equation 1 rather than Equation 3.

¹¹ Two main approaches have been used in the literature to define a fractional process x _t . The first, which is adopted in Hosking (1981), among others, defines a stationary fractional process as an infinite order moving average of innovations: and defines a nonstationary I(d) process as the partial sum of an I(d − 1) process (Velasco, 1999a, b). The second, which is used in Robinson (1994) and Phillips (1999), truncates the fractional difference filter and defines for all values of d. For a more detailed discussion of the definitions and their implications, see Shimotsu and Phillips (2006).

¹² This section draws heavily from HLT (2006).

¹³ Most of the previous studies on inflation dynamics and inflation persistence have been conducted for the case of the US economy and several other industrialized countries. They used the GDP deflator or Harmonized CPI for the case of the EU countries since these price series are reported seasonally adjusted as well. However, in our case there is no consistent dataset that provides the CPI or GDP deflator for all the countries of our sample as seasonally adjusted. Therefore, we are forced to apply the X12 seasonal adjustment method of the US Census Bureau which is widely accepted.

¹⁴ Based on the AIC and Schwarz Information Criterion (SIC) we selected an ARMA(1, 1) specification for all countries although for some cases a higher order ARMA(p, q) specification could also be selected. However the qualitative results derived by these alternative specifications were shown to be very similar to the ones obtained by the estimated ARMA(1, 1) models.

¹⁵ Our sample does not include the recent members of the Eurozone, namely, Cyprus, Malta, Slovakia and Slovenia.

¹⁶ Based on the AIC and SIC we selected an AR(1) specification for all countries although for some cases a higher order AR(p) specification could also be selected. However the qualitative results derived by these alternative specifications were shown to be very similar to the ones obtained by the estimated AR(1) models.

¹⁷ An alternative approach to study time-variation in parameters is the use of split samples and rolling regressions. Following O’Reilly and Whelan (2005), Batini (2006) and Pivetta and Reis (2007) we also applied rolling regressions to examine the time-varying behaviour of the coefficient of inflation persistence. To save space our results are available upon request. In addition we also applied recursive estimation of the AR coefficient and we found that the overall results are consistent with those obtain from rolling regressions. These results are also available upon request.

¹⁸ Stock and Watson (1996, 1998) proposed an alternative estimation method the time varying parameter-MUB estimation which corrects for possible distortion in estimates. However, in our case no distortion is estimates was detected.

¹⁹ The estimated equation suggested by Beechey and Österholm (2007, 2009) features homoscedastic disturbances. There are some studies, Cogley and Sargent (2005) and Sims and Zha (2006) which found evidence of heteroscedasticity in the US inflation rates. However, our testing for conditional heteroscedasticity provided no evidence at the 5% critical value for the presence of conditional heteroscedasticity for all cases.

²⁰ Canova et al. (2007) and Gambetti et al. (2008) argued that the use of a SVAR model is a more appropriate specification to study for the individual features inflation such as persistence and volatility. They argued that in the presence of conditional heteroscedasticity, persistence and volatility should not depend on a single source of variation. Although this argument may be true, in our case this is not valid as we examine only one feature of inflation that of persistence.

²¹ For the case of China the algorithm did not converge because of the small sample.