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Inflation Persistence Before and After Inflation Targeting: A Fractional Integration Approach

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Abstract

We investigate the persistence in the inflation series for 13 OECD countries that explicitly adopted an inflation targeting (IT) regime before 1992. Mean reversion and stationarity as well as mean reversion and non-stationarity exist in the pre-IT period, while mean reversion and stationarity characterize the post-IT period. Inflation exhibits fractional integration behavior over the entire sample period, the pre-IT period, and, in most cases, also in the post-IT period. The adoption of IT coincides with a structural break in all inflation series and marks a decrease in the point estimates of inflation persistence in most countries.

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Notes

  1. Recent contributions on inflation persistence in the US include Kumar and Okimoto [2007], Pivetta and Reis [2007], and Mehra and Reilly [2009]. Beechey and Österholm [2009], Batini [2006] and Meller and Nautz [2012] consider inflation persistence in the euro area, while Gadea and Mayoral [2006] examine inflation persistence in 21 OECD countries

  2. Whether inflation follows a stationary or nonstationary process possesses theoretical implications, since a number of macroeconomic models [Dornbusch 1976; Taylor 1979, 1980; Calvo 1983; and Ball 1993] assume stationary inflation. Additionally, models such as Fuhrer and Moore [1995] and Blanchard and Galí [2007] suggest that inflation persistence captures structural characteristics of the economy that do not likely respond to policy actions. Thus, a policy of IT should exert no effect on inflation persistence. Others such as Batini [2006], Beechey and Österholm [2009], Benati [2008], and Mehra and Reilly [2009] present evidence that inflation persistence varies across monetary regimes

  3. Examples include Nelson and Plosser [1982], Fuhrer and Moore [1995], Cogley and Sargent [2001], Stock [2001], Cecchetti and Debelle [2006], Pivetta and Reis [2007], and Zhang et al. [2008] for the US; O’Reilly and Whelan [2005] and Beechey and Österholm [2009] for Europe and Levin and Piger [2004] and Levin et al. [2004] for a group of OECD countries. Barsky [1987], Ball and Cecchetti [1990], and Brunner and Hess [1993] suggest that the US inflation contains a unit root. The unit-root property appears to occur in a wide array of countries examined in O’Reilly and Whelan [2005] and Cecchetti et al. [2007].

  4. Baillie [1996] provides an extensive review of the concepts of fractional integration in economic series. Long-memory processes are defined in both time and frequency domains. In the time domain, a process exhibits long memory, if its autocorrelation function, k=1, 2, …, decreases at a hyperbolic rate rather than the exponential decay in a covariance-stationary ARMA process. In the frequency domain, the spectrum for a long-memory process diverges to infinity at the zero frequency. In practical applications, long memory emerges when the series possesses a pole on a part of the spectrum close to the zero frequency [Granger and Joyeux 1980].

  5. The misspecification of the short-run dynamics of the ARFIMA model may invalidate the estimation of the fractional integration parameter [Gil-Alana 2004]. The task of identifying p and q for an ARMA process by a simple analysis of the autocorrelation and partial autocorrelation functions proves nearly impossible. Schmidt and Tscherning [1993], Crato and Ray [1996], and Smith et al. [1997] consider various information criteria and assess, by Monte Carlo simulations, the performance of these criteria for a fractionally integrated true model against ARMA and ARFIMA alternative models. Their results suggest that for an ARFIMA(p, d, q) data-generating process (DGP), the identification of the true model may not occur for small or moderate sample size.

  6. We transform the seasonally adjusted price data P t into annualized monthly (quarterly) percentage rate of inflation using π t =12 × 100log(P t /P t−1) for monthly data and π t =4 × 100log(P t /P t−1) for quarterly data.

  7. Prior to switching to IT, six of the 13 countries in the sample (Chile, Iceland, Israel, Norway, Sweden, and the UK) used exchange rates as nominal anchors in stabilization programs, while four (South Korea, Mexico, South Africa, and Switzerland) used the money supply. Australia, Canada, and New Zealand did not specify a nominal anchor before switching to IT.

  8. Baillie [1996] considers four possible outcomes when considering the PP and KPSS tests jointly. First, reject the PP, but not the KPSS statistic, which provides evidence of a stationary series. Second, reject the KPSS, but not the PP statistic, suggesting a unit-root process. Third, do not reject both statistics, suggesting insufficient information on the long-memory characteristics of the series. Fourth, reject both statistics, which provides evidence of a process between I(0) and I(1) or a fractionally integrated process.

  9. The PP test uses Newey–West [1987] standard errors to account for serial correlation and adopts lags chosen deterministically following the rule of thumb int[4(T/100)2/9] [Newey and West 1994]. The KPSS test uses the quadratic spectral kernel. Andrews [1991] and Newey and West [1994] indicate that the latter kernel yields more accurate estimates of the long-run variance than the Bartlett kernel in finite samples. The bandwidth comes from an automatic bandwidth selection routine. Hobijn et al. [2004] find that the combination of the automatic bandwidth selection and the quadratic spectral kernel yields the best small sample test performance in Monte Carlo simulations.

  10. Sample autocorrelations also indicate long memory as all inflation series reveal a slow rate of decay. None exhibit exponential decay like stationary data. For Chile, Israel, and Mexico, the autocorrelations fall at a faster rate, while those corresponding to the remaining countries exhibit sinusoidal behavior that decays slowly. In either case, the autocorrelations exhibit a persistent pattern of moderately high values. Mexico displays the largest autocorrelation at lag 1 (0.92), followed by Israel (0.869) and Chile (0.864), while Switzerland displays the lowest autocorrelation at lag 30 (0.127), followed by Korea (0.154) and Australia (0.178).

  11. From an empirical perspective, the estimates of d usually vary significantly with the choice of m. Too small an m leads to imprecise estimates because of a large standard deviation. Too large an m leads to a biased estimate of d. A large literature focuses on the choice of optimal bandwidth [Delgado and Robinson 1996 and Hurvich et al. 1998].

  12. Hurvich et al. [1998] find that the choice of α=0.5, originally suggested by Geweke and Porter-Hudak [1983], and extensively used in empirical applications, leads to inferior performance to the optimal choice in reasonable samples.

  13. Although Phillips [2007] suggests that we remove deterministic linear trends from the series before the application of the MLP estimator, we also estimate the persistence of the inflation series before and after the IT adoption without detrending the data at the suggestion of a referee. For all countries, the estimates of d without detrending rise relative to their values with detrended data in the pre-IT period. In the post-IT period, the estimates rise only for Canada, Israel, and Mexico. For the remaining countries, the estimates instead fall slightly using the detrended model. The Kumar-Okimoto and Hassler-Olivares test results are also generally invariant to detrending. The main exceptions are Australia (the Kumar-Okimoto test results reverse from insignificant to significant), Chile (both test results reverse from insignificant to significant), and South Africa (both test results reverse from significant to insignificant). Without detrending, the difference in the estimates of persistence for the pre- and post-IT periods are much smaller than we previously found, resulting in the failure to reject the null hypothesis of equality. We note, however, that the regression of the rate of inflation on time in these three countries as well as in the remaining ten countries produces a significantly negative linear trend estimate. We interpret this to imply that ignoring the trend in the MLP regressions leads to misspecification problems.

  14. The frequency of observations does not affect our findings, since similar results also occur using quarterly data.

  15. Since 1980, monetary policy implemented three distinct regimes in South Africa. From 1980 to 1989, monetary policy did not successfully contain inflation. From 1990 to 2000, a significant improvement in the performance of the South African Reserve Bank (SARB) occurred as average inflation fell from 13.06 to 8.87 percent. Since the SARB did not pursue an explicit inflation target, we can characterize this period as implicit IT. From 2000 till the present, the SARB pursues low inflation with an average inflation equal to 5.21 percent. This period differs from the second in that the SARB pursues an official and explicitly stated inflation target. Consequently, we conduct additional tests to assess the importance of the second period. First, we include the second period in the IT period. The results do not differ qualitatively from those reported in the tables. We can reject the nulls of d=0 and d=1 at the 1 percent level, and the MLP regression estimates of d vary from 0.539 for α=0.70 to 0.420 for α=0.80. Second, we test whether the explicit IT regime proved marginally more successful than the implicit targeting regime. We do not find that that occurs. We reject the null of d=1 at the 1 percent level, but we cannot reject the null of d=0 for α=0.70, 0.75, and 0.80. The MLP estimates of d vary from 0.170 for α=0.70 to 0.289 for α=0.80. Thus, persistence in the explicit IT regime, where the SARB wanted to keep inflation within the target band of 3-6 percent, exceeds its actual level under the assumption that the SARB followed the more eclectic and heterogeneous policy of the previous period. This perverse outcome could occur, ceteris paribus, because of the wide targeting band. A lower and narrower target band could improve the credibility of the SARB [Gupta and Uwilingiye 2012], causing inflationary expectations to converge to a focal point [Demertzis and Viegi 2008], resulting in an increase in monetary policy credibility and a decline in inflation persistence.

  16. The Kumar-Okimoto and Hassler-Olivares test results are also generally invariant to detrending. The main exceptions are Australia (the Kumar-Okimoto test results reverse from insignificant to significant), Chile (both test results reverse from insignificant to significant), and South Africa (both test results reverse from significant to insignificant). Without detrending, the difference in the estimates of persistence for the pre- and post-IT periods are much smaller than we previously found, resulting in the failure to reject the null hypothesis of equality.

  17. We thank an anonymous referee for this suggestion.

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Acknowledgements

We acknowledge the helpful comments of two anonymous referees. Any remaining errors reflect our own work.

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    Giorgio Canarella & Stephen M Miller

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Canarella, G., Miller, S. Inflation Persistence Before and After Inflation Targeting: A Fractional Integration Approach. Eastern Econ J 43, 78–103 (2017). https://doi.org/10.1057/eej.2015.36

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  • DOI: https://doi.org/10.1057/eej.2015.36

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