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Empirical Economics

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01.03.2014

Detecting multiple breaks in long memory the case of U.S. inflation

verfasst von: Uwe Hassler, Barbara Meller

Erschienen in: Empirical Economics | Ausgabe 2/2014

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Abstract

Multiple structural change tests by Bai and Perron (Econometrica 66:47–78, 1998) are applied to the regression by Demetrescu et al. (Econ Theory 24:176–215, 2008) in order to detect breaks in the order of fractional integration. With this instrument we tackle time-varying inflation persistence as an important issue for monetary policy. We determine not only the location and significance of breaks in persistence, but also the number of breaks. Only one significant break in U.S. inflation persistence (measured by the long-memory parameter) is found to have taken place in 1973, while a second break in 1980 is not significant.

Vorheriger Artikel Smooth transition trends and labor force participation rates in the United States

Nächster Artikel Measuring monetary policy with empirically grounded identifying restrictions

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For a review on changing inflation persistence in EMU member states see Tillmann (2012) and Meller and Nautz (2012).

Such a feature is sometimes called “mean-reversion” although Phillips and Xiao (1999) argue that this is a misnomer given the nonstationarity.

The model in (6) introduces a nonlinearity in \(\Delta ^d y_t\) which is not present under the null in (1). Baillie and Kapetanios (2007) and Baillie and Kapetanios (2008) found evidence in favour of nonlinearity in addition to long memory in many economic and financial time series. Contrary to (6), however, they instead assume a smooth transition autoregression or a similar nonlinear \(I(0)\) model for \(\Delta ^d y_t\). An investigation of their tests under breaks in memory is beyond the scope of the present paper.

The critical values are available from an unpublished appendix to Bai and Perron (2003b) posted on the homepage of Pierre Perron.

Tables containing corresponding information as reported in Table 1 are available for all variations to the simulation set-up reported in this subsection.

Seasonality is accounted for by twelve monthly dummies (\(dum_{seas}\)), the break in mean is accounted for by a mean dummy (\(dum_\mu \)) taking on the value one before and the value 0 after \([\tau _0 \,T]\). The variable \(y_t\) is the residual of the regression of \(p_t\) on \(dum_\mu \) and \(dum_{seas}\).

As an alternative to the sequential procedure we also allow for two mean shifts simultaneously and obtain similar break points and \(p\) values.

Bai and Perron (1998) also investigate a double maximum test, not considered in this paper. The number of break points is found by taking the maximum over all \(sup F(m)\) test statistics, where \(m={1,2,...,5}\). This maximum value is then compared to critical values in order to determine the significance. This suggests that in our analysis there is only one break point.

As becomes evident in Fig. 5, the power of the test increases with the difference in the order of integration before and after the break. Another factor is the total number of observations in the whole sample, see Fig. 6. If the difference in the order of integration is at least 0.3 and the sample size is 500, the test has a rejection rate of more than 80 % if there are at least 150 observations left before and after the break.

This interpretation is inferred directly from Proposition 3 in Demetrescu et al. (2008) and the derivations of this paper.

The order of integration was estimated to be 0.22 for \(B=T^{0.70}\) with a 90 % confidence interval \([0.01, 0.43]\). However, the estimation depends heavily on single observations.

The events are not described in order to indicate causality but rather in order to integrate the break date into its historical background.

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Titel: Detecting multiple breaks in long memory the case of U.S. inflation
verfasst von: Uwe Hassler
Barbara Meller
Publikationsdatum: 01.03.2014
Verlag: Springer Berlin Heidelberg
Erschienen in: Empirical Economics / Ausgabe 2/2014
Print ISSN: 0377-7332
Elektronische ISSN: 1435-8921
DOI: https://doi.org/10.1007/s00181-013-0691-8

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