Panel Stationarity Test with Structural Breaks*

Abstract

In this paper, we extend the heterogeneous panel data stationarity test of Hadri ["Econometrics Journal", Vol. 3 (2000) pp. 148-161] to the cases where breaks are taken into account. Four models with different patterns of breaks under the null hypothesis are specified. Two of the models have been already proposed by Carrion-i-Silvestre "et al." ["Econometrics Journal", Vol. 8 (2005) pp. 159-175]. The moments of the statistics corresponding to the four models are derived in closed form via characteristic functions. We also provide the exact moments of a modified statistic that do not asymptotically depend on the location of the break point under the null hypothesis. The cases where the break point is unknown are also considered. For the model with breaks in the level and no time trend and for the model with breaks in the level and in the time trend, Carrion-i-Silvestre "et al." ["Econometrics Journal", Vol. 8 (2005) pp. 159-175] showed that the number of breaks and their positions may be allowed to differ across individuals for cases with known and unknown breaks. Their results can easily be extended to the proposed modified statistic. The asymptotic distributions of all the statistics proposed are derived under the null hypothesis and are shown to be normally distributed. We show by simulations that our suggested tests have in general good performance in finite samples except the modified test. In an empirical application to the consumer prices of 22 OECD countries during the period from 1953 to 2003, we found evidence of stationarity once a structural break and cross-sectional dependence are accommodated. Copyright (c) Blackwell Publishing Ltd and the Department of Economics, University of Oxford, 2008.

The long-run behaviour of the terms of trade between primary commodities and manufactures: a panel data approach

“…The proof of the previous result can be found in Hadri (2000). Furthermore, Hadri and Rao (2008) show that in the presence of breaks, that is for the models in Equations (3) to (6), the individual means, The Hadri and Rao (2008) test critically relies on the assumption that the individual time series in the panel are independent from each other. 10 To allow for cross-section dependence, Hadri and Rao recommend employing an AR-based bootstrap method, the steps of which are as follows: First, to account for serial correlation Equation (11) …”

“…In a recent paper, Hadri and Rao (2008) extend the previous setup to allow for the presence of one-time structural breaks. More specifically, they postulate the following models of structural break under the null hypothesis:…”

“…Lastly, beef and zinc can be viewed as trendless series that show evidence of a one-time positive level shift after the break, which does not corroborate the PS hypothesis either. At this point, it could well be argued that while the Hadri and Rao (2008) procedure accounts for unknown structural breaks, it is limited insofar as only a single break is permitted for each individual in the panel. However, informal visual inspection of the residuals from the chosen models reveals no evidence of further structural breaks, apart from the presence of potential outlier observations.…”

“…the existence of a unit root), appears more suitable to assess the PS hypothesis because this hypothesis, as originally postulated, implies the existence of a long-run declining deterministic trend in relative commodity prices. For this purpose, we employ the residual-based Lagrange multiplier (LM) panel stationarity tests put forward by Hadri and Rao (2008), who extend the Hadri (2000) tests to accommodate one-time structural breaks and cross-section dependence.…”

Real interest parity: A note on Asian countries using panel stationarity tests

“…Using a panel stationarity testing procedure recently advocated by Hadri and Rao (2008) that allows for structural breaks and cross-sectional dependency, we are unable to reject the stationarity of Asian real interest rate differentials. JEL Classification: C33; F36; G15 Keywords: Heterogeneous dynamic panels, real interest parity, mean reversion, panel stationarity test.…”