Testing structural stability in heterogeneous panel data

Abstract

This paper introduces a new test for structural instability among only some individuals at the end of a sample in a panel regression model. Most tests for structural breaks in the literature are appropriate when the break is relatively long lasting and happens in the middle of a sample. The distribution of the corresponding test statistic is suitably found using asymptotics in which the number of observations before and after the break point go to infinity. However, it is often at the end of a sample that researchers and policy-makers alike are interested in testing for instability. Andrews (2003) proposes a test for structural break which was shown to be particularly useful when the number of post-break observations is small. Unlike the well known Predictive Failure test of Chow (1960), the critical values of Andrews’s (1993) test statistic are calculated using parametric sub-sampling methods making the test robust to non-normal, heteroskedastic and serially correlated errors. The extension of the test to panel data, under the assumption of cross sectional independence, is relatively straightforward as shown in Mancini-Griffoli and Pauwels (2006). This extension assumes an alternative hypothesis that all individuals exhibit a break, as in other tests for structural breaks in the panel literature. Yet, these tests do not allow the interesting alternative that only some - and not all - individuals are affected by a break. This paper addresses such question by introducing a standardized Z statistic built from Andrews (2003) statistics averaged across individuals.Methodologically, the proposed procedure is similar to the approach in Im et al. (2003) which, while focussing on the different question of unit root tests, also considers an average of separate statistics. The test statistic is shown to follow a normal distribution as the number of individuals goes to infinity by using the Lindeberg-Feller Central Limit Theorem (LFCLT). This greatly simplifies the computation of the critical values with respect to Andrews (2003). As in Andrews (2003), though, the proposed statistic is robust to non-normal, heteroskedastic, serially correlated errors and when the instability occurs at the end of a given sample. Lastly, the test covers the cases of parameter heterogeneity or homogeneity pre- and post-instability. Moreover, it is straightforward to extend the proposed test statistic and the associated asymptotic results to accommodate the presence of cross sectional dependency. A series of Monte Carlo experiments show that the proposed structural break test performs very well in finite sample. The experiments accommodate serial correlation in the error terms with a mixture of different distributions for the innovations. Monte Carlo results indicate that the test has good size and power with relatively few time series and moderate serial correlation within cross sections. For high levels of serial correlation, the performance of the test improves as the number of time series observations, T, increases. Lastly, the test has good power and size for partial instabilities, when the instabilities are of a small magnitude.Finally, this paper considers an empirical application of the test to demonstrate its practical usefulness. The question of detecting the effects of Euro on trade has been at the center of lively debates in academic and policy circles alike. However, the papers that have tackled the issue have not provided strong empirical evidence in support of the presumed effect. This is largely due to two empirical issues: the few datapoints available after the Euro’s introduction and the heterogeneity of the trade effect over different countries. Given both these characteristics, the test introduced in this paper is particularly well suited. Results show a break at the 10% significance level in Eurozone trade starting in 1998, thereby supporting to the belief commonly expressed in the literature.