Testing for a Structural Break in Dynamic Panel Data Models with Common Factors

This paper develops a method for testing for the presence of a single structural break in panel data models with unobserved heterogeneity represented by a factor error structure. The common factor approach is an appealing way to capture the effect of unobserved variables, such as skills and innate ability in studies of returns to education, common shocks and cross-sectional dependence in models of economic growth, law enforcement acts and public attitudes towards crime in statistical modelling of criminal behaviour. Ignoring these variables may result in inconsistent parameter estimates and invalid inferences. We focus on the case where the time frequency of the data may be yearly and thereby the number of time series observations is small, even if the sample covers a rather long period of time. We develop a Distance type statistic based on a Method of Moments estimator that allows for unobserved common factors. Existing structural break tests proposed in the literature are not valid under these circumstances. The asymptotic properties of the test statistic are established for both known and unknown breakpoints. In our simulation study, the method performed well, both in terms of size and power, as well as in terms of successfully locating the time at which the break occurred. The method is illustrated using data from a large sample of banking institutions, providing empirical evidence on the well-known Gibrat's `Law'.