Testing Homogeneity and Unit Root Restrictions in Panels
Sammanfattning: This thesis is divided into two distinct parts. The first part contains three chapters, co-authored with Joakim Westerlund, that deal with the analysis of unit root testing, and the second part consists of two chapters on slope homogeneity testing. Chapter 2 continues and extends the analysis in Westerlund (Empirical Economics 37:517–531, 2009), who demonstrates that the performance of the popular LLC (Levin et al., Journal of Econometrics 98:1–24, 2002) panel unit root test depends critically on the choice of lag truncation used when correcting for serial correlation, and that it is only when this parameter is set as a function of time that the power raises above size. The purpose Chapter 2 is to propose a modified test that does not suffer from this drawback. The new test is not only simpler to compute but also superior in terms of small-sample performance, which is illustrated using as an example purchasing power parity for less developed countries. Chapter 3 considers panel unit root testing when there is uncertainty about the deterministic trend. In doing so, it takes PANIC (Bai and Ng, Econometrica 72:1127-1177, 2004), one of the most general and popular panel unit root tests, and demonstrates how it can be modified to determine the extent of both the deterministic trend and non-stationarity of the data. Chapter 4 offers an in-depth analysis of the dynamic and cross-sectional properties of crime using data covering 21 Swedish counties from 1975 to 2010. The results suggest that the crimes considered are non-stationary, and that this cannot be attributed to county-specific disparities alone, but that there are also a small number of common stochastic trends to which groups of counties tend to revert. With this result in mind, we investigate the relationship between unemployment and crime using novel panel cointegration techniques. Overall, the results do not support cointegration, and suggest that previous findings of a significant relationship between unemployment and crime might be spurious. Chapter 5 proposes a test of slope homogeneity for panel data models that is robust to unspecified error serial dependence and heteroscedasticity. The proposed test is an adjusted version of the dispersion-type test suggested by Pesaran and Yamagata (Journal of Econometrics 142, 50–93, 2008) and is shown to have a standard normal distribution, as N, T → ∞. Using Monte Carlo experiments, it is demonstrated that the proposed test performs well in small samples, even when the degree of serial dependence is large. Chapter 6 considers the issue of slope homogeneity testing in panel data models with non-spherical errors. It proposes a bootstrap test of the slope homogeneity hypothesis that is robust to cross-sectional and serial dependence in the errors. The chapter also proposes a bootstrap sequential test that enables differentiation between units with a common slope coefficient vector and units for which the hypothesis of equal slope coefficients fails. Asymptotic properties of the bootstrap tests are derived by letting the time series dimension of the panel increase to infinity, and a small Monte Carlo study is conducted to investigate the small-sample properties.
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