Nonstationary Panels, Panel Cointegration, and Dynamic Panels: Volume 15

This chapter provides an overview of topics in nonstationary panels: panel unit root tests, panel cointegration tests, and estimation of panel cointegration models. In addition it surveys recent developments in dynamic panel data models.

This chapter reviews developments to improve on the poor performance of the standard GMM estimator for highly autoregressive panel series. It considers the use of the ‘system’ GMM estimator that relies on relatively mild restrictions on the initial condition process. This system GMM estimator encompasses the GMM estimator based on the non-linear moment conditions available in the dynamic error components model and has substantial asymptotic efficiency gains. Simulations, that include weakly exogenous covariates, find large finite sample biases and very low precision for the standard first differenced estimator. The use of the system GMM estimator not only greatly improves the precision but also greatly reduces the finite sample bias. An application to panel production function data for the U.S. is provided and confirms these theoretical and experimental findings.

This chapter uses fully modified OLS principles to develop new methods for estimating and testing hypotheses for cointegrating vectors in dynamic panels in a manner that is consistent with the degree of cross sectional heterogeneity that has been permitted in recent panel unit root and panel cointegration studies. The asymptotic properties of various estimators are compared based on pooling along the ‘within’ and ‘between’ dimensions of the panel. By using Monte Carlo simulations to study the small sample properties, the group mean estimator is shown to behave well even in relatively small samples under a variety of scenarios.

In this chapter we extend the concept of serial correlation common features to panel data models. This analysis is motivated both by the need to develop a methodology to systematically study and test for common structures and comovements in panel data with autocorrelation present and by an increase in efficiency coming from pooling procedures. We propose sequential testing procedures and study their properties in a small scale Monte Carlo analysis. Finally, we apply the framework to the well known permanent income hypothesis for 22 OECD countries, 1950–1992.

To test the hypothesis of a difference stationary time series against a trend stationary alternative, Levin & Lin (1993) and Im, Pesaran & Shin (1997) suggest bias adjusted t-statistics. Such corrections are necessary to account for the nonzero mean of the t-statistic in the case of an OLS detrending method. In this chapter the local power of panel unit root statistics against a sequence of local alternatives is studied. It is shown that the local power of the test statistics is affected by two different terms. The first term represents the asymptotic effect on the bias due to the detrending method and the second term is the usual location parameter of the limiting distribution under the sequence of local alternatives. It is argued that both terms can offset each other so that the test has no power against the sequence of local alternatives. These results suggest to construct test statistics based on alternative detrending methods. We consider a class of t-statistics that do not require a bias correction. The results of a Monte Carlo experiment suggest that avoiding the bias can improve the power of the test substantially.

In this chapter, we study the asymptotic distributions for ordinary least squares (OLS), fully modified OLS (FMOLS), and dynamic OLS (DOLS) estimators in cointegrated regression models in panel data. We show that the OLS, FMOLS, and DOLS estimators are all asymptotically normally distributed. However, the asymptotic distribution of the OLS estimator is shown to have a non-zero mean. Monte Carlo results illustrate the sampling behavior of the proposed estimators and show that (1) the OLS estimator has a non-negligible bias in finite samples, (2) the FMOLS estimator does not improve over the OLS estimator in general, and (3) the DOLS outperforms both the OLS and FMOLS estimators.

There has been extensive research on testing for unit roots in the presence of structural change and on testing for unit roots in panels. This chapter takes a small step towards combining the two research agendas.We propose a unit root test for non-trending data in the presence of a one-time change in the mean for a heterogeneous panel.The date of the break is determined endogenously.We perform simulations to investigate the power of the test,and apply the test to a data set of annual unemployment rates for 17 OECD countries from 1955 to 1990.

This chapter develops a new limit theory for panel data with large numbers of cross section, n, and time series, T, observations. The results apply when n and T tend to infinity simultaneously and provide useful tools for obtaining convergencies in probability and in distribution in cases where the panel data may be cross sectionally heterogenous in a fairly general way. We demonstrate how the new theory can be applied to derive asymptotics for a panel regression where regressors are generated by a local to unit root process with heterogenous localizing coefficients across cross section.

Several stationarity tests in heterogeneous panel data models are proposed in this chapter. By allowing maximum degree of heterogeneity in the panel, two different ways of pooling information from independent tests, the group mean and the Fisher tests, are used to develop the panel stationarity tests. We consider the case of serially correlated errors in the level and trend stationary models. The small sample performances of the tests are investigated via Monte Carlo simulations. The simulation experiments reveal good small sample performances. In the presence of serial correlation, either the group mean or the Fisher tests based on individual KPSS tests with l2 and LMC tests with p = 1 are recommended for use in empirical work due to their good small sample performances.

We consider the problem of instrumental variable estimation of semipara-metric dynamic panel data models. We propose several new semiparametric instrumental variable estimators for estimating a dynamic panel data model. Monte Carlo experiments show that the new estimators perform much better than the estimators suggested by Li & Stengos (1996) and Li & Ullah (1998).

This chapter conducts a Monte Carlo investigation into small sample properties of some of the dynamic panel data estimators that have been applied to estimate the growth-convergence equation using Summers-Heston data set. The results show that the OLS estimation of this equation is likely to yield seriously upward biased estimates. However, indiscriminate use of panel estimators is also risky, because some of them display large bias and mean square error. Yet, there are panel estimators that have much smaller bias and mean square error. Through a judicious choice of panel estimators it is therefore possible to obtain better estimates of the parameters of the growth-convergence equation. The growth researchers may make use of this potential.