Essays on Non-Stationary Panel Analysis

Abstract

This thesis consists of three self-contained essays on non-stationary panel data. We propose novel approaches to both cointegration and unit root analysis in panel data models. The main contribution of this thesis is allowing for the presence of cross¬section dependence through the specification of an approximate common factor model. Early studies assumed that time series in the panel data were either indepen¬dent or that cross-section dependence could be controlled by including time effects. In macroeconomic, microeconomic and financial applications, cross-section depen¬dence is more a recurrent than a rare characteristic and it is usually caused by the presence of common shocks (oil price shocks or financial crises) or the existence of local productivity spillover effects. Ignoring these factors can lead to spurious statistical inference. More exactly, in the case of unit root testing, the unaccounted cross-section dependence might lead one to conclude that panel data is actually I(0) stationary when in fact it might be I(1) non-stationary. Similarly, the panel data cointegration test statistics might indicate than there are more cointegrating relations than there exist. Thus, recent studies proposed several alternatives to over¬come this limitation. One popular approach is the factor structure applied to the error process, an approach that we employ throughout this thesis.

In the first essay we extend the univariate Carrion-i-Silvestre, Kim and Perron (2009) GLS-based unit root tests with multiple structural breaks to panel data. The proposed statistics are general enough that they allow for cross-section dependence and multiple structural breaks in both the level and the trend of the units of the panel. We evaluate the finite-sample properties of these statistics via Monte Carlo simulations. Our simulation study shows that the panel tests perform well, espe¬cially for the cases of known structural breaks. We apply these statistics to a panel of annual data covering the period 1870-2008 for 19 OECD countries. We find strong evidence in favor of I(0) stationarity when we apply the unit root tests to idiosyncratic component. However, the empirical analysis also shows that the I(1) non-stationarity of the real per capita GDP is captured by the common factor.

In the second essay we propose a test statistic to determine the cointegration rank of VAR processes both in a unit-by-unit analysis and in a panel data frame¬work. The cross-section dependence is accounted for through the specification of a common factor model, which covers situations where there is cointegration among the cross-section dimension. We perform a Monte Carlo experiment in order to investigate the small-sample properties of the proposed panel statistic and the sim-ulation results indicate a good performance of the tests in terms of empirical size and power. We show that in some cases not accounting for common factors when they are present can lead to overestimating the cointegrating rank. We apply our proposed tests to two empirical applications using the variables involved in the money demand equation and the monetary exchange model. The money demand model detects two stochastic trends while the monetary exchange model detects three stochastic trends.

In the third essay of this dissertation we investigate the cointegration relation between output, physical capital, human capital, public capital and labor for 17 Spanish regions observed over the period 1964-2000. The novelty of our approach is that we allow for cross-section dependence between the members of the panel using a common factor model. This is interesting because we allow the model specification to capture unobservable variables (technological progress, total factor productivity) to be proxied by the common factors, something that has not been widely addressed in the literature. To see if the variables are cointegrated or not, we employ two different techniques at the panel level. More exactly, we compare the statistics from the single-equation method of Westerlund (2008) and Banerjee and Carrion-i-Silvestre (2011, 2013) with those from the VAR framework of Carrion¬i-Silvestre and Surdeanu (2011). Moreover, using the VAR method, we identify at least one common cointegrating relation among output, physical capital, human capital, public capital and labor. Finally, we use several estimators to estimate the long-run relation between these variables.