Cointegration in panel data

Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)




Chihwa Kao


Cointegration, Panel data

Subject Categories

Economics | Statistics and Probability


This dissertation investigates an asymptotic theory of cointegration in panel data covering spurious regression, residual based tests for cointegration, and estimation and inference of cointegrating regressions, where the cross section and time series dimensions are comparable in magnitude. A fixed effect least squares dummy variable (LSDV) regression model is selected throughout the paper. The error terms are assumed to be identically and independently distributed, so that the law of large numbers and central limit theorem for triangular arrays can be applied in a straightforward way.

We first examine a spurious regression problem in panel data and show that the spurious coefficient estimator is consistent but the conventional t-statistic is divergent. We can derive from the latter that ignoring properties of integrated processes in panel data will lead to false inferences about the relationship among the integrated variables as the sample size becomes large.

Next, we propose several residual-based tests for cointegration with the null hypothesis of no cointegration. The Dickey-Fuller (DF) test and the Augmented Dickey-Fuller (ADF) test have asymptotic properties very similar to the unit roots based upon raw residuals. Monte Carlo simulations indicate that the ADF test does not improve the DF test in general.

The asymptotic properties of estimation and inference of cointegrating regression are studied. The LSDV estimators based on the ordinary least squares (OLS) have a non-negligible finite sample bias although they are superconsistent (the convergence rate of ${1\over T}$ instead of ${1\over\sqrt T}).$ Monte Carlo simulations find that the bias-corrected OLS estimators do not improve over the simple OLS estimators.

Finally, we apply the asymptotic theory of cointegrating regressions recently developed by Kao and Chiang (1997) to Coe and Helpman's (1995) international R&D spillovers regression. Conventional OLS may lead to false inference about the coefficients. The OLS with bias-correction, and the Fully-Modified (FM) and the Dynamic OLS (DOLS) estimations produce different predictions about the impact of foreign R&D on total factor productivity although all of the estimations support that domestic R&D is related to total factor productivity. Our empirical results tend to reject Coe and Helpman's hypothesis that international spillovers are trade-related.


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