Spurious Regression and Residual-Based Tests for Cointegration in Panel Data When the Cross-Section and Time-Series Dimensions are Comparable

In the first half of the paper we study spurious regressions in panel data when the cross-section and time-series dimensions are comparable. Asymptotic properties of the least-squares dummy variable (LSDV) estimator and other conventional statistics are examined. We show that the LSDV estimatoris consistent for its true value, but the t-statistic diverges so that inferences about the regression coefficient, are wrong with the probability that goes to one. The asymptotics of LSDV are also different from those of the spurious regression in the pure time series. This has an important consequence for residual-based cointegration tests in panel data, because the null distribution of residual-based cointegration tests depends on the asymptotics of LSDV. In the second half of the paper we study residual-based tests for cointegration regression in panel data. We study Dickey-Fuller (DF) tests and an augmented Dickey-Fuller (ADF) test to test the null of no cointegration. Asymptotic distributions of the tests a re derived and Monte Carlo experiments are conducted to evaluate finite sample properties of the proposed tests.