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In the first half of the paper I study spurious regressions in panel data. Asymptotic properties of the least-squares dummy variable (LSDV) estimator and other conventional statistics are examined. The asymptotics of LSDV estimator are 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 estimator. In the second half of the paper I study residual-based tests for cointegration regression in panel data. I study Dickey–Fuller (DF) tests and an augmented Dickey–Fuller (ADF) test to test the null of no cointegration. Asymptotic distributions of the tests are derived and Monte Carlo experiments are conducted to evaluate finite sample properties of the proposed tests.