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This study examines the finite-sample bias of S. Johansen's likelihood ratio tests for cointegration using the Monte Carlo method. Response surface analysis is employed to obtain approximations to the finite-sample critical values and illustrate the individual roles of the sample size, the dimension of the variable system, and the lag order in determining the finite-sample bias of Johansen's tests. The study further shows the importance of lag length selection for Johansen's tests and the performance of standard lag selection criteria in choosing the proper lag length is investigated. Monte Carlo results concerning the sensitivity of Johansen's tests to non-normal innovations are also reported.