Bivariate time series models have been used extensively to analyze the relationship between pairs of economic variables. Various tests have been proposed that can be used to examine the adequacy of specific models. The empirical literature is noteworthy for the frequency with which different authors using different tests reach different conclusions, and for the apparent lack of evidence for certain relationships strongly suggested by economic theory. The objective of this study is to use Monte Carlo methods to examine the size and power of alternative tests, and to relate these findings to the analytical structure of the tests.