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The Approximate Slopes of Econometric Tests

John Geweke

Abstract

In this paper the concept of approximate slope, introduced by R. R. Bahadur, is used to make asymptotic global power comparisons of econometric tests. The approximate slope of a test is the rate at which the logarithm of the asymptotic marginal significance level of the test decreases as sample size increases, under a given alternative. A test with greater approximate slope may therefore be expected to reject the null hypothesis more frequently under that alternative than one with smaller approximate slope. Two theorems, which facilitate the computation and interpretation of the approximate slopes of most econometric tests, are established. These results are used to undertake some illustrative comparisons. Sampling experiments and an empirical illustration suggest that the comparison of approximate slopes may provide an adequate basis for evaluating the actual performance of alternative tests of the same hypothesis.