On the Consistency of Joint and Paired Tests for Non-Nested Regression Models

This paper examines the consistency properties of some tests of a null model against a single non-nested alternative and against multiple non-nested alternatives (paired and joint tests, respectively). Consistency of the tests is evaluated. First, even when all possible paired comparisons are made, paired tests may be inconsistent unless the true alternative is used. A joint test can be consistent when the paired Wald test based on the comprehensive model may be inconsistent, thereby formalizing the notion that a joint test may be more widely consistent then a paired test. Finally we show that when a fixed alternative for the paired test is true, the power of a joint test can never exceed that of the paired test.