The Effect of Nuisance Parameters on Size and Power; Lm Tests in Logit Models

In econometrics, most null hypotheses are composite, dividing the parame ters into parameters of interest and nuisance parameters. Typically, a composite hypothesis can be tested using two or more testing procedures. Competing testing procedures are commonly compared using size-corrected powers. What is often overlooked is that the size-corrected critical value of a test can be sensitive to the set of admissible values of the nuisance parameters, and hence its size-corrected power. As a result, different choices for the admissible set can produce different conclusions about which test is best. This fact complicates the interpretation of Monte Carlo power studies because in many cases there is no natural definition of the set of admissible values. We find this fact to be crucial when choosing a Lagrange Multiplier test in the case of a logit model. A theoretical explanation for this effect is developed using large parameter asymptotics