Hypothesis testing in the presence of nuisance parameters

Abstract

How to deal with nuisance parameters is an important problem in econometrics because of the non-experimental nature of economic data. This paper suggests a new approach to dealing with such parameters in the context of hypothesis testing. It involves calculating p-values conditional on values for key nuisance parameters and then taking a weighted average of these values with the weights reflecting the likelihood or posterior probabilities of these values being true. Two specific applications are discussed. These are testing linear regression coefficients in the presence of first-order autoregressive (AR(1)) disturbances and testing for AR(1) disturbances in the dynamic linear regression model. For the former testing problem, a Monte Carlo experiment demonstrates that the new procedure typically provides more accurate inferences than the accepted conventional tests.