Variable Augmentation Specification Tests in the Exponential Family

This paper motivates, exposits, and develops the variable augmentation specification test (VAST) approach from the perspective of generalized linear exponential family, which includes several parametric families widely used in applied econometrics and statistics. The approach is equivalent to score tests and link tests and serves to both unify and simplify the computation of score tests in such models using the Engle-Davidson-MacKinnon technique of artificial regression. Specification tests for both the mean and the variance components are treated symmetrically. Several theoretical applications are discussed.