This paper examines the finite-sample power of tests of structural inv
ariance and superexogeneity hypotheses in econometric models with cont
emporaneous conditioning variables. We consider both direct parametric
tests of superexogeneity, as well as indirect procedures based on tem
poral stability tests for the parameters of interest. Our Monte Carlo
analysis reveals that both types of tests may lack power in interestin
g classes of models. An empirical illustration investigates the supere
xogeneity of the short-term interest rate in a dynamic specification f
or the U.S. term structure.