On the Sensitivity of Kernel-based Tests of Conditional Moment Restrictions ∗

This paper extends the analysis of Godfrey and Orme (1996), on the behaviour of parametric conditional moment tests in the presence unconsidered local alternatives, to that of kernel-based tests of conditional moment restrictions. Particular attention is paid to tests of separate moment conditions. The theoretical results presented in this paper provide a method of identifying whether, or not, a given test will be sensitive to a particular type of (unconsidered) local model misspecification and how any such sensitivity manifests itself. Insensitivity helps isolate possible sources of misspecification, whilst a characterisation of the sensitivity can aid the construction of robust procedures.