Refined exogeneity tests in linear dynamic panel data models

Exogeneity tests are investigated in linear dynamic panel data models, estimated by GMM. Because in that context usually just internal instruments are being exploited, misclassification of explanatory variables renders either a specific subset of instruments invalid or yields inefficient estimates. Rather than testing all overidentifying restrictions by the Sargan-Hansen test, the focus is on subsets using either the incremental Sargan-Hansen test or a Hausman test. Although it is known in the literature that the Sargan-Hansen test suffers when using many instruments, it is  yet unclear in what way the incremental test is affected. Therefore, test statistics are considered in which the number of employed instruments is deliberately restricted. Two possible refinements are proposed. The procedure of Hayakawa (2014), which forces a block diagonal structure on the weighting matrix in order to reduce problems stemming from taking its inverse, is generalized to the incremental test and a finite sample corrected variance estimate for the vector of contrasts is derived from which two new Hausman test statistics are constructed. Simulation is used to investigate finite sample performance. One of corrected Hausman test statistics and a specific implementation of the incremental Sargan-Hansen test, both using only the one-step residuals calculated under the null hypothesis, are found to perform best in terms of size.