The purpose of this research is to produce statistical tests and methods for the construction of confidence regions that are valid for the general k-endogenous variable, overidentifying instruments, model. In addition there are several subsidiary goals. First, the work will be extended to the general GMM framework. It is very likely that the distribution of test statistics carries over to nonlinear and nonspherical models, but works needs to be done on those details which rely on the significance of the first stage simply because the standard GMM approach doesn't have a separately identified first stage. Second, the distinction between included and excluded exogenous variables needs to be clarified in computing the degrees of freedom for the `switched-LR` and `switched-LM` statistics. Third, recent work by others will be extended which provide diagnostics for finding `weak instruments.` It is clear that simple tests of first-stage significance are inadequate. Fourth, the practical significance of the methods developed will be demonstrated by applying them to real data. In particular, the widespread adoption in labor economics of natural experiments as a source of instruments should provide a good `test bed.` Inference using the above methods will be compared to the traditional methods currently employed.
