Inference on subsets of parameters in GMM without assuming identification

Joint with: Sophocles Mavroeidis

We construct an upper bound on the limiting distributions of the identification robust GMM statistics for testing hypotheses that are specified on subsets of the parameters. The upper bound corresponds to the limiting distribution that results when the unrestricted parameters are well identified. It therefore leads to more powerful tests than those that result from using projection arguments on tests on all the parameters. The upper bound only applies when the unrestricted parameters are estimated using the continuous updating estimator.

The critical values that result from the upper bound lead to conservative tests when the unrestricted parameters are not well-identified. The identification robust GMM statistics resemble identification statistics when we evaluate them at a value of the hypothesized parameter that is distant from the true one. The power of these statistics is therefore governed by the least identified parameter so a weakly identified parameter implies that the power for tests on any of the parameters is low.

For more information, contact Frank Schorfheide.