Model‐selection tests for conditional moment restriction models

We propose a Vuong‐type model‐selection test for models defined by conditional moment restrictions. The moment restrictions that define the models can be standard equality restrictions that point‐identify the model parameters, or moment equality or inequality restrictions that partially identify the model parameters. The test uses a new average generalized empirical likelihood criterion function designed to incorporate full restriction of the conditional model. We also introduce a new adjustment to the test statistic that makes it asymptotically pivotal whether the candidate models are nested or non‐nested. The test uses simple standard normal critical values and is shown to be asymptotically similar, to be consistent against all fixed alternatives, and to have non‐trivial power against n − 1 / 2 ‐local alternatives. Monte Carlo simulations demonstrate that the finite sample performance of the test is in accordance with the theoretical prediction.