In this paper we derive the asymptotic distribution of the test statistic of a generalized version of the integrated conditional moment (ICM) test of Bierens (1982, 1984), under a class of Vn-local alternatives, where n is the sample size. The generalized version involved includes neural network tests as a special case, and allows for testing misspecification of dynamic models. It appears that the ICM test has nontrivial local power. Moreover, we show that under the assumption of normal errors the ICM test is asymptotically admissible, in the sense that there does not exist a test that is uniformly more powerful. The asymptotic size of the test is case-dependent: the critical values of the test depend on the data-generating process. In this paper we derive case-independent upperbounds of the critical values

IF THE SENDER'S PREFERENCES are monotonic in the Receiver's action, then it is known that the Sender reveals its type in every sequential equilibrium of a Sender-Receiver game with verifiable messages (see, e.g., Milgrom (1981)). Monotonicity is a natural condition in social situations such as buyer-seller relationships; but there are obviously other situations in which the ideal action for a Sender varies with its type. Accordingly, we generalize Milgrom's result by replacing monotonicity with more general conditions on the Sender's preferences, which are sufficient for existence and uniqueness of a fully revealing equilibrium in verifiable message games. These conditions include all games in which preferences satisfy the conditions which Crawford-Sobel (1982) imposed on cheap talk games.

Moment based tests for mispecification of parametric models (e.g., of mean equals variance in a Poisson model) are studied. The moment restrictions under test are embedded in an extension of the model so that the moment test is a score test of the hypothesis that a vector of added parameters is zero. Second-order asymptotic properties of the likelihood ratio version of this test are studied. Unlike the conventional test, the likelihood ratio version is Bartlett correctable. The correction depends on the curvature at the origin of the function used to incorporate the moment restriction in the extended model.