This paper analyzes the properties of standard estimators, tests, and confidence sets (CS's) for parameters that are unidentified or weakly identified in some parts of the parameter space. The paper also introduces methods to make the tests and CS's robust to such identification problems. The results apply to a class of extremum estimators and corresponding tests and CS's that are based on criterion functions that satisfy certain asymptotic stochastic quadratic expansions and that depend on the parameter that determines the strength of identification. This covers a class of models estimated using maximum likelihood (ML), least squares (LS), quantile, generalized method of moments, generalized empirical likelihood, minimum distance, and semi-parametric estimators. The consistency/lack-of-consistency and asymptotic distributions of the estimators are established under a full range of drifting sequences of true distributions. The asymptotic sizes (in a uniform sense) of standard and identification-robust tests and CS's are established. The results are applied to the ARMA(1, 1) time series model estimated by ML and to the nonlinear regression model estimated by LS. In companion papers, the results are applied to a number of other models.

This paper is concerned with tests and confidence intervals for parameters that are not necessarily point identified and are defined by moment inequalities. In the literature, different test statistics, critical-value methods, and implementation methods (i.e., the asymptotic distribution versus the bootstrap) have been proposed. In this paper, we compare these methods. We provide a recommended test statistic, moment selection critical value, and implementation method. We provide data-dependent procedures for choosing the key moment selection tuning parameter κ and a size-correction factor η.

In this paper, we derive and experimentally test a theoretical model of speculation in multi-period asset markets with public information flows. The speculation arises from the traders’ heterogeneous posteriors as they make different inferences from sequences of public information. This leads to overpricing in the sense that price exceeds the most optimistic belief about the real value of the asset. We find evidence of speculative overpricing in both incomplete and complete markets, where the information flow is a gradually revealed sequence of imperfect public signals about the state of the world. We also find evidence of asymmetric price reaction to good news and bad news, another feature of equilibrium price dynamics under our model. Markets with a relaxed short-sale constraint exhibit less overpricing.