Irregular Identification, Support Conditions, and Inverse Weight Estimation

摘要: In weighted moment condition models, we show a subtle link between identification and estimability that limits the practical usefulness of estimators based on these models. particular, if it is necessary for (point) weights take arbitrarily large values, then parameter interest, though point identified, cannot be estimated at regular (parametric) rate said to irregularly identified. This depends relative tail conditions can as slow in some examples n−1/4. nonstandard convergence lead numerical instability and/or standard errors. We examine two model examples: (i) binary response under mean restriction introduced by Lewbel (1997) further generalized cover endogeneity selection, where estimator this class models density special regressor, (ii) treatment effect exogenous selection (Rosenbaum Rubin (1983)), resulting average one variant propensity score. Without strong support conditions, similar well known “identified infinity” converge slower than parametric rate, since essentially, ensure identification, requires variables values sets with small probabilities, or thin sets. For above, derive rates propose conducts inference using adaptive procedures are analogous Andrews Schafgans (1998) sample model.