Set Identified Linear Models
研究了在非完整线性矩条件下参数β的识别与估计，给出了识别集为有界凸集的刻画，并提出了超数限制有效性的检验及置信区域构建方法。
Before quoting, please ask for the fully revised version We analyze the identification and estimation of parameters β satisfying the incomplete linear moment restrictionsE(z>(xβ−y)) = E(z>u(x))where z is a set of instruments and u(z) an unknown bounded scalar function. We first provide empirically relevant examples of such a set-up. Second, we show that these conditions set identify β where the identified set B is bounded and convex. We provide a sharp characterization of the identified set not only when the number of moment conditions is equal to the number of parameters of interest but also in the case in which the number of conditions is strictly larger than the number of parameters. We derive a necessary and sufficient condition of the validity of supernumerary restrictions, which generalizes the familiar Sargan condition. Third, we provide new results on the asymptotics of analog estimates. When B is a strictly convex set, we also construct a test of the null hypothesis, β0 ∈ B, whose level is asymptotically exact and which relies on the minimization of the support function of the set B −{β0}. Inverting this test makes it possible to construct confidence regions with uniformly exact coverage probabilities. Results of some Monte Carlo experiments are presented.