DEMAND ANALYSIS AS AN ILL-POSED INVERSE PROBLEM WITH SEMIPARAMETRIC SPECIFICATION
研究一种半参数估计量，通过假设残差与工具变量均值独立来纠正非参数回归中的内生性，重点分析联合正态条件下的不适定逆问题，并给出检验、估计量构造及大样本性质，蒙特卡洛实验和消费者需求应用展示了方法的优劣。
In this paper we are concerned with analyzing the behavior of a semiparametric estimator that corrects for endogeneity in a nonparametric regression by assuming mean independence of residuals from instruments only. Because it is common in many applications, we focus on the case where endogenous regressors and additional instruments are jointly normal, conditional on exogenous regressors. This leads to a severely ill-posed inverse problem. In this setup, we show first how to test for conditional normality. More importantly, we then establish how to exploit this knowledge when constructing an estimator, and we derive the large sample behavior of such an estimator. In addition, in a Monte Carlo experiment we analyze its finite sample behavior. Our application comes from consumer demand. We obtain new and interesting findings that highlight both the advantages and the difficulties of an approach that leads to ill-posed inverse problems. Finally, we discuss the somewhat problematic relationship between endogenous nonparametric regression models and the recently emphasized issue of unobserved heterogeneity in structural models.