This project studies identification and estimation in models with independent variables correlated with nonseparable errors if an instrumental variable is available. The first part compares two identification methods of the average structural function (ASF), used in the recent nonparametric simultaneous equations literature. The first uses the conditional moment restriction (CMR) and identifies the ASF only if the model is structurally separable. The second uses the error of a first stage, the control variate, to identify the ASF. Extensions include investigation of the structural model, i.e. invariant in the first stage, the nature of other identification methods as local instrumental variables and other estimands as the quantile structural function. Preliminary analysis indicates that the conditional moment restriction approach does not identify anything structural, thereby clarifying the role of control function in the identification of causal relationships. In the second part, the theory developed in the first part is applied to the nonlinear regression model with nonclassical measurement error and practical estimators are developed for its parameters.
Both applications look at the existing difficult problem in the literature from a completely different perspective. The first application clarifies the relationship between the CMR and causal analysis. The existing literature has used the CMR without realizing the nature of its identified object. The second application tackles the nonclassical measurement error problem, which has not been satisfactorily addressed in the literature.
Broad Impact: The first application is expected to decrease the prominence of CMR in the literature. The second application is expected to have an immediate impact on empirical practice.
