Conditional Moment Restrictions and Triangular Simultaneous Equations

We show that in the nonparametric triangular simultaneous equations model, the mean independence conditional moment restriction (CMR) identifies a causal relation between the dependent variable and an endogenous covariate, only if the model is structurally separable in observable covariates and unobservable random errors. If the CMR is used in a nonseparable population model, the average structural function (ASF) is not recovered. However, the ASF is recovered from the average CMR (ACMR) based on independence of the endogenous covariate and the random error given a control variate. We also provide a condition under which the nonseparable model is nonparametrically just identified from the population distribution of the observables, so that under this assumption the nonseparable triangular simultaneous equations model does not restrict their population distribution