Conditional Moment Restrictions and Triangular Simultaneous Equations∗

We examine whether a causal interpretation can be given to the function identified by the conditional moment restriction (CMR). It is shown that in a general nonseparable triangular system the CMR does not identify the average structural function (ASF) nor any other structural object. This implies that the CMR identifies a causal relation only if the model is structurally separable in observable covariates and unobservable random errors. This excludes for instance random coefficient models in which the CMR in general does not identify the average response. Because we discuss identification by CMR in a general nonseparable triangular system, we provide a condition under which this system is nonparametrically just identified from the population distribution of the observables, so that under this condition there is a one-to-one correspondence between the population distribution of the observables and the triangular nonseparable system. An implication of our results is that empirical researchers should use other methods than CMR if they want to estimate the average response in a random coefficient model.