Conditional Moment Restrictions and Triangular Simultaneous Equations

Joint with: Geert Ridder

We examine whether a causal interpretation can be given to the function identified by the conditional moment restriction (CMR). It is shown that in general the CMR does not identify the average structural function (ASF) nor any other structural object. It is further shown that the CMR does not identify the average derivative either. We conclude that the CMR identifies a causal relation only if the model is structurally separable in observable covariates and unobservable random errors. 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 the population distribution of the observables.

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