CHAPTER 1 Identification of Nonadditive Structural Functions ∗

When latent variates appear nonadditively in a structural function the effect of a ceteris paribus change in an observable argument of the function can vary across people measured as identical. Models that admit nonadditive structural functions permit responses to policy interventions to have probability distributions. Knowledge of the distributions of responses is important for welfare analysis and it is good to know what conditions secure identification of these distributions. This lecture examines some aspects of this problem. Early studies of identification in econometrics dealt almost exclusively with linear additive “error” models. The subsequent study of identification in nonlinear models was heavily focused on additive error models until quite recently1 and only within the last ten years has there has been extensive study of identification in nonadditive error models. This lecture examines some of these recent results, concentrating onmodelswhich admit nomore sources of stochastic variation than there are observable stochastic outcomes. Models with this property are interesting because they are direct generalizations of additive error models and of the classical linear simultaneous equation models associated with the work of the Cowles Commission, and because the addition of relatively weak nonparametric restrictions results in models which identify complete structural functions or specific local features of them. Nonparametric restrictions are interesting because they are consonant with the information content of economic theory. Even if parametric or semiparametric restrictions are imposed when estimation and inference are done, it is good to know nonparametric identification conditions because they tell us what core elements of the model are essential for identification and which are in