On the Identification of Nonparametric Structural Models

In this paper we study the identiiability of nonparametric models, that is, models in which both the functional forms of the equations and the probability distributions of the disturbances remain unspeciied. Identiiability in such models does not mean uniqueness of parameters but rather uniqueness of the set of predictions of interest to the investigator. For example, predicting the eeects of changes, interventions, and control. We provide suucient and necessary conditions for identifying a set of causal predictions of the type: \Find the distribution of Y , assuming that X is controlled by external intervention", where Y and X are arbitrary variables of interest. Whenever identiiable, such predictions can be expressed in closed algebraic form, in terms of observed distributions. We also show how the identifying criteria can be veriied qualitatively, by inspection, using the graphical representation of the structural model. When compared to standard identiiability tests of linear models (e.g., rank and order), our criteria serve to segregate tests that hold universally from those that are artifacts of the linearity assumption.