| Chapter 1 studies the problem of identification of the long regression E(y | x, z) when the short conditional distributions P(y | X) and P(z | x) are known but the long conditional distribution P(y | x, z) is not known. This problem often arises when a researcher utilizes data from two separate data sets. An identification region is isolated containing feasible values of the long regression, and it is shown that this region forms a sharp bound on the long regression. Following this completely nonparametric analysis, the identifying power yielded by exclusion restrictions across distinct covariate values is examined. Such restrictions cause the identification region to shrink, in many cases to a single point.;Chapter 2 extends this analysis to incorporate monotone instrumental variable (MIV) assumptions. An IV assumption on one of the covariates, x or z, says that E(y | x, z) is constant across distinct values of this covariate. This assumption is invariably of questionable credibility. I relax the IV assumption to an MIV one. An MIV assumption on one of the covariates, x or z, says that E(y | x, z) is monotonically increasing in that covariate. The MIV assumption yields an identification region, containing all feasible values that the long regression can take. This identification region is often tight enough to yield useful inferences.;Chapter 3 examines nonparametric identification in production analysis. The behavioral and technological assumptions of producer theory can be combined with production data to test for consistency of the theory, and to aid identification of the production technology. Since the theory applies to an individual firm, the production data must be of a time-series nature. Nonparametric techniques for addressing the consistency and identification questions are well developed in the literature. However, to apply these techniques a researcher must assume that the firm's technology is invariant; the time-series data is derived from a firm facing fixed technological constraints. In contrast, I make the weaker assumption of technological progressivity; the firm's technological opportunities are (weakly) increasing over time. The techniques developed in this chapter can be applied by a researcher who is wary of assuming technological invariance, but is willing to entertain the progressivity assumption. |
