Title:

Essays in theoretical econometrics

The first chapter proposes an alternative (`dual regression') to the quantile regression process for the global estimation of conditional distribution functions. Dual regression provides all the interpretational power of the quantile regression process while largely avoiding the need for `rearrangement' to repair the intersecting conditional quantile surfaces that quantile regression often produces in practice. The method can be appropriately modified to provide full structural distribution function estimates of the single equation instrumental variables model. In the second chapter, I consider nonparametric identification in nonseparable triangular models. I construct a conditional independence representation which coincides with a normalized version of the structural function in the outcome equation. I illustrate the methodology by estimating a semiparametric nonseparable triangular model with an endogenous regressor. An empirical application to the estimation of gasoline demand functions in the United States is given, and I find that the estimated demand functions are mostly downwardsloping once endogeneity of prices has been accounted for. In the third chapter, I give a falsifiable characterization of a conditional exogeneity restriction imposed upon a vector of instruments given the first stage disturbance in a nonseparable triangular model. I assume that at least two instrumental variables are available, one continuous and one binary or discrete, and use exogenous shifts in their values to generate sets of transformations under which the distribution of observables is invariant. This invariance property is shown to be equivalent to the conditional exogeneity restriction. This result can be used for testing the validity of the available instruments. The fourth and final chapter describes the set of overidentifying restrictions generated by nonmonotonicity of the relationship between the endogenous variable and a continuous instrument in a nonseparable triangular model. The graph of `inverse' functions of a nonmonotone conditional quantile function with respect to the instrument is shown to identify observationally equivalent subpopulations. A procedure for constructing such `inverse' functions is proposed and illustrated with an empirical example.
