Abstract:

This dissertation examines the effects of measurement error in non-linear econometric models. In particular, it considers the case where the measurement error is correlated with other observables in the econometric model so that standard estimation procedures based on a classical model for measurement error are no longer feasible.

The first chapter examines the effect of mismeasured discrete regressors in binary choice models. Under a minimal set of assumptions, the model is only partially identified and I derive bounds for some of the parameters of interest. If the misclassification is conditionally independent of the other regressors, the model is point identified and I propose a estimation strategy. If the misclassification rates are not independent of the other regressors, I propose an identification strategy and develop a [Special characters omitted.] consistent, asymptotically normal estimator using the method of sieves. Monte Carlo simulations suggest good finite sample properties and the method is illustrated with a study using data from the Current Population Survey.

The second chapter extends the scope of the previous chapter to general single index models. It shows that the parameters in the index model are identified in the presence of an additional random variable that is correlated with the unobserved true underlying variable but unrelated to the measurement error. It also proposes modifications to the standard weighted partial derivative estimation methods to estimate the parameters on the continuously distributed regressors as well as a method for estimating the marginal effect of the misclassified repressor.

The third chapter estimates a price elasticity using a flexible demand specification on survey data where prices are observed with error and are correlated with household characteristics. The demand function is modeled as a polynomial (and also including trigonometric terms) in the unobserved true prices and the form of the dependency between the observed prices and household characteristics is modeled parametrically. The flexible specifications allow us to observe that price elasticities vary across the price distribution, something missed in previous work using linear demand specifications.