Estimation of nonlinear models with measurement error using marginal information

Empirical researchers often use survey data to estimate models that are nonlinear in the independent variables. A problem with survey data is that they contain measurement errors because of inaccurate reporting by the respondents. The identification and estimation of models in which mismeasured variables enter nonlinearly still pose formidable problems. In this thesis, I discuss the identification and estimation of such models using accurate marginal information on variables that are mismeasured in the survey. Such information is often available in administrative data. The thesis consists of two chapters.; The first chapter develops a new consistent estimator for models that are nonlinear in the mismeasured variables. Without additional information, such models are not identified. The new estimator assumes that there is accurate, i.e. free of measurement errors, information on the marginal distribution of the contaminated variables, usually in a second sample or an administrative data source. I show that this information identifies the distribution of the true variables given the contaminated variables and the other error-free independent variables. This distribution is needed to identify the parameters of interest. The estimator is shown to be consistent and asymptotically normally-distributed under mild regularity conditions. The estimator performs well in Monte Carlo experiments. I apply the estimator to a proportional hazard duration model for censored welfare spells. I also discuss the extensions to discrete independent variables and measurement errors that are correlated with the true value of the variables.; The second chapter discusses the case that the measurement error is correlated with both the true regressor and the error of the regression in a linear regression model. According to existing results, there is no finite bound on the regression coefficients. I show that tight finite bounds on the parameters can be found using accurate marginal information if the distribution of the contaminated regressor contains enough information on the distribution of the true one. The new approach is also applicable if the regressor is a dichotomous variable. In this case, the marginal information can be used to infer the relation between the true and mismeasured value of the regressor.