The identification and the root n consistent estimation of nonlinear models with measurement error in the regressors using instrumental variables is a long-standing problem in econometrics and statistics. This project provides a practical solution to this problem through extensive use of Fourier analysis and the theory of generalized functions, combined with semiparametric estimation methods. The methods investigated rely on parametric assumptions regarding the regression function to achieve root n consistency, but avoid any parametric constraints on the distribution of all the variables. Two alternative trade-offs between the strength of the assumptions on the mismeasured covariates and on the instruments are considered, one of which is directly applicable to panel data settings. The usefulness of the proposed approaches is illustrated through examples drawn from production function analysis, Engel curve estimation, epidemiology and nutrition studies, for which public data are readily available.
Most econometrics and statistics textbooks describe how to eliminate the bias due to the presence of covariate measurement error in linear regression analysis through the use of so-called instrumental variables. This project provides generalizations of this approach that are applicable to nonlinear models. The methods devised during this study will be helpful, because nonlinearity and measurement error are bound to be simultaneously present in a number of applications in economics. For instance, household expenditure on a given type of goods or services is typically a nonlinear function of household income, a variable that is notoriously misreported. Nonlinear responses to mismeasured quantities are also common in biostatistics and epidemiology, where exposures (to pathogens or contaminants) are typically measured with error and where the physiological response to the exposure is typically nonlinear. More generally, whenever human subjects are involved, a nonlinear response to mismeasured inputs is the rule rather than the exception, and this holds equally for economic behavior as for physiological responses to diseases or medications. A computer program implementing these methods will be made publicly available.
