SOME ASPECTS OF MEASUREMENT ERROR IN A CENSORED REGRESSION-MODEL

When a linear model with a censored dependent variable is written as a regression model, the model is nonlinear in the explanatory variables. This means that when the explanatory variables are measured with error, estimation by instrumental variables will not lead to consistent estimates of the parameters. My approach to the problem involves assuming that the variables measured with error can be represented by a reduced form equation and estimating the parameters of the censored regression model by the least absolute deviations estimator. This estimator is based on the median of the distribution of the dependent variable rather than the mean, and the median is not affected by censoring in the lower tail. Hence the estimator is consistent under general conditions. I also consider the problem of testing for the presence of measurement error.