A Note on the Estimation of Linear Regression Models with Heteroskedastic Measurement Errors

I consider the estimation of linear regression models when the independent variables are measured with errors whose variances differ across observations, a situation that arises, for example, when the explanatory variables in a regression model are estimates of population parameters based on samples of varying sizes. Replacing the error variance that is assumed common to all observations in the standard errors-in-variables estimator by the mean measurement error variance yields a consistent estimator in the case of measurement error heteroscedacticity. However, another estimator, which I call the Heteroskedastic Errors in Variables Estimator (HEIV), is, under standard assumptions, asymptotically more efficient. Simulations show that the efficiency gains are likely to appreciable in practice. In addition, the HEIV estimator, which is the ordinary least squares regression of the dependent variable on the best linear predictor of the true independent variables, is simple to compute with standard regression software.