Cost Function Estimation with Proportional Errors in Variables

A model with proportional errors in variables arising naturally in microeconomics is considered. Unlike the classical additive errors case, all OLS parameter estimates exhibit attenuation bias that does not depend on the limiting distribution of the data. The distribution of OLS estimators is developed. With no intercept, a simple correction of OLS based on mean predictions is identified that is consistent and asymptotically normal. With an intercept, a readily available additional moment based on sample data identifies the parameters. In neither case are additional restrictions or use of extra-sample data as instruments required as for common errors-in-variables methods.