Extremum Estimation when the Predictors are Estimated from Large Panels

Much is written about the use of factors estimated by the method of principal components from large panels in linear regression models. In this paper, we provide an analysis for non-linear estimation and establish the conditions under which the estimated factors can be treated as though they were observable. The results can be used to estimate probabilities as in probit type analysis as well as classification of observations into types conditional on covariates. Comparison with traditional generated regressors is also made.