Minimum distance estimation of dynamic models with errors-in-variables

Empirical analysis often involves using inexact measures of desired predictors. The bias created by the correlation between the problematic regressors and the error term motivates the need for instrumental variables estimation. This paper considers a class of estimators that can be used when external instruments may not be available or are weak. The idea is to exploit the relation between the parameters of the model and the least squares biases. In cases when this mapping is not analytically tractable, a special algorithm is designed to simulate the latent predictors without completely specifying the processes that induce the biases. The estimators perform well in simulations of the autoregressive distributed lag model and the dynamic panel model. The methodology is used to re-examine the Phillips curve, in which the real activity gap is latent.