Local identifiability of the factor analysis and measurement error model parameter

Measurement error regression models are factor analysis models, the latent ‘correct’ regressors are the factors. There is however no common statistical method between the factor analysis and the regression model, because the covariance elements that are known identifying constituents of the former model are unknown in the latter. Instead, the idea that the data come from the same regression model, as with panel data, but can be grouped in two or more groups, each group having its own different regrressor generating process, is shown to supply credible restrictions. We generalize and compare relevant identifiability criteria and corresponding asymptotically efficient estimators that are recursive in the number of overidentifying restrictions.