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We present a general theory of consistent estimation for possibly misspecified parametric models based on recent results of Domowitz and White. This theory extends the unification of Burguete, Gallant, and Souza by allowing for heterogeneous, time-dependent data and dynamic models. The theory is applied to yield consistency results for quasi-maximum-likelihood and method of moments estimators. Of particular interest is a new generalized rank condition for identifiability.
Bates et al. (Thu,) studied this question.