## Artificial Regressions

Russell Davidson and James G. MacKinnon

All popular nonlinear estimation methods, including nonlinear least squares (NLS), maximum likelihood (ML), and the generalized method of moments (GMM), yield estimators which are asymptotically linear. Provided the sample size is large enough, the behavior of these nonlinear estimators in the neighborhood of the true parameter values closely resembles the behavior of the ordinary least squares (OLS) estimator. A particularly illuminating way to see the relationship between any nonlinear estimation method and OLS is to formulate the artificial regression that corresponds to the nonlinear estimator.

An artificial regression is a linear regression in which the regressand and regressors are constructed as functions of the data and parame...

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