Practitioners' Corner: Double Length Artificial Regressions

Recently, applied econometricians have become familiar with the idea that artificial regressions may offer a convenient way to compute many test statistics. One well-known family of artificial regressions is the outer product of the gradient (OPG) family. However, available evidence indicates that using tests based on the OPG regression can be very misleading. A procedure that often can replace it is the double-length artificial regression (DLR), which can be considered as a generalization of both the Gauss-Newton regression and the squared-residuals regression. A discussion includes applications to the nonlinear regression model as well as tests for functional form. DLRs potentially are very useful. While they generally have good finite-sample properties, they are applicable to far more situations than Gauss-Newton and squared-residuals artificial regressions. They also can be used as part of maximization algorithms and should be considered to routinely test regression equations for functional form.

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