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.