Ramsey RESET test

The Ramsey Regression Equation Specification Error Test (RESET) test (Ramsey, 1969) is a general specification test for the linear regression model. More specifically, it tests whether non-linear combinations of the estimated values help explain the endogenous variable. The intuition behind the test is that, if non-linear combinations of the explanatory variables have any power in explaining the exogenous variable, then the model is mis-specified.

Technical summary

Consider the model

:

The Ramsey test then tests whether has any power in explaining $y$. This is executed by estimating the following linear regression

: ,

and then testing, by a means of a F-test whether through are zero. If the null-hypothesis that all regression coefficients of the non-linear terms are zero is rejected, then the model suffers from mis-specification.

For a univariate "x" the test can also be performed by regressing on the truncated power series of the explanatory variable and using an F-Test for

:

Test rejection implies the same insight as the first version mentioned above.

:

References

* Ramsey, J.B. "Tests for Specification Errors in Classical Linear Least Squares Regression Analysis", J. Royal Statist. Soc. B., 31:2, 350-371 (1969).