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 exogenous 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


 * $$\hat{y}=E\{y|x\}=\beta x.$$

The Ramsey test then tests whether $$(\beta_1 x)^2, (\beta_2 x)^3...,(\beta_{k-1} x)^k$$ has any power in explaining $$y$$. This is executed by estimating the following linear regression


 * $$\hat{y}=\beta x + \beta_1\hat{y}^2+...+\beta_{k-1}\hat{y}^k+\epsilon$$,

and then testing, by a means of a F-test whether $$\beta_1~$$ through $$~\beta_{k-1}$$ 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.