Ramsey reset test

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The Ramsey regression equation specification error test (Reset) test (Ramsey, 1969) is a general model (mis-)specification test for the linear regression model. More speficically, 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.

[edit] Technical summary

Consider the model

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

The Ramsey test then tests wheter (β1x)2,(β2x)3...,(βkx)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\hat{y}^k+\epsilon,

and then testing, by a means of a F-test whether \beta_1~ thru ~\beta_k are zero. If the null-hypothesis that all regression coefficients of the non-linear terms are zero is rejected, then the model sufffers from mis-specification.

[edit] References

  • Ramsey, J.B. "Tests for Specification Errors in Classical Linear Least Squares Regression Analysis", J. Royal Statist. Soc. B., 32, 350-371 (1969).
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