Ramsey RESET test

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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.

[edit] Technical summary

Consider the model

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

The Ramsey test then tests whether (β1x)2,(β2x)3...,(βk − 1x)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.

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

~H_0:\beta_i=0 \quad \forall i=1,\ldots,k-1.

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

y=\beta x + \beta_1x^2+...+\beta_{k-1}x^k+u. \,

[edit] 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).