What does the Ramsey RESET test tell me about model misspecification?

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AcadiFi · Accepted Answer

The Ramsey RESET (Regression Equation Specification Error Test) detects omitted variables and incorrect functional forms by checking whether powers of the fitted values add explanatory power to the original regression.

Procedure: estimate the original model and save fitted values y_hat. Run an augmented regression that adds y_hat^2, y_hat^3, and possibly higher powers as extra regressors. Test the joint hypothesis that these added coefficients are zero using an F-test. If you reject, the original model is misspecified.

The intuition: if the true relationship is nonlinear or includes interaction terms you've omitted, a polynomial in the fitted values can capture some of that missing structure. If the original model was correctly specified, powers of y_hat should add nothing.

Consider Thornwick Aerospace earnings modeled linearly against R&D spending and revenue. Analyst Sigrid Halvorsen runs RESET with y_hat^2 and y_hat^3 added. The F-statistic is 12.4 with p-value 0.00003. She rejects correct specification. She then experiments with a log-log specification and finds RESET no longer significant, suggesting the underlying relationship was multiplicative rather than additive.

Limitations: RESET does not tell you what the correct form is, only that something is wrong. It is also sensitive to heteroskedasticity and should be combined with other diagnostics. Low power in small samples is common.

Despite limitations, RESET is a standard first-pass check for specification issues and CFA candidates should recognize it on the exam.

What does the Ramsey RESET test tell me about model misspecification?

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