8.6 Testing functional form: RESET

Ramsey’s RESET test asks whether powers of the fitted values add explanatory power. If the true relation is non-linear in the regressors, the squares and cubes of \(\hat Y = Xb\) will pick up some of the neglected curvature. The test adds \(\hat Y^2\) and \(\hat Y^3\) (or more powers) to the regression and applies the \(F\) test of Theorem 7.4.1 to their coefficients. It is a general-purpose check rather than a test against a specific alternative: a rejection says that something is wrong with the specification, often the functional form or an omitted variable correlated with powers of the fitted values, without saying what. The test is approximate, because \(\hat Y\) is itself estimated, but its \(F\) distribution is a good guide.

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