Ramsey RESET test

In

The test was developed by James B. Ramsey as part of his Ph.D. thesis at the University of Wisconsin–Madison in 1968, and later published in the Journal of the Royal Statistical Society in 1969.^[1][2]

Technical summary

Consider the model

${\displaystyle {\hat {y}}=E\{y\mid x\}=\beta x.}$

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

${\displaystyle y=\alpha x+\gamma _{1}{\hat {y}}^{2}+\cdots +\gamma _{k-1}{\hat {y}}^{k}+\varepsilon ,}$

and then testing, by a means of a F-test whether ${\displaystyle \gamma _{1}~}$ through ${\displaystyle ~\gamma _{k-1}}$ are zero. If the null-hypothesis that all ${\displaystyle \gamma ~}$ coefficients are zero is rejected, then the model suffers from misspecification.

See also

• Harvey–Collier test

References