Ramsey RESET test

In statistics, the Ramsey Regression Equation Specification Error Test (RESET) test is a general specification test for the linear regression model. More specifically, it tests whether non-linear combinations of the explanatory variables help to explain the response variable. The intuition behind the test is that if non-linear combinations of the explanatory variables have any power in explaining the response variable, the model is misspecified in the sense that the data generating process might be better approximated by a polynomial or another non-linear functional form.

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 an 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

1. Ramsey, J. B. (1969). "Tests for Specification Errors in Classical Linear Least Squares Regression Analysis". Journal of the Royal Statistical Society, Series B. 31 (2): 350–371. JSTOR 2984219.
2. Ramsey, J. B. (1974). "Classical model selection through specification error tests". In Zarembka, Paul (ed.). Frontiers in Econometrics. New York: Academic Press. pp. 13–47. ISBN 0-12-776150-0.

Further reading

• Long, J. Scott; Trivedi, Pravin K. (1993). "Some Specification Tests for the Linear Regression Model". In Bollen, Kenneth A.; Long, J. Scott (eds.). Testing Structural Equation Models. London: Sage. pp. 66–110. ISBN 0-8039-4506-X.
• Thursby, J. G.; Schmidt, P. (1977). "Some Properties of Tests for Specification Error in a Linear Regression Model". Journal of the American Statistical Association. 72: 635–641. doi:10.1080/01621459.1977.10480627. JSTOR 2286231.
• Wooldridge, Jeffrey M. (2016). Introductory Econometrics – A Modern Approach (Sixth ed.). Cengage Learning. pp. 273–278. ISBN 978-1-305-27010-7.