Ramsey Reset Test

Question 1

What is the Ramsey Reset Test?

Answer 1

The ramsey reset test checks for incorrect functional form in a regression model.

It is a diagnostic test for detecting omitted variables, incorrect transformations, or non-linear relationships.

Question 2

Testing Procedure, H0, H1

Answer 2

Testing procedure:
1) Estimate the original model, save the fitted values (y-hat)

y = B0 + B1x1 + … + Bkxk + u

2) Then run an augmented regression that includes the powers of y-hat

y = B0 + B1x1 + … + v(y-hat)^2 + v1(y-hat)^3 + … + e

3) Conduct an F-test for the joint significance of the added terms.

H0: v = v1 = … = 0 (model correctly specified)

H1: At least one vj does not equal 0. (model misspecification)

Question 3

What is the F-statistic for the reset test?

Answer 3

F-Statistic

q - number of added fitted terms
u - augmented regression
r - orginal regression

F = (RSSr - RSSu)/q
/
(RSSu) / (n-k-q)

Question 4

What does the test imply…

Answer 4

A significant test implies the model might need additional variables or transformation of existing ones (e.g., logs, polynomials).

It is a general specification test, not tied to any specific omitted variable.

It does not tell you what the problem is — only that a problem may exist.