The RESET specification test for nonlinearity in a random sample (due to Ramsey (1969))

is the following. The null hypothesis is a linear regression Y Æ X0¯Åe with E[e j X] Æ 0. The parameter ¯ is estimated by OLS yielding predicted values b Yi . Then a second-stage least squares regression is estimated including both Xi and b Yi Yi Æ X0 i

e¯Å

¡

b Yi

¢2 e°Å eei The RESET test statistic R is the squared t-ratio on e°.

A colleague suggests obtaining the critical value for the test using the bootstrap. He proposes the following bootstrap implementation.

• Draw n observations (Y ¤

i ,X¤

i ) randomly from the observed sample pairs (Yi ,Xi ) to create a bootstrap sample.

• Compute the statistic R¤ on this bootstrap sample as described above.

• Repeat this B times. Sort the bootstrap statistics R¤, take the 0.95th quantile and use this as the critical value.

• Reject the null hypothesis if R exceeds this critical value, otherwise do not reject.

Is this procedure a correct implementation of the bootstrap in this context? If not, propose amodification.