Question

3. Compare the fits of Equations 26 and 27 using the F-test. If the two equations are significantly different in overall fit, we can conclude that it's likely that Equation 26 is misspecified While the Ramsey RESET test is fairly easy to use, it does little more than signal when a major specification error might exist. If you encounter a sig nificant Ramsey RESET test, then you face the daunting task of figuring out exactly what the error is! Thus, the test often ends up being more useful in "supporting" (technically, not refuting) a researcher's contention that a given specification has no major specification errors than it is in helping find an otherwise undiscovered flaw.16 As an example of the Ramsey RESET test, let's return to the chicken demand model of this chapter to see if RESET can detect the known specifica tion error (omitting the price of beef) in Equation 9. Step one involves run- ning the original equation without PB Y, 30.7 0.09PCt +0.25YD (0.03) (0.005) t-2.76 +46.1 R2 9895 N 29 (annual 1974-2002) RSS 83.22 For step two, we take Ýt from, Equation 9, calculate Y,Yi, and Y, and then reestimate Equation 9 with the three new terms added in: (0.59) .77) (0.17) -0.00 IYİ + 0.0000020 + et (0.002) (0.000006) R2 -,991 N 29 (annual 1974-2002) RSS 57.43 In step three, we compare the fits of the two equations by using the F-test. Specifically, we test the hypothesis that the coefficients of all three of the added terms are equal to zero HA: otherwise

Answer 1

The reduced model is just another way of stating our hypothesis. But in more complex situations this is not the only reduced model that we can write, there are others we could look at The general linear test is stated as an Fratio: SSE(R)-SSEF)/dR diF) SSE(F)/dfF This is a very general test. You can apply any full and reduced model and test whether or not the difference between the full and the reduced model is significant just by looking at the difference in the SSE appropriately. This has an F distribution with (R-dfF), afF degrees of freedom, which correspond to the numerator and the denominator degrees of freedom of this F ratic.

here R stands for reduced model

F stands for full model

here df Full model is 23

M = 3

F = 3.44

critical value = f.inv.rt(0.05,3,23) = 3.03   {using Excel}

since TS > critical value

we reject the null hypothesis