Relative Efficiency of OLS Under Heteroskedasticity

a. From Eq. (5.9) we have

n / n 2 n / n 2

var(p 0ls) = e x2^i2 / (Ex2) = °2 Ex2x8 / (Ex2)

i=1 i=1 i=1 i=1

where xi = Xi — X. For Xi = 1,2,.., 10 and 8 = 0.5, 1, 1.5 and 2. This is tabulated below.

 P

"P2

b. Apply these four Wald statistics to the equation relating real per-capita con­sumption to real per-capita disposable income in the U. S. over the post World War II period 1959-2007. The SAS program that generated these Wald statistics is given below

 + p(n — 1) 1 + p(n — 1)

 22

c21mx2xi c22mx2x2

 dF/dx is for discrete change of dummy variable from 0 to 1 z and P>|z| correspond to the test of the underlying coefficient being 0

One can also run logit and probit for the unemployment variable and repeat this for females. This is not done here to save space.

 dF/dx is for discrete change of dummy variable from 0 to 1

z and P > |z| correspond to the test of the underlying coefficient being 0

 dF/dx is for discrete change of dummy variable from 0 to 1 z and P> |z| correspond to the test of the underlying coefficient being 0