Using our cross-section Energy/GDP data set in Chapter 3, problem 3.16 consider the following two models: Model 1: logEn = + logRGDP + u

Using our cross-section Energy/GDP data set in Chapter 3, problem 3.16 consider the following two models:

Model 1: logEn = α + βlogRGDP + u Model 2: En = α + βRGDP + v Make sure you have corrected the W. Germany observation on EN as described in problem 3.16 part (d).

(a) Run OLS on both Models 1 and 2. Test for heteroskedasticity using the Goldfeldt/Quandt Test. Omit c = 6 central observations. Why is heteroskedasticity a problem in Model 2, but not Model 1?

(b) For Model 2, test for heteroskedasticity using the Glejser Test.

(c) Now use the Breusch-Pagan Test to test for heteroskedasticity on Model 2.

(d) Apply White’s Test to Model 2.

(e) Do all these tests give the same decision?

(f) Propose and estimate a simple transformation of Model 2, assuming heteroskedasticity of the form σ2i = σ2RGDP2.
(g) Propose and estimate a simple transformation of Model 2, assuming heteroskedasticity of the form σ2i = σ2(a + bRGDP)2.
(h) Now suppose that heteroskedasticity is of the form σ2i = σ2RGDPγ where γ is an unknown parameter. Propose and estimate a simple transformation for Model 2. Hint: You can write σ2i as exp{α + γlogRGDP} where α = logσ2.
(i) Compare the standard errors of the estimates for Model 2 from OLS, also obtain White’s heteroskedasticity-consistent standard errors. Compare them with the simpleWeighted Least Squares estimates of the standard errors in parts (f), (g) and (h). What do you conclude?