Describe the steps you would use to undertake whites test

Question

1. Consider the following two estimated least squares regressions, with standard errors in parentheses:

At =	26.19	+0.6248B1	-0.4398A
	(2.73)	(0.006)	(0.074)
R2 =	0.999
(A/B)t =	25.921/Bk	+0.6246	-0.4315t
	(2.22)	(0.007)	(0.060)
R2 =	0.875

(a) Assuming that the second equation has been estimated to remove heteroscedasticity, what assumption has been made about the error variance in first equation ?

(b) Assuming that there is indeed heteroscedasticity, provide the properties possessed by the LS estimator that was used to estimate first equation.

(c) Assuming that there is indeed heteroscedasticity as modelled, provide the properties possessed by the IS estimator that was used to estimate second equation.

(d) Describe the steps you would use to undertake White's test for homoscedasticity for first equation.

2. Consider the following partitioned regression model: where is the variance covariance matrix of the error terms. Find the formula for the GLS estimator and suggest a feasible GLS estimator.

3. Consider the simple linear regression model y_t = β₀ + β₁x₁ + ∈_t where the errors exhibit second-order autocorrelation: ∈_t = ρ₂∈_t-2 + μ_t

(a) Calculate the autocovariance function (y(s) = cou(∈_t, ∈_t-s )) under the assumption that et is a weakly covariance stationary process

(b) Assuming ρ₂ is known, derive the GLS estimator of β₁.

(c) Describe how one would calculate an asymptotically efficient two-step estimator of β₁ if ρ2 were unknown.

 

Answer 1

The evaluation of assignment as illustrate below you have to assume for the solutions of all questions. 1. Consider the subsequent 2 estimated least squares regressions, through standard errors in parentheses: At = 26.19 +0.6248B1 -0.4398A (2.73) (0.006)(0.074) R2 =0.999 (A/B)t =25.921/Bk +0.6246 -0.4315t (2.22) (0.007) (0.060) R2 =0.875 (a) Assuming that the 2nd equation has been estimated to eliminate heteroscedasticity, what assumption has been made about the error variance in 1st equation? (b) Assuming that there is certainly heteroscedasticity, give the properties possessed via the LS estimator that was used to estimate first equation. (c) Assuming that there is indeed heteroscedasticity as modelled, provide the properties possessed by the IS estimator that was employed to estimate second equation. (d) Explain the steps you would use to undertake White's test for homoscedasticity for first equation.