2. [7+3+5+10] Consider the following model where et is i.i.d and |p| < 1. Yt = Bo+B1xt + ut Ut = put-1 + et, t = 1, 2, … … · ‚T, (a) Show that variance of the usual OLS estimator (0² / Σ(x+ - x)²) underestimates the true variance of the OLS estimator. (b) The value of the Durbin-Watson statistic turned out to be 1.4. Compute an estimate of p, the serial correlation parameter, based on the value of the Durbin-Watson statistic. (c) Suppose you also wish to test for serial correlation using Durbin's alternative test (Durbin's h- test) at the 5 percent significance. After estimating the original regression on the entire 80 sam- ples, you saved the residuals and estimated the following auxiliary regression. Et = 0.07 + 0.08æt+ 0.3 êt_1 (0.04) (0.02) (0.1) (Standard errors are in parentheses.) Give the value of the test statistic, and your conclusion (accept or reject the null hypothesis of no serial correlation). (d) Regardless of your answers to parts (a)-(c), suppose you believe that serial correlation is indeed present. Elaborate on FGLS procedure.

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2. [7+3+5+10] Consider the following model
where
et
is i.i.d and |p| < 1.
Yt
= Bo+B1xt + ut
Ut
= put-1 + et, t = 1, 2, … … · ‚T,
(a) Show that variance of the usual OLS estimator (0² / Σ(x+ - x)²) underestimates the true variance
of the OLS estimator.
(b) The value of the Durbin-Watson statistic turned out to be 1.4. Compute an estimate of p, the serial
correlation parameter, based on the value of the Durbin-Watson statistic.
(c) Suppose you also wish to test for serial correlation using Durbin's alternative test (Durbin's h-
test) at the 5 percent significance. After estimating the original regression on the entire 80 sam-
ples, you saved the residuals and estimated the following auxiliary regression.
Et
=
0.07 + 0.08æt+ 0.3 êt_1
(0.04) (0.02)
(0.1)
(Standard errors are in parentheses.) Give the value of the test statistic, and your conclusion
(accept or reject the null hypothesis of no serial correlation).
(d) Regardless of your answers to parts (a)-(c), suppose you believe that serial correlation is indeed
present. Elaborate on FGLS procedure.
Transcribed Image Text:2. [7+3+5+10] Consider the following model where et is i.i.d and |p| < 1. Yt = Bo+B1xt + ut Ut = put-1 + et, t = 1, 2, … … · ‚T, (a) Show that variance of the usual OLS estimator (0² / Σ(x+ - x)²) underestimates the true variance of the OLS estimator. (b) The value of the Durbin-Watson statistic turned out to be 1.4. Compute an estimate of p, the serial correlation parameter, based on the value of the Durbin-Watson statistic. (c) Suppose you also wish to test for serial correlation using Durbin's alternative test (Durbin's h- test) at the 5 percent significance. After estimating the original regression on the entire 80 sam- ples, you saved the residuals and estimated the following auxiliary regression. Et = 0.07 + 0.08æt+ 0.3 êt_1 (0.04) (0.02) (0.1) (Standard errors are in parentheses.) Give the value of the test statistic, and your conclusion (accept or reject the null hypothesis of no serial correlation). (d) Regardless of your answers to parts (a)-(c), suppose you believe that serial correlation is indeed present. Elaborate on FGLS procedure.
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