Deck 5: Multiple Regression

Question 1

$\begin{array} {| l| } \hline\text { AVG } = 77 \\\text { RANGE: } 30 - 100 \\\\\text { A - } 4 \\\text { B - } \\\text { C - 2 } \\\text { D - } \\\text { F - 2 }\\\hline\end{array}$

-Given Y_i = $\hat { \beta } _ { 0 }$ + $\hat { \beta } _ { 1 }$ X1_i + $\hat { \beta } _ { 2 }$ X2_i + $\hat { \beta } _ { 2 }$ X3_i + e_i, write the auxiliary regression required to perform the Park test for heteroskedasticity.

Answer 1

ln(e_i²) = α₀ + α₁ ln(X1_i) + ε_i ; assuming X1 is the culprit variable

Question 2

$\begin{array} {| l| } \hline\text { AVG } = 77 \\\text { RANGE: } 30 - 100 \\\\\text { A - } 4 \\\text { B - } \\\text { C - 2 } \\\text { D - } \\\text { F - 2 }\\\hline\end{array}$

-Describe the weighted least-squares procedure.

Answer 2

Suppose the error terms from SAVING_i = $\beta _ { 0 }$ + $\beta _ { 1 }$ INCOME_i + u_i are heteroskedastic in that the variance of the error terms varies with INCOME. Multiply through the original regression by 1/INCOME. $$\frac { S A V I N G _ { i } } { I N C O M E _ { i } } = \beta _ { 0 } \frac { 1 } { I N C O M E _ { i } } + \beta _ { 1 } \frac { I N C O M E _ { i } } { I N C O M E _ { i } } + \frac { u _ { i } } { I N C O M E _ { i } }$$ $$\left( \frac { u _ { i } } { I N C O M E _ { i } } \right)$$ are the new error terms. They will be homoskedastic if the variance of the u_i's is proportional to the square of INCOME.

Question 3

$\begin{array} {| l| } \hline\text { AVG } = 77 \\\text { RANGE: } 30 - 100 \\\\\text { A - } 4 \\\text { B - } \\\text { C - 2 } \\\text { D - } \\\text { F - 2 }\\\hline\end{array}$

-What is generalized least-squares?

Answer 3

Y_t - $\rho$ Y_t-1 = $\beta _ { 0 }$ (1- $\rho$ ) + $\beta _ { 1 }$ (X_t - $\rho$ X_t-1) + u_t - $\rho$ u_t-1

Question 4

$\begin{array} {| l| } \hline\text { AVG } = 77 \\\text { RANGE: } 30 - 100 \\\\\text { A - } 4 \\\text { B - } \\\text { C - 2 } \\\text { D - } \\\text { F - 2 }\\\hline\end{array}$

-Describe the Hildreth-Lu Scanning procedure.

Question 5

$\begin{array} {| l| } \hline\text { AVG } = 77 \\\text { RANGE: } 30 - 100 \\\\\text { A - } 4 \\\text { B - } \\\text { C - 2 } \\\text { D - } \\\text { F - 2 }\\\hline\end{array}$

-Describe the maximum likelihood procedure.

Question 6

$\begin{array} {| l| } \hline\text { AVG } = 77 \\\text { RANGE: } 30 - 100 \\\\\text { A - } 4 \\\text { B - } \\\text { C - 2 } \\\text { D - } \\\text { F - 2 }\\\hline\end{array}$

-Draw a diagram indicative of negative serial correlation. Be sure to label the axes.

Question 7

$\begin{array} {| l| } \hline\text { AVG } = 77 \\\text { RANGE: } 30 - 100 \\\\\text { A - } 4 \\\text { B - } \\\text { C - 2 } \\\text { D - } \\\text { F - 2 }\\\hline\end{array}$

-Describe 3 ways to estimate ? in a generalized least-squares regression.

Question 8

$\begin{array} {| l| } \hline\text { AVG } = 77 \\\text { RANGE: } 30 - 100 \\\\\text { A - } 4 \\\text { B - } \\\text { C - 2 } \\\text { D - } \\\text { F - 2 }\\\hline\end{array}$

-What do you recommend in a situation where GLS does not remedy autocorrelation? Explain.

Question 9

$\begin{array} {| l| } \hline\text { AVG } = 77 \\\text { RANGE: } 30 - 100 \\\\\text { A - } 4 \\\text { B - } \\\text { C - 2 } \\\text { D - } \\\text { F - 2 }\\\hline\end{array}$

-Given Y_i = $\hat { \beta } _ { 0 }$ + $\hat { \beta } _ { 1 }$ X1_i + $\hat { \beta } _ { 2 }$ X2_i + e_i, describe the White test for heteroskedasticity making sure to specify the auxiliary regression in this case.

Question 10

$\begin{array} {| l| } \hline\text { AVG } = 77 \\\text { RANGE: } 30 - 100 \\\\\text { A - } 4 \\\text { B - } \\\text { C - 2 } \\\text { D - } \\\text { F - 2 }\\\hline\end{array}$

-Are the standard errors of the coefficients in a regression expected to increase or decrease after Newey-West is applied? Explain why?

Question 11

The Durbin-Watson statistic is invalid in autoregressive models, models without a constant term, and models with n = 9.

Question 12

Application of the Newey-West technique will alter the estimates of the P-values on the structural parameters.

Question 13

R-squared is biased downward in a regression suffering from serial correlation.

Question 14

Serial correlation is when E[u_i u_j] = 0 for all i $\neq$ j.

Question 15

Autocorrelation increases the probability of a TYPE II error on a test of significance on a given structural parameter.

Question 16

Weighted least-squares is efficient when E[u_i²] $\neq$ E[u_j²] = $\sigma$ ² for all i $\neq$ j.

Question 17

R-squared from a GLS regression is directly comparable to the R-squared from the same regression estimated using OLS.

Question 18

A regression with a Durbin-Watson statistic close to 4 most likely suffers from negative autocorrelation.

Question 19

The error terms (u_t) from a regression are white noise when u_t ~ N(0, $\sigma$ ²).

Question 20

In the presence of autocorrelated error terms, GLS yields BLUE parameter estimates.