1. Consider the model
Y,. = a+ fix , + yZ +11,, i=1,...,n, - iid(0,172),
(a) Derive the Ordinary Least Squares estimator of fi .
(35%)
(b) Show that :6' is an unbiased estimator.
(c) Consider now the estimator b = (YMAX+ Ymin) /2 , where Y mAx and X mAx
(X ,VMX X111111)/2
represent the maximum sample values of logY and logX, rim, and X,,,„ are the minimum sample values. Explain which estimator, p or g , is preferable.
2. Below is the Eviews output from a model that attempts to explain the determinants of wages in the US, using a sample of 751 individuals from the 1976 National Longitudinal Survey of Youths.
Dependent Variable: LWAGE
Method: Least Squares
Included observations: 751
Variable Coefficient Std. Error t-Statistic Prob.
C 0.359837 0.138917 2.590310 0.0098
EDUC 0.070022 0.006918 10.12226 0.0000
EXPER 0.073828 0.013873 5.321542 0.0000
EXPERSQ -0.001932 0.000659 -2.932331 0.0035
BLACK -0.220327 0.033702 -6.537483 0.0000
MARRIED -0.021918 0.006723 -3.260104 0.0012
R-squared 0.232704 Mean dependent var 1.662692
Adjusted R-squared 0.227555 S.D. dependent var 0.416248
S.E. of regression 0.365836 Akaike info criterion 0.834692
Sum squared resid 99.70760 Schwarz criterion 0.871614
Log likelihood -307.4269 F-statistic 45.18855
Durbin-Watson stat 2.051298 Prob(F-statistic) 0.000000
_ _
where LWAGE is the log of the individual's hourly wage in dollars;
C is the intercept (or constant);
EDUC is the number of years of schooling the individual has;
EXPER is the number of years of potential labour market experience the individual has; EXPERSQ is the square of EXPER;
BLACK is a dummy variable which takes the value of I if the individual is of black ethnic origin, otherwise it takes a value of 0;
MARRIED is a dummy variable which takes the value of 1 if the individual is married, otherwise it takes a value of 0.
a) Interpret the estimated coefficients. (30%) .
b) Calculate and interpret the turning point for the effect of labour market experience on the log of the wage. (40%)
c) Test whether an individual's ethnicity has a significant effect on their wage. (30%)
3. A model relating US expenditure in imported goods (Y) with personal disposable income (DI) has been estimated with US annual data from 1968 to 1987, with the following results (t-ratios in brackets)
log = - 751.5- 0.574 DI - 19.0 Time,
(-5.67) (-8.68) a -5.44
R2 = 0. 359
Time = 1968, 1969,...
(a) Interpret the coefficient estimates obtained from the regression.
(35%)
(b) Comment on the global significance of the regression.
(35%)
(c) Obtain a 90% confidence interval for the coefficient on disposable income
(DI).
(30%)
4. A production functions for the primary metals industry has been estimated by OLS for a sample of 27 US states, using value-added output (Y), labour (L) and capital (K) :
log = 1.17 +0.60 log Li +0.38 log K Estimated covariance matrix
|
|
Constant
|
log L
|
log K
|
|
Constant
|
1.17
|
|
|
|
log L
|
-0.019
|
0.015
|
|
|
log K
|
0.001
|
-0.00096
|
0.007
|
6-2= 0.266, TSS = 236.3
TSS is the total sum of squares and 6: is the regression's estimated variance.
(a) Interpret and test the significance of the coefficients in the estimated model. (30%)
(b) Test the hypothesis that the capital share is the same as the labour share. (40%)
(c) A researcher, using the Breusch-Pagan test, claims that the errors are heteroskedastic. Explain what this procedure involves and how he reached that result.