Econometrics- Assignment I
This assignment carries 25 points (25% of the total score). If you are
submitting hand-written answers, please write legibly, illegible
answers will not be marked. Plagiarism is strictly forbidden. If you
copy from one another, both who copied and who let his paper get
copied will be given a score of zero.
Problem 1
Consider a k-variables linear regression model, i.e.,
Y = X 1β1 + X 2 β2 + ε,
(
Where, X1 is N  k1
) , X 2 is (N  k2 ) and k = k1 + k2 . As you may recall, adding columns
to the X matrix (including additional regressors in the model) gives positive definite increase in R2.
The adjusted R2 ( R 2 ) attempts to avoid this phenomenon of ever increase in R2. Show that the
additional k2 number of variables (regressors) in this model increases R 2 if the calculated F-statistic
in testing the joint statistical significance of coefficients of these additional
regressors
(β2 ) is larger than one.
(5 points)
Problem 2
Let X1 , X2 , ⋯, XN be a random sample of size n from normal distribution with mean µ and
variance σ2 .
a). Find the maximum likelihood estimator of σ2  2 .
b). Find the asymptotic distribution of the maximum likelihood estimator
obtained in part (a).
(2 points)
of σ2  2
(3 points)
Problem 3
In this question we look at the relation between the logarithm of weakly earnings and years
of education. Using data from the national longitudinal study of youth, we find the
following results for a regression of log weekly earnings and years of education,
experience, experience squared and an intercept:
Log (earnings) = 4.016 + 0.092 . educi + 0.079 .expei + 0.002 . experi 2
( 0.222) ( 0.008)
( 0.025)
(0.001)
a).Construct a 95% confidence interval for the effect of years of education on log
weakly earnings.
(2 point)
b).Consider an individual with 10 year of experience. What would you expect to be
the return to an additional year of experience for such an individual
(the effect on log weakly earnings)?
(3 point)
c).
Labour economist studying the relation between education and earnings are often
concerned about what they call “ability bias”. Suppose that individuals differ in ability,
and that the correct specification of the regression function is one that includes ability:
log ( earnings )I = β1 + β 2 ⋅ educI + β 3 ⋅ experI − β 4 ⋅ experI2 + β5 ⋅ abilityI + εI .
In this regression, what do you expect the sign of β5 (the coefficient on ability) to be?
(1 point)
d).
What do you think the sign of the correlation between ability and years of education?
(1 point)
e).
If we estimate the
regression function with ability included, do you think that the
estimated value of β 2 will be greater or less than what it was in the regression without
ability? Explain.
(1 point)
Problem 4
A. Does identification state have any implication on the estimation of the econometric
parameters? How? (1 point)
B. What is the difference between autocorrelation and multicollinearity? (1 point)
C. State briefly the four stages in econometric researches? (1 point)
D. Discuss the difference between structural models and reduced form models? (2 point)
E. Why do you study econometrics in your field of study? (2 point)