OLLSCOIL NA hÉIREANN MÁ NUAD
NATIONAL UNIVERSITY OF IRELAND MAYNOOTH
DEPARTMENT OF ECONOMICS, FINANCE AND ACCOUNTING
M.A. IN ECONOMICS
JANUARY 2019
EC606A ECONOMETRICS
Professor Donal O’Neill
Time allowed: 1.5 hours
Answer Sections A and B. All Sections are of equal worth.
EC606A ECONOMETRICS
EXAMINATION JANUARY 2018
Answer Sections A and B. All Sections are of equal worth.
SECTION A
Answer three questions from this Section. Answers for each question should be no more than two
pages long.
1. Suppose that you have been given data Assume that the data are generated according to an
exponential probability density:
where
One possible estimator for λ is given by .
Is this estimator unbiased? Is it a consistent estimator of λ?
2. White’s robust standard errors are useful for estimating a model in which the error term is
heteroscedastic, because they provide us with the most efficient estimator without having to be
specific about the nature of the heteroscedasticity. Evaluate this statement.
3. Consider the regression model where Z=3X. A colleague
warns that you may have troubling estimating the parameters of this model, but that the problem
will go away provided you have a large enough sample. How would you evaluate this advice?
4. P-values are useful in econometrics because they provide researchers with information on the
probability that the null-hypothesis is true and also help us determine the economic significance
of the estimated effects. Evaluate this statement.
SECTION B
Answer one of the following three questions.
1. a. Explain the differences between the Wald, likelihood Ratio and Lagrange Multiplier approaches to
hypothesis testing.
b. Consider the data generating process
i. Write the null hypothesis H0: β4=5 and β 2+ β3 =0and 2β5-4β6=0 in Rβ-q notation.
ii. Discuss how would test these conjectures in practice assuming that is known.
iv. Discuss how you would test the null-hypothesis
2.
Suppose you are interested in estimating the relationship between wages and obesity. To do this you
consider estimating the following regression model.
2
W =β 1+ β 2 Obesity+ e e i N (0 , σ )
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where W is a measure of an individual’s wage and Obesity is a measure of how obese the individual is.
a. What do economists mean when they talk about the causal effect of obesity on wages?
b. Explain why the OLS estimator of the above equation is unlikely to provide a consistent estimator
of the casual effect of obesity on wages. What effect will the OLS estimator estimate?
c. The hormone FGF21 regulates how much sugar we eat. In a recent study in Denmark, scientists
found that patients with a particular defective variant of the hormone FGF21 were 20% more likely
to be higher consumers of sugar. How might an econometrician use this medical information to
estimate the causal effect of obesity on wages. Be careful to outline both the advantages and
potential pitfalls associated with your suggested approach.
3. Suppose that Y is randomly generated according to an exponential model.
That is, f(yi|)=(1/)exp(-yi/)
For this distribution we know that .
i. Derive the maximum likelihood estimator for θ. How would you estimate the variance of the
maximum likelihood estimator?
ii. Discuss how you would estimate θ using the method of moments estimator given the moment
condition E [ y ]=θ. Is θ underidentified, exactly identified or over identified in this instance.
Explain your answer.
iii. Suppose in addition, you were told that Is θ underidentified, exactly identified or
over identified given this additional information. Explain your answer.
iv. Discuss how to derive the optimal GMM estimator for θ using both of the moment conditions
provided.
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