Question 1 (Panel Data) (40 points)
Suppose that you have a dataset of ten players on a sports team, whom you monitor
for ve seasons. For each of the players, you observe the total goals scored, and the total
amount of time spent on the eld, and the total number of injuries received by the player
during each season. Suppose that between the second and the third seasons, two of the team
players (players #3 and #8) were replaced.
(a) (5 points) Is your dataset a long or a short, a balanced or an unbalanced panel, and
why?
(b) (8 points) Brie
y discuss the key advantages of panel data.
(c) (8 points) Suppose that you estimate the following pooled OLS model:
Yit = 1 + 2X2it + 3X3it + uit; (1)
where Yit are the goals scored by player i in season t, X2it are player’s eld time, and
X3it is the number of player’s injuries. When estimating such a pooled OLS model,
what are the assumptions which you are making about the model coecients, and about
heterogeneity between the players in your sample?
(d) (5 points) What is meant by the term nuisance parameter?
(e) (7 points) What are the consequences of excluding a nuisance parameter which is corre-
lated with other regressors from this model?
(f) (7 points) In the context of your answers to parts (d) and (e), explain how does the
xed-eects LSDM model improve upon the pooled OLS model.
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Question 2 (Simultaneous Equations Models) (40 points)
Consider the following simultaneous equations model, representing a market for gasoline:
Qd
t = 1 + 2Pt + 3It + ut (2)
Qs
t = 1 + 2Pt + vt (3)
Qd
t = Qs
t (4)
where Qd
t is the equilibrium quantity demanded in period t, Qs
t is the equilibrium quantity
supplied, Pt is the equilibrium price of gasoline, and It is the consumers’ income. Equation
(2) represents the demand curve for gasoline, equation (3) is the supply curve, and equation
(4) is the market-clearing condition. In your dataset, you have monthly data on equilibrium
quantity Qt, prices Pt and incomes It.
(a) (4 points) Which variables are endogenous, and which are exogenous in this simultaneous
equations model?
(b) (4 points) In general, what is the dierence between the endogenous and exogenous
variables?
(c) (4 points) What are the structural parameters in this model?
(d) (8 points) Suppose that you estimate equation (2) using OLS. That is, suppose you
regress equilibrium quantity Qt on equilibrium price Pt and income It. How reliable are
your resulting estimates ^ 1, ^ 2 and ^ 3?
(e) (10 points) Derive the reduced-form equations for this model (there’s two).
(f) (5 points) Suppose that you estimate the reduced-form equations using the OLS. What
are the statistical properties (bias/eciency) of your reduced-form estimates?
(g) (5 points) Is this model fully identied? Why (or why not)?
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Question 3 (GRETL) (20 points)
This question requires the use of GRETL. Download and open the Table 20.2: Selected
Macroeconomic Data, U.S. 1970 – 1999 dataset from the Gujarati textbook. The structure
of the dataset is as follows:
Y1 = Gross Domestic Product, Billions of dollars
Y2 = Money Supply, Billions of dollars
X1 = Gross Private Domestic Investment, Billions of dollars
X2 = Federal Government Expenditure, Billions of dollars
X3 = Interest Rate on 6-Month Treasury Bills, Percent
Consider the following simultaneous equations model:
X3t = 1 + 2Y2t + 3Y1t + ut (5)
Y1t = 1 + 2X3t + 3X1t + vt (6)
(a) (15 points) Obtain unbiased estimates of the structural parameters in this model using
GRETL (just print and attach your regression output).
(b) (5 points) Generate and print the residual plots from this model.
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