Conceptual questions
1. (5 pts) Explain the following time series concepts:
a. Covariance stationary time series
b. Autocovariance and autocorrelation
c. Weak dependence
d. White noise
e. Autoregressive models
2. (5 pts) Difference-in-difference estimator:
Suppose a new policy was implemented in the state of Ohio in 2007 that greatly reduced the cost
of filing for a divorce, both in terms of monetary fees and paperwork. In the neighboring state of
Pennsylvania, suppose the cost of filing for divorce has not changed from before 2007 to after
2007. You have collected two cross sections of divorce data from the years 2005 and 2009, for a
random set of counties in both states. Suppose you propose the following regression model, with
no additional factors controlled for, to study how the new policy has influenced the number of
divorces in Ohio versus Pennsylvania:

Where:
= Number of divorces per 100 residents in the county
= Dummy variable, =1 if the year is 2009
= Dummy variable, =1 if the county is in Ohio
Error term
Which parameter measures the differential effect of the new policy on divorce rates in Ohio,
compared to Pennsylvania? Suppose the policy increases divorce rate, what must be true about
this parameter?
3. (15 pts) Panel data estimators:
a. Consider the following generic fixed effects model, along with a two-period (), randomly
sampled panel data set with dependent variable  and independent variable
Where:
: Value of and for individual at time
: Dummy variable, equal 1 if the observation belongs to the second period ()
: Unobserved (time-invariant effect)
: Error term
Suppose you would like to estimate the above equation using the first-differenced
approach. Write the first-differenced equation you will estimate (Let denotes the first
difference operator). Is it true that the first-differenced estimator is always unbiased?
Explain.
b. Explain the differences between the first-differenced estimation, the fixed-effect
estimation and the random-effect estimation.
c. Suppose that for an individual, total sleep time and total work time are jointly determined
by the following equations:

Where:
= total minutes slept per night
= total working minutes spent working per week
= years of schooling
= age, in years
Under what conditions can we estimate/ identify the parameters of the above system of
equations? How can we test these conditions? Describe the procedure to estimate the
above system of equations using 2SLS.

4. (5pts) Logit and probit models
Let grad be a dummy variable for whether a student-athlete at a large university graduates in five
years. Let hsGPA and SAT be high school grade point average and SAT score, respectively. Let
study be the number of hours spent per week in an organized study hall. Suppose that, in using
data on 420 student-athletes, the following logit model is obtained:
Where: is the logit function
Suppose and . What is the probability of graduation for a student-athlete who spent 14 hours per
week in study hall? For a student-athlete who spent 7 hours per week in study hall?