Download Econ 472 Econometrics Homework #3 1. Consider teh equation Σ

Econ 472
Econometrics
Homework #3
1. Consider teh equation
yt =
n
X
β i xti + εt , t = 1, 2, .., T.
i=0
a) Compute
T
X
E
t=1
where
b
εt = yt −
b) Compute
n
X
i=0
T
X
E
t=1
c) Compute
E
t=1
ybt =
b xti .
β
i
b
εt yt .
T
X
where
b
εt εt
b
εt ybt
n
X
i=0
Explain the intuition for your results.
b xti .
β
i
2. Consider the equation
yt
=
n
X
β i xti + εt , t = 1, 2, .., T ;
i=0
Eεt
Eεt εs
= 0;
⎧ 2
⎨ σ
ρσ 2
=
⎩
0
1
if t = s
if |t − s| = 1 .
if |t − s| > 1
Estimates of β are derived usin OLS:
b
a) What is E β?
³ ´
b ?
b) What is D β
b = (X 0 X)−1 X 0 y.
β
c) Suggest a test of
H0
HA
: ρ=0
: ρ=
6 0.
3. It is commonly believed that people move from areas of bad opportunities
to areas of good opportunities. Thus, we see the Northeast losing population and the Sunbelt gaining population. Gather data on population
of eac stta and unemployment rate in each state for the years 1990 and
1991. Let
DP OPi =
P OPi,1991 − P OPi,1990
P OPi,1990
for each state i, and explain DP OPi as a function of unemployment rate in
1990 and/or 1991. Add some other explanatory variables to help explain
population changes. Test to see whether the effect of unemployment is
statistically significant. Hint: you can find the necessary data in Alderman Library in “Employment and Earnings.”
2