Economics 467: Economic Forecasting
State University of New York at Binghamton
Department of Economics
Spring 2010
Midterm II
Theexamcons
istso
fthreequest
ionsontwo pages. Each question is of equal value.
1. Consider the model
y
t
=
c
+
φy
t
−
1
+
ε
t
+
θε
t
−
1
,where
ε
t
∼
WN
¡
0
,σ
2
ε
¢
is a white noise sequence.
(a) Write the loglikelihood function needed to estimate this model.
(b) Why do we want to maximize the funciton in part (a) as opposed to minimizing a function as we
did with OLS?
(c) Consider the null hypothesis
H
0
:
θ
= 0. Write the loglikelihood function needed to estimate the
model under the null hypothesis.
(d) Write the test statistic needed to test the null hypothesis in part (c) as well as note its distribution.
(e) Do we know the sign of the test statistic? If so, what is it and why?
2. Consider the model
y
t
=
μ
+
βx
t
+
ε
t
,whereboth
ε
t
∼
WN
¡
0
,σ
2
ε
¢
and
x
t
∼
WN
¡
0
,σ
2
x
¢
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 Fall '11
 HENDERSON
 Economics, Econometrics, Regression Analysis, Null hypothesis, Hypothesis testing, Likelihood function, federal funds rate

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