Download An economist interested in studying the effect of trade

Economics 329 Econometrics
Sanjay DeSilva
Midterm Exam
Fall 2006
Name: _______________________
Question 1
An economist interested in studying the effect of trade policy on GDP growth runs the
following cross-country regression for a sample of 26 countries.
Yi  ˆ0  ˆ1 X i  ei
Y = GDP growth rate in percentage points.
X = Average tariff rate in percentage points.
The following is a partial list of results she obtains by running an OLS regression.
ˆ1  0.15
y
e
x
2
i
  (Yi  Y ) 2  200
2
i
 168
2
i
  ( X i  X ) 2  1000
a. Based on the information above, construct the ANOVA table for this regression.
Sums
Degrees of Freedom Means
Explained/Regression
Residual
Total
b. Calculate R 2 , Adjusted R 2 and the F-statistic for overall significance of the
regression.
R2
Adjusted R 2
F-statistic
Economics 329 Econometrics
Sanjay DeSilva
Midterm Exam
Fall 2006
c. Calculate the variance of ˆ1 , the slope coefficient.
d. Carry out a hypothesis test to verify that tariffs do in fact reduce economic
growth. Denote the null and alternative hypotheses, compute the relevant test
statistics, and write the decision rule.
H0 :
H1 :
Test Statistic:
Decision Rule: Reject H 0 if ________________________
Economics 329 Econometrics
Sanjay DeSilva
Midterm Exam
Fall 2006
Question 2
A more sophisticated multiple regression model that attempts to answer the same
question, i.e. the effect of trade policy on economic growth, is shown below.
GROWTH i  ˆ0  ˆ1.TARIFFi  ˆ2 .QUOTAi  ˆ3 .GDPi  ˆ4 .SSAi  ˆ5 .EAi  ei
GROWTH
TARIFF
QUOTA
GDP
SSA
EA
= GDP growth rate in percentage points
= Average tariff rate in percentage points
= Index of trade quotas
= GDP per capita
= Dummy variable for Sub Saharan African countries
= Dummy variable for East Asian counties.
a. In this model, TARIFF and QUOTA are both measures of trade policy. Set up a
hypothesis test that would help to establish whether trade policies significantly
influence economic growth. Note the null hypothesis, construct the test statistic
and report the decision rule (Don’t attempt to find numerical answers).
H0 :
Test Statistic:
Decision Rule: Reject H 0 if ________________________
Economics 329 Econometrics
Sanjay DeSilva
Midterm Exam
Fall 2006
b. When the QUOTA variable was added, the economist reports that the absolute
value of the coefficient ˆ1 decreases (say, for example, to -0.05) but its standard
error increased. Briefly explain why this may have happened.
Decrease of ˆ1 :
Increase of Var ( ˆ1 ):
c. Suppose both ˆ1 and ˆ2 become statistically insignificant but the SSA dummy is
significantly negative and the EA dummy is significantly positive. Draw a scatter
plot of a relationship between tariffs and growth that is consistent with this
finding.
Economics 329 Econometrics
Sanjay DeSilva
Midterm Exam
Fall 2006
d. Suppose the economist wants to find out whether the effect of tariff reduction on
economic growth is greater from island nations than for countries with land
borders. Sketch how this test can be carried out using a regression. Write out the
regression equation/s and the set-up of a hypothesis test (null hypothesis and the
test statistic).
e. Suppose you want to find out whether tariffs impede growth less than quotas. Set
up a hypothesis test (report the null hypothesis and the test statistic)
Question 3
Consider the theoretical (population) regression Yi   0  1 X i  ui . The OLS method
obtains the following estimate for the slope coefficient, ˆ1 
a. Show that ̂1 
x y  kY

x
i
i
2
i
i i
where ki 
x y
x
i
i
2
i
xi
(Note: y and Y are different).
 xi2
Economics 329 Econometrics
Sanjay DeSilva
Midterm Exam
Fall 2006
b. Using the equation for the population regression, show that
ˆ1   kiYi  1   ki ui
c.
2
Starting from the definition of variance, show that Var ( ˆ1 ) = E  k i ui 
2
d. In order to simplify Var ( ˆ1 ) = E  k i ui  to the more familiar form that we use
for a simple classical regression, what additional assumptions are needed?