Download Econometrics Problem Set 1 2008

Econometrics Problem Set 1
2008.10
1. Assume that you are in charge of the central monetary authority on a mythical
country. You are given the following historical data on the quantity of money and
national income（both on millions of dollars）：
Year
Quantity of
money
National
income
Year
Quantity of
money
National
income
1998
18
4
2003
12
3
1999
2000
2001
2002
13
15
8
9
3
3
3
2
2004
2005
2006
2007
18
6
10
12
3
2
3
4
(1) Estimate the regression of national income on the quantity of money . ( 要交
STATA 報表)
(2) How do you interpret the intercept and slope of the regression line？
(3) Calculate mean , standard error, minimum and maximum by STATA.
( 要交 STATA 報表)
2. Let Y and X denote the labor force participation rate of women in 1972 and 1968,
respectively, in each of 19 cities in the United States. The regression output for this
data set is shown in Table 2.10.It was also found that SSR=0.0358 and SSE=0.0544.
Suppose that the model
Y=β0+β1X+ε satisfies the usual regression assumptions.
(a) Compute Var(Y) and Cor(Y,X).
(b) Suppose that the participation rate of women in 1968 in a given city is 45%.
What is the estimated the participation rate of women in 1972 for the same city?
(c) Suppose further that the mean and variance of the participation rate of women in
1968 are 0.5 and 0.005, respectively. Construct the 95% confidence interval for
the estimate in (b).
(d) Construct the 95% confidence interval for the slope of the true regression line,
β1..
(e) Test the hypothesis: H0 : β1 = 1 versus H1 : β1 > 1 at the 5% significance level.
Table 2.10 Regression output when Y is regressed on X for the labor force
participation rate of women.
Variable
Coefficient
Standard Deviation
t-test
p-value
Constant
X
0.203311
0.656040
0.0976
0.1961
2.08
3.35
0.0526
<0.0038
n=19
R 2  0.397
Ra2 =0.362
 =0.0566
d.f. =17
3. In order to investigate the feasibility of starting a Sunday edition for a large
metropolitan newspaper, information was obtained from a sample of 34
newspapers concerning their daily and Sunday circulations (in thousands).
(1) Fit a regression line predicting Sunday circulation from Daily circulation.
(2) Obtain the 95% confidence intervals for  0 and 1 .
(3) Is there a significant relationship between Sunday circulation and Daily
circulation? Justify your answer by a statistical test. Indicate what hypothesis
you are testing and your conclusion.
(4) What proportion of the variability in Sunday circulation is accounted for by
Daily circulation?
(5) Provide an interval estimate (based on 95% level) for the true average
Sunday circulation of newspapers with Daily circulation of 500,000.
(6) The particular newspaper that is considering a Sunday edition has a Daily
circulation of 500,000. Provide an interval estimate ( based on 95%) for the
predicted Sunday circulation of this paper.
(7) Another newspaper being considered as a candidate for a Sunday edition has
a Daily circulation of 2,000,000. Provide an interval estimate for the
predicted Sunday circulation for this paper?