Introduction to Econometrics
Worksheet week # 5
1. Thomas Brugging and David Rose estimated a regression for the annual team revenue
for Major League Baseball franchises, using 78 observations (standard deviations in
parentheses):
Ri = −1522.5 + 53.1
9.1)
Pi + 1469.4
233.6)
Mi + 1322.7
1363.6)
Si − 7376.3
2255.7)
Ti ,
where:
Ri . . . team revenue from attendance, broadcasting, and concessions
(in thousands of dollars)
Pi . . . the i-th team’s winning rate (their winning percentage multiplied
by a thousand, 1000 = highest)
Mi . . . the population of the i-th team’s metropolitan area (in millions)
Si . . . a variable equal to 1 if the i-th team’s stadium was built before 1940,
0 otherwise
Ti . . . a variable equal to 1 if the i-th team’s city has two Major League
Baseball teams, 0 otherwise
(a) Test the statistical significance of the coefficients, comment on their signs.
(b) The authors originally expected a negative coefficient for S. Their explanation
for the unexpected positive sign was that teams in older stadiums have greater
revenue because they are better known and have more faithful fans. Since this
β is just one observation from the sampling distribution of β’s, do you think
they should have changed their expected sign?
(c) On the other hand, Keynes reportedly said, “When I am wrong, I change my
mind; what do you do?” If one β lets you realize an error, shouldn’t you be
allowed to change your expectation?
(d) Assume that you team is in last place with P = 350. According to this regression
equation, would it be profitable to pay $4 million a year to a free agent who
would raise the team’s winning rate (P) to 500? Be specific.
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2. In 1986 Frederick Schut and Peter VanBergeijk published an article in which they
attempted to see if the pharmaceutical industry practiced international price discrimination
by estimation by estimating a model of the prices of pharmaceuticals in
a cross section of 32 countries. The authors felt that if price discrimination existed,
then the coefficient of per capita income in a properly specified price equation would
be strongly positive. The reason they felt that the coefficient of per capita income
would measure price discrimination went as follows: the higher the ability to pay,
the lower (in absolute value) the price elasticity of demand for pharmaceuticals and
the higher the price a price discriminator could charge. In addition, the authors expected
that prices would be higher if pharmaceutical patents were allowed and that
prices would be lower if price controls existed, if competition was encouraged, or if
the pharmaceutical market in a country was relatively large. Their estimates were:
Pi = 38.22+ 1.43
0.21)
GDPNi − 0.6
0.22)
CV Ni + 7.31
6.12)
PPi − 15.63
6.93)
DPCi − 11.38
7.16)
IPCi ,
where:
Pi . . . the pharmaceutical price level in the i-th country divided by that
of the United States
GDPNi . . . per capita domestic product in the i-th country divided by that of
the United States
CV Ni . . . per capita volume of consumption of pharmaceuticals in the i-th
country divided by that of the United States
PPi . . . a variable equal to 1 if patents for pharmaceutical products are
recognized in the i-th country and equal to 0 otherwise
DPCi . . . a variable equal to 1 if the i-th country applied strict price controls
and 0 otherwise
IPCi . . . a variable equal to 1 if the i-th country encouraged price competition
and 0 otherwise
(a) Develop and test appropriate hypotheses concerning the regression coefficients
using the t-test at the 5 percent level. Do you think Schut and VanBergeijk
concluded that international price discrimination exists? Why or why not?
(b) Set up 90 percent confidence intervals for each of the estimated slope coefficients.
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