Introduction to Econometrics
Worksheet week # 11
1. Consider the following model that explains major league baseball players’ salaries:
log(salary) = β0 + β1years + β2gamesyr + β3bavg + β4hrunsyr + β5rbisyr+
+β6srunsyr + β7fldperc + β8allstar + β9frstbase + β10scndbase+
+β11thrdbase + β12shrtstop + β13catcher + ε ,
The variables used in the model are the
following:
salary ... 1993 total salary
years ... years in the league
gamesyr ... average games played a year
bavg ... career batting average
hrunsyr ... home runs per year
rbisyr ... runs batted in per year
srunsyr ... runs scored per year
fldperc ... career fielding perc
allstar ... percentage of years as all-star
frstbase ... = 1 if playing first base
scndbase ... = 1 if playing second base
thrdbase ... = 1 if playing third base
shrtstop ... = 1 if playing shortstop
catcher ... = 1 if playing catcher.
You are given the data baseball.xls with
the following variables:
salary ... 1993 total salary
years ... years in the league
games ... career games played
bavg ... career batting average
hruns ... career home runs
rbis ... career runs batted in
sruns ... career runs scored
fldperc ... career fielding perc
yrsallst ... years as all-star
position ... = 0 if outfield,
= 1 if first base
= 2 if second base
= 3 if third base
= 4 if shortstop
= 5 if catcher
(a) Use the file baseball.xls for this exercise:
i. Open the file in Excel, save it as baseball.csv (comma separated values) files.
ii. Load the file in Gretl.
(b) Define the new variables you need for the regression.
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(c) Estimate the model.
(d) Test for heteroskedasticity using the White test and Breusch-Pagan test.
(e) Reestimate the model to remedy for heteroskedasticity if it is present.
(f) Explain why dummy for outfield players is not included.
(g) Is the average salary of outfield players different from the salary of the first base
players?
(h) Suppose you decided to include dummy for outfield players instead of the dummy
for first base players. What regression results would you obtain in this case?
(i) Test the null hypothesis that there is no difference in average salary across
positions, once other factors have been controlled for.
2. Estimate the impact of GDP on the housing prices level in the UK using quarterly
time series data from Q1 1975 to Q2 2011. Consider the following model:
h pricet = β0 + β1GDPt + et
(a) Load the data house.gdt into Gretl and estimate the model.
(b) Test for the presence of AR(1) autocorrelation (positive or negative) in the error
term. Define the hypothesis, test statistic, and interpret the results.
(c) Include lagged housing prices into the model and estimate by OLS:
h pricet = α0 + α1GDPt + α2h pricet−1 + ut
(d) Test for autocorrelation of higher order using the analysis of residuals from the
model with lagged housing prices.
(e) Reestimate the model with four lags of housing prices, and test for the autocorrelation
of the error term in this model:
h pricet = γ0+γ1GDPt+γ2h pricet−1+γ3h pricet−2+γ4h pricet−3+γ5h pricet−4+vt
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