Problem Set 5
Economics 321
(Due at the Start of Class, Thursday, July 13)
1. Suppose a researcher is interested in estimating the impact of gasoline
taxes (xi) on per capita gallons of gasoline consumed per year (yi). Assume
tax is measured in cents per gallon. The researcher has data from 51 states for
a 10 year period for a total of 510 observations. The researcher estimates the
linear model yi=1+1xi+iand calculate b1to be -0.90. Supp ose instead
of measuring taxes in cents per gallon, the researcher measures taxes in dollars
per gallon where the new model is yi=2+2x
i+i,and .x
i=xi=100:What
will be the estimate on 2?
Now suppose that taxes are estimated in cents as in the …rst case, but
consumption is measured as gallons consumed per month, where y
i=yi=12.
The model now is of the form y
i=3+3xi+i. What will be the estimate
on 3?
2. Suppose a researcher is interested in estimating the linear model yi=
+xi+i:In a sample of 48 points, the following descriptive statistics are
generated:
_
x= 30;
_
y= 63
48
P
i=1
(xi_
x)2= 6900
48
P
i=1
(yi_
y)2= 29;000
48
P
i=1
(xi_
x)(yi_
y) = 13;800
The OLS estimates generate a value of s2
e= 36
(a) What are the OLS estimates of and ?
(b) What is the standard error of the estimate of ?
(c) What is the R2for this model?
3. A pharmaceutical company is interested in estimating the impact of a new
drug on cholesterol levels. They enroll 200 people in a clinical trial. People are
randomly assigned dosage levels or they are randomly assigned into the control
group. Half of the people are given dosages of the new drug and half of the
people are given a sugar pill with no active ingredient. To examine the impact
of dosage on reductions in cholesterol levels, the authors of the study regress
change in cholestorel levels (Y) on dosage level (X). For people in the control
group, x=0, and for people in the treatment group, x measures milligrams of
active ingredient. The model they estimate is of the form yi=+ xi+i. In
this case, the authors …nnd a statistically signi…cant and negative coe¢ cient on
the estimate for -larger dosages reduce cholesterol levels. Is this an unbiased
estimate of the impact of dosage on change in cholesterol level? Why or why
not? Do you expect the estimate to be too large or too small?
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