University of Illinois Roger Koenker
Dept. of Econometrics Fall 2006
Econ 508
Applied Econometrics
Problem Set 2
Since the “oil shock’ of 1973 there has been a continuing controversy about tax policy for
gasoline and other petroleum distillates. A crucial component of any such debate is a reliable
model for demand. In this problem set we will analyze U.S. postwar demand for gasoline and
some implications for tax policy.
A general dynamic model for the demand for gasoline is (see Harvey 8.4.1)
yt=α0+ (α1yt−1+
r−1
X
j=1
δj∆yt−j) + xtβ+
s−1
X
j=0
γj∆xt−j+ut(1)
where all variables are in natural logarithms, ∆yt=yt−yt−1, and
yt= per capita personal consumption on gasoline in thousands of gallons (at annual rates)
x0
t= (zt, pt)
zt= per capita personal income (in 1000’s of 1982 $ at annual rates)
pt= real price/gallon of gasoline in 1982 $ (1 gallon = $ at 1982 prices)
Data on these variables has been extracted from DRI tapes. There are quarterly observations,
from 1947.1 to 1997.1, available from the class website as gasq.data.
1. Estimate model (1) with r= 2, s = 2,and use Schwarz’s BIC criterion to simplify the
model.
2. Compute the long-run income and price elasticities corresponding to your final model.
Compare with results you would get from the simple static model with α1= 0, and
δj=γj= 0 for all j. Try to interpret the differences. What revenue implication do these
long run elasticities have for contemplated increases in the gasoline tax. If the current tax
rate is 14 cents per gallon, what would be the net per-capita revenue gain expected from
the imposition of an additional 10, 20 and 50 cent per gallon tax?
3. Plot the impulse response functions for your final model for both income and price changes.
Interpret. Put the model in error-correction form (Harvey §8.5) and reinterpret.
4. The constant elasticity equilibrium model has some implausible features from a policy
analysis standpoint. An alternative somewhat more appealing equilibrium model is the
following:
yt=β0+β1zt+β2pt+β3(pt)2+β4ptzt+ut(2)
1
