13. In Evidence of a shift in the short-run price elasticity of gasoline de- man

Question

13. In Evidence of a shift in the short-run price elasticity of gasoline de- mand" by J. Hughes, C. Knittel and D. Sperling, the authors estimate the following demand equation: where Gje is per capita gasoline consumption in gallons in month j and year t, P is the real retail price of gasoline in month j and year t, Yje is real per capita disposable income in month j and year t, ej represents unobserved demand factors that vary at the month level and ejt is a mean zero error term (f) The table presents the adjusted R-squared statistic for the two regressions. What does this number mean? If we caleulated the unadjusted R-squared values, can we say whether these are larger or smaller than the adjusted R-squared values of 0.84 and 0.94 in this table? (g) Under the linear specification for the period 1975-1980 the co- efficient on the Price variable is7.252. What is the implied elasticity of demand, assuming the linear model, if during a June month per capita demand was 40 gallons, and price was 1.70? (h) What is the implied elasticity of demand if during July demand is 5 gallons higher (due to a month specific effect) and price is the same? (i) Under teir demand specification the demand elasticity varies within each period. Therefore the authors calculate an average elasticity of demand across each period. Do you think a time weighted or quantity weighted average is more reasonable and why? G) The authors specify a model where there is an interaction between price and income: where 3 is the coeflicient on the interaction term. Derive the price elasticity of demand using this model specification. (k) Explain how the demand estimates can be used to quantify in- terfuel substitution? Table1 Basic Model: Double Log 1975 1980 2001 2006 .697 0.042 In(Y) 04670.530 0.044 0-0.122 0.615 0.929) 0.587) (0.009) (0.058) (0 006) In(P) -0.335 0.024) -0079.** 0.010 Feb 0.019) Mar -0019 0.008 0.006) 0.021 0.016) 0.013 0011) 0.020 0.010) 0.024 0.005 May 0.026 Jun 0.000 0.004) 0.031 0.040 0.010) Aug 00420.04 0.004) Sep 0.028*0.039 0.005) 0.008 (0005) Oct 0.002 Nov0.080.032 0.012) 0.004) 0.85 0.027 (p 001) 0.94 011

Explanation / Answer

Thanks for the question.
Answer:-
a) The authors have assumed that price elasticity is constant.
b) The intercept term 0 tells that per capita gasoline consumption is antilog(-1.697) when price and income are kept at zero.
The coefficient 1 tells that if the price increases by one percent then on average gasoline consumption will fall by 0.042 percent keeping income constant.
The coefficient 2 tells that if income increase by one percent demand for gasoline on average increases by 0.53 percent keeping price of gasoline fixed.
c) The €j factors refers to the price of substitutes to the gasoline such as LPG, biodiesel etc. which affects its demand .
d) t-statistic = i/Se(i), i={0, 1, 2 }
For 0 ; t = -1.697/0.587 = -16.64
1; t= -0.042/0.009 = -4.67
2; t= 0.530/0.058 = 9.14
e) The *** tells that these variables are statistically significant in determining gasoline demand. The t-statistic help in checking for statistical significance. Higher the tabsolute t-value significant are the variables.
*We are supposed to do only four sub-parts. For solution to other parts please post as a different question please upvote if possible.

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