I know that the Betas represent the elasticities, but nothing else of what the q

Question

I know that the Betas represent the elasticities, but nothing else of what the question (all parts) is asking of me. Any help would be greatly appreciated!

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 Gjt is per capita gasoline consumption in gallons in month j and year t, Pt is the real retail price of gasoline in month j and year t, Yjt is real per capita disposable income in month j and year t, j represents unobserved demand factors that vary at the month level and Eit 1S a mean zero error term (a) What have the authors assumed about the price elasticity of de- mand when they wrote down the demand equation in this form? (b) Referring to table 1, assuming the authors have obtained umbiased estimates of the parameters Bo, B1,32, what do they mean? (c) Interpret the values of the monthly observed demand factors j What are these relative to? What can you say about the yearly pattern of gasoline demand from these coefficients? (d) From the information presented in table 1 calculate the appro- priate t-statistics for each of the Bs to test if it is statistically different from 0. (e) What do the next to some of the entries in the table indicate? How are thev related to the t-statistics vou calculated? (f) The table presents the adjusted R-squared statistic for the two regressions. What does this number mean? If we calculated 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?

Explanation / 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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