Instrumental Variable Estimation Consumption of gasoline is a critical component of household expenditures, and increasingly, it is the focus intense public policy debate given the concern over greenhouse emissions. For these reasons alone economists would like to find accurate estimates of price elasticity of demand for gasoline by American consumers. The data file gasoline. csv contains monthly data on U. S. consumption of gasoline from 1978 to 2002. a) Estimate a simple linear demand equation by regressing the quantity of gas (QUANTGAS) consumed on the price of a gallon of gas (PRICEGAS). What is your estimate of the price coefficient from the OLS estimation?
b) Use your OLSEs to express the price elasticity of demand evaluated at the average price of gas. Does it make economic sense? [Hint: express the price elasticity when demand is linear.]
c) Now introduce per capita personal income (PERSINCOME) as a regressor in the linear demand model and re-estimate using OLS. How has your estimate of price coefficient changed?
d) Do you think that the above regression suffers from omitted variable bias? If so, can you sign the bias?
e) Give reasons why you should suspect that the gasoline price would be correlated with error term even after you introduced personal income into the regression. Evaluate the monthly sales of autos in the U. S. (AUTOSALES) serve as a good instrument for price of gas? Explain.
f) Estimate the first stage of a two stage least squares estimation by regressing price of gasoline on the sales of autos. Perform a test that determines whether auto sales is a "strong instrument."
g) Can you suggest another instrument that is likely to be a better instrument than auto sales?
h) Now perform the second stage of the TSLS estimation and report any change in the size of the coefficient on gasoline price as a result of using the instrumental variable.
i) Is the TSLS estimate of the price coefficient statistically significant? Do you have any reason to doubt the reported values of the standard errors from the second stage of in (e)? Explain.
j) Suppose you were instead interested in studying how the supply of gas is influenced by its price. Would you feel comfortable regressing the quantity of gas produced on its price? Why?
k) Also included in the dataset is the BLS monthly price index for consumer purchases of "transportation services" over the same sample period (TRANSINDEX). Perform TSLS estimation using this price index as an instrument.
l) Now use both CARSALES and TRANSINDEX as instruments for gas prices and report the results of J-statistic test of the hypothesis that the two are valid instruments.
m) Based on your empirical results using these data, decide what you consider the "best" estimate of the price coefficient, explaining your reasoning.
[Binary Dependent Variable] The dataset PS6data (affairs).dta contains the results from a survey of 601 individuals regarding extramarital affairs taken from Psychology Today. While the nature of this survey is a bit unseemly, the data give us the opportunity to practice binary dependent variable techniques. Below is a table with brief descriptions of the variables contained in the dataset. The dummy variable "affair" indicates whether the respondent had an affair. Explanatory variables include "male," "age," "yrsmarried," "kids," "religion," "educ," "occup," and "rating." id survey respondent identifier male =1 if male, =0 if female age age of respondent in years yrsmarried years married kids =1 if have kids, =0 if no kids religious 5 = very religious., 4 = somewhat religious, 3 = slightly religious, 2 = not at all religious, 1 = anti-religious educ years of formal schooling occup ccupation, measured by Hollingshead Occupational Scale (ranges from 1 (menial jobs) to 9 (major professional jobs) rating rate happiness in marriage (5 = very happily married, 4= happier than average, 3 = average, 2 = somewhat unhappy, 1 = very unhappy) naffairs number of affairs within last year affair =1 if had at least one affair