Econ7103 Homework 5 Solved

You have access to imaginary vehicle sales data from 2017 (instrumentalvehicles.csv). You are interested in estimating the hedonic price of an additional mile per gallon as part of a larger analysis of willingness to pay for fuel efficiency. In your data, you have the following variables:

Variable

price car mpg weight height length

1 Python

Description
Sales price of the vehicle in USD
Class of the vehicle. =1 if the vehicle is a sedan, =0 if the vehicle is an SUV Fuel efficiency in miles per gallon
Weight of the vehicle in pounds
Height of the vehicle in inches
Length of the vehicle in inches

Table 1: Variable descriptions for homework 6.

1. Run the ordinary-least-squares regression of price on mpg, the car indicator variable, and a constant. Report and interpret the coefficient on miles per gallon (do not construct a table).
2. What forms of endogeneity are you concerned about when estimating the coefficient on mpg?
3. To correct for this endogeneity, you would like to use instrumental variables. Specifically, you are

   interested in the system of equations:
   pricev = β0 + β1mpgv + β2carv + ev (1)

   mpgv =γ0 +γ1zv +γ2carv +uv, (2)

   where zv is the value of the instrument for vehicle v and ev and uv are error terms. Report the estimated second-stage coefficients, standard errors or confidence intervals, and the first-stage F-statistic for the excluded instrument in the same table for the following procedures (just us a regular F-statistic for this exercise rather than the robust Montiel-Olea-Pflueger F-statistic):

   1. (a)  Perform two-stage-least-squares estimation by hand using weight as the excluded instrument. (First regress mpg on all of the instruments. Save the fitted values from the first stage mˆpg and use the fitted values in place of the endogenous variable in the second stage price regression.)
   2. (b)  Perform two-stage-least-squares estimation by hand using weight2 as the excluded instrument.
   3. (c)  Perform two-stage-least-squares estimation by hand using height as the excluded instrument.
   4. (d)  In words, what are the different exclusion restrictions required for parts (a)-(c)? Does this seem reasonable for these instruments?
   5. (e)  Compare and contrast the estimated coefficient on mpg from parts (a)-(c). What explains the discrepancies?
4. Calculate the IV estimate using GMM with weight as the excluded instrument. (Look for the Linear- models function IVGMM). Report the estimated second-stage coefficient and standard error or confidence interval for mpg What factors account for the differences in the standard errors?

1

2 Stata

1. Use the ivregress liml command to compute the limited information maximum likelihood estimate using weight as the excluded instrument. Report your second-stage results in a nicely-formatted table using outreg2. Use heteroskedasticity-robust standard errors.
2. Use weakivtest to estimate the Montiel-Olea-Pflueger effective F-statistic. What is the 5% critical value, the F-statistic, and conclusion?

2