Economics7103 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 
Description 
price 
Sales price of the vehicle in USD 
car 
Class of the vehicle. =1 if the vehicle is a sedan, =0 if the vehicle is an SUV 
mpg 
Fuel efficiency in miles per gallon 
weight 
Weight of the vehicle in pounds 
height 
Height of the vehicle in inches 
length 
Length of the vehicle in inches 
Table 1: Variable descriptions for homework 6. 
1 Python 
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): 
(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 ˆ mpg and 
use the fitted values in place of the endogenous variable in the second stage price regression.) 
(b) Perform two-stage-least-squares estimation by hand using weight2 as the excluded instrument. 
(c) Perform two-stage-least-squares estimation by hand using height as the excluded instrument. 
(d) In words, what are the different exclusion restrictions required for parts (a)-(c)? Does this seem 
reasonable for these instruments? 
(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? 
12 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