Problem Set: USDOT Airfare Dataset
In this exercise you will use panel data methods to examine data from the Domestic Airline Consumer Airfare Report, courtesy of the U.S. Department of Transportation (USDOT). For convenience, I have posted the required data on my personal website: https://ditraglia.com/data/usdot.csv. This file contains information on average airfares on different routes throughout the U.S. between 1997 and 2000. A route is a pair of cities between which you can fly non-stop: e.g. Philadelphia-Chicago. The columns in usdot.csv
are as follows:
Name | Description |
---|---|
year |
Year of a given observation (1997, 1998, 1999, or 2000) |
route_id |
Unique numeric identifier for each route (pair of cities) |
distance |
Distance between the pair of cities (miles) |
passengers_daily |
Average number of passengers per day who flew this route |
airfare |
Average one-way airfare on this route (nominal U.S. $) |
market_share |
Market share of largest carrier on this route (decimal) |
Exercises
Exercise 1: Simple OLS model
Consider an OLS regression of the log of airfare
on market_share
, log(dist)
, log(dist)^2
, and a full set of year dummies.
- Why might it make sense to include year dummies in this regression? Do the estimated coefficients for the time dummies make sense in light of this explanation?
- Interpret the estimated coefficient on
market_share
in this regression, along with the associated 95% confidence interval based on “plain-vanilla,” i.e. non-roust, standard errors. - Repeat (b) accounting for potential heteroskedasticity and clustering. What is the appropriate level at which to cluster in this example? How do your results change?
Exercise 2: Airfare elasticities
- Recall that elasticities measure the sensitivity of one variable to another. The elasticity of \(Y\) wrt \(X\) is given by \(\frac{d Y/Y}{dX/X}\). Compute the derivative of the logarithm, \(\frac{d\log(Y)}{dY}\), rearrange, and express the formula for elasticity in terms of logarithms. Hint: You formula should have only logarithms in it!
- What is the elasticity of
airfare
with respect todistance
? Use your formula from (a) to derive an expression for the elasticity in your log-log model. Hint: Your formula should give the elasticity depending on model coefficients anddistance
. - Use this expression to add the variable
elasticity
to your data set.elasticity
should contain airfare elasticities for each route. Visualise this variable in a figure. - Comment on your findings. Do the estimated elasticities make economic sense?
Exercise 3: Route fixed effects
Suppose that we decided to add route fixed effects to the regression from above.
- What inference issue do fixed effects solve? Why might adding route fixed effects make sense here?
- Typeset the estimation equation. If we add route fixed effects, will we be able to estimate the elasticity of
airfare
with respect todistance
? Why or why not? Hint: This depends on whether we can include time-invariant regressors in our model. Can we do that in fixed effects? - Carry out the fixed effects regression, clustering standard errors appropriately. How do your results compare to those from above? Suggest a possible explanation for any differences that you find.