For this exercise, use the data in AIRFARE.RAW, but only for the year 1997.
(i) A simple demand function for airline seats on routes in the United States is
Log(passen) = β10 + α1 log(fare) + β11 log(dist) + βl2 [log(dist)]2 + u1,
where
passen = average passengers per day.
fare = average airfare.
dist = the route distance (in miles).
If this is truly a demand function, what should be the sign of α1?
(ii) Estimate the equation from part (i) by OLS. What is the estimated price elasticity?
(iii) Consider the variable concen, which is a measure of market concentration. (Specifically, it is the share of business accounted for by the largest carrier.) Explain in words what we must assume to treat concen as exogenous in the demand equation.
(iv) Now assume concen is exogenous to the demand equation. Estimate the reduced form for log(fare) and confirm that concen has a positive (partial) effect on\ogifare).
(v) Estimate the demand function using IV. Now what is the estimate price elasticity of demand? How does it compare with the OLS estimate?
(vi) Using the IV estimates, describe how demand for seats depends on route distance.