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For this exercise, use the data in AIRFARE, but only for the year $1997 .$(i) A simple demand function for airline seats on routes in the United States is$\log ($passen$)=\beta_{10}+\alpha_{1} \log ($ fare $)+\beta_{11} \log (d i s t)+\beta_{12}[\log (d i s t)]^{2}+u_{1}$where$$\begin{aligned} \text {passen} &=\text { average passengers per day, } \\ \text {fare} &=\text { average airfare, and } \\ d i s t &=\text { the route distance (in miles) } \end{aligned}$$If this is truly a demand function, what should be the sign of $\alpha_{1} ?$(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 log(fare).(v) Estimate the demand function using IV. Now whate? How does it compare with the OLS estimate?(vi) Using the IV estimates, describe how demand for seats depends on route distance.

(i) The sign of $\alpha_{1}$ is expected to be negative as higher the average airfare, lower should be the passengers per day (ii) The estimated price elasticity is given by the coefficient of log(fare) which is $-0.391$ (tstat = -5.82) (iii) (iv) see video (v) $-1.17$ more sensitivity than OLS estimate (vi) U-shape - see video

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Chapter 16

Simultaneous Equations Models

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Turan K.

May 30, 2021

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part one. The demand function should be downward sloping, So I'll for one Is smaller than zero. Right? Mhm. As price increases, quantity demanded for error, travel decreases are to the estimated price elasticity is mhm minus pulling 3 9. 1 with 80 statistic of -5 points eight. This estimated elasticity is highly significant. Or three. We would assume that passenger demand depends only on airfare so that once price is controlled for passengers are indifferent about the fraction of travel accounted for by the largest carrier. Hard for this is what we get when we estimate the reduced form equation for log of airfare. Yeah, the coefficient on concentration bearable is highly significant. With a T statistic Of 6.3. The estimated coefficient shows a positive relationship between concentration and as there, if concentration of the industry increases by 10 point airfare is estimated to increase by almost four. Yeah percent. Yeah. Charge five. Using concentration as an instrument for airfare, We find the estimated price elasticity to B -1.17. With a standard error of .389. Yeah. The estimate estimated elasticity is much greater in magnitude than the old estimate. This instrumental variable estimate suggest that A one increase in fair let's do is slightly more than 1%. Drop in passenger demand. The standard error of this ivy estimate is much larger compared with the old L. S. Standard error but the ivy estimate is still significant. Okay. Yeah, Part six Estimated coefficient on lock of distance is -2.176. And the coefficient on the log of distance square Is pulling 187. Yeah. So the relationship between block of passenger and lock of distance. Yes and U. Shape. And we can illustrate that on the following grafts we can find the value of lack of distance that minimize lock of passenger. And that value is calculated by taking the estimated value of the coefficient on log distance, Flip the sign so we have 2.176 divided by the coefficient on lock of distance, square point 187 And that gives 5.82. Right? That is the lock of distance. And when we convert to distance, this value is equivalent you 337 yeah, months.

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