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Use the data set in AIRFARE to answer this question. The estimates can be compared with those inComputer Exercise $10,$ in this Chapter.(i) Compute the time averages of the variable concen; call these concenbar. How many differenttime averages can there be? Report the smallest and the largest.(ii) Estimate the equationIfare $_{i t}=\beta_{0}+\delta_{1} y 98_{t}+\delta_{2} y 99_{t}+\delta_{3} y 00_{t}+\beta_{1}$ concen $_{i t}+\beta_{2} l d i s t_{i}+\beta_{3} l d i s t s q_{i}+$ $\gamma_{1}$ concenbar $_{i}+a_{i}+u_{i t}$ by random effects. Verify that $\hat{\boldsymbol{\beta}}_{1}$ is identical to the FE estimatecomputed in $\mathrm{Cl} 0 .$ (iii) If you drop ldist and ldistsq from the estimation in part (i) but still include concenbar, whathappens to the estimate of $\hat{\beta}_{1}$ ? What happens to the estimate of $\gamma_{1} ?$(iv) Using the equation in part (ii) and the usual RE standard error, test $H_{0} : \gamma_{1}=0$ against the two-sided alternative. Report the $p$ -value. What do you conclude about RE versus FE for estimating$\beta_{1}$ in this application?(v) If possible, for the test in part (iv) obtatistic (and, therefore, $p$ -value) that is robust to arbitraryserial correlation and heteroskicity. Does this change the conclusion reached in part (iv)?

(i) (ii) See video, same estimate (iii) $\beta_1$ is the same but $\gamma_1$ changes sign (iv) RE produces similar results to FE (v) Conclusion does not change

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Chapter 14

Advanced Panel Data Methods

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part one. The variable consent represent concentration is defined to be the same as the variable B M k T s H r. It's okay. Show the fraction of the market of the biggest carrier. Thanks. Constant bar is the time averages of consent. And there can be 1000 149 different values of consent bar. It is so because 1149 is the number of, um, ID or there years should be there either the city or the county. Okay, so it's the same as the number of I d. That is interior. Mhm. The minimum value of constant bar is okay, 0.1862 So about 10%. And the largest value of consent bar is 0.9997 So for a certain I'd the biggest carrier. Mm. There may be only one carrier for that. I d. For that subject. Yeah. And for part two, you will look at the panel on the left of the screen and you can confirm that it's a little bit small. You can confirm that there estimate on variable consent is the same to what we get when We estimate the equation which fixed effects. Our three. If we drop the distant variables from the estimation in part one, but still include consent bar, you should find that data one stays the same later. One is the estimate on consent. You can get 0.169 with standard barrel of 0.2 0.2 94 and four gamma one. They estimate On constant bar, you get minus 0.709 with a standard barrel of point Oh 71 So this one doesn't sheen. Same in magnitude and significance. But the estimate on consent bar now flip sign. The reason could be the distant variables are probably correlated with consent bar and so admitting them leads to a bias in constant bar, and the bio sign is complicated. Consumer picks up much of the bias, probably because it is less harm variant than consent. In part for using the usual standard error from random effect. Estimate we contest the null hypothesis gamer. One equals zero against the two sided alternative. You may see that this variable is significant at the 1% level, so we reject. It's not hypothesis at the one person level for beta one. You may find out from part two that it doesn't matter whether we use random effects are fixed effect because we get the same result. He her five I went try, um, the robust standard era, the one that is robust. You had to risk elasticity, and I have the same conclusion as in part four.

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