# Estimate The Above Equation By Pooled OLS

**C10 **Use the data in AIRFARE.RAW for this exercise. We are interested in estimating the model

log( *fare**it*) 5 ***t *1 **1*concen**it *1 **2log(*dist**i*) 1 **3[log(*dist**i*)]2

1 *a**i *1 *u**it *, *t *5 1, …, 4,

where ***t *means that we allow for different year intercepts.

(i) Estimate the above equation by pooled OLS, being sure to include year dummies. If *concen *5 .10, what is the estimated percentage increase in *fare*?

(ii) What is the usual OLS 95% confidence interval for **1? Why is it probably not reliable? If you have access to a statistical package that computes fully robust standard errors, find the fully robust 95% CI for **1. Compare it to the usual CI and comment.

(iii) Describe what is happening with the quadratic in log(*dist*). In particular, for what value of *dist *does the relationship between log( *fare*) and *dist *become positive? [*Hint: *First figure out the turning point value for log(*dist*), and then exponentiate.] Is the turning point outside the range of the data?

(iv) Now estimate the equation using random effects. How does the estimate of **1 change?

(v) Now estimate the equation using fixed effects. What is the FE estimate of **1? Why is it fairly similar to the RE estimate? (*Hint**: *What is **ˆ for RE estimation?)

(vi) Name two characteristics of a route (other than distance between stops) that are captured by *a**i*. Might these be correlated with *concen**it*?

(vii) Are you convinced that higher concentration on a route increases airfares? What is

your best estimate?

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