The median starting salary for new law school graduates is determined by log(sal

Question

The median starting salary for new law school graduates is determined by log(salary) = beta_0 + beta_1LSAT + beta_2GPA + beta_3log (libvol) + beta_4log(cost) + beta_5rank + u, where LSAT is the median LSAT score for the graduating class, GPA is the median college GPA for the class, libvol is the number of volumes in the law school library, cost is the annual cost of attending law school, and rank is a law school ranking (with rank = 1 being the best). (i) Explain why we expect beta_5 lessthanorequalto 0. (ii) What signs do you expect for the other slope parameters? Justify your answers. (iii) Using the data in LAWSCH85, the estimated equation is log(salary) = 8.34 + .0047 LAST + .248 GPA + .095 log (libvol) + .038 log(cost) - .0033 rank n = 136, R^2 = .842. What is the predicted ceteris paribus difference in salary for schools with a median GPA different by one point? (Report your answer as a percentage.) (iv) Interpret the coefficient on the variable log(libvol). (v) Would you say it is better to attend a higher ranked law school? How much is a difference in ranking of 20 worth in terms of predicted starting salary?

Explanation / Answer

Part-i

We expect beta_5<=0 as we expect that as the ranking of law school increase, its rating decrease (as 1=best rank) and so will leads to decrease in salary.

Part-ii

We expect positive sign for LSAT as improvement in graduating class LSAT score will lead to increase in salary.

We expect positive sign for GPA as improvement in median college GPA will lead to increase in salary.

We expect positive sign for libvol as improvement in more law volumes will lead to increase in salary as more understanding will be gained.

Part-iii

We observe that corresponding to a unit increase in median GPA there is 24.8% increase in salary, ceteris paribus.

Part-iv

Ceteris paribus, corresponding to 1% increase in library volume there is 0.095% increase in starting salary.

Part-v

A school with high ranking means the school is worst as rank=1 is the best and we would say it is not better to attend a higher ranked law school.

Corresponding to 20 ranking increase there is 20*(-0.0033)*100 = -6.6% or 6.6% decrease in starting salary,

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