Question

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

$$ \begin{aligned} \log (\text { salary })=& \beta_{0}+\beta_{1} L S A T+\beta_{2} G P A+\beta_{3} \log (\text { libvol })+\beta_{4} \log (\text { cost }) \\ &+\beta_{5} \operatorname{rank}+u \end{aligned} $$

where \(L S A T\) is the median LSAT score for the graduating class, \(G P A\) is the median collegi GPA for the class, libvol is the number of volumes in the law school library, cost is the an nual cost of attending law school, and \(\operatorname{rank}\) is a law school ranking (with \(\operatorname{rank}=1\) bein the best).

(i) Explain why we expect \(\beta_{5} \leq 0\).

(ii) What signs do you expect for the other slope parameters? Justify your answers.

(iii) Using the data in LAWSCH85.RAW, the estimated equation is

$$ \begin{aligned} {\log (\text { salary) }}=& 8.34+.0047 L S A T+.248 G P A+.095 \log (\text { libvol }) \\ &+.038 \log (\cos t)-.0033 \operatorname{rank} \\ n=& 136, R^{2}=.842 \end{aligned} $$

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?

Answer 1

i) We expect B5 to be less than zero because the lower the rank, the higher the median starting salary.

ii) B1 and B2 would be greater than 0 because higher the LSAT score and GPA higher should be the median starting salary, whereas we can assume B4 and B5 to measure the quality of school and be greater than 0. It implies higher is the quality of school higher would be the median starting salary.

iii) For GPA difference by 1 point and all other ceteris paribus, the difference in median starting salary would be: 0.248 * 100 = 24.8% on an average.

iv) B4 = 0.095

The above coefficient of log(libvol) implies that if the library volume of books increases by 1%, then the median starting salary would increase by 0.095% on average.

v) No, a higher ranked school must not be attended, and a lower rank should always be preferred. If there is a difference in ranking of 20, then predicted median starting salary changes by 20 * 0.0033 * 100 = 6.6%

Answer 2

1) we expect b5 < 0 as b5 represent sensitivity of salary to law school ranking . As rank of law school goes high then median starting salary for new law school graduates decreases. As low rank being the best.Due to this inverse relation between salary and rank, Coefficient of rank, b5 will be neagative (i.e <0)

ii) B1 will be positive as median LSAT score for the graduating class increases, salary of gradutae increases. So B1 >0

and B2 will be positive as college median GPA increase , salary of graduates increases, B3 will be positive as if there are more volumes in library, there is more chance of getting higher salary, so B3 >0 and B4 will be >0 as if annual cost is high , that indictaes more facilities for students, hence it makes students better there by attaining high salaries , hence B4 >0 and B5 <0 due to explaination in answer in part 1

iii) predicted ceteris paribus difference in salary for schools with a median GPA different by one point

= coefficient of GPA

=0.248

= 24.8% (in percentage) As coefficient of GPA = % change in slary/unit change in GPA)

iv)coefficient on the variable log(libvol). = % change in salary/ % change in libvol

Interpretation :How much will be the percentage change in salry due to % change in library volumes . It represents sensitivity of library volumes to salary

v)No, it is better to attend a Lower ranked law school instead of igher rank school as there is inverse relation exists between rank of law school and salry.

difference in ranking of 20 worth in terms of predicted starting salary = 20*(-0.0033)

= -0.066

= -6.6%

so due to difference in ranking of 20, salry decrease by 6.6% or if rank is lower by 20 units , then salary attained will be 6.6% higher