Department of Ag and Resource Economics UC Davis

ARE 106 Homework 1

Fall 2017

DUE: 1:40pm Thursday, October 26 (i.e., before class)

Important: – You must write your answers on the sheet on pg 3 of this assignment

and you must attach explanations and derivations of your answers.

– Please turn your homework in at lecture.

– Late homeworks will automatically be given a score of zero.

This homework assignment is based on Problem 3.4 in Wooldridge.

Here are three models for the median starting salary of law school graduates in 1985.

0 1

0 1 2

0 1 2 3 4 5

1. log( )

2. log( )

3. log( ) log( ) log(cos )

i i i

i i i i

i i i i i i i

salary LSAT u

salary LSAT GPA u

salary LSAT GPA libvol t rank u

Each observation i represents a school. You can read the data from the internet directly

into Stata using the command:

“use http://fmwww.bc.edu/ec-p/data/wooldridge/lawsch85, clear”

The variables in the dataset are:

1. rank law school ranking

2. salary median starting salary

3. cost law school cost

4. LSAT median LSAT score

5. GPA median college GPA

6. libvol no. volumes in lib., 1000s

7. faculty no. of faculty

8. age age of law sch., years

9. clsize size of entering class

10. north =1 if law sch in north

11. south =1 if law sch in south

12. east =1 if law sch in east

13. west =1 if law sch in west

14. lsalary log(salary)=log of median starting salary

15. studfac student-faculty ratio

16. top10 =1 if ranked in top 10

17. r11_25 =1 if ranked 11-25

18. r26_40 =1 if ranked 26-40

19. r41_60 =1 if ranked 41-60

20. llibvol log(libvol)

21. lcost log(cost)

Department of Ag and Resource Economics | UC Davis |

1) How many law schools are in the dataset? | |

2) Explain how to interpret β1 in Model 1. | |

3) Explain how to interpret β1 in Model 2. | |

4) In Model 2, do you expect β1 and β2 to be positive or negative? Explain. | |

5) Estimate Model 1. | |

a. If School A has median LSAT that is one point higher than School B, what is the | |

predicted difference between the log median salary for each school’s | |

graduates? | |

b. Explain what the R2 measures in your regression. | |

6) Estimate Model 2. |

a. Why is ˆ1 in Model 2 different from ˆ1 in Model 1?

b. Why is the R2 in Model 2 higher than Model 1?

7) Estimate Model 3.

a. Why is ˆ1 in Model 3 so small compared to ˆ1 in Model 1?

b. Suppose School A and School B have the same values for all the variables on

the right hand side in Model 3, except School A is ranked 10 places higher than

School B. What is the difference in predicted difference in log median salary

between the two schools?

c. Suppose School A and School B have the same values for all the variables on

the right hand side in Model 3, except School A costs $10,000 and School B

costs $15,000. What is the difference in predicted difference in log median

salary between the two schools?

d. Suppose a school were to double its cost. Would you expect graduates from

the program to earn higher salaries? Why?

Department of Ag and Resource Economics UC Davis

Name: Discussion Time:

ARE 106 Answer Sheet for Homework 1

Fall 2017

Please write your answers to each question on the appropriate line. Each of the 12 parts

questions is worth two points.

You will get a zero on this homework if you do not attach your computer output to

this sheet.

(1) Number of schools:

(2) Explain

(3) Explain

(4) Answer yes or no: β1 β2

Explain

(5a) Predicted difference:

(5b) Explain

Department of Ag and Resource Economics UC Davis

(6a) Why?

(6b) Why?

(7a) Why?

(7b) Predicted difference: (7c) Predicted difference:

(7d) Yes or no? Why

Free points are given to anyone who completes the homework including attaching computer output.

TA use only

Available

Points Score

Score 24 Free points 11 |

Total 35 |

Divide by 5 to get recorded score 7 |