UNIVERSITY OF LONDON BSc UNASSESSED EXAMINATION 2010 (Problem Set A11)For Internal Students of Royal Holloway
DO NOT TURN OVER UNTIL TOLD TO BEGIN
EC3333 : ECONOMETRICS EC3333R: ECONOMETRICS
Deadline: 18 January 2011 (Noon)
Attempt All questions.
The format requirements:
1. Type up your work, using any software of your favorite. If you ar代写英国留学生作业using MS Word, you type mathematics using Insert/Symbol or
Insert/Object/Equations.
2. Save the file as PDF. To do so, us "Print As" and set "Printer Name" as
"Adobe PDF." A MS Word file is also acceptable.
3. Students will need to submit all coursework via Turnitin/JISC. The
course number is 222622 and the password is EC333310
4. Please do not add a cover page.
5. Save both Word and STATA log files by your name (e.g.,
AdamSmith.doc, AdamSmith.log) and upload both to Turnitin/JISC. In
addition, submit only the first page of the Word file to the Department
Office (H209) before the deadline.
6. For questions required STATA outputs, report summary statistics as
Table 6.1 and summarize regression results as Table 7.1. Give each
table a title and attach all tables at the end of your course work. Do
not copy and paste STATA outputs to your answer.
EC3333 and EC3333R © Royal Holloway and Bedford New College 2010
Question 1
Consider the regression model
Yi 1Xi ui
for i=1,2,…,n.
a) Derive 1
ˆ
the OLS estimator for 1 .
[5 marks]
b) Show that 1
ˆ
a linear estimator.
[5 marks]
c) Show that 1
ˆ
is conditionally unbiased.
[5 marks]
d) Derive the conditional variance of the estimator 1
ˆ
.
[5 marks]
e) Describe Gauss-Markov conditions and theorem for 1
ˆ
given the model.
[5 marks]
f) Show Gauss-Markov theorem for 1
ˆ
given the model.
[10 marks]
(Total 35 Marks)
Question 2
Many sociologies and demographers hypothesize that women’s fertility choice depend onthe sex composition of earlier born children. If women prefer mixed-sex composition, theywould stop fertility sooner after having one girl and one boy at the two births, comparedthose with a same sex composition (e.g. Angrist and Evan’s article in 1998 published in theAmerican Economic Review; posted on http://www.1daixie.com/liuxueshengzuoye/Moodle). To examine this, download from Moodlefertility.dta, which contains 254,654 women from 1980 US Census who have at least 2children. See data descriptions on Moodle. Answer the following questions:
a) Use boy1st and boy2nd to generate samesex1 an indicator for same sex of the firsttwo births. Check if samesex1 replicated samesex in the data.
[5 marks]
b) Construct a table (called Table 1) to show the percent of women aged 21-35 whohave two or more children by the sex composition of children.
[5 marks]
c) Run a regression of having a third child (morekids) on the indicator for same sexcomposition (samesex). Is the hypothesis consistent with the regression result?
[5 marks]
TURN OVER
d) Mothers’ age can also affect fertility choice. Does controlling for the mother’s agechange the result in (c)?
[5 marks]
e) It’s likely that the preference for mixed sex composition differ across races, after
controlling for mothers’ age. Use F-test to test the importance of race dummies.
[5 marks]
f) If the sex composition of children indeed affects fertility choice, it might also affect
women’s labor supply. Run three regressions such as models (c), (d) and (e) but with
weeks worked in 1979 (weeksm1) as the dependent variable. Construct a table
(called Table 2) to summarize the estimation results. Discuss how the relationship
between the sex composition of children and women’s labor supply changes across
the specifications.
[10 marks]
(Total 35 Marks)
Question 3
The Bertrand and Hallock (2000) study (posted on Moodle) compares totalcompensation among top executives by gender in a a large set of U.S. public tradedcorporations in the 1990s. Let Female be an indicator for female. Their benchmark resultis
, 2.65.(0.05)
0.44
(0.01)
ln(earnings) 6.48 Female u SER (1)a) Interpret the estimated coefficient on Female.
[5 marks]
b) Does this regression suggest that female top executives earn less than top maleexecutives? Does this regression suggest that there is gender discrimination?
Explain.
[5 marks]
Two new variables, MarketValue the market value of the firm (a measure of firm size, inmillions of dollars) and Return the stock return (a measure of firm performance, inpercentage points), are added to the regression:earnings Female MarketValue Re turn u
(0.003)
0.004
(0.004)
0.37 ln( )
(0.04)
0.28
(0.03)
ln( ) 3.86 (2)
c) Interpret the estimated coefficient on Female.
[5 marks]
d)代写英国留学生论文 Interpret the estimated coefficient on ln(MarmetValue).
[5 marks]
e) Interpret the estimated coefficient on Return.
[5 marks]
TURN OVER
f) Discuss the omitted variable bias problem in model (1). Why model (1) overstatesthe gender wage differential?
[5 marks]
(Total 30 Marks)
END