Quantitative Methods in Finance
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BFIP013 Quantitative Methods in Finance
This seminar relates to nonlinear models and dummy variables (in week 8). The
seminars will provide a forum for discussion with respect to the following questions.
As preparation for the seminar, you should attempt the questions in advance.
Please retain a copy of your answers, which you can then use in the seminars to discuss
with the tutor (to monitor your understanding).
Question 1:
Use the data in cps.dta to estimate the following wage equation:
1 2 3 4ln( )WAGE EDUC EXPER UNION u
(a) Report the results. Interpret the estimates of β2, β3 and β4. Are these estimates
significantly different from zero?
(b) Suppose you wish to test the hypothesis that a year of education a year of experience
have statistically significant joint effect on ln(WAGE). What null and alternative
hypothesis would you set up?
(c) What is the restricted model, assuming that the null hypothesis is true?
(d) Test the hypothesis in (b) in two ways: (i) using the appropriate STATA command,
and (ii) calculate manually the relevant test statistic.
(e) Test the hypothesis that an extra year of education increases the wage rate by at
least 10% against the alternative that it is less than 10%.
(f) Re estimate the model with the additional variables EDUC x EXPER, EDUC2 and
EXPER2 . Interpret the estimated coefficients. Are the estimated coefficients
significantly different from zero?
(g) For the new model, find expressions for the marginal effects
ln( ) and ln( ) .WAGE EDUC WAGE EXPER Is the effect of EDUC and
EXPER on lnWAGE statistically significant in the model estimated in part (f)?
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Question 2:
Use the data in eawe22.dta.
(a) Regress WEIGHT04 on HEIGHT and save the fitted values as YHAT.
(b) Perform a RESET test of functional misspecification including (i) YHAT2, (ii)
YHAT3. What do you conclude in both cases?
Question 3:
In the file stockton_dummy.dta we have data from January 1991 to December 1996 on
house prices, square footage and other characteristics of 4682 houses that were sold in
Stockton, California.
(a) Generate the annual dummy variables d91, d92, d93, d94, d95, d96 and give a label
mentioning the year of the house being sold.
(b) Estimate the following model:
1 2 3 1 2 3 4 592 93 94 95 96PRICE SQFT AGE D D D D D u
where PRICE = house price, SQFT = the size of the house, AGE = the age of the
house, and D92, D93, D94, D95, D96 are annual dummy variables, omitting the
dummy variable for year 1991.
(c) Discuss the estimated coefficients on SQFT and AGE, including their
interpretation, signs, and statistical significance.
(d) Discuss the estimated coefficients on the dummy variables.
(e) What would have happened if we had included a dummy variable for 1991?
Question 4:
Use the data in wage2.dta.
(a) Estimate the model:
0 1 2 3 4 5 6 7log( ) expwage educ er tenure married black south urban u
and report the results. Holding other factors fixed, what is the approximate difference
in monthly salary between blacks and nonblacks? Is this difference statistically
significant?
(b) (i) Add the variables exper2 and tenure2 to the equation and show that they are
jointly insignificant at 10% significance level.
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(ii) Based on the model estimated at (i), test the statistical significance of
experience and tenure, respectively.
(c) Extend the original model to allow the return to education to depend on race and
test whether the return to education does depend on race.
(d) Consider the original model and apply the Chow test in order to test whether there
are wage differences between married and unmarried.