Financial Econometrics

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Final Examination
Semester 2 / Year 2018
COURSE
COURSE CODE
TIME
DEPARTMENT
LECTURER
: FINANCIAL ECONOMETRICS
: BBFN3523
: 2 1/2 HOURS
: FACULTY OF BUSINESS AND MANAGEMENT
: DR. JOHN ENG YONG HENG
Student’s ID
Batch No.
:
:
INSTRUCTIONS TO CANDIDATES:
1) This question paper consists of 7 pages, 5 questions, and a t-table.
2) Answer ALL questions in the answer booklet provided within the duration allocated.
3) Return your answer booklet along with the question papers.
FINANCIAL ECONOMETRICS
Question 1
a) Basic labor economics theory tells us that among many variables, education is an important
determinant of wages. You have collected the following data of 13 individuals and decided to estimate
the regression line as Y = β0 + β1X
Table 1
Impact of Education on Wages
(Y, in RM)
(X)
Mean Hourly Wage
Years of Schooling
4.4567
6
5.7700
7
5.9787
8
7.3317
9
7.3182
10
6.5844
11
7.8182
12
7.8351
13
11.0223
14
10.6738
15
10.8361
16
13.6150
17
13.5310
18
Observation
1
2
3
4
5
6
7
8
9
10
11
12
13
i) Calculate
0 and
1
manually for the regression line Y = β0 + β1X
.
(8 marks)
ii) If an individual has 20 years of education, what is the mean hourly wage (in RM) would you guess
that individual had?
(4 marks)
b) Consider the following regression results:
= 798.7 – 1.18 × STR
n = 420, R2 = 0.051, SER = 18.6
i) How would the slope coefficient of student-teacher STR change, if you decided one day to
measure testscores in 100s, i.e., a test score of 650 became 6.5? Would this have an effect on
your interpretation?
(4 marks)
ii) Do you think the regression R2 will change? Why or why not?
1/7
(4 marks)
(Total 20 marks)
FINANCIAL ECONOMETRICS
Question 2
a) Consider the following regression equation for the Johor state (standard errors in parentheses):
P̂t  4.00  0.010PRPt  0.030PRBt  0.20YD t
(0.005)
(0.020)
R 2  0.98
(0.04)
n  29
where: Pt = per capita pounds of chicken consumed in time period t
PRPt = the price of chicken in time period t
PRBt = the price of beef in time period t
YDt = per capita disposable income in time period t
i) Hypothesize signs and specify the appropriate null and alternative hypotheses for the coefficients
of each of these variables.
(4 marks)
ii) State your decision rules and then test your hypotheses on the above results using the t-test at a 5%
level of significance.
(4 marks)
iii) If you could add one variable to the regression, what variable would you add? Why?
(2 marks)
b) In a research, you have obtained measurements of height in inches of 30 female and 80 male
students (Studenth) at a shopping center. A regression of the height on a constant and a dummy
variable (Femme), which takes a value of one for females and is zero otherwise, yields the following
result:
= 69.0 – 4.89×Femme , R2 = 0.40, SER = 2.0
(0.3) (0.57)
i) What is the interpretation of the intercept? What is the interpretation of the slope? How tall are
females, on average?
(6 marks)
ii) Test the hypothesis that females, on average, are shorter than males, at the 1% level.
(4 marks)
(Total 20 marks)
2/7
FINANCIAL ECONOMETRICS
Question 3
a) You would like to find the effect of gender and marital status on earnings. As a result, you consider
running the following regression:
ahei= β0 + β1×DFemmei + β2×DMarri + β3×DSinglei + β4×educi+...+ ui
Where ahe is average hourly earnings, DFemme is a dummy variable which takes on the value of "1" if
the individual is a female and is "0" otherwise, DMarr is a dummy variable which takes on the value of
"1" if the individual is married and is "0" otherwise, DSingle takes on the value of "1" if the individual
is not married and is "0" otherwise. The EViews regression program which you are using either returns
a message that the equation cannot be estimated or drops one of the coefficients. Why do you think that
is? What advice do you suggest to this problem?
(5 marks)
b) The faculty dean of a university has some disagreement with I. M. Smart (the director of the
Computer Center) about an equation that Smart built to understand the number of applications that the
school received from high school seniors. In need of an outside opinion, they turn to you to help them
evaluate the following regression results (standard errors in parentheses):
N̂ t  150  180A t  1.50 ln Tt  30.0Pt
(90)
R  0.50
2
(1.50)
N  22
(60.0)
(annual)
where: Nt = the number of high school seniors who apply for admission in year t
At = the number of people on the admission staff who visit high schools full time
spreading information about the school in year t
Tt = dollars of tuition in year t
Pt = the percent of the faculty in year t that had PhDs in year t
How would you respond if they asked you to:
i) Discuss the expected signs of the coefficients.
(3 marks)
ii) Compare these expectations with the estimated coefficients by using the appropriate tests.
(3 marks)
iii) Evaluate the possible econometric problems that could have caused any observed differences
between the estimated coefficients and what you expected.
(3 marks)
3/7
FINANCIAL ECONOMETRICS
Question 3 (Cont’)
iv) Determine whether the semilog function for T makes theoretical sense.
(3 marks)
v) Make any suggestions you feel are appropriate for another run of the equation.
(3 marks)
(Total 20 marks)
Question 4
a) A model of the number of cars sold in the United States from 1980 through 2004 produced the
following results (standard errors in parentheses):
Ĉt
= 3738 - 48.0Pt + 10.0Yt + 6.0At - 360.0Rt
(12.0)
(2.0) (2.0) (120.0)
R2 = 0.85
DW = 1.86
N = 25 (annual)
where: Ct = thousands of cars sold in year t
Pt = price index for domestic cars in year t
Yt = disposable income (billions of dollars) in year t
At = billions of dollars of auto industry advertising expenditures in year t
Rt = the interest rate in year t
i) Hypothesize the expected signs of the coefficients and test the appropriate null hypotheses at the 1%
level.
(3 marks)
ii) What econometric problems appear to be present in this equation? Support your answer.
(3 marks)
iii) Suppose you were now told that the simple correlation coefficients between P, A, and Y were all
between 0.88 and 0.94 and that a Breush-Pagan test produced a surprisingly low NR2. Would your
answer to part ii) above change? Why or why not? How would it change?
(4 marks)
iv) What suggestions would you have for another run of this regression?
(2 marks)
4/7
FINANCIAL ECONOMETRICS
Question 4 (Cont’)
b) If you run a regression in which the dependent variable and one or more independent variables are
spuriously correlated, the result is a spurious regression, and the t-scores and overall fit of such
spurious regressions are likely to be overstated and untrustworthy. One problem with time-series data
is that independent variables can appear to be more significant than they actually are if they have the
same underlying trend as the dependent variable. To test for non-stationarity, Dickey-Fuller test is
employed to test the null hypothesis of whether a unit root is present in an autoregressive model.
Describe and explain the test procedure.
(8 marks)
(Total 20 marks)
Question 5
a) Consider the following distributed lag model:
Yt = β0 + β1Xt + β2Xt-1 + β3Xt-2 + β4Xt-3 + ut
where ut = φ1 ut-1 + ũt , AR(1) error term.
ũt is serially uncorrelated, and X is strictly exogenous.
Using the two equations of the model above, derive the ADL form of the model.
(5 marks)
b) Two authors published a study in 1992 of the effect of minimum wages on teenage employment
using a U.S. state panel. The paper used annual observations for the years 1977-1989 and included all
50 states. The estimated equation is of the following type
(Eit )= β0 + β1 (Mit /Wit ) +
D2i + ... +
D50i +
B2t + ... +
B13t + uit,
where E is the employment to population ratio of teenagers, M is the nominal minimum wage, and W is
average wage in the state. In addition, other explanatory variables, such as the prime-age male
unemployment rate, and the teenage population share were included.
i) Briefly discuss the advantage of using panel data in this situation rather than pure cross sections or
time series.
(5 marks)
5/7
FINANCIAL ECONOMETRICS
Question 5 (Cont’)
ii) Estimating the model by OLS but including only time fixed effects results in the following output
it = 0 - 0.33 × (Mit /Wit ) + 0.35(SHYit) – 1.53 × uramit; R2 = 0.20
(0.08)
(0.28)
(0.13)
where SHY is the proportion of teenagers in the population, and uram is the prime-age male
unemployment rate. Coefficients for the time fixed effects are not reported. Numbers in parenthesis are
homoskedasticity-only standard errors.
Comment on the above results. Are the coefficients statistically significant? Since these are level
regressions, how would you calculate elasticities?
(5 marks)
iii) Adding state fixed effects changed the above equation as follows:
it = 0 + 0.07 × (Mit /Wit ) – 0.19 × (SHYit) – 0.54 × uramit; 2 = 0.69
(0.10)
(0.22)
(0.11)
Compare the two results. Why would the inclusion of state fixed effects change the coefficients in this
way?
(5 marks)
(Total 20 marks)
________ 000_________
6/7
FINANCIAL ECONOMETRICS
7/7
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