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Semester One 2019
Examination Period
Faculty of Business and Economics
EXAM CODES:
ETF2100-ETF5910
TITLE OF PAPER:
Introductory (Applied) Econometrics – PAPER 1
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2 hours writing time
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10 minutes
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Page 1 of 13
Page 2 of 13
ETF2100/5910 Introductory Econometrics
There are five (5) questions on pages 2 to 9, and statistical tables on pages 10 to 13.
Answer all five (5) questions.
Note that Question 1 has two parts. Part 1 is for ETF2100 students only while part 2 is for
ETF5910 students only.
Question 1
(18 marks)
Part 1 for ETF2100 students only
Consider the following simple regression model
yi  1  2 xi  ei


where E  ei | xi   0, var  ei | xi    2 and cov ei , e j | x  0 for i  j . Suppose application of
the least squares rule to this equation with number of observations N  8 yields b1  10, b2  2,
and that other information we obtain is SSE  12 , R 2  0.7 and
0.1
 b , b | x   4
cov
1 2
 0.1 0.25


Are the following statements true or false? Clearly indicate which statements are true or false
and support your choice with a brief statement.
(c)
The coefficient 2 is the elasticity of yi with respect to a 1% change in xi .
(2 marks)
The coefficient estimate b2 is significantly different from zero at the 5% level.
(3 marks)
The total sum squares ( SST ) is 125.
(2 marks)
(d)
(e)
The variance of the error terms, ̂2 is 2.
 b  b | x   3
var
1
2
(f)
(g)
The prediction for y0 when x0  2 is 14.
(2 marks)
The estimated variance for the forecast error for the prediction in (f) is 7.
(4 marks)
(a)
(b)
(2 marks)
(3 marks)
Part 2 for ETF5910 students only
(a)
The estimates b1 and b2 are called least squares estimates because they minimize the
squares  b1  1  and  b2  2  .
2
2
(3 marks)
(b)
The errors are heteroskedastic because the two variances on the diagonal of
  b , b | x  are not equal.
(3 marks)
cov
1 2
(c)
The assumption var  ei | x   2 implies that large errors are not more likely for some
xi than for others.
(d)
(3 marks)
Because the estimators b1 and b2 are random variables, they can take different values
in different samples.
(3 marks)
Page 3 of 13
ETF2100/5910 Introductory Econometrics
(e)
Because least squares estimates are unbiased they will always be equal to the true
parameter values.
(3 marks)
(f)
If economic theory suggests that xi has a positive relationship with yi , it makes sense
to use a right-tail test when testing significance of 2 .
Question 2
(3 marks)
(28 marks)
Consider the following model that relates the proportion of a household's budget spent on
alcohol (walc) to total expenditure (totexp), age of the household head (age), and the number
of children in the household (nk).
walci  1  2 ln  totexpi   3agei  4 nki  ei
(2.1)
(a)
What signs would you expect on the coefficients 2 , 3 and 4 ? Why?
(b)
The EViews output for the least squares estimation of (2.1) is below. Report the results
(2 marks)
in the standard format.
(3 marks)
Table 2.1
Dependent Variable: WALC
Method: Least Squares
Date: 04/28/15 Time: 11:36
Sample: 1 500
Included observations: 500
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
LOG(TOTEXP)
AGE
NK
0.014861
0.032703
-0.002204
-0.014834
0.036955
0.008152
0.000400
0.006087
0.402140
4.011542
-5.514748
-2.436796
0.6878
0.0001
0.0000
0.0152
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
0.080343
0.074780
0.064552
2.066844
662.6771
14.44381
0.000000
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
0.059748
0.067111
-2.634708
-2.600992
-2.621478
1.990082
(c)
Interpret the estimates b2 , b3 and b4 . Do you think the results make sense from a logical
(4 marks)
point of view?
(d)
Are there any variables that you might exclude from the equation? Why? (5 marks)
(e)
Commodities are regarded as luxuries if 2  0 and necessities if 2  0 . Test
H 0 : 2  0 against H1 : 2  0 and comment on the outcome.
(4 marks)
(f)
Find a 95% interval estimate for the change in the budget share for alcohol consumption
when total expenditure changes by 1%. Interpret the results.
(5 marks)
(g)
Explain the purpose of RESET (REgression Specification Error Test)? Outline how
RESET is done for equation (2.1)
(5 marks)
ETF2100/5910 Introductory Econometrics
Question 3
Page 4 of 13
(20 marks)
Consider the following regression model for wage.
ln  wagei   1  2 educi  3experi  4 experi 2  5nonwhitei  ei
(3.1)
where wagei = earnings per hour for a person i.
educi = years of education for the corresponding person i.
experi = years of experience for the corresponding person i.
nonwhitei = 1 if the person i is not a white person.
Some EViews output related to the model (3.1) is reported in Tables 3.1, 3.2, 3.3 and 3.4 below.
(a)
Table 3.1 is the EViews output for the least squares estimation of equation (3.1). Report
the results in the usual way and interpret the estimated coefficients for educ and
(5 marks)
nonwhite . Do they make intuitive sense?
(b)
Construct a 95% confidence interval for 2 and interpret the result. Can you use this
confidence interval to make a conclusion about whether the level of education has an
(4 marks)
impact on wage? Explain.
(c)
Perform an appropriate test using a 5% significance level to test whether wage responds
to years of experience. Table 3.2 below will be useful.
(5 marks)
(d)
Equation (3.1) was re-estimated for male and female observations separately. Consider
the following models:
For female
ln  wagei   1  2 educi  3experi  4experi 2  5nonwhitei  eFi
For male
ln  wagei   1   2educi   3experi   4experi 2   5nonwhitei  eMi
We assume that E  eMi | x   E  eFi | x   0 , var  eMi | x    2M , var  eFi | x    2F , and
eMi and eFi are independent of each other.
Table 3.3 is the EViews output when only male observations are included and Table
3.4 is the EViews output when only female observations are included.
Assuming that  2M   2F , test whether there is any evidence to suggest that the wage
equations for males and females are different. That is test the hypothesis
H 0 : 1  1, 2   2 , 3   3 , 4   4 , 5   5
(6 marks)
Page 5 of 13
ETF2100/5910 Introductory Econometrics
Table 3.1
Dependent Variable: LOG(WAGE)
Method: Least Squares
Sample: 1 1000
Included observations: 1000
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
EDUC
EXPER
EXPER^2
NONWHITE
0.330762
0.108705
0.036873
-0.000594
-0.170716
0.091358
0.006069
0.004440
0.000103
0.051549
3.620492
17.91258
8.305028
-5.742988
-3.311745
0.0003
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
F-statistic
Prob(F-statistic)
0.307908
0.305126
0.460814
211.2880
110.6676
0.000000
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Durbin-Watson stat
0.0000
0.0000
0.0010
2.166837
0.552806
1.293344
1.317883
0.572625
Table 3.2
Dependent Variable: LOG(WAGE)
Method: Least Squares
Sample: 1 1000
Included observations: 1000
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
EDUC
NONWHITE
0.815104
0.102825
-0.162413
0.085041
0.006266
0.054568
9.584862
16.40894
-2.976354
0.0000
0.0000
0.0030
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
F-statistic
Prob(F-statistic)
0.221538
0.219976
0.488233
237.6560
141.8649
0.000000
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Durbin-Watson stat
2.166837
0.552806
1.406946
1.421669
0.427249
Table 3.3: Only male observations included
Method: Least Squares
Sample: 1 1000 IF FEMALE=0
Included observations: 506
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
EDUC
EXPER
EXPER^2
NONWHITE
0.520269
0.098110
0.042960
-0.000667
-0.204453
0.116940
0.007881
0.005950
0.000139
0.073038
4.449005
12.44949
7.220527
-4.801108
-2.799258
0.0000
0.0000
0.0000
0.0000
0.0053
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
F-statistic
Prob(F-statistic)
0.349506
0.344312
0.441544
97.67571
67.29587
0.000000
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Durbin-Watson stat
2.297458
0.545288
1.212756
1.254520
0.598303
Page 6 of 13
ETF2100/5910 Introductory Econometrics
Table 3.4: Only female observations included
Dependent Variable: LOG(WAGE)
Method: Least Squares
Sample: 1 1000 IF FEMALE=1
Included observations: 494
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
EDUC
EXPER
EXPER^2
NONWHITE
0.156461
0.117306
0.031572
-0.000535
-0.123338
0.132677
0.008688
0.006120
0.000142
0.067288
1.179266
13.50129
5.159068
-3.766533
-1.832992
0.2389
0.0000
0.0000
0.0002
0.0674
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
F-statistic
Prob(F-statistic)
Question 4
0.304742
0.299055
0.442402
95.70665
53.58399
0.000000
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Durbin-Watson stat
2.033042
0.528414
1.216872
1.259408
0.659827
(16 marks)
Reconsider the model for wage in (3.1)
(a)
Equation (3.1) was estimated and the residuals are plotted against educ in the graph
below. What does the graph suggest to you?
(2 marks)
2.0
1.5
1.0
residual
0.5
0.0
-0.5
-1.0
-1.5
-2.0
0
4
8
12
16
20
EDUC
(b)
Use the least squares results in Table 4.1 below to perform the White test for
heteroskedastic errors. Make sure to write the test equation, the hypotheses to be tested,
and the test statistic.
(5 marks)
(c)
What are the consequences of heteroskedasticy on your least squares estimators?
(4 marks)
(d)
It is suspected that the error variance is of the form  i2  exp  1   2 educi  . Explain
how you would transform the model (3.1) to eliminate heteroskedasticity.
(5 marks)
Page 7 of 13
ETF2100/5910 Introductory Econometrics
Table 4.1
Dependent Variable: RESID^2
Method: Least Squares
Sample: 1 1000
Included observations: 1000
Variable
Coefficient Std. Error
C
EDUC^2
EDUC*EXPER
EDUC*EXPER^2
EDUC*NONWHITE
EDUC
EXPER^2
EXPER*EXPER^2
EXPER*NONWHITE
EXPER
EXPER^2^2
EXPER^2*NONWHITE
NONWHITE^2
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
F-statistic
Prob(F-statistic)
Question 5
-0.052723
-1.54E-05
0.000766
-3.47E-05
-0.042066
0.012566
0.000786
-1.96E-05
-0.016997
-0.004562
2.46E-07
0.000546
0.593341
0.057122
0.045659
0.308050
93.66118
4.982950
0.000000
0.254518
0.000932
0.001373
3.20E-05
0.016936
0.029253
0.001172
4.06E-05
0.010668
0.020703
4.56E-07
0.000249
0.236883
t-Statistic
Prob.
-0.207149
-0.016539
0.557759
-1.084679
-2.483919
0.429558
0.670458
-0.482367
-1.593363
-0.220331
0.539490
2.190291
2.504782
0.8359
0.9868
0.5771
0.2783
0.0132
0.6676
0.5027
0.6297
0.1114
0.8257
0.5897
0.0287
0.0124
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Durbin-Watson stat
0.211288
0.315333
0.495806
0.559606
1.044917
(18 marks)
Figure 5.1 below plots the amount of ice cream consumption in litres over time. There are 30
monthly observations spanning from March 2010 to August 2012.
Figure 5.1
.56
.52
.48
icecr
.44
.40
.36
.32
.28
.24
0
4
8
12
16
20
24
28
32
time
(a)
Comment on the features of the data. What does the graph suggest to you? (3 marks)
Page 8 of 13
ETF2100/5910 Introductory Econometrics
(b)
Consider the following model that explains ice cream consumption.
icecrt  1  2 pricet  3incomet  4tempt  et
(5.1)
where
icecr
price
income
temp
= monthly consumption of ice cream per head (in litres)
= price of ice cream (per litre)
= average family income per week (in dollars)
= average temperature (in Celsius)
Equation (5.1) was estimated by least squares and the EViews output is in Table 5.1
below.
Table 5.1
Dependent Variable: ICECR
Method: Least Squares
Sample: 1 30
Included observations: 30
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
PRICE
INCOME
TEMP
0.307985
-1.044414
0.003308
0.006225
0.265778
0.834357
0.001171
0.000802
1.158806
-1.251759
2.823722
7.762213
0.2571
0.2218
0.0090
0.0000
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
F-statistic
Prob(F-statistic)
0.718994
0.686570
0.036833
0.035273
22.17489
0.000000
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Durbin-Watson stat
0.359433
0.065791
-3.641296
-3.454469
1.021170
Briefly interpret the estimated coefficients for price and temp and comment on their
statistical significance.
(2 marks)
(c)
What assumption is violated when the errors are serially correlated? What are the
effects of this violation on the least squares estimators?
(5 marks)
(d)
The following EViews output (Table 5.2) is obtained from a Lagrange Multiplier (LM)
test for first order serial correlation applied to equation (5.1). Use the LM test at the 5%
significance level to test for a first order autoregressive error. Make sure to specify the
null and alternative hypotheses and the test statistic.
(3 marks)
Table 5.2
Breusch-Godfrey Serial Correlation LM Test:
F-statistic
Obs*R-squared
4.111588
4.237064
Prob. F(1,25)
Prob. Chi-Square(1)
0.0534
0.0396
Page 9 of 13
ETF2100/5910 Introductory Econometrics
(e)
The model was re-estimated assuming the existence of AR(1) errors. The EViews
output is in Table 5.3 below.
(5 marks)
Table 5.3
Dependent Variable: ICECR
Method: Least Squares
Sample (adjusted): 2 30
Included observations: 29 after adjustments
Convergence achieved after 17 iterations
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
PRICE
INCOME
TEMP
AR(1)
0.271011
-0.892396
0.003203
0.006405
0.400940
0.292444
0.829537
0.001599
0.001105
0.207975
0.926712
-1.075775
2.002716
5.797086
1.927830
0.3633
0.2927
0.0566
0.0000
0.0658
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
F-statistic
Prob(F-statistic)
Inverted AR Roots
0.796047
0.762055
0.032565
0.025452
23.41860
0.000000
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Durbin-Watson stat
0.358517
0.066760
-3.855556
-3.619815
1.548859
.40
Table 5.4 below contains information on the data for ice cream consumption, the
corresponding prices, income and average temperature for August, September and
October, 2012. Forecast the ice cream consumption for September and October, 2012.
Table 5.4
2012
icecr
price
income
temp
0.55
0.26
90
18
September
0.28
95
21
October
0.27
91
24
August
END OF PAPER
ETF2100/5910 Introductory Econometrics
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ETF2100/5910 Introductory Econometrics
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ETF2100/5910 Introductory Econometrics
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ETF2100/5910 Introductory Econometrics
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