 |
AEM810S- APPLIED ECONOMETRICS- 1ST OPP- JUNE 2023 |
|
|
1 Page 1 |
▲back to top |
n Am I BI A u n IVE RS ITY
OF SCIEnCE Ano TECHnOLOGY
FACULTY OF COMMERCE, HUMAN SCIENCES AND EDUCATION
DEPARTMENT OF ECONOMICS, ACCOUNTING AND FINANCE
QUALIFICATION:
BACHELOR OF ECONOMICS HONOURS DEGREE
QUALIFICATION CODE: 08HECO LEVEL:
8
COURSE CODE: AEM810S
COURSE NAME: APPLIED ECONOMETRICS
SESSION:
JUNE 2023
DURATION:
3 HOURS
MARKS:
100
FIRST OPPORTUNITY QUESTION PAPER
EXAMINER($) Prof. Tafirenyika Sunde
MODERATOR: Dr. Reinhold Kamati
INSTRUCTIONS
1. Answer ALL the questions.
2. Write clearly and neatly.
3. Number the answers clearly.
PERMISSIBLE MATERIALS
1. Ruler
2. Calculator
THIS QUESTION PAPER CONSISTS OF 4 PAGES
1
|
|
2 Page 2 |
▲back to top |
QUESTION 1 [20 MARKS]
a) What is the difference between time-series and cross-sectional data?[5]
b) Explain the purpose of the following diagnostic tests and state their hypotheses
and decision rules.
i. Normality
[2]
ii. Autocorrelation
[2]
iii. Heteroscedasticity
[2]
iv. Ramsey RESET
[2]
V. CUSUM
[2]
c) Given the following unrestricted OLS regression equation
Ye = B0 + B1X1t + B2Xu + B3X3 c + B4 X4 c + B5X5c + et
i. State the hypothesis and decision rule used to test whether X2, X3 and X4
are redundant variables.
[4]
ii. If the explanatory variables in question c) i. are redundant, how would
the adjusted coefficient of determination be affected?
[1]
QUESTION 2 [20 MARKS]
a) What properties of time series data would make Ordinary Least Squares (OLS)
results spurious?
[4]
b) State the characteristics of the spurious OLS regression equation. [4]
c) Why should one conduct the unit-roots tests?
[4]
d) State the Augmented Dickey-Fuller (ADF) equations used to test for unit roots.
[4]
e) Compare and contrast the Dickey-Fuller and the Augmented Dickey-Fuller tests
for unit roots
[4]
QUESTION 3 [20 MARKS]
a) Under what circumstances do you use the ARDL econometrics method?
b) Given Gross Domestic Product (Y), Capital (K) and Labour (L) variables, where
Y is the dependent variable, and K and L are independent variables, answer
the following questions:
i. Write the ARDL equation for the three variables.
[4]
2
|
|
3 Page 3 |
▲back to top |
ii. How do you test for cointegration using the above equation in b) i.? State
the hypothesis and decision rule.
[4]
iii. If cointegration is confirmed, state the ARDL-ECM for these three
variables.
[4]
iv. Write down the short-run and long-run parameters in the ARDL-ECM
equation.
[4]
v. Explain the importance of the coefficient of the error correction term in
the ARDL-ECM model.
[4]
QUESTION 4 (20 marks)
The results below relate to the model, which has GDP per capita (GDPC) as the dependent
variable and capital (CAPITAL), Government Consumption Expenditure (GCE), exports
(EXPORT) and imports (IMPORT) as the independent variables. Use the information to:
a) Interpret the bounds test results in Table 1.
[4]
b) Interpret the significance of the short-run coefficients.
[4]
c) Interpret the meaning of the long-run coefficient results.
[4]
d) Interpret the diagnostic tests shown (note that the probability values are in brackets).
[4]
e) Given the results in (d) above, what is your overall conclusion about the robustness of
the estimated model?
[4]
Table 1: Bounds Test
F-statistic
Asymptotic
10%
5%
1%
Source: Authors' compilation
10bound
2.260
2.620
3.410
Model 1
8.6670
11 bound
3.350
3.790
4.680
3
|
|
4 Page 4 |
▲back to top |
Table 2: Model 1 ARDL Error Correction Results
De~endent Variable: ~GDPC)
Variable
Coefficient
~GDPPCt-i
0.718561
~CAPITAL
0.023534
~CAPITALt-l
0.023481
~GCE
0.098649
~GCEt-l
0.064403
~EXPORT
0.193348
~EXPORTt-i
0.170057
~IMPORT
-0.107918
~IMPORTt-i
-0.089017
ECTt-l
-0.092793
R-squared
Adjusted R-squared
x2 Serial
x2 ARCH
x2 Normal
x2 RESET
Std. Error t-Statistic Prob.
0.109843 6.541717 0.0000
0.007184 3.275855 0.0021
0.007666 3.063024 0.0038
0.040458 2.438287 0.0190
0.041016 1.570206 0.1237
0.052318 3.695652 0.0006
0.049054 3.466700 0.0012
0.039872 -2.706626 0.0097
0.041593 -2.140167 0.0381
0.018807 -4.933906 0.0000
0.779004
0.707051
0.345567 (0.7686)
0.359706 (0.5526)
0.364725 (0.8333)
0.609020 (0.4443)
Source: Authors' compilation
QUESTION 5 [20 marks]
(a) What is the difference between a static and a dynamic model?
[2]
(b) State an AR(2) model using the variable GDP.
[2]
(c) State a distributed lag model (OLM) using variable GDPas the dependent
varible and PCE as the independent variable.
[2]
(d) State the Auto Regressive Distributed Lag Model (ARDL) using the variable
GDP and gross fixed capital formation (GFCF), where GDP is the dependent
variable.
[4]
(e) Given the following estimated ARDL equation where GDP is gross domestic
product, PCE is personal consumption expenditure, and POI is personal
disposable income.
GDPt = 50 + 0.5GDPt-i + 0.4PCEt + 0.2PCEt-i + 0.2PDlt + 0.lPDlt
i. What are the instantaneous impact multipliers associated with PCE
and POI?
[2]
ii. What are the cumulative short-run multipliers of PCE and POI after one
period?
[2]
iii. Determine the long-run multipliers with respect to PCE and POI.
[6]
4