AEM702S- APPLIED ECONOMETRICS - JAN 2020pdf :: NUST past examination papers between 2020 and 2024

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AEM702S- APPLIED ECONOMETRICS - JAN 2020pdf

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NAMIBIA UNIVERSITY

OF SCIENCE AND TECHNOLOGY

FACULTY OF HEALTH AND APPLIED SCIENCES

DEPARTMENT OF MATHEMATICS AND STATISTICS

QUALIFICATION: BACHELOR OF SCIENCE IN APPLIED MATHEMATICS AND STATISTICS

QUALIFICATION CODE: 07BAMS

NQF LEVEL: 7

COURSE NAME: APPLIED ECONOMETRICS

MODELLING

SESSION: JANUARY 2020

DURATION: 3 HOURS

COURSE CODE: AEM702S

PAPER: THEORY

MARKS: 100

SECOND OPPORTUNITY/SUPPLEMENTARY EXAMINATION

EXAMINER Mr SP KASHIHALWA

MODERATOR; | PROF P. NJUHO

INSTRUCTIONS

Answer ALL the questions in the booklet provided.

2. Show clearly all the steps used in the calculations.

All written work must be done in blue or black ink and sketches must

be done in pencil.

4. You may not start to read the questions printed on the subsequent

pages of this question paper until instructed that you may do so by

the invigilator

PERMISSIBLE MATERIALS

1. Non-programmable calculator without a cover.

2. Attached statistical tables (t-table, d-table and F-table).

THIS QUESTION PAPER CONSISTS OF 4 PAGES (Including this front page) and 3 attachments.

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QUESTION 1 [20 MARKS]

1.1 Explain the following terminologies as they are applied in Econometrics

1.1.1 Classical econometrics

[2]

1.1.2 Autocorrelation

[2]

1.1.3 Autoregressive model

[2]

1.1.4 Indirect Least Square

[2]

1.1.5 Reduced form equation

[2]

1.2 Suppose the Lorenzo curve is given by the following function:

L(x) = In(« + 1)

Compute the Gini-Coefficient

[10]

QUESTION 2 [28 MARKS]

An econometrician used a multi variable regression model: Y = By + Bi INF + B2CO +

B3i + ByPMIm + BsPMIs + u4;, to predict the GDP growth rate in Namibia using key

macroeconomic indicators such as inflation

(INF), Crude Oil(CO), interest rate(i), Manufacturing (PMIm)and Services (PMIs).

The E-VIEWS output is given below.

Variable

Coefficient |

Inflation

-0.57278

Crude oil

0.02914

Interest rate

0.42451

PMI Manufacturing | -0.57157

PMI Services

0.07338

Intercept

31.35076

Std.error

0.099731

0.478308

0.80499

0.20544

0.08669

12641.63

t-statistics

R-square

0.988909

0.498544

2.1

Find the t-values for the model

[3]

2.2 Suppose the output above is for a linear-log model, interpret the coefficient for crude oil

[2]

2.3 Interpret the R-square

[2]

2.4 Investigate if the indicator crude oil is significant at 5% level

[4]

2.5 Suppose we suspect the presence of autocorrelation in the above model

2.5.1 What could be the cause of autocorrelation

[4]

2.5.2 State the important assumptions underlying the DW statistic

[5]

2.5.3 Validate or invalidate the statement in 2.5(assuming n = 15)

[6]

2.5.4 If the statement in 2.5 is true, what will you do

[2]

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QUESTION 3 [18 MARKS]

3.1 An econometrician wants to estimate the effect of FDI(X) on GDP(Y) using the following

model 1: ¥ = By + BoX + uj.

3.1.1 Find the elasticity of the model

[4]

3.2 Suppose the researcher uses the following model 2 given below, instead of the above

model 1.

Y = ay + 2X1 + 3X2 + Up;

3.2.1 Identify the specification error in model 2 if model 1 is the truth model.

3.2.2 State the consequences of the specification error identified in 3.2.1.

[4]

3.2.3 Find the w2;, in model 2.

[2]

3.2.4 If the variance of uz; in model 2 is variable. What will be the consequences?

[6]

QUESTION 4 [34 MARKS]

4.1

The Keynesian model of income determination can be summarized by two simple

mathematical equations:

National Income identity: ¥, = C,; + I;

Consumption function: C; = Bo + BiY, tu, ; O< fy <1,

where Y; is income, C, is consumption, and /, is private investment.

4.1.1 Derive the reduced form equation for income.

[3]

4.1.2 Derive the reduced form equation for consumption.

[3]

4.1.3 Explain why government should pass policies that discourage C;.

[2]

4.1.4 Briefly describe the features of 2SLS.

[5]

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4.2

Regression of per capita personal expenditure (PPCE) on per capita disposable income

(PPDI) and lagged PPCE gave the following results:

PPCE, = —1242.169 + 0.6033PPDI, + 0.4106PPCE;_;

se = (402.5784) (0.15021)

(0.1546)

d=1.0056 ,durbin h=5.119

|f we assume that this model resulted from a Koyck-type transformation

4.2.1 Find the Koyck model: median lag.

[3]

4.2.2 Find the Koyck model: mean lag.

[3]

4.2.3. Name the features of the Koyck transformation.

[4]

4.2.4 Explain why d statistic may not be used to detect a (first-order) serial correlation in

autoregressive models.

[2]

4.3 If we assume that this model resulted from Almon-type transformation

4.3.1 Estimate the original coefficient of PPD and PPCE,.

[4]

4.3.2 Name and define the method used to estimate the Koyck and adaptive

expectations models consistently.

[3]

4.3.3. Name any 2 practical problems we must resolve, before we apply the Almon

technique.

[2]

END

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t Table

cum. prob

one-tail

two-tails

100

1000

t 50

0.50

1.00

0.000

t 75

0.25

0.50

1.000

0.816

0.765

0.741

0.727

0.718

0.711

0.706

0.703

0.700

0.697

0.695

0.694

0.692

0.691

0.690

0.689

0.688

0.687

0.686

0.685

0.684

0.683

0.681

0.679

0.678

0.677

0.675

0.674

50%

t 80

0.20

0.40

1.376

1.061

0.978

0.941

0.920

0.906

0.896

0.889

0.883

0.879

0.876

0.873

0.870

0.868

0.866

0.865

0.863

0.862

0.861

0.860

0.859

0.858

0.857

0.856

0.855

0.854

0.851

0.848

0.846

0.845

0.842

60%

t gs

0.15

0.30

1.963

1.386

1.250

1.190

1.156

1.134

1.119

1.108

1.100

1.093

1.088

1.083

1.079

1.076

1.074

1.071

1.069

1.067

1.066

1.064

1.063

1.061

1.060

1.059

1.058

1.057

1.056

1.055

1.050

1.045

1.043

1.042

1.037

1.036

70%

t 90

0.10

t 95

0.05

t 975

0.025

0.20

0.10

0.05

3.078

1.886

1.638

1.533

1.476

1.440

1.415

1.397

1.383

1.372

1.363

1.356

1.350

1.345

1.341

1.337

1.333

1.330

1.328

1.325

1.323

1.321

1.319

1.318

1.316

4.315

1.314

1.313

1.311

1.310

1.303

1.296

1.292

1.290

1.282

6.314

2.920

2.353

2.132

2.015

1.943

1.895

1.860

1.833

1.812

1.796

1.782

1.771

1.761

1.753

1.746

1.740

1.734

1.729

1.725

1.721

1.717

1.714

1.711

1.708

1.706

1.703

1.701

1.699

1.697

1.684

1.671

1.664

1.660

1.646

12.71

4.303

3.182

2.776

2.571

2.447

2.365

2.306

2.262

2.228

2.201

2.179

2.160

2.145

2.131

2.120

2.110

2.101

2.093

2.086

2.080

2.074

2.069

2.064

2.060

2.056

2.052

2.048

2.045

2.042

2.021

2.000

1.990

1.984

1.962

1.282

80%

1.645

90%

1.960

95%

Confidence Level

t 99

0.01

0.02

31.82

6.965

4.541

3.747

3.365

3.143

2.998

2.896

2.821

2.764

2.718

2.681

2.650

2.624

2.602

2.583

2.567

2.552

2.539

2.528

2.518

2.508

2.500

2.492

2.485

2.479

2.473

2.467

2.462

2.457

2.423

2.390

2.374

2.364

2.330

2.326

98%

t 995

0.005

0.01

t o99

0.001

0.002

t 9995

0.0005

0.001

63.66

9.925

5.841

4.604

4.032

3.707

3.499

3.355

3.250

3.169

3.106

3.055

3.012

2.977

2.947

2.921

2.898

2.878

2.861

2.845

2.831

2.819

2.807

2.797

2.787

2.779

2.771

2.763

2.756

2.750

2.704

2.660

2.639

2.626

2.581

2.576

99%

318.31

22.327

10.215

7.173

5.893

5.208

4.785

4.501

4.297

4.144

4.025

3.930

3.852

3.787

3.733

3.686

3.646

3.610

3.579

3.552

3.527

3.505

3.485

3.467

3.450

3.435

3.421

3.408

3.396

3.385

3.307

3.232

3.195

3.174

3.098

3.090

99.8%

636.62

31.599

12.924

8.610

6.869

5.959

5.408

5.041

4.781

4.587

4.437

4.318

4.221

4.140

4.073

4.015

3.965

3.922

3.883

3.850

3.819

3.792

3.768

3.745

3.725

3.707

3.690

3.674

3.659

3.646

3.551

3.460

3.416

3.390

3.300

3.291

99.9%

t-table.xls 7/14/2007

6 Page 6

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T-14

Tables

.100

3.46

3.11

.050

5.32

4.46

.025

7.57

6.06

.010

11.26

8.65

.001

25.41

18.49

.100

.050

.025

.010

.001

.100

.050

.025

.010

001

3.36

5.12

7.21

10.56

22.86

3.29

4.96

6.94

10.04

21.04

3.01

4.26

5.71

8.02

16.39

2.92

4.10

5.46

7.56

14.91

.100

3.23

2.86

.050

4.84

3.98

.025

6.72

5.26

.010

9.65

7.21

.001

19.69

13.81

-100

3.18

2.81

.050

4.75

3.89

.025

6:55

5.10

‘a

-010

9.33

6.93

.001

18.64

12.97

.100

-050

.025

.010

.001

.100

.050

.025

.010

.001

3.14

4.67

6.41

9.07

17.82

3.10

4.60

6.30

8.86

17.14

2.76

3.81

4.97

6.70

12.31

2.73

3.74

4.86

6.51

11.78

.100

-050

-025

.010

001

3.07

4.54

6.20

8.68

16.59

2.70

3.68

4.77

6.36

11.34

.100

.050

.025

.010

.001

3.05

4.49

6.12

8.53

16.12

2.67

3.63

4.69

6.23

10.97

.100

.050

.025

.010

.001

3.03

4.45

6.04

8.40

15.72

2.64

3.59

4.62

6.11

10.66

Degrees of freedom in the numerator

2.92

4.07

5.42

7.59

15.83

2.81

3.86

5.08

6.99

13.90

2.73

3.71

4.83

6.55

12.55

2.66

3.59

4.63

6.22

11.56

2.61

3.49

4.47

5.95

10.80

2.56

3.41

4.35

5.74

10.21

2.52

3.34

4.24

5.56

9.73

2.49

3.29

4.15

5.42

9.34

2.46

3.24

4.08

5.29

9.01

2.44

3.20

4.01

5.19

8.73

2.81

3.84

5.05

7.01

14.39

2.69

3.63

4.72

6.42

12.56

2.61

3.48

4.47

5.99

11.28

2.54

3.36

4.28

5.67

10.35

2.48

3.26

4.12

5.41

9.63

2.43

3.18

4.00

5.21

9.07

2.39

3.11

3.89

5.04

8.62

2.36

3.06

3.80

4.89

8.25

2.33

3.01

3.73

4.77

7.94

2.31

2.96

3.66

4.67

7.68

2.73

3.69

4.82

6.63

13.48

2.61

3.48

4.48

6.06

11.71

2.52

3.33

4.24

5.64

10.48

2.45

3.20

4.04

5.32

9.58

2.39

315

3.89

5.06

8.89

2.35

3.03

3.77

4.86

8.35

2.31

2.96

3.66

4.69

7.92

2.27

2.90

3.58

4.56

7.57

2.24

2.85

3.50

4.44

7.27

2.22

2.81

3.44

4.34

7.02

2.67

3.58

4.65

6.37

12.86

2.55

3.37

4.32

5.80

11.13

2.46

3:22

4.07

5.39

9.93

2.39

3.09

3.88

5.07

9.05

2.33

3.00

3.73

4.82

8.38

2.28

2.92

3.60

4.62

7.86

2.24

2.85

3.50

4.46

7.44

2.21

2.79

3.41

4.32

7.09

2.18

2.74

3.34

4.20

6.80

2.15

2.70

3.28

4.10

6.56

2.62

3.50

4.53

6.18

12.40

2.51

3.29

4.20

5.61

10.70

2.41

3.14

3.95

5.20

9.52

2.34

3.01

3.76

4.89

8.66

2.28

2.91

3.61

4.64

8.00

2.23

2.83

3.48

4.44

7.49

2.19

2.76

3.38

4.28

7.08

2.16

2.71

3.29

4.14

6.74

2.13

2.66

3.22

4.03

6.46

2.10

2.61

3.16

3.93

6.22

2.59

3.44

4.43

6.03

12.05

2.47

3.23

4.10

5.47

10.37

2.38

3.07

3.85

5.06

9.20

2.30

2.95

3.66

4.74

8.35

2.24

2.85

3.51

4.50

7.71

2.20

2.77

3.39

4.30

7.21

2.15

2.70

3.29

4.14

6.80

2.12

2.64

3.20

4.00

6.47

2.09

2,59

3.12

3.89

6.19

2.06

2.55

3.06

3.79

5.96

2.56

3.39

4.36

5.91

11.77

2.44

3.18

4.03

5.35

10.11

2.35

3.02

3.78

4.94

8.96

2.27

2.90

3.59

4.63

8.12

2.21

2.80

3.44

4.39

7.48

2.16

2.71

3.31

4.19

6.98

2.12

2.65

3.21

4.03

6.58

2.09

2.59

3.12

3.89

6.26

2.06

2.54

3.05

3.78

5.98

2.03

2.49

2.98

3.68

5.75

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