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考试助攻:Subject of Economics Degree of MSc Resit Degree Exam Basic Econometrics, ECON5002

2018-08-09 08:00 星期四 所属: 考试助攻 浏览:936

 

Subject of Economics

Degree of MSc Resit Degree Exam

Basic Econometrics, ECON5002

Wednesday, 02 August 2017,14:30 – 16:30

 考试助攻,天才写手

Instructions to students:

· No candidate will be permitted to leave within the first hour or the last half hour of this exam.

· Both entry and exit to the examination hall shall be at the absolute discretion of the invigilator.

· Students should answer ONE question from Section A and ONE question from Section B.

 

Materials supplied:

· Tables: Table D.2 – Percentage Points of t Distribution on Final Page

 

Materials allowed:

· Calculators:

 

o You may use Business School approved models only: Casio FX-83GT/Casio-83GT+, Casio FX-85GT/Casio FX-85GT+, Sharp EL531WH, Aurora AX-582BL.

 

· Students are entitled to use a single A4 double-sided sheet of pre-written notes

 

Using exam answer sheets

· Always use a black pen.

· Complete personal information on all white sheets supplied before the exam begins.

· Write your answer to each question on a SEPARATE white answer sheet, using BOTH sides if required. For this exam, the required number of white answer sheets is 2.

· Request yellow continuation sheets to continue an answer if one white sheet is not enough.

· Use the standard character set, printed below, when hand writing in data boxes. E.g. Student ID, Date of Birth, Question Number. Keep your characters inside the boxes.

· You must return all white answer sheets to the invigilator even if you have not attempted all questions.

 

This page has been left blank for student notes – anything written here will not be marked.

 

Section A

 

You must answer one question from this section.

You must use ONE WHITE answer sheet per question. To provide an answer that exceeds the space on the answer sheet, please raise your hand to request a YELLOW answer sheet.

 

1. Consider the simple regression with a constant

Yi = α + βXi + ui, i = 1, . . . , n. (1)

1.1. Verify the following numerical properties for the OLS estimator:

image.png

where  uˆi  = Yi  Yˆi Yˆi  = αˆ + βˆXi and  αˆ  and  βˆ denote  the OLS

estimators of α and β, respectively. [20%]

1.2. Set β = 0 in model (1), that is, consider the model

Yi = α + ui, i = 1, . . . , n. (2)

Assume that ui i.i.d.(0, σ2), that is, the errors ui are independent and identically distributed across i, with mean zero and variance σ2.

Show that the OLS estimator of α, αˆ, is equal to Y¯  = n1 Σn Yi

and the variance of αˆ is σ2/n. [20%]

1.3. Verify which of the numerical properties described in sub-question

1.1.  hold for the OLS estimator of model (2). [10%]

 

2. Let F (FEMALE) be a variable which takes the value “0” for male and “1” for female. Similarly, the variable M (MALE) takes on the value “1” for male and “0” for female. Y denotes the Earnings.

For a given parameter θ, let θˆ denote its OLS estimator.

2.1. Derive the OLS estimators of αF and αM for the regression model

Yi = αF Fi + αM Mi + ui, i = 1, . . . , n (3) Show that αˆF  = Y¯F , the average of the Yi’s only for females, and

αˆM = Y¯M , the average of the Yi’s only for males. [20%]

 

                                                                                                                                                    Continued overleaf

2.2. Consider the regression

Yi = α + βFi + ui, i = 1, . . . , n. (4) Substitute M  =  1 F  in (3) and show that α  =  αM  and β   =

αF  αM . [10%]

2.3. Derive the OLS estimators of α and β for model (4). Show that αˆ = αˆM  and βˆ = αˆF     αˆM , where αˆF  and αˆM  have been derived in sub-question 2.1. [20%]

 

 

 

 

Section B

 

You must answer one question from this section.

You must use ONE WHITE answer sheet per question. To provide an answer that exceeds the space on the answer sheet, please raise your hand to request a YELLOW answer sheet.

 

3. Consider the following wage-determination equation for the British econ- omy for the period 1950-1969:

 

Wt = 8.582 + 0.364 P Ft + 0.004 P Ft−1 2.560 Ut

(1.129) (0.080) (0.072) (0.658)

(5)

where

 

W= wages and salaries per employee. PF= prices of final output at factor cost.

U= unemployment in Great Britain as a percentage of the total number of employees in Great Britain.

t= time, measured in years.

The figures in parenthesis are standard errors. The R2 of the regression is 0.873.

3.1. Interpret briefly the  preceding equation. [12.5%]

3.2. What is the rationale for the introduction of P Ft−1?. [12.5%]

 

 

                                                                                                Continued overleaf

3.3. Should the variable P Ft−1 be dropped from the model? Explain

your answer. [12.5%]

3.4. Suppose that you are asked to estimate the elasticity of wages and salaries per employee with respect to the price of final output. How would you modify the regression model (5) to accomplish your task? [12.5%]

 

4. Consider the Cobb-Douglas production function

Y  = β1Lβ2 Kβ3 (6)

where Y = output, L = labour input, and K = capital input.

Dividing equation (6) through by K, we get

(Y /K) = β1 (L/K)β2 Kβ2+β31 (7)

Taking the natural log of (7) and adding the error term, we obtain

ln (Y /K) = β0 + β2 ln (L/K) + (β2 + β3  1) ln (K) + u (8) where β0 = ln(β1).

4.1. Suppose you had data to run the regression (8). How would you test the hypothesis that there are constant returns to scale, that is, (β2 + β3) = 1? [17%]

4.2. If there are constant returns to scale, how would you interpret re- gression (8)? [16%]

4.3. Suppose we divide (6) by L rather than by K. Assuming constant returns to scale, how would you interpret this regression? [17%]

 

                                                                                                    END OF QUESTION PAPER

APPENDIX D: STATISTICAL TABLES 961

 

 

TABLE D.2 PERCENTAGE POINTS OF THE t DISTRIBUTION

image.pngExample

Pr (t > 2.086) = 0.025

Pr (t > 1.725) = 0.05 for df = 20

Pr (|t | > 1.725) = 0.10

t

0 1.725

 

Pr

df

0.25

0.50

0.10

0.20

0.05

0.10

0.025

0.05

0.01

0.02

0.005

0.010

0.001

0.002

1

1.000

3.078

6.314

12.706

31.821

63.657

318.31

2

0.816

1.886

2.920

4.303

6.965

9.925

22.327

3

0.765

1.638

2.353

3.182

4.541

5.841

10.214

4

0.741

1.533

2.132

2.776

3.747

4.604

7.173

5

0.727

1.476

2.015

2.571

3.365

4.032

5.893

6

0.718

1.440

1.943

2.447

3.143

3.707

5.208

7

0.711

1.415

1.895

2.365

2.998

3.499

4.785

8

0.706

1.397

1.860

2.306

2.896

3.355

4.501

9

0.703

1.383

1.833

2.262

2.821

3.250

4.297

10

0.700

1.372

1.812

2.228

2.764

3.169

4.144

11

0.697

1.363

1.796

2.201

2.718

3.106

4.025

12

0.695

1.356

1.782

2.179

2.681

3.055

3.930

13

0.694

1.350

1.771

2.160

2.650

3.012

3.852

14

0.692

1.345

1.761

2.145

2.624

2.977

3.787

15

0.691

1.341

1.753

2.131

2.602

2.947

3.733

16

0.690

1.337

1.746

2.120

2.583

2.921

3.686

17

0.689

1.333

1.740

2.110

2.567

2.898

3.646

18

0.688

1.330

1.734

2.101

2.552

2.878

3.610

19

0.688

1.328

1.729

2.093

2.539

2.861

3.579

20

0.687

1.325

1.725

2.086

2.528

2.845

3.552

21

0.686

1.323

1.721

2.080

2.518

2.831

3.527

22

0.686

1.321

1.717

2.074

2.508

2.819

3.505

23

0.685

1.319

1.714

2.069

2.500

2.807

3.485

24

0.685

1.318

1.711

2.064

2.492

2.797

3.467

25

0.684

1.316

1.708

2.060

2.485

2.787

3.450

26

0.684

1.315

1.706

2.056

2.479

2.779

3.435

27

0.684

1.314

1.703

2.052

2.473

2.771

3.421

28

0.683

1.313

1.701

2.048

2.467

2.763

3.408

29

0.683

1.311

1.699

2.045

2.462

2.756

3.396

30

0.683

1.310

1.697

2.042

2.457

2.750

3.385

40

0.681

1.303

1.684

2.021

2.423

2.704

3.307

60

0.679

1.296

1.671

2.000

2.390

2.660

3.232

120

0.677

1.289

1.658

1.980

2.358

2.617

3.160

0.674

1.282

1.645

1.960

2.326

2.576

3.090

Note: The smaller probability shown at the head of each column is the area in one tail; the larger probability is the area in both tails.

Source: From E. S. Pearson and H. O. Hartley, eds., Biometrika Tables for Statisticians, vol. 1, 3d ed., table 12, Cambridge University Press, New York, 1966. Reproduced by permission of the editors and trustees of Biometrika.

Before your exam answers are collected:

 

Please ensure that you have written the course code (on the front of this exam paper), your student ID, date of birth and the number of the question that you have attempted on each answer sheet.

 

Put your exam answers in the order of the question number, ensuring that yellow answer sheets follow the appropriate white answer sheet.

 

Do not place any other exam materials, including the exam paper, beside the A3 answer sheets.

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