Exercises

For

Principles of Econometrics, Fourth Edition

R. CARTER HILL

Louisiana State University

WILLIAM E. GRIFFITHS

University of Melbourne

GUAY C. LIM

University of Melbourne

JOHN WILEY & SONS, INC

New York / Chichester / Weinheim / Brisbane / Singapore / Toronto

CONTENTS

Answers for Selected Exercises in:

Probability Primer

1

Chapter 2

The Simple Linear Regression Model

3

Chapter 3

Interval Estimation and Hypothesis Testing

12

Chapter 4

Prediction, Goodness of Fit and Modeling Issues

16

Chapter 5

The Multiple Regression Model

22

Chapter 6

Further Inference in the Multiple Regression Model

29

Chapter 7

Using Indicator Variables

36

Chapter 8

Heteroskedasticity

44

Chapter 9

Regression with Time Series Data: Stationary Variables

51

Chapter 10

Random Regressors and Moment Based Estimation

58

Chapter 11

Simultaneous Equations Models

60

Chapter 15

Panel Data Models

64

Chapter 16

Qualitative and Limited Dependent Variable Models

66

Appendix A

Mathematical Tools

69

Appendix B

Probability Concepts

72

Appendix C

Review of Statistical Inference

76

29 August, 2011

PROBABILITY PRIMER

Exercise Answers

EXERCISE P.1

(a)

X is a random variable because attendance is not known prior to the outdoor concert.

(b)

1100

(c)

3500

(d)

6,000,000

EXERCISE P.3

0.0478

EXERCISE P.5

(a)

0.5.

(b)

0.25

EXERCISE P.7

(a)

f (c )

0.15

0.40

0.45

(b)

1.3

(c)

0.51

(d)

f (0,0) 0.05 f C (0) f B (0) 0.15 0.15 0.0225

1

Probability Primer, Exercise Answers, Principles of Econometrics, 4e (e)

A

5000

6000

7000

(f)

f (a)

0.15

0.50

0.35

1.0

EXERCISE P.11

(a)

0.0289

(b)

0.3176

(c)

0.8658

(d)

0.444

(e)

1.319

EXERCISE P.13

(a)

0.1056

(b)

0.0062

(c)

(a) 0.1587 (b) 0.1265

EXERCISE P.15

(a)

9

(b)

1.5

(c)

0

(d)

109

(e)

−66

(f)

−0.6055

EXERCISE P.17

(a)

4a b( x1 x2 x3 x4 )

(b)

14

(c)

34

(d)

f (4) f (5) f (6)

(e)

f (0, y ) f (1, y ) f (2, y )

(f)

36

2

2

CHAPTER

Exercise Answers

EXERCISE 2.3

(a)

The line drawn for part (a) will depend on each student’s subjective choice about the position of the line. For this reason, it has been omitted.

(b)

b2 1.514286

b1 10.8

2

4

6

8

10

Figure xr2.3 Observations and fitted line

1

2

3

4

5

6

x

y

(c)

Fitted values

y 5.5

x 3.5

ˆ

y 5.5

3

Chapter 2, Exercise Answers Principles of Econometrics, 4e

4

Exercise 2.3 (Continued)

(d)

ˆ

ei

0.714286

0.228571

−1.257143

0.257143

−1.228571

1.285714

ˆ

ei 0.

(e)

ˆ