Basic econometrics

The McGraw-Hill Series

Economics

ESSENTIAl s OI ECONOMK s

Brue. McConnell. and Flynn

Essentials oi Economỉcs

Second Edirìon

Mandcl

Economics: The Basics

First Edition

Schiỉỉer

Essentials út Economics

Seventh Edition

PRINCIPLES OF ECONOMICS

Colander

Econumics, Mĩcroeconomics,

and Macroeconomics

Seventh Edition

Frank and Bernanke

Principles oi Economics.

Principles of Microeconomics.

Principles of Macroeconomics

Fourth Edition

Frank and Bernanke

Brieí Rditions: Principles «f

Economics, Principles of

Microeconomics, Prìnciples of

ỈVIacroeconomics

First Edition

McConnelI, Brue. and Flynn

Economỉcs, Microeconomìcs,

and Macroeconomics

Eighteenth Edition

McConnell, Brue, and Klynn

Brỉef Kditiuns: Eeonomics.

Mỉcroeconomics,

ỈYlacroeconomics

First Edition

Miller

Fĩrst anEighteenth Schille ThEỉeventh Samuelso Econoir Econamics Principle de Macroeconomic Econoi r mEdition nsToday o, Edition anomfMicroeconomics Microeconomic daEdition Today yNordhau , ands,Thse Máicr ,soro

Slavin

Economics, Microeconomics,

and Macroeconomics

Ninth Edition

ECONOM1CS OF SOCIAL ISSUES

Guell

Issues in Economics Todav

Fourth Edition

Sharp. Regìster, and Grìmes

Economics of Social Issues

Eighteenth Eđition

ECONOMETRICS

Gujarati and Porter

Basic Econometrìcs

Fifth Editìon

Giýarati and Porter

Essentìals oi Econometrĩcs

Fourth Edition

MANAGER1AL ECONOMICS

Baye

Managerial Econoniĩcs and Business

Strategy

Sixth Edìtion

Brickley, Smith, and Zimmerman

Managerial Econumics and

Organizatĩonal Architecture

Fìfth Edition

Thomas and Maurìce

Managerial Economics

Ninth Edition

1NTRRMEDIATE ECONOMICS

Bernheim and Whinston

Mĩcroeconomics

First Edition

Dornbusch. Fischer, and Startz

Macrncconomics

ADVANCED ECONOMICS Seventh Fran ỊVIicroeconomic Rome AdTenth Third \ ance k r Edition Edition d Edition Macroeconomíc s and Behavios r

MONEY AND BANKING

Cecchetti

Money, Banking, and Financìal

Markets

Second Edition

URBAN ECONOMICS

OSuIlivan

Urban Economics

Seventh Eđition

LABOR ECONOMICS

Borjas

Labor Economics

Fourth Edition

McConnell. Brue. and Macpherson

Contempurarỵ Labor Economics

Eighth Edition

PUBLIC FINANCE

Rosen and Gayer

Public Kinance

Eighth Edition

Seidman

Public Pinance

First Edition

ENVIRONMENTAL ECONOMICS

Field and Field

Emironmenta) Economics:

An Introduction

Fifth Ediíion

INTERNATIONAL ECONOMICS

Appleyard, Reld, and Cobb

[nternatìonal Economics

Sixth Edition

Kĩng and King

Internatỉonal Kconomics.

Globalization, and Policv:A Reader

Fifth Editìon

Puge Fourteenth Inu-rnationa l l Economic Edition s

Số hóa bởi Trung tâm Học liệu – ĐH TN http://www.lrc-tnu.edu.vn

Basi c

Econometric s

Fifth Edition

Damodar N. Cujarati

Pro/ipssor ỉùmeritus of Hmnamùs.

I niteii Stíttes Militarv icaderny, \\c.st Point

Dawn c. Porter

t niversity of -So (lí/lí'7-/1 i'.fiỉifnrnia

Asian Network

for Higher Education

No.

Me

Grauu

Boston Burr Ridge. IL Dubuque. IA Madison. Wl New York San Francisco St Louis

Bangkok Bogota Caracas Kuala Lumpur Lisbon London Maơrid Mexico City

Milan Montreal Nfìw Delhi Santiago Seoul Singapore Sydney Taipei Toronto Số hóa bởi Trung tâm Học liệu – ĐH TN http://www.lrc-tnu.edu.vn

BASIC ECONOMbTRICS

[ntemational Edỉtion 2009

Exclusive righis hy McGrau-HiM Education (Asia), for manufacture and export. This book can nót be re￾exported from the couniry lo u hich í! is sold by McGraw-Hill. This International Edition is nót to be sold

or purehased in Ntirth America :ind con tai ns eonteni thát is differeni from iỉs North American version.

Publishcd by McGrau -Hill/Iru in. a business unit ót" The McGrav\ -Hin Companies. ì ne. 1221 Avenụe of the

Americas. Nêu- Ýork. NY 10020. Copyright © 2009. 2003. 1995. 1988. 1978 b> The McGraw-Hil1

Companies, Inc. AU rights reserved. No part of this publication may be reproduceđ or distributed in any

íbrm or by any means, orsiored in a daiabase or retrie\ ai system. without the prior written consent of The

McGrau -HiII Companĩes. Inc. including. bui nót lìmited lo. in an) network or other electronic storage or

transmìssion. or broađcasi for distance learning.

Some ancìHaries, including electronic and print components. ma) noi be avaĩlable to customers outside the

United States.

lo 09 08 07 06 05 04 03 02

20 09

CTF BJE

nhen ordering this title, liSI' ISBN: 978-007-127625-2 or Mím): 007-127625-4

Prỉntcd in Singapore

\\ \\ \\ .mhhe.com

Số hóa bởi Trung tâm Học liệu – ĐH TN http://www.lrc-tnu.edu.vn

t h e Author s

Damodar N. Gujarati

After teaching for more than 25 years át the City University of New York and 17 years in the

Department ofSocìal Sciences, u.s. Military Academy át West Point, New York, Dr. Gujarati

is currently Proĩessor Emeritus of economics átthe Academy. Dr. Giỹarati received his

M.Com. degree from the University of Bombay in 1960, his M.B.A. degree from the

University of Chicago in 1963, and his Ph.D. degree from the University of Chicago in 1965.

Dĩ. Gujarati has published extensively in recognized national and internationaljournals, such

as the Revievv ofEconomics and Statistics, the Economic Journaỉ, the Journaỉ ofFinancỉal

and Quantitatìve Anatysis. and the Joumal of Business. Dr. Giỳarati was a member of the

Board of Editors of the Joumal of Quantitaứve Economics, the otĩìcialjournal of the Indian

Econometric Society. Dr. Gujarati is also the author ofPensions and the New York City Fiscaỉ

Crisis (the American Enterprise Institute, 1978), Government and Business (McGraw-Hill,

1984), and Essentials of Econometrìcs (McGraw-Hill, 3d ed., 2006). Dr. Gujaratĩ's books

ôn econometrics have been translated into sevcral languages.

Dr. Guịarati was a Visiting Protessor át the University of Shcfficld, U.K.. (1970-1971), a

Visiting Fulbright Proícssor to India (1981-1982), a Visiting Professor in the School of

Management of the Natìonal University of Singapore {Ì 985-1986). and a Visiting Professor

of Econometrics, University of New South Wales, Australia (summer of 1988). Dr. Gujarati

has lectured extensively ôn micro- and macroeconomic topics in countries such as Australia,

China, Bangladesh. Germany, India, Israel. Mauritius, and the Republic of South Korea.

Dawn c. Porter

Dawn Porter has been an assỉstant professor in the lnformation and Opcrations Manage￾ment Department át the Marshall School of Business of the University of Southern

Caliíornia since the tai Ì of 2006. She currently teaches both introductory undergraduate

and MBA statistics in the business school. Prior to joining the faculty át usc, tròm

2001-2006. Dawn was an assistant protessor át the McDonough School of Business át

Georgetovvn University, and beforc thai was a visitĩng professor in the psychology depart￾mcnt át the Graduate School ofArts and Sciences át NYU. Át NYU she taught a number of

advanced statistical methods courses and was also an ĩnstructor át the Stern School of

Business. Her Ph.D. is (rom the Stẹrn School in Statistics.

Dawn's areas of research interest include categorical analysis, agreement measures,

multivariate modeling, and applications to the tìcld of psychology. Her current research ex￾amines online auction models from a statistieal perspective. She has presented her research

át the Joint Statistical Meetings, the Decision Sciences ỉnstitute meetings, the International

Ginni Conferenc aOutsid Sh(NYU Economic co-autho e hae)e Mae Medica so alsfse academìcs r an ô,o [ne n vvorke ndl lnformatio Essentìaìs NYUCenter . Toyd,. aDaw s an. Rs adn Un variou Systems statistica of has Corporation Business s bee s -eommerc ,ln severa consultan employe Sttttistics, , IBM l universitie edt an fo a. Cosmaire rsd man a statistic statistica 2nsy includin othe d,s lúc eđition semina rl mạịo consultan .g an th,dMcGraw-Hil er Ne seriescompanies Londo wt f Yor .n Daw r KPMG Schoo kl Universit , includin Irwin n ils, o alsInc ,f 2008 y og ..

Hi

Số hóa bởi Trung tâm Học liệu – ĐH TN http://www.lrc-tnu.edu.vn

For Joan Gujarati, Diane Gujarati-Chesnut,

Charles Chesnut, and my grandchildren,

"Tommy" and Laura Chesnut.

—DNG

For Judy, Lee, Brett, Bryan, Amy, and Autumn Porter.

Bin especially for mv adoring father, Terry.

—DCP

Số hóa bởi Trung tâm Học liệu – ĐH TN http://www.lrc-tnu.edu.vn

Brie f Content s

Preface xvỉ

Acknovvledgments xix

Introduction Ì

PART ONE

Single-Equation Regression Models 13

Ì The Nature of Regression Analysis

2 Two-Variable Regression Analysis:

Some Basic Iđeas

3 T\vo-Variab!e Regressíon Model: The

Problem of Estimation

4 Classical Normal Linear Regression

Model (CNLRM)

5 Two-Variable Regression: Interval

Estimation and Hypothesis Testing

6 L:\tensions of the Two-Variable

Linear Regression Model

7 Multiple Regression Analysis: The

Problem of Estimation

8 Multiple Regression Analysis: The

Problem of Inference

9 Dummy Variable Regression Models

PART TWO

Rclaxing the Assumptions

ót'the Classical Model 315

lo Multicollinearity: What Happens

li"the Regressors Are Correlatcd?

Ì Ì Heteroscedasticỉty: What Happens [f

thó Error Variance Is Nonconstant?

12 Autocorrelation: What Happens [f

tho Error Terms Are Correlated?

13 [ conometric Modeling: Model

Speciíìcation and Diagnostic Testing

PART THREE

Topics in Econometrics 523

14 Nonlinear Regression Models 525

15 Qualitative Response Regression

Models 541

16 Panel Data Regressíon Models 591

17 Dynamic Econometric Mođels:

Autoregressive and

Distributed-Lag Models 617

PART FOUR

Simultaneous-Equation Models and Time

Serĩes Econometrics 671

18 Simultaneous-Equation Models 673

19 The Identiíication Problem 689

20 Simultaneous-Equation Methods 711

21 Time Series Econometrics: Some

Basic Concepts 737

22 Time Series Econometrics:

Forecasting 773

APPENDICES

A A Review of Some

Statistical Concepts SOI

B Rudiments of Matrix Algebra 838

c

D

E

The Matrix Approach to

Linear Regression Model

Statistical Tables

Computer Output of EVievvs,

MINITAB. Excel. and STATA

Economic Data ôn the

World Wide Web

SELECTED BIBLIOGRAPHY 902

849

877

Số hóa bởi Trung tâm Học liệu – ĐH TN http://www.lrc-tnu.edu.vn

Content s

Preface xvi

Ackncmledgments xìx

Introduction Ì

1.1 \v hát Is Econometrics? Ì

1.2 Why a Separate Discipline? 2

1.3 Mcthodology of Econometrics 2

/. Statement ofTheory ót Hvpothesìs 3

2. Specification of the Mathematical Motiel

of Consumptỉon 3

.í. Specựication of the Econometrìc Model

of Consumption 4

4. Obtaining Da ta 5

5. Estimation of the Econometric Model 5

ứ. Hypothesis Testing 7

Forecasting or pređictìon 8

<S' Use oi'the Modeifor Controi

OI- Poiicy Purposes 9

(_ hoosing among Competing Models 9

1.4 Tvpcs ofEconometrics lo

1.5 Mathematĩcal and Statistical Prerequisites Ì Ì

1.6 The Role ofthe Computer Ì Ì

1.7 Suìiuestionsfor Further Readine 12

PART ONE

SINGLE-EQUATION REGRESSION

MODELS 13

CHAPTER ì

The Naturc ofRegression Analvsis 15

1-1 Hisiorĩcal Origin of the Term Regression 15

1.2 The Modern Interpretation of Regression 15

/\,I'IÌ/>ỈIS M

1.3 Suuisiical versus Dctcrministic

Relationships 19

1.4 kcLMVssitMi versus Causation Ì1

)

Ì .5 Rcmcssion versus Correlation 20 Ì1. .76 ] lerminolog \n;il hếỉli. e> • N.HLir p-s si, ì. ,ft Smm s 2 . ni} ót Iiac\ yc2 ạnathua c.\ <hd Notatio Source ni ni I22 Hít ì ! him sn út o 2f 25 Dati I i tbr Economic

Summary and Conclusions 28

Exercises 29

CHAPTER 2

Two-Variable Regression Analysis: Some

Basĩc Ideas 34

2.1 A Hypothetical Example 34

2.2 The Concept of Population Regression

Punction (PRF) 37

2.3 The Meaning ofthe Term Linear 38

Linearity in the Variabìes 38

Linearity in the Parameters 38

2.4 Stochastic Speciíìcation of PRF 39

2.5 The Signiíĩcance of the Stochastic

Disturbance Tcrm 41

2.6 The Sample Regression Punction (SRF) 42

2.7 Illustrative Examples 45

Summary andConclusions 48

Exercises 48

CHAPTER 3

Tvvo-Variable Regression ModehThe

Problem of Estimation 55

3.1 The Method of Ordinary Least Squares 55

3.2 The Classical LinearRegression Modcl: The

Assumptions Underlying the Method

of Least Squares 61

A Worci about TheseAssumptions 68

3.3 Precision or Standard Errors

ofLeast-Squares Estimates 69

3.4 Properties of Least-Squares Estimators:

The c ìuuss—Míirkov Thcorcm 7 Ì

3.5 The Coeữìcieiit of Determination r

2

:

A Measure of "Goodness ót" hít" 73

3.6 A Numerical Example 78

3-7 lllustrative Examples 81

3.ỈA8. ÌA Dcmaiio Summar Exercise trót'ị ÌViiriance \ppendi incarit i INot cast-Square east-Squarữ esx ôyss aiu n 83an n oi Mont \5 ld" Unbiasedncs Lcast-Square 9Conclusion Slandar ss Estimạtor e2 Kstimator Cạrldo Error Experimẹnt sss 8s Prop s 9 bsti 9s 4 2 3 n cs 93

Số hóa bởi Trung tâm Học liệu – ĐH TN http://www.lrc-tnu.edu.vn

Contenls vii

3A.4 Covariance Between fi\ and £2 93

3A.5 The Least-Squares Estimator of ơ2

93

3A.6 Minịmuim-Variance Property

of Least-Squares Estimators 95

3A.7 Consistency of Least-Squares Estimators 96

CHAPTER 4

Classical Normal Linear Regression

Model (CNLRM) 97

4.1 The Probability Distribution

of Disturbances Ui 97

4.2 The Normality Assụmption for li, 98

Whx the NormaỊitỵ Assumption? 99

4.3 Properties of OLS Estimators under

the Normality Assưmption I 00

4.4 The Method of Maximum

Likelihood (ML) 102

Summary and Conclusions 102

Appendix 4A 103

4A.1 Maximum Likelihood Estimation

of T\vo-Variable Regressìon Model 103

4A.2 Maximum Likelihood Estimatĩon

of Foocỉ Expenditure in India 105

Appendix 4A Exercises 105

CHAPTER 5

T>\o-Variable Regression: Interval

Estimation and Hypothesis Testing 107

5. ì Statistical Prerequisites 107

5.2 Intcrval Estimation: Some Basic Ideas 108

5.3 Contìdence Intervals for Regression

CoeAìcients fi\ and ti: 109

í ontitỉciH V ỉntcrval loi- /í; / nụ

Ctnựitlence hìicrval ft>r p\ li tui $2

Sitnuỉtaitetĩítxtv ì ỉ i

5.4 Coníìdence [ntcrval for à

2

I l I

5.5 Hypothcsis Testiim: Gcncral Comments Ì 13

5.6 Ì lypothesis Testing:

The ConHdence-lnterval Approach Ì 13

5.7 Hypothcsi TheOnc-SUlcd T\vo-Siiictl í7Ị'v//w TCIÌHỊ: Tcst-c*t-Sỉmiỉíìcanc ttctinỵ tin- SÌí>Mfictmcc oi Regmsskm s icnỉs Testing the Siiỉiiiticuncc orOI- The : Onc-Taĩ/ Twti-Tưil Tesi e I Approac Ti"./ / oi Tcsĩ ỉ? h Ìrĩ ỈU Ì Hỉ 5 1

; The ý

1

5.8 I ụ pothesis Tcstina: Somc PracTÌcnl Aspccts I Ìĩc\t ỉ M" 1

tỉyfU)thi.-\h Tiu- \U\imn\i // lơy ". ít t i'/»////.« " í»)• "Rvivt-' /ìttỉi " ti

7V?f "ZỂTO " Mí// Hvpothesis anci the "2-1" Ruỉe

o/Thumb 120

Forming the Nuil and Aỉternative

Hvpotheses 121

Choosing a. the Leveì of Signiýicance ì 21

The Exaci Leveì of Signiýicance:

The p Vaỉue 122

Statisticaỉ Signiýìcance versus Practicaỉ

SìỊỊtíiýicance 123

The Choice between Confidence-Ịntervaỉ

an tỉ Test-of-Signifieance Approuches

to Hvpathesis Testing ỉ 24

5.9 Regression Analysis and Analysis

of Variance 124

5.10 Application of Regression Analysis:

The Problem of Prediction 126

Mean Pretiiction ì27

hĩdìviduaì Preiỉictitm 138

5.1 Ì Reporting the Results of Regression

Analysis 129

5.12 Evaluating the Rcsults of Regression

Analysis 130

Nartttality Tcsls /30

Other Tcsts oỊModel AíiecỊiiacy 132

Summary and Conclusions 134

Excrcises 135

Appendix 5A 143

5A.1 Probability Distributions Rclated

to the Normal Distribution 143

SA.2 Derivation of Equation (5.3.2) 145

5A.3 Derivaúon of Equation (5.9.1 I 145

5A.4 Derivations ót* Equations (5.10.2)

mui (5.10.6) 145

iiiriưtỉic I>f Meo lì Pivilictitm 145

liiriam c ót ImÌÌYĨtỉitíti PtVíih Hon Ì4(\

CHAPTER 6

Extensions of the Two-Variable Linear

6.1 Reuression ihrouuh the Oriiỉìn 147 Regressio/--n f Model 147 6. 6.324 Kunetiona Scalin Rcnrcssio I Mímut>ran/l Rc\>rcssiu>i-thn>UỊỉh-(hizhỉ dnhon/ KormôUnit n Standarđirc ss ỉnHTprcttition lít'Réiircssio of Mcasuremen d Varíable n ModiMt s15 15 /ĩ4s Ì "75 UtHỈcl ỊĨ0 l

6.56 ị\o\x Scmìlo Nlodc \lodcl ts 15 ưo 1* Modcls Mcasur 9 0 :e Lo hlasticitv a Liu an: Thd Ìe i Loii-L.inca n Log r >

Số hóa bởi Trung tâm Học liệu – ĐH TN http://www.lrc-tnu.edu.vn

viii Contents

Haw tu Mcasure the Grxnvth Raiư:

The Log—Lin híodel 162

The Lin—Log Modeỉ ỉ64

6.7 Reciprocal Models 166

Log Hvperbolư or Logarithmic Reciprocaỉ

Modeỉ ỉ 72

6.8 Choice of Functìonal Form 172

6.9 A Note ôn the Nature of the Stochastic Error

Tcrm: Additivc versus Multiplicative

Stochastic ErrorTerm 174

Summary and Conclusions 175

Exercises 176

Appendix 6A 182

6A.1 Derivation of Least-Squares Estimators

for Regression through the Origin 182

6A.2 Proof thát a Standardizcd Variable

Has Zero Mean and Unit Variance 183

6A.3 Logarithms 184

6A.4 Growth Rate Formulas 186

6A.5 Box-Cox Regression Model 187

CHAPTER 7

Multỉple Regression Analysis:

The Problem of Estĩmation 188

7.1 TheThree-Variable Modcl: Notation

and Assumptions 188

7.2 [nterpretation of Multiple R.egression

Equation 191

7.3 The Meaning of Partial Regression

CoeíTìcients 191

7.4 OLS and ML Estimation ofthe Partial

Regression Coeíììcients 192

OLS Estimaỉors ỉ 92

Variances í!Hi! Standơrd Errors

o/OLS Estimators ỉ 94

Properties ofOLS Estimators 195

Maximum Likelihood Estimators Ỉ96

7.5 The Multiple Cocữìcient of Determination R2

7.7 7.86 R A Simpl opeciíìcatio oanfnd Multipl Corrclatio Regression ỉmpaci Change Illustrativ the Regressio Multípl en Regression ônn in Bia e R Exampl e the Dependent More Cocíììcien s 19 ônn 20 in Standardized Variables 6 0 the: than lntroductio 19 e Contex t 8 Onel Variable Regressor n to ofa Ị Unitỉ 99 99 2

anComparing d the AdịusteTHd RĨO 20R1

2 Values 203

AUocating R

:

among Regressors 206

The Game "ạf Maximizing R2

206

7.9 The Cobb-Douglas Production Function:

More ôn Functional Form 207

7.10 Polynomiai Regression Models 210

7.11 Partial Correlation Coeíĩìcients 213

Explanation o/Simpỉe and Partiáĩ

Correiation Coẹfficients 2Ỉ3

Iníerpretation ofSimple and Partiaỉ

Correiaũon Coefficients 214

Summary and Conclusions 21 5

Exercises 216

Appendix 7A 227

7A.1 Derivation of OLS Estimators

Given in Equations (7.4.3) to (7.4.5) 227

7A.2 Equality bctvveen the Coeíĩìcients of PGNP

in Equations (7.3.5) and (7.6.2) 229

7A.3 Derivation of Equation (7.4.19) 229

7A.4 Maximum Likclihood Estimation

ofthe Multiplc Regression Model 230

7A.5 EViews Output of the Cobb-Douglas

Production Function in

Equation (7.9.4) 231

CHAPTER 8

Multiple Regression Analysis: The Problem

of Inĩerence 233

8.1 The Normality Assumptỉon Once Atỉain 233

8.2 Hypothesis Testing in Multiple Recression:

General Comments 234

8.3 Hypothesis Testing about Individual

Regression Coeíỉìcients 235

8.4 Testing the Overall Sìunitìcance of the Sample

Regression 237

The Anaỉysis of Varỉance Approach to Testing the

Overall Significance nỉ an Observed Muỉtìpỉe

Regression: The F Test 238

Testing the Overali Signiýìcance ofa Muỉtìpie

AnRegression: important The Rlationship behveen F Tesi 240 R2 Regression Testing the Overall in Terms Signựỉcance o/R of a Muỉtìpỉe and F 241 2

8.56 TestinRestricte Coeflficient Equalit oiThe angy th "ỉncremental" t-Test d Restriction Expỉanatory e Leas s Equalit 24t Approach Squares 6 ys ofTw 24: Variable 8 or Testin o 249 Regressio "Margìnaỉ g 242 Linea 243 n r " í 'ontribution

Số hóa bởi Trung tâm Học liệu – ĐH TN http://www.lrc-tnu.edu.vn

8.7 Testíng for Structural or Parameter Stability

of Regression Models: TheChow Test 254

8.8 Prediction with Multiple Regression 259

8.9 The Troika of Hypothesis Tests: The

Likelihood Ratio (LR), Wald (W), and

Lagrange Multiplier (LM) Tests 259

8.10 Testing the Functional Form ofRegression:

Choosing betvveen Linear and Log-Linear

Regression Models 260

Summary and Conclusions 262

Exercises 262

Appendix SA: Likelihood

Ratio (LR)Test 274

CHAPTER 9

Dummv Variable Regressĩon Models 277

9.1 The Nature of Dummy Variables 277

9.2 ANOVA Models 278

Caution in the Use of Dummv Variables 28!

9.3 ANOVA Models with Two Ọualitative

Variables 283

9.4 Regression with a Mixture of Quantitative

and Ọualitative Regressors: The ANCOVA

Modèls 283

9.5 The Dummy Variablc Altcrnative

to the Chow Test 285

9.6 Interaction Eíĩects Using Dummy

Variables 288

9.7 The Use of Dummy Variables in Scasonal

Analysis 290

9.8 Piecewise Lĩnear Regression 295

9.9 Panel Data Regression Models 297

9.10 Somc Technical Aspects oithe Dummy

Variable Technique 297

The Interpreíation oi Dumtny Varìables

in Semiỉogarithmic Regressions 297

9.121 Topic AAppendi wit Summar Exercise hĩsConcludin Dummy What Dumm sa foDummy yxs Happens 30 r9AanyFurthe Variabìes Variables and dg Regresso 5 : Conclusion Semilogarithmi Exampỉ rVariable? Stud ựer the y 31 30 mui s 30 30 Dependenl Variabỉe 4 0 0 Heteroscedasticity Autocorreỉaùon c4 Regressio 299 n 299 298

Con ten ts ìx

PART TWO

RELAXING THE ASSUMPTIONS OF THE

CLASSICAL MODEL 315

CHAPTER 10

Multicollinearity: What Happens

If the Regressors Are Correlated? 320

10.1 The Nature of Multicollinearity 321

10.2 Estimation in the Presence of Perfect

Multicollinearity 324

10.3 Estimation in the Presence of "High"

bút "Imperfect" Multicollinearity 325

10.4 Multicollinearity: Much Ado about Nothing?

Theoretical Consequences

of Multicollinearity 326

10.5 Practical Consequences

of Multicollinearity 327

Large Variances anđ Covariances

ofOLS Estimators 328

Wìder Cọnfidence Intervals 330

"ỉnsignificant" t Ratios 330

A Hig/i R2

bút Few Signiýìcant í Ratios 331

Sensitivity a('OLS Estimators and Their

Startdard Errors to Smaỉỉ Changes in Data 331

Consequences of Micronumerosity 332

10.6 An lllustrative Example 332

10.7 Detection of Multicollinearity 337

10.8 Remcdial Measures 342

Do Nothing 342

RuIe-of-Thumb Procedures 342

10.9 ỉs Multicollinearity Necessarily BadV Maybe

Noi. If the Objective Is Prediction Only 347

10.10 An Extended Examplc: The Lonuley

Data 347

Summary and Conclusĩons 350

Exercises 351

CHAPTER 11

Heteroscedasticity: \Vhat Happens If

th11.1 The Naturc of Heteroscedasticity 365 11.e324ErrooConsequence ThOLSquare f eHeteroscedasticit Heteroscedasticit rDifference SMeiho Varianc Estimatio s (GLS d osefn)oGeneralize Ifbenvcen isn37Usin Nonconstant thy1e g37Presenc OL04dOLS SLcas ein thand ?e Presenc 36GLS 5 e3 73

Số hóa bởi Trung tâm Học liệu – ĐH TN http://www.lrc-tnu.edu.vn

X Contents

OLS Estimation AlỉowingJòr

Heteroscedasticity 3 74

OLS Estimation Disregarding

Heteroscedastỉcity 3 74

Á Technicaì Note 376

11.5 Detectìon of Heteroscedasticity 376

lnformat Methods 3 76

Formaỉ Methods 3 78

11.6 Remedial Measures 389

When ơiĩs Known: The Method ofWeìghted

Least Squares 3X9

When ơi Is Noi Known 391

11.7 Concluding Examples 395

11.8 A Caution about Overreacting

to Heteroscedasticity 400

Summary and Conclusions 400

Exercises 401

Appendix Ì ÌA 409

11A.1 Proofof Equation (Ì 1.2.2) 409

11 A.2 The Method of Weighted Least

Squares 409

ì TA.3 Proof thát E(â2

) +Õ1

in the Presence

of Heteroscedasticity 410

11 A.4 White's Robust Standard Errors 41 Ì

CHAPTER12

Autocorrelation: What Happens If the Error

Terms Are Correlated? 412

12. Ì The Nature of the Problem 413

12.2 OLS Estimatỉon ỉn the Presence

of Autocorrelation 418

12.3 The BLUH Estỉmator in the Presence

of Autocorrelation 422

12.4 Consequences of Usỉng OLS

in the Prcsencc of Autocorrelation 423

OLS Estímatìon Aỉlowing

for Autocorrelation 423

OLS Estimation Disregarding

12.65 Detectin Relationshi i1960-200 n thAutocorrelation in. nIV. li./e in. Graphical Busỉnes Durbin-Watson The The A GenemlTest So g5 Autocorrelatio p Breusch-Godfrey (BO 42 RunsTesí Mâm- Tests betwee s8 Secto Method nr Wage 423 o 43 nf oỷAutocorrelation: th42 dTest of es 429ì Unite an Autocorrelation? 9 d 434 Productivit d States Hem, v 438 440

12.7 What to Do when You Find Autocorrelation:

Remedial Measures 440

12.8 Model Mis-Specification versus Pure

Autocorrelation 441

12.9 Correcting for (Pure) Autocorrelation:

The Method of Generalized Least

Squares (GLS) 442

wken p ỉs Known 442

When p ỉs Nót Known 443

12.10 The Newey-West Method of Correcting

the OLS Standard Errors 447

Ì 2.11 OLS versus FGLS and HÁC 448

12.12 Ađditional Aspects ofAutocorrelation 449

Dummy Varỉabtes andAutocomlatừm 449

ARCHand GARCH Modeh 449

Coexìstence of Autocorreỉation

arnì Heteroscedasticity 450

12.13 A Concluding Example 450

Summary and Conclusỉons 452

Exerciscs 453

Appendix 12A 466

ì 2A. ì Proof thát the Error Term Vi in

Equation (12.1.1 Ì) ls Autocorrelated 466

12A.2 Proof of Equations (12.2.3), (12.2.4),

anđ (12.2.5) 466

CHAPTER13

Econometric Modeling: IVlodel Spcciíìcation

and Diagnostic Testing 467

13.1 Model Selection Criteria 468

13.2 Types of Speciíìcation Errors 468

13.3 Consequences of Model Specỉíìcatioii

Errors 470

Underfitting a Modeỉ (Omừtìng a Rclevant

Variable) 471

ỉnclusìon lít an Irrelevant Variabỉe

(Overfittiiĩg a Model) 473

13.4 Tests of Specitìcation Errors 474

13. 13.56 Error Erro Incrrec Functional Detecting (Overfittinga Errors Tests VaríableY Variablẽ rsTer otfm for Omitted Variables and Measuremen Speciíìcatio of4S Measurement Measurement Xthe 482 6 Form 4X3 Model) Presence nto 48 477 fthe2 475 Stochasti in(tỉ the Unnecessary c Dependent Expkmaỉory Incorrecí tiiriahlcs

Số hóa bởi Trung tâm Học liệu – ĐH TN http://www.lrc-tnu.edu.vn

Contents xi

13.7 Nested versus Non-Nested Models 487

ì 3.8 Tests ofNon-Nested Hypotheses 488

The Discrímination Approach 488

The DiscerningApproach 488

13.9 Model Selection Criteria 493

The R

2 Criterion 493

Adjusted R

1

493

Akaikes ĩnýòrmation Criterion (AJC) 494

Sckwarz's In/ormation Criterion (SIC) 494

Maỉhnvs s Cp Criterion 494

Á ÌVord ofCàutlon ahout Model

Selection Criteria 495

fòrecast Chi-SíỊuarc (x1

) 496

13.10 Adđitional Topĩcs in Econometric

Modeline 496

Outỉiers, Leverage, anđ ỉnftuence 496

Recursive Least Squares 49H

Chow's Prediction Paiỉure Test 498

Missing Data 499

13.11 Concludintĩ Examples 500

/. A Modeỉ oý Houriy Wage Determination 500

2. Reo! Consumption Function for the United

States. Ì947-2000 505

13.12 Non-Normal Errors and Stochastic

Regressors 509

/. What Happens í/the Error Term is Noi

Normally Distributed? 509

2. Stochastic Explanatory Varíabỉes 510

13.13 A Word to the Practitioner 5 Ì I

Summarv and Conclusions 5 12

Exeicises 513

Appendix 13A 519

13A.1 The Proof thát E{bi2) = 02 + foi>ĩ2

[Equation ( 13.3.3)] 519

ì SA.2 The Consequences of Including an Irrelevant

Varíable: The Unbíasedness Property 520

13A.3 The ProofofEquation (13.5.10) 521

PART THREE CHAPTER 14 14.1 Intrinsically Linearand Intrinsically TOPIC Nonlinea 14.3A. 24 Nonlinea Regressio Estimatio ThSerIProofo NRegressio ECONOMETRIC rnRegressìo Model offEquatio LineasModel rn52nanModel 7(13.6.2 d Nonlinea ssS)5252525525r 3

14.3 Estimating Noniinear Regression Models:

The Trial-and-Error Method 527

14.4 Approaches to Estimating Nonlinear

Regression Mođels 529

DirecỀ Search Oi- Trial-and-Error

or Derivative-Free Method 529

Dĩrcci Opiimizaĩion 529

iterative Linearization Method 530

14.5 Illustrative Examples 530

Summary and Conclusions 535

Exercises 535

Appendix 14A 537

14A. ì Derivation of Equations (14.2.4)

and (14.2.5) 537

14A.2 The Linearization Method 537

14A.3 Lĩnear Approximation ofthe Exponential

Function Givcn in Equation (14.2.2) 538

CHAPTER 15

Qualitative Response Regression IModels 541

15.1 The Naturc of Qualitative Rcsponse

Models 541

15.2 The Linear Probability Model (LPM) 543

Non-Normality oJ the Disturbances Ui 544

Heteroscedastic ỉ ariances

o/ the Disturbances 544

Non/ủựUỉment ọ/ 0 < E( y, I X.) 5 l 545

Questionable Value of R as a Measure

of Goodness ofFit 546

15.3 Applicaùons of LPM 549

15.4 Alternatives to LPM 552

15.5 The Logit Model 553

15.6 Estimation of the Logit Modcl 555

Daia át the ĩndividuaỉ Level 556

Grouped or Repỉicated Dư ta 556

15.7 The Grouped Logit (Glogit) Model: A

Numerical Example 558

Inierpretation oJ the Estimated Logil

15.98 Thor [ndividua eModeỉ Probit Dam: orinRegression The ProbiLogi the Vaỉue individuaỉ Datã Probit Modelfor Marginal t Mode gprobit t 558Estimation Mode l Datla Modeỉs fol of 56 567 r Ẹffecl tựa Ungroupe a6 1 Regressor with 570 571 Ungrouped Grouped d Ưnit in the Various Change

Số hóa bởi Trung tâm Học liệu – ĐH TN http://www.lrc-tnu.edu.vn

xỉ! Cnrttents

15.10 Logìt and Probĩt Models 571

15.11 The Tobit Model 574

lUustration ofthe Tobit Madeỉ: Ray Fair's Mndeỉ

of Extramarítaí AỌairs 575

15.12 Modeling Count Data: The Poisson

Regression Model 576

15.13 Further Topìcs in Qualitative Response

Regression Models 579

Ordinal Logit anđ Probu Mờdels 580

Muỉtinomiaỉ Logit and Probĩt Models 5M)

Dumtion Modets 580

Summary and Conclusions 581

Exercises 582

Appendix I5A 589

ì 5A. Ì Maximum Likelihood Estimation ofthe Logit

and Probit Models for Individual (Ungrouped)

Data 589

CHAPTER 16

Panel Data Regression Models 591

16.1 Why Panel Data? 592

16.2 Panel Data: An Illustrative Example 593

16.3 Pooled OLS Regression or Constant

Coefficients Model 594

16.4 The Fĩxed Effect Least-Squares Dummy

Variable (LSDV) Model 596

A Caution in the ưse oi the Fixed Effect

LSDV Modeỉ 598

16.5 The Fixed-Effect Within-Group <WG)

Estimator 599

16.6 The Random Eữects Modcl (REM) 602

Breusch and Pagan Lagrange

Muitipiier Test 605

16.7 Properties of Various Esiimators 605

16.8 Fixcd EITects versus Random Eữects Model:

Some Guidelines 606

16.9 Pancl Data Regressions: Some Concluding

Comments 607

CHAPTER 17 an17.1 The Rolc of "Time," or "Lag." Dvnamĩ 17. 16.1d20Distributed-La SomThiumar Exercise nceEconomic Econometri Reason e niustrativ ys 61anssd3 fo Conclusion g61reModel c Example 8LagModels s 62ss2s 6161: 60Autoregressiv 72 7 e

17.3 Estimation of Distributed-Lag Models 623

Ad Hoe Estimation ofDistributed-Lag

Modeỉs 623

Ì 7.4 The Koyck Approach to Distributed-Lag

Models 624

The Median Lag 627

The Mean Lag 627

ì 7.5 Rationalization of the Koyck Model: The

Adaptive Expectations Model 629

17.6 Another Rationalization of the Koyck Model:

The Stock Adjustment, or Partial Adjustment.

Model 632

ì 7.7 Combination of Adaptive Expectations

and Partial Adjustment Models 634

Ì 7.8 Estimation of Autoreeressive Models 634

17.9 The Method of Instrumental

Variables (IV) 636

ì 7.10 Detecting Autocorrelatĩon in Autoreeressive

Modeis: Durbin /ỉ Test 637

17.11 A Numerical Example: The Demand for

Money in Canada, 1979-1 to 1988-IV 639

17.12 [llustratìve Examples 642

17.13 The Almon Approach to Distributcd-Lag

Models: The AI mon or Polvnomial Distributed

Lag(PDL) 645

ì 7.14 Causality in Economics: The Granser

Causality Test 652

The Cranger Test 653

A Note ôn Causaíity mui Exogeneity 657

Summary and C onclusions 658

Exercises 659

Appendix 17A 669

ì 7A.1 The Sargan Test tbr the Validity

of lnstruments 669

PART FOUR

SIMULTANEOUS-EQUATION

MODELS ANDTIME SẼR1ES

CHAPTER 18 18.1 The Nature of Simultaneous-Equation ECONOMETRIC Simultaneous-Equatio 18.23 Examplc ThModeli Inconsistenc e Simultaneous-Equatio s s67o43fySimultaneous-Equaúo SofOL67nS1Model Estimatoi n Bias s -676n3"

Số hóa bởi Trung tâm Học liệu – ĐH TN http://www.lrc-tnu.edu.vn

Contents xiii

18.4 The Simultaneous-Equation Bias: A Numerical

Example 682

Summary and Conclusions 684

Exercises 684

CHAPTER 19

The Identiíication Problem 689

19.1 Notations and Deíìnitions 689

19.2 The Identiíìcation Problem 692

ưnderidentiýìcatìon 692

Just, or Exact, ỉdentỉficatìon 694

Overiđentìficatìon 697

19.3 Rules íbr Identitìcation 699

The Order Condition of ỉdentìfiabilìty 699

The Ranh Condition of Identịftabiỉity 700

19.4 ATest of Simultancity 703

Hausman Specịftcaíion Test 703

19.5 Tests for Exogeneity 705

Summary and Conclusions 706

Exercỉses 706

CHAPTER 20

Simultaneous-Equation Methods 711

20.1 Approaches to Estimation 71 Ì

20.2 Recursive Models and Ordinary

Least Squares 712

20.3 Estimation of a Just Identiíìed Equation: The

Method of Indirect Least Squares (ILS) 715

An Ilỉustrative Example 715

Properties o/ĨLS Estimators 718

20.4 Estimation ót"an Overidentitìed Equation:

The Mcthod ofTwo-Stage Least Squares

(2SLS) 718

20.5 2SLS: A Numerical Example 721

20.6 Illustrative Examplcs 724

Summary and Conclusions 730

Exercises 730

Appendix 20A 735

20A.1 Bias ìn the [ndirect Least-Squares

CHAPTER 21 Tim20A. S1.o1me2eSerie Estĩmatio Estimator Estimator Serie ABasi LooscskConcept Econometrics 73nást8oSelecte 73fStandar 56 sd 73u.sd 7Error :. Economi s of2SLc TimS e

21.2 KeyConcepts 739

21.3 Stochastic Processes 740

Stationary Stochastic Processes 740

Nonstatìonary Stochastic Processes 74 ỉ

21.4 Unit Root Stochastic Process 744

21.5 Trend Stationary (TS) and DiíTerence

Staĩionary (DS) Stochastic Processes 745

21.6 Integrated Stochastic Processes 746

Properties oi/ntegrated Serìes 747

21.7 The Phenomenon of Spurious

Regression 747

21.8 Tests of Stationarìty 748

/. Graphỉcal Anatysis 749

2. Autocorreỉation Function (ACFt

anả Corrvlogram 749

Statisticaì Sigrứficance of Autocorreiatìon

Coefficierits 753

21.9 The Lĩnh Root Test 754

TheAugmented Díckẹy-Fuiier (ADF)

Tesí 757

Testing the Signựỉcance ofMore than One

c<it>fficiem: The F Test 758

The Philiips Perron (PP) Unit

Root Tests 758

Testing for Strucíurai Changes 75H

Ả Critique of the Vnỉt Rom Tests 75V

21.10 Transíòrming Nonstationary Time Series 760

DỊffẽrenceStatiơnary Processes 760

TrendStatỉonary Processes 761

21.11 Cointegration: Regression of a Unit

Root Time Series ôn Anothcr Unit Root

Time Series 762

Testing for Cointegration 763

Cointegratìon an ti Error Correction

Mechanìsm (ECM) 764

21.12 Some Economic Applications 765

Summary and Conclusions 768

CHAPTER 22 22.1 Approaches to Economic Porecasting 773 TimForecastin c Serie Exercise Exponentiai Singỉemuitaneous-Equation Models .4VAR g RỈA s 77 Econometrics s Modeh 76 ỈAEquation Regrvssion Models 3 774 9 Modeỉs Smoothing 775 : 774 Methods Regrẹssion 774 774

Số hóa bởi Trung tâm Học liệu – ĐH TN http://www.lrc-tnu.edu.vn