Basic Econometrics (Fifth Edition) PDF

guj75772_IFC.qxd 01/08/2008 10:06 AM Page 2 The McGraw-Hill Series Economics ESSENTIALS OF ECONOMICS Slavin MONEY AND BANKING Brue, McConnell, and Flynn Economics, Microeconomics, Cecchetti...

guj75772_IFC.qxd 01/08/2008 10:06 AM Page 2 The McGraw-Hill Series Economics ESSENTIALS OF ECONOMICS Slavin MONEY AND BANKING Brue, McConnell, and Flynn Economics, Microeconomics, Cecchetti Essentials of Economics and Macroeconomics Money, Banking, and Financial Second Edition Ninth Edition Markets Mandel Second Edition ECONOMICS OF SOCIAL ISSUES Economics: The Basics Guell URBAN ECONOMICS First Edition Issues in Economics Today O’Sullivan Schiller Fourth Edition Urban Economics Essentials of Economics Seventh Edition Sharp, Register, and Grimes Seventh Edition Economics of Social Issues Eighteenth Edition LABOR ECONOMICS PRINCIPLES OF ECONOMICS Borjas Colander ECONOMETRICS Labor Economics Economics, Microeconomics, Fourth Edition Gujarati and Porter and Macroeconomics Basic Econometrics McConnell, Brue, and Macpherson Seventh Edition Fifth Edition Contemporary Labor Economics Frank and Bernanke Eighth Edition Gujarati and Porter Principles of Economics, Essentials of Econometrics Principles of Microeconomics, PUBLIC FINANCE Fourth Edition Principles of Macroeconomics Rosen and Gayer Fourth Edition MANAGERIAL ECONOMICS Public Finance Frank and Bernanke Baye Eighth Edition Brief Editions: Principles of Managerial Economics and Business Seidman Economics, Principles of Strategy Public Finance Microeconomics, Principles of Sixth Edition First Edition Macroeconomics Brickley, Smith, and Zimmerman First Edition ENVIRONMENTAL ECONOMICS Managerial Economics and McConnell, Brue, and Flynn Organizational Architecture Field and Field Economics, Microeconomics, Fifth Edition Environmental Economics: and Macroeconomics An Introduction Thomas and Maurice Eighteenth Edition Fifth Edition Managerial Economics McConnell, Brue, and Flynn Ninth Edition Brief Editions: Economics, INTERNATIONAL ECONOMICS Microeconomics, INTERMEDIATE ECONOMICS Appleyard, Field, and Cobb Macroeconomics International Economics Bernheim and Whinston First Edition Sixth Edition Microeconomics Miller First Edition King and King Principles of Microeconomics International Economics, Dornbusch, Fischer, and Startz First Edition Globalization, and Policy: A Reader Macroeconomics Fifth Edition Samuelson and Nordhaus Tenth Edition Economics, Microeconomics, Pugel Frank and Macroeconomics International Economics Microeconomics and Behavior Eighteenth Edition Fourteenth Edition Seventh Edition Schiller The Economy Today, The Micro ADVANCED ECONOMICS Economy Today, and The Macro Romer Economy Today Advanced Macroeconomics Eleventh Edition Third Edition guj75772_fm.qxd 05/09/2008 11:15 AM Page i Basic Econometrics Fifth Edition Damodar N. Gujarati Professor Emeritus of Economics, United States Military Academy, West Point Dawn C. Porter University of Southern California Boston Burr Ridge, IL Dubuque, IA New York San Francisco St. Louis Bangkok Bogotá Caracas Kuala Lumpur Lisbon London Madrid Mexico City Milan Montreal New Delhi Santiago Seoul Singapore Sydney Taipei Toronto guj75772_fm.qxd 05/09/2008 11:15 AM Page ii BASIC ECONOMETRICS Published by McGraw-Hill/Irwin, a business unit of The McGraw-Hill Companies, Inc., 1221 Avenue of the Americas, New York, NY, 10020. Copyright © 2009, 2003, 1995, 1988, 1978 by The McGraw-Hill Companies, Inc. All rights reserved. No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written consent of The McGraw-Hill Companies, Inc., including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning. Some ancillaries, including electronic and print components, may not be available to customers outside the United States. This book is printed on acid-free paper. 1 2 3 4 5 6 7 8 9 0 VNH/VNH 0 9 8 ISBN 978-0-07-337577-9 MHID 0-07-337577-2 Publisher: Douglas Reiner Developmental editor: Anne E. Hilbert Editorial coordinator: Noelle Fox Associate marketing manager: Dean Karampelas Lead Project manager: Christine A. Vaughan Full-service project manager: Michael Ryder, ICC Macmillan Inc. Lead production supervisor: Carol A. Bielski Design coordinator: Joanne Mennemeier Media project manager: Srikanth Potluri, Hurix Systems Pvt. Ltd. Cover design: Brittany Skwierczynski Typeface: 10/12 TimesNewRomanPS Compositor: ICC Macmillan Inc. Printer: R. R. Donnelley Library of Congress Cataloging-in-Publication Data Gujarati, Damodar N. Basic econometrics / Damodar N. Gujarati, Dawn C. Porter. — 5th ed. p. cm. Includes bibliographical references and index. ISBN-13: 978-0-07-337577-9 (alk. paper) ISBN-10: 0-07-337577-2 (alk. paper) 1. Econometrics. I. Porter, Dawn C. II. Title. HB139.G84 2009 330.01
5195—dc22 2008035934 www.mhhe.com guj75772_fm.qxd 05/09/2008 11:15 AM Page iii About the Authors Damodar N. Gujarati After teaching for more than 25 years at the City University of New York and 17 years in the Department of Social Sciences, U.S. Military Academy at West Point, New York, Dr. Gujarati is currently Professor Emeritus of economics at the Academy. Dr. Gujarati 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. Dr. Gujarati has published extensively in recognized national and international journals, such as the Review of Economics and Statistics, the Economic Journal, the Journal of Financial and Quantitative Analysis, and the Journal of Business. Dr. Gujarati was a member of the Board of Editors of the Journal of Quantitative Economics, the official journal of the Indian Econometric Society. Dr. Gujarati is also the author of Pensions and the New York City Fiscal Crisis (the American Enterprise Institute, 1978), Government and Business (McGraw-Hill, 1984), and Essentials of Econometrics (McGraw-Hill, 3d ed., 2006). Dr. Gujarati’s books on econometrics have been translated into several languages. Dr. Gujarati was a Visiting Professor at the University of Sheffield, U.K. (1970–1971), a Visiting Fulbright Professor to India (1981–1982), a Visiting Professor in the School of Management of the National University of Singapore (1985–1986), and a Visiting Professor of Econometrics, University of New South Wales, Australia (summer of 1988). Dr. Gujarati has lectured extensively on 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 assistant professor in the Information and Operations Manage- ment Department at the Marshall School of Business of the University of Southern California since the fall of 2006. She currently teaches both introductory undergraduate and MBA statistics in the business school. Prior to joining the faculty at USC, from 2001–2006, Dawn was an assistant professor at the McDonough School of Business at Georgetown University, and before that was a visiting professor in the psychology depart- ment at the Graduate School of Arts and Sciences at NYU. At NYU she taught a number of advanced statistical methods courses and was also an instructor at the Stern School of Business. Her Ph.D. is from the Stern School in Statistics. Dawn’s areas of research interest include categorical analysis, agreement measures, multivariate modeling, and applications to the field of psychology. Her current research ex- amines online auction models from a statistical perspective. She has presented her research at the Joint Statistical Meetings, the Decision Sciences Institute meetings, the International Conference on Information Systems, several universities including the London School of Economics and NYU, and various e-commerce and statistics seminar series. Dawn is also a co-author on Essentials of Business Statistics, 2nd edition, McGraw-Hill Irwin, 2008. Outside of academics, Dawn has been employed as a statistical consultant for KPMG, Inc. She has also worked as a statistical consultant for many other major companies, including Ginnie Mae, Inc., Toys R Us Corporation, IBM, Cosmaire, Inc., and New York University (NYU) Medical Center. iii guj75772_fm.qxd 05/09/2008 11:15 AM Page iv 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. But especially for my adoring father, Terry. —DCP guj75772_fm.qxd 05/09/2008 11:15 AM Page v Brief Contents Preface xvi PART THREE Acknowledgments xix Topics in Econometrics 523 Introduction 1 14 Nonlinear Regression Models 525 15 Qualitative Response Regression PART ONE Models 541 Single-Equation Regression Models 13 16 Panel Data Regression Models 591 1 The Nature of Regression Analysis 15 17 Dynamic Econometric Models: Autoregressive and 2 Two-Variable Regression Analysis: Distributed-Lag Models 617 Some Basic Ideas 34 3 Two-Variable Regression Model: The PART FOUR Problem of Estimation 55 Simultaneous-Equation Models and Time 4 Classical Normal Linear Regression Series Econometrics 671 Model (CNLRM) 97 18 Simultaneous-Equation Models 673 5 Two-Variable Regression: Interval Estimation and Hypothesis Testing 107 19 The Identification Problem 689 6 Extensions of the Two-Variable 20 Simultaneous-Equation Methods 711 Linear Regression Model 147 21 Time Series Econometrics: Some 7 Multiple Regression Analysis: The Basic Concepts 737 Problem of Estimation 188 22 Time Series Econometrics: 8 Multiple Regression Analysis: The Forecasting 773 Problem of Inference 233 9 Dummy Variable Regression Models 277 APPENDICES A A Review of Some PART TWO Statistical Concepts 801 Relaxing the Assumptions B Rudiments of Matrix Algebra 838 of the Classical Model 315 C The Matrix Approach to 10 Multicollinearity: What Happens Linear Regression Model 849 If the Regressors Are Correlated? 320 D Statistical Tables 877 11 Heteroscedasticity: What Happens If E Computer Output of EViews, the Error Variance Is Nonconstant? 365 MINITAB, Excel, and STATA 894 12 Autocorrelation: What Happens If F Economic Data on the the Error Terms Are Correlated? 412 World Wide Web 900 13 Econometric Modeling: Model Specification and Diagnostic Testing 467 SELECTED BIBLIOGRAPHY 902 v guj75772_fm.qxd 05/09/2008 11:15 AM Page vi Contents Preface xvi Summary and Conclusions 28 Acknowledgments xix Exercises 29 Introduction 1 CHAPTER 2 I.1 What Is Econometrics? 1 Two-Variable Regression Analysis: Some I.2 Why a Separate Discipline? 2 Basic Ideas 34 I.3 Methodology of Econometrics 2 2.1 A Hypothetical Example 34 1. Statement of Theory or Hypothesis 3 2.2 The Concept of Population Regression 2. Specification of the Mathematical Model Function (PRF) 37 of Consumption 3 2.3 The Meaning of the Term Linear 38 3. Specification of the Econometric Model Linearity in the Variables 38 of Consumption 4 Linearity in the Parameters 38 4. Obtaining Data 5 2.4 Stochastic Specification of PRF 39 5. Estimation of the Econometric Model 5 2.5 The Significance of the Stochastic 6. Hypothesis Testing 7 Disturbance Term 41 7. Forecasting or Prediction 8 2.6 The Sample Regression Function (SRF) 42 8. Use of the Model for Control 2.7 Illustrative Examples 45 or Policy Purposes 9 Summary and Conclusions 48 Choosing among Competing Models 9 Exercises 48 I.4 Types of Econometrics 10 I.5 Mathematical and Statistical Prerequisites 11 CHAPTER 3 I.6 The Role of the Computer 11 Two-Variable Regression Model: The I.7 Suggestions for Further Reading 12 Problem of Estimation 55 PART ONE 3.1 The Method of Ordinary Least Squares 55 3.2 The Classical Linear Regression Model: The SINGLE-EQUATION REGRESSION Assumptions Underlying the Method MODELS 13 of Least Squares 61 CHAPTER 1 A Word about These Assumptions 68 3.3 Precision or Standard Errors The Nature of Regression Analysis 15 of Least-Squares Estimates 69 1.1 Historical Origin of the Term Regression 15 3.4 Properties of Least-Squares Estimators: 1.2 The Modern Interpretation of Regression 15 The Gauss–Markov Theorem 71 Examples 16 3.5 The Coefficient of Determination r2: 1.3 Statistical versus Deterministic A Measure of “Goodness of Fit” 73 Relationships 19 3.6 A Numerical Example 78 1.4 Regression versus Causation 19 3.7 Illustrative Examples 81 1.5 Regression versus Correlation 20 3.8 A Note on Monte Carlo Experiments 83 1.6 Terminology and Notation 21 Summary and Conclusions 84 1.7 The Nature and Sources of Data for Economic Exercises 85 Analysis 22 Appendix 3A 92 Types of Data 22 3A.1 Derivation of Least-Squares Estimates 92 The Sources of Data 25 3A.2 Linearity and Unbiasedness Properties The Accuracy of Data 27 of Least-Squares Estimators 92 A Note on the Measurement Scales 3A.3 Variances and Standard Errors of Variables 27 of Least-Squares Estimators 93 vi guj75772_fm.qxd 05/09/2008 11:15 AM Page vii Contents vii 3A.4 Covariance Between β̂1 and β̂ 2 93 The “Zero” Null Hypothesis and the “2-t” Rule 3A.5 The Least-Squares Estimator of σ2 93 of Thumb 120 3A.6 Minimum-Variance Property Forming the Null and Alternative of Least-Squares Estimators 95 Hypotheses 121 3A.7 Consistency of Least-Squares Estimators 96 Choosing α, the Level of Significance 121 The Exact Level of Significance: CHAPTER 4 The p Value 122 Classical Normal Linear Regression Statistical Significance versus Practical Model (CNLRM) 97 Significance 123 The Choice between Confidence-Interval 4.1 The Probability Distribution and Test-of-Significance Approaches of Disturbances ui 97 to Hypothesis Testing 124 4.2 The Normality Assumption for ui 98 5.9 Regression Analysis and Analysis Why the Normality Assumption? 99 of Variance 124 4.3 Properties of OLS Estimators under 5.10 Application of Regression Analysis: the Normality Assumption 100 The Problem of Prediction 126 4.4 The Method of Maximum Mean Prediction 127 Likelihood (ML) 102 Individual Prediction 128 Summary and Conclusions 102 5.11 Reporting the Results of Regression Appendix 4A 103 Analysis 129 4A.1 Maximum Likelihood Estimation 5.12 Evaluating the Results of Regression of Two-Variable Regression Model 103 Analysis 130 4A.2 Maximum Likelihood Estimation Normality Tests 130 of Food Expenditure in India 105 Other Tests of Model Adequacy 132 Appendix 4A Exercises 105 Summary and Conclusions 134 Exercises 135 CHAPTER 5 Appendix 5A 143 Two-Variable Regression: Interval 5A.1 Probability Distributions Related Estimation and Hypothesis Testing 107 to the Normal Distribution 143 5.1 Statistical Prerequisites 107 5A.2 Derivation of Equation (5.3.2) 145 5.2 Interval Estimation: Some Basic Ideas 108 5A.3 Derivation of Equation (5.9.1) 145 5.3 Confidence Intervals for Regression 5A.4 Derivations of Equations (5.10.2) Coefficients β1 and β2 109 and (5.10.6) 145 Confidence Interval for β2 109 Variance of Mean Prediction 145 Confidence Interval for β1 and β2 Variance of Individual Prediction 146 Simultaneously 111 5.4 Confidence Interval for σ2 111 CHAPTER 6 5.5 Hypothesis Testing: General Comments 113 Extensions of the Two-Variable Linear 5.6 Hypothesis Testing: Regression Model 147 The Confidence-Interval Approach 113 Two-Sided or Two-Tail Test 113 6.1 Regression through the Origin 147 One-Sided or One-Tail Test 115 r2 for Regression-through-Origin Model 150 5.7 Hypothesis Testing: 6.2 Scaling and Units of Measurement 154 The Test-of-Significance Approach 115 A Word about Interpretation 157 Testing the Significance of Regression 6.3 Regression on Standardized Variables 157 Coefficients: The t Test 115 6.4 Functional Forms of Regression Models 159 Testing the Significance of σ2: The χ2 Test 118 6.5 How to Measure Elasticity: The Log-Linear 5.8 Hypothesis Testing: Some Practical Aspects 119 Model 159 The Meaning of “Accepting” or “Rejecting” a 6.6 Semilog Models: Log–Lin and Lin–Log Hypothesis 119 Models 162 guj75772_fm.qxd 05/09/2008 11:15 AM Page viii viii Contents How to Measure the Growth Rate: Allocating R2 among Regressors 206 – The Log–Lin Model 162 The “Game’’ of Maximizing R2 206 The Lin–Log Model 164 7.9 The Cobb–Douglas Production Function: 6.7 Reciprocal Models 166 More on Functional Form 207 Log Hyperbola or Logarithmic Reciprocal 7.10 Polynomial Regression Models 210 Model 172 7.11 Partial Correlation Coefficients 213 6.8 Choice of Functional Form 172 Explanation of Simple and Partial 6.9 A Note on the Nature of the Stochastic Error Correlation Coefficients 213 Term: Additive versus Multiplicative Interpretation of Simple and Partial Stochastic Error Term 174 Correlation Coefficients 214 Summary and Conclusions 175 Summary and Conclusions 215 Exercises 176 Exercises 216 Appendix 6A 182 Appendix 7A 227 6A.1 Derivation of Least-Squares Estimators 7A.1 Derivation of OLS Estimators for Regression through the Origin 182 Given in Equations (7.4.3) to (7.4.5) 227 6A.2 Proof that a Standardized Variable 7A.2 Equality between the Coefficients of PGNP Has Zero Mean and Unit Variance 183 in Equations (7.3.5) and (7.6.2) 229 6A.3 Logarithms 184 7A.3 Derivation of Equation (7.4.19) 229 6A.4 Growth Rate Formulas 186 7A.4 Maximum Likelihood Estimation 6A.5 Box-Cox Regression Model 187 of the Multiple Regression Model 230 7A.5 EViews Output of the Cobb–Douglas CHAPTER 7 Production Function in Equation (7.9.4) 231 Multiple Regression Analysis: The Problem of Estimation 188 CHAPTER 8 7.1 The Three-Variable Model: Notation Multiple Regression Analysis: The Problem and Assumptions 188 7.2 Interpretation of Multiple Regression of Inference 233 Equation 191 8.1 The Normality Assumption Once Again 233 7.3 The Meaning of Partial Regression 8.2 Hypothesis Testing in Multiple Regression: Coefficients 191 General Comments 234 7.4 OLS and ML Estimation of the Partial 8.3 Hypothesis Testing about Individual Regression Coefficients 192 Regression Coefficients 235 OLS Estimators 192 8.4 Testing the Overall Significance of the Sample Variances and Standard Errors Regression 237 of OLS Estimators 194 The Analysis of Variance Approach to Testing the Properties of OLS Estimators 195 Overall Significance of an Observed Multiple Maximum Likelihood Estimators 196 Regression: The F Test 238 7.5 The Multiple Coefficient of Determination R2 Testing the Overall Significance of a Multiple and the Multiple Coefficient Regression: The F Test 240 of Correlation R 196 An Important Relationship between R2 and F 241 7.6 An Illustrative Example 198 Testing the Overall Significance of a Multiple Regression on Standardized Variables 199 Regression in Terms of R2 242 Impact on the Dependent Variable of a Unit The “Incremental” or “Marginal” Contribution Change in More than One Regressor 199 of an Explanatory Variable 243 7.7 Simple Regression in the Context 8.5 Testing the Equality of Two Regression of Multiple Regression: Introduction to Coefficients 246 Specification Bias 200 8.6 Restricted Least Squares: Testing Linear 7.8 R2 and the Adjusted R2 201 Equality Restrictions 248 Comparing Two R2 Values 203 The t-Test Approach 249 guj75772_fm.qxd 05/09/2008 11:15 AM Page ix Contents ix The F-Test Approach: Restricted Least PART TWO Squares 249 RELAXING THE ASSUMPTIONS OF THE General F Testing 252 8.7 Testing for Structural or Parameter Stability CLASSICAL MODEL 315 of Regression Models: The Chow Test 254 8.8 Prediction with Multiple Regression 259 CHAPTER 10 8.9 The Troika of Hypothesis Tests: The Multicollinearity: What Happens Likelihood Ratio (LR), Wald (W), and If the Regressors Are Correlated? 320 Lagrange Multiplier (LM) Tests 259 10.1 The Nature of Multicollinearity 321 8.10 Testing the Functional Form of Regression: 10.2 Estimation in the Presence of Perfect Choosing between Linear and Log–Linear Multicollinearity 324 Regression Models 260 10.3 Estimation in the Presence of “High” Summary and Conclusions 262 but “Imperfect” Multicollinearity 325 Exercises 262 10.4 Multicollinearity: Much Ado about Nothing? Appendix 8A: Likelihood Theoretical Consequences Ratio (LR) Test 274 of Multicollinearity 326 10.5 Practical Consequences CHAPTER 9 of Multicollinearity 327 Dummy Variable Regression Models 277 Large Variances and Covariances of OLS Estimators 328 9.1 The Nature of Dummy Variables 277 Wider Confidence Intervals 330 9.2 ANOVA Models 278 “Insignificant” t Ratios 330 Caution in the Use of Dummy Variables 281 A High R2 but Few Significant t Ratios 331 9.3 ANOVA Models with Two Qualitative Sensitivity of OLS Estimators and Their Variables 283 Standard Errors to Small Changes in Data 331 9.4 Regression with a Mixture of Quantitative Consequences of Micronumerosity 332 and Qualitative Regressors: The ANCOVA 10.6 An Illustrative Example 332 Models 283 10.7 Detection of Multicollinearity 337 9.5 The Dummy Variable Alternative 10.8 Remedial Measures 342 to the Chow Test 285 Do Nothing 342 9.6 Interaction Effects Using Dummy Rule-of-Thumb Procedures 342 Variables 288 10.9 Is Multicollinearity Necessarily Bad? Maybe 9.7 The Use of Dummy Variables in Seasonal Not, If the Objective Is Prediction Only 347 Analysis 290 10.10 An Extended Example: The Longley 9.8 Piecewise Linear Regression 295 Data 347 9.9 Panel Data Regression Models 297 Summary and Conclusions 350 9.10 Some Technical Aspects of the Dummy Exercises 351 Variable Technique 297 The Interpretation of Dummy Variables CHAPTER 11 in Semilogarithmic Regressions 297 Heteroscedasticity: What Happens If Dummy Variables and Heteroscedasticity 298 Dummy Variables and Autocorrelation 299 the Error Variance Is Nonconstant? 365 What Happens If the Dependent Variable 11.1 The Nature of Heteroscedasticity 365 Is a Dummy Variable? 299 11.2 OLS Estimation in the Presence 9.11 Topics for Further Study 300 of Heteroscedasticity 370 9.12 A Concluding Example 300 11.3 The Method of Generalized Least Summary and Conclusions 304 Squares (GLS) 371 Exercises 305 Difference between OLS and GLS 373 Appendix 9A: Semilogarithmic Regression 11.4 Consequences of Using OLS in the Presence with Dummy Regressor 314 of Heteroscedasticity 374 guj75772_fm.qxd 05/09/2008 11:15 AM Page x x Contents OLS Estimation Allowing for 12.7 What to Do When You Find Autocorrelation: Heteroscedasticity 374 Remedial Measures 440 OLS Estimation Disregarding 12.8 Model Mis-Specification versus Pure Heteroscedasticity 374 Autocorrelation 441 A Technical Note 376 12.9 Correcting for (Pure) Autocorrelation: 11.5 Detection of Heteroscedasticity 376 The Method of Generalized Least Informal Methods 376 Squares (GLS) 442 Formal Methods 378 When ρ Is Known 442 11.6 Remedial Measures 389 When ρ Is Not Known 443 When σ 2i Is Known: The Method of Weighted 12.10 The Newey–West Method of Correcting Least Squares 389 the OLS Standard Errors 447 When σ 2i Is Not Known 391 12.11 OLS versus FGLS and HAC 448 11.7 Concluding Examples 395 12.12 Additional Aspects of Autocorrelation 449 11.8 A Caution about Overreacting Dummy Variables and Autocorrelation 449 to Heteroscedasticity 400 ARCH and GARCH Models 449 Summary and Conclusions 400 Coexistence of Autocorrelation Exercises 401 and Heteroscedasticity 450 Appendix 11A 409 12.13 A Concluding Example 450 11A.1 Proof of Equation (11.2.2) 409 Summary and Conclusions 452 11A.2 The Method of Weighted Least Exercises 453 Squares 409 Appendix 12A 466 11A.3 Proof that E(σ̂ 2 ) σ2 in the Presence 12A.1 Proof that the Error Term vt in of Heteroscedasticity 410 Equation (12.1.11) Is Autocorrelated 466 11A.4 White’s Robust Standard Errors 411 12A.2 Proof of Equations (12.2.3), (12.2.4), and (12.2.5) 466 CHAPTER 12 Autocorrelation: What Happens If the Error CHAPTER 13 Terms Are Correlated? 412 Econometric Modeling: Model Specification and Diagnostic Testing 467 12.1 The Nature of the Problem 413 12.2 OLS Estimation in the Presence 13.1 Model Selection Criteria 468 of Autocorrelation 418 13.2 Types of Specification Errors 468 12.3 The BLUE Estimator in the Presence 13.3 Consequences of Model Specification of Autocorrelation 422 Errors 470 12.4 Consequences of Using OLS Underfitting a Model (Omitting a Relevant in the Presence of Autocorrelation 423 Variable) 471 OLS Estimation Allowing Inclusion of an Irrelevant Variable for Autocorrelation 423 (Overfitting a Model) 473 OLS Estimation Disregarding 13.4 Tests of Specification Errors 474 Autocorrelation 423 Detecting the Presence of Unnecessary Variables 12.5 Relationship between Wages and Productivity (Overfitting a Model) 475 in the Business Sector of the United States, Tests for Omitted Variables and Incorrect 1960–2005 428 Functional Form 477 12.6 Detecting Autocorrelation 429 13.5 Errors of Measurement 482 I. Graphical Method 429 Errors of Measurement in the Dependent II. The Runs Test 431 Variable Y 482 III. Durbin–Watson d Test 434 Errors of Measurement in the Explanatory IV. A General Test of Autocorrelation: Variable X 483 The Breusch–Godfrey (BG) Test 438 13.6 Incorrect Specification of the Stochastic Why So Many Tests of Autocorrelation? 440 Error Term 486 guj75772_fm.qxd 09/09/2008 12:15 PM Page xi Contents xi 13.7 Nested versus Non-Nested Models 487 14.3 Estimating Nonlinear Regression Models: 13.8 Tests of Non-Nested Hypotheses 488 The Trial-and-Error Method 527 The Discrimination Approach 488 14.4 Approaches to Estimating Nonlinear The Discerning Approach 488 Regression Models 529 13.9 Model Selection Criteria 493 Direct Search or Trial-and-Error The R2 Criterion 493 or Derivative-Free Method 529 Adjusted R2 493 Direct Optimization 529 Akaike’s Information Criterion (AIC) 494 Iterative Linearization Method 530 Schwarz’s Information Criterion (SIC) 494 14.5 Illustrative Examples 530 Mallows’s Cp Criterion 494 Summary and Conclusions 535 A Word of Caution about Model Exercises 535 Selection Criteria 495 Appendix 14A 537 Forecast Chi-Square (χ2) 496 14A.1 Derivation of Equations (14.2.4) 13.10 Additional Topics in Econometric and (14.2.5) 537 Modeling 496 14A.2 The Linearization Method 537 Outliers, Leverage, and Influence 496 14A.3 Linear Approximation of the Exponential Recursive Least Squares 498 Function Given in Equation (14.2.2) 538 Chow’s Prediction Failure Test 498 Missing Data 499 CHAPTER 15 13.11 Concluding Examples 500 Qualitative Response Regression Models 541 1. A Model of Hourly Wage Determination 500 2. Real Consumption Function for the United 15.1 The Nature of Qualitative Response States, 1947–2000 505 Models 541 13.12 Non-Normal Errors and Stochastic 15.2 The Linear Probability Model (LPM) 543 Regressors 509 Non-Normality of the Disturbances ui 544 1. What Happens If the Error Term Is Not Heteroscedastic Variances Normally Distributed? 509 of the Disturbances 544 2. Stochastic Explanatory Variables 510 Nonfulfillment of 0 ≤ E(Yi | Xi) ≤ 1 545 13.13 A Word to the Practitioner 511 Questionable Value of R2 as a Measure Summary and Conclusions 512 of Goodness of Fit 546 Exercises 513 15.3 Applications of LPM 549 Appendix 13A 519 15.4 Alternatives to LPM 552 13A.1 The Proof that E(b1 2) = β2 + β3b3 2 15.5 The Logit Model 553 [Equation (13.3.3)] 519 15.6 Estimation of the Logit Model 555 13A.2 The Consequences of Including an Irrelevant Data at the Individual Level 556 Variable: The Unbiasedness Property 520 Grouped or Replicated Data 556 13A.3 The Proof of Equation (13.5.10) 521 15.7 The Grouped Logit (Glogit) Model: A 13A.4 The Proof of Equation (13.6.2) 522 Numerical Example 558 Interpretation of the Estimated Logit Model 558 PART THREE 15.8 The Logit Model for Ungrouped TOPICS IN ECONOMETRICS 523 or Individual Data 561 15.9 The Probit Model 566 Probit Estimation with Grouped CHAPTER 14 Data: gprobit 567 Nonlinear Regression Models 525 The Probit Model for Ungrouped 14.1 Intrinsically Linear and Intrinsically or Individual Data 570 Nonlinear Regression Models 525 The Marginal Effect of a Unit Change 14.2 Estimation of Linear and Nonlinear in the Value of a Regressor in the Various Regression Models 527 Regression Models 571 guj75772_fm.qxd 09/09/2008 12:15 PM Page xii xii Contents 15.10 Logit and Probit Models 571 17.3 Estimation of Distributed-Lag Models 623 15.11 The Tobit Model 574 Ad Hoc Estimation of Distributed-Lag Illustration of the Tobit Model: Ray Fair’s Model Models 623 of Extramarital Affairs 575 17.4 The Koyck Approach to Distributed-Lag 15.12 Modeling Count Data: The Poisson Models 624 Regression Model 576 The Median Lag 627 15.13 Further Topics in Qualitative Response The Mean Lag 627 Regression Models 579 17.5 Rationalization of the Koyck Model: The Ordinal Logit and Probit Models 580 Adaptive Expectations Model 629 Multinomial Logit and Probit Models 580 17.6 Another Rationalization of the Koyck Model: Duration Models 580 The Stock Adjustment, or Partial Adjustment, Summary and Conclusions 581 Model 632 Exercises 582 17.7 Combination of Adaptive Expectations Appendix 15A 589 and Partial Adjustment Models 634 15A.1 Maximum Likelihood Estimation of the Logit 17.8 Estimation of Autoregressive Models 634 and Probit Models for Individual (Ungrouped) 17.9 The Method of Instrumental Data 589 Variables (IV) 636 17.10 Detecting Autocorrelation in Autoregressive CHAPTER 16 Models: Durbin h Test 637 Panel Data Regression Models 591 17.11 A Numerical Example: The Demand for Money in Canada, 1979–I to 1988–IV 639 16.1 Why Panel Data? 592 17.12 Illustrative Examples 642 16.2 Panel Data: An Illustrative Example 593 17.13 The Almon Approach to Distributed-Lag 16.3 Pooled OLS Regression or Constant Models: The Almon or Polynomial Distributed Coefficients Model 594 Lag (PDL) 645 16.4 The Fixed Effect Least-Squares Dummy 17.14 Causality in Economics: The Granger Variable (LSDV) Model 596 Causality Test 652 A Caution in the Use of the Fixed Effect The Granger Test 653 LSDV Model 598 A Note on Causality and Exogeneity 657 16.5 The Fixed-Effect Within-Group (WG) Summary and Conclusions 658 Estimator 599 Exercises 659 16.6 The Random Effects Model (REM) 602 Appendix 17A 669 Breusch and Pagan Lagrange 17A.1 The Sargan Test for the Validity Multiplier Test 605 of Instruments 669 16.7 Properties of Various Estimators 605 16.8 Fixed Effects versus Random Effects Model: Some Guidelines 606 PART FOUR 16.9 Panel Data Regressions: Some Concluding SIMULTANEOUS-EQUATION Comments 607 MODELS AND TIME SERIES 16.10 Some Illustrative Examples 607 ECONOMETRICS 671 Summary and Conclusions 612 Exercises 613 CHAPTER 18 Simultaneous-Equation Models 673 CHAPTER 17 Dynamic Econometric Models: Autoregressive 18.1 The Nature of Simultaneous-Equation and Distributed-Lag Models 617 Models 673 18.2 Examples of Simultaneous-Equation 17.1 The Role of “Time,’’ or “Lag,’’ Models 674 in Economics 618 18.3 The Simultaneous-Equation Bias: 17.2 The Reasons for Lags 622 Inconsistency of OLS Estimators 679 guj75772_fm.qxd 05/09/2008 11:15 AM Page xiii Contents xiii 18.4 The Simultaneous-Equation Bias: A Numerical 21.2 Key Concepts 739 Example 682 21.3 Stochastic Processes 740 Summary and Conclusions 684 Stationary Stochastic Processes 740 Exercises 684 Nonstationary Stochastic Processes 741 21.4 Unit Root Stochastic Process 744 CHAPTER 19 21.5 Trend Stationary (TS) and Difference The Identification Problem 689 Stationary (DS) Stochastic Processes 745 21.6 Integrated Stochastic Processes 746 19.1 Notations and Definitions 689 Properties of Integrated Series 747 19.2 The Identification Problem 692 21.7 The Phenomenon of Spurious Underidentification 692 Regression 747 Just, or Exact, Identification 694 21.8 Tests of Stationarity 748 Overidentification 697 1. Graphical Analysis 749 19.3 Rules for Identification 699 2. Autocorrelation Function (ACF) The Order Condition of Identifiability 699 and Correlogram 749 The Rank Condition of Identifiability 700 Statistical Significance of Autocorrelation 19.4 A Test of Simultaneity 703 Coefficients 753 Hausman Specification Test 703 21.9 The Unit Root Test 754 19.5 Tests for Exogeneity 705 The Augmented Dickey–Fuller (ADF) Summary and Conclusions 706 Test 757 Exercises 706 Testing the Significance of More than One Coefficient: The F Test 758 CHAPTER 20 The Phillips–Perron (PP) Unit Simultaneous-Equation Methods 711 Root Tests 758 20.1 Approaches to Estimation 711 Testing for Structural Changes 758 20.2 Recursive Models and Ordinary A Critique of the Unit Root Tests 759 Least Squares 712 21.10 Transforming Nonstationary Time Series 760 20.3 Estimation of a Just Identified Equation: The Difference-Stationary Processes 760 Method of Indirect Least Squares (ILS) 715 Trend-Stationary Processes 761 An Illustrative Example 715 21.11 Cointegration: Regression of a Unit Properties of ILS Estimators 718 Root Time Series on Another Unit Root 20.4 Estimation of an Overidentified Equation: Time Series 762 The Method of Two-Stage Least Squares Testing for Cointegration 763 (2SLS) 718 Cointegration and Error Correction 20.5 2SLS: A Numerical Example 721 Mechanism (ECM) 764 20.6 Illustrative Examples 724 21.12 Some Economic Applications 765 Summary and Conclusions 730 Summary and Conclusions 768 Exercises 730 Exercises 769 Appendix 20A 735 20A.1 Bias in the Indirect Least-Squares CHAPTER 22 Estimators 735 Time Series Econometrics: 20A.2 Estimation of Standard Errors of 2SLS Forecasting 773 Estimators 736 22.1 Approaches to Economic Forecasting 773 CHAPTER 21 Exponential Smoothing Methods 774 Single-Equation Regression Models 774 Time Series Econometrics: Simultaneous-Equation Regression Some Basic Concepts 737 Models 774 21.1 A Look at Selected U.S. Economic Time ARIMA Models 774 Series 738 VAR Models 775 guj75772_fm.qxd 05/09/2008 11:15 AM Page xiv xiv Contents 22.2 AR, MA, and ARIMA Modeling of Time Expected Value 808 Series Data 775 Properties of Expected Values 809 An Autoregressive (AR) Process 775 Variance 810 A Moving Average (MA) Process 776 Properties of Variance 811 An Autoregressive and Moving Average (ARMA) Covariance 811 Process 776 Properties of Covariance 812 An Autoregressive Integrated Moving Correlation Coefficient 812 Average (ARIMA) Process 776 Conditional Expectation and Conditional 22.3 The Box–Jenkins (BJ) Methodology 777 Variance 813 22.4 Identification 778 Properties of Conditional Expectation 22.5 Estimation of the ARIMA Model 782 and Conditional Variance 814 22.6 Diagnostic Checking 782 Higher Moments of Probability 22.7 Forecasting 782 Distributions 815 22.8 Further Aspects of the BJ Methodology 784 A.6 Some Important Theoretical Probability 22.9 Vector Autoregression (VAR) 784 Distributions 816 Estimation or VAR 785 Normal Distribution 816 Forecasting with VAR 786 The χ2 (Chi-Square) Distribution 819 VAR and Causality 787 Student’s t Distribution 820 Some Problems with VAR Modeling 788 The F Distribution 821 An Application of VAR: A VAR Model of the Texas The Bernoulli Binomial Distribution 822 Economy 789 Binomial Distribution 822 22.10 Measuring Volatility in Financial Time Series: The Poisson Distribution 823 The ARCH and GARCH Models 791 A.7 Statistical Inference: Estimation 823 What to Do If ARCH Is Present 795 Point Estimation 823 A Word on the Durbin–Watson d and the ARCH Interval Estimation 824 Effect 796 Methods of Estimation 825 A Note on the GARCH Model 796 Small-Sample Properties 826 22.11 Concluding Examples 796 Large-Sample Properties 828 Summary and Conclusions 798 A.8 Statistical Inference: Hypothesis Testing 831 Exercises 799 The Confidence Interval Approach 832 The Test of Significance Approach 836 References 837 APPENDIX A A Review of Some Statistical Concepts 801 APPENDIX B A.1 Summation and Product Operators 801 Rudiments of Matrix Algebra 838 A.2 Sample Space, Sample Points, B.1 Definitions 838 and Events 802 Matrix 838 A.3 Probability and Random Variables 802 Column Vector 838 Probability 802 Row Vector 839 Random Variables 803 Transposition 839 A.4 Probability Density Function (PDF) 803 Submatrix 839 Probability Density Function of a Discrete B.2 Types of Matrices 839 Random Variable 803 Square Matrix 839 Probability Density Function of a Continuous Diagonal Matrix 839 Random Variable 804 Scalar Matrix 840 Joint Probability Density Functions 805 Identity, or Unit, Matrix 840 Marginal Probability Density Function 805 Symmetric Matrix 840 Statistical Independence 806 Null Matrix 840 A.5 Characteristics of Probability Null Vector 840 Distributions 808 Equal Matrices 840 guj75772_fm.qxd 05/09/2008 11:15 AM Page xv Contents xv B.3 Matrix Operations 840 C.9 Prediction Using Multiple Regression: Matrix Matrix Addition 840 Formulation 861 Matrix Subtraction 841 Mean Prediction 861 Scalar Multiplication 841 Variance of Mean Prediction 862 Matrix Multiplication 841 Individual Prediction 862 Properties of Matrix Multiplication 842 Variance of Individual Prediction 862 Matrix Transposition 843 C.10 Summary of the Matrix Approach: An Matrix Inversion 843 Illustrative Example 863 B.4 Determinants 843 C.11 Generalized Least Squares (GLS) 867 Evaluation of a Determinant 844 C.12 Summary and Conclusions 868 Properties of Determinants 844 Exercises 869 Rank of a Matrix 845 Appendix CA 874 Minor 846 CA.1 Derivation of k Normal or Simultaneous Cofactor 846 Equations 874 B.5 Finding the Inverse of a Square Matrix 847 CA.2 Matrix Derivation of Normal Equations 875 B.6 Matrix Differentiation 848 ˆ 875 CA.3 Variance–Covariance Matrix of  References 848 CA.4 BLUE Property of OLS Estimators 875 APPENDIX C APPENDIX D The Matrix Approach to Linear Regression Statistical Tables 877 Model 849 C.1 The k-Variable Linear Regression APPENDIX E Model 849 Computer Output of EViews, MINITAB, C.2 Assumptions of the Classical Linear Excel, and STATA 894 Regression Model in Matrix Notation 851 C.3 OLS Estimation 853 E.1 EViews 894 An Illustration 855 E.2 MINITAB 896 Variance-Covariance Matrix of β̂ 856 E.3 Excel 897 Properties of OLS Vector β̂ 858 E.4 STATA 898 C.4 The Coefficient of Determination R2 in Matrix E.5 Concluding Comments 898 Notation 858 References 899 C.5 The Correlation Matrix 859 C.6 Hypothesis Testing about Individual APPENDIX F Regression Coefficients in Matrix Economic Data on the World Wide Web 900 Notation 859 C.7 Testing the Overall Significance of Regression: Analysis of Variance in Matrix Selected Bibliography 902 Notation 860 Name Index 905 C.8 Testing Linear Restrictions: General F Testing Using Matrix Notation 861 Subject Index 909 guj75772_fm.qxd 05/09/2008 11:15 AM Page xvi Preface Objective of the Book The first edition of Basic Econometrics was published thirty years ago. Over the years, there have been important developments in the theory and practice of econometrics. In each of the subsequent editions, I have tried to incorporate the major developments in the field. The fifth edition continues that tradition. What has not changed, however, over all these years is my firm belief that econometrics can be taught to the beginner in an intuitive and informative way without resorting to matrix algebra, calculus, or statistics beyond the introductory level. Some subject material is inherently technical. In that case I have put the material in the appropriate appendix or refer the reader to the appropriate sources. Even then, I have tried to simplify the technical material so that the reader can get an intuitive understanding of this material. I am pleasantly surprised not only by the longevity of this book but also by the fact that the book is widely used not only by students of economics and finance but also by students and researchers in the fields of politics, international relations, agriculture, and health sciences. All these students will find the new edition with its expanded topics and concrete applications very useful. In this edition I have paid even more attention to the relevance and timeliness of the real data used in the text. In fact, I have added about fifteen new illustra- tive examples and more than thirty new end-of-chapter exercises. Also, I have updated the data for about two dozen of the previous edition’s examples and more than twenty exercises. Although I am in the eighth decade of my life, I have not lost my love for econometrics, and I strive to keep up with the major developments in the field. To assist me in this endeavor, I am now happy to have Dr. Dawn Porter, Assistant Professor of Statistics at the Marshall School of Business at the University of Southern California in Los Angeles, as my co-author. Both of us have been deeply involved in bringing the fifth edition of Basic Econometrics to fruition. Major Features of the Fifth Edition Before discussing the specific changes in the various chapters, the following features of the new edition are worth noting: 1. Practically all of the data used in the illustrative examples have been updated. 2. Several new examples have been added. 3. In several chapters, we have included extended concluding examples that illustrate the various points made in the text. 4. Concrete computer printouts of several examples are included in the book. Most of these results are based on EViews (version 6) and STATA (version 10), as well as MINITAB (version 15). 5. Several new diagrams and graphs are included in various chapters. 6. Several new data-based exercises are included in the various chapters. 7. Small-sized data are included in the book, but large sample data are posted on the book’s website, thereby minimizing the size of the text. The website will also publish all of the data used in the book and will be periodically updated. xvi guj75772_fm.qxd 05/09/2008 11:15 AM Page xvii Preface xvii 8. In a few chapters, we have included class exercises in which students are encouraged to obtain their own data and implement the various techniques discussed in the book. Some Monte Carlo simulations are also included in the book. Specific Changes to the Fifth Edition Some chapter-specific changes are as follows: 1. The assumptions underlying the classical linear regression model (CLRM) introduced in Chapter 3 now make a careful distinction between fixed regressors (explanatory variables) and random regressors. We discuss the importance of the distinction. 2. The appendix to Chapter 6 discusses the properties of logarithms, the Box-Cox trans- formations, and various growth formulas. 3. Chapter 7 now discusses not only the marginal impact of a single regressor on the dependent variable but also the impacts of simultaneous changes of all the explanatory variables on the dependent variable. This chapter has also been reorganized in the same structure as the assumptions from Chapter 3. 4. A comparison of the various tests of heteroscedasticity is given in Chapter 11. 5. There is a new discussion of the impact of structural breaks on autocorrelation in Chapter 12. 6. New topics included in Chapter 13 are missing data, non-normal error term, and stochastic, or random, regressors. 7. A non-linear regression model discussed in Chapter 14 has a concrete application of the Box-Cox transformation. 8. Chapter 15 contains several new examples that illustrate the use of logit and probit models in various fields. 9. Chapter 16 on panel data regression models has been thoroughly revised and illus- trated with several applications. 10. An extended discussion of Sims and Granger causality tests is now included in Chap- ter 17. 11. Stationary and non-stationary time series, as well as some of the problems associated with various tests of stationarity, are now thoroughly discussed in Chapter 21. 12. Chapter 22 includes a discussion on why taking the first differences of a time series for the purpose of making it stationary may not be the appropriate strategy in some situations. Besides these specific changes, errors and misprints in the previous editions have been cor- rected and the discussions of several topics in the various chapters have been streamlined. Organization and Options The extensive coverage in this edition gives the instructor substantial flexibility in choos- ing topics that are appropriate to the intended audience. Here are suggestions about how this book may be used. One-semester course for the nonspecialist: Appendix A, Chapters 1 through 9, an overview of Chapters 10, 11, 12 (omitting all the proofs). One-semester course for economics majors: Appendix A, Chapters 1 through 13. guj75772_fm.qxd 05/09/2008 11:15 AM Page xviii xviii Preface Two-semester course for economics majors: Appendices A, B, C, Chapters 1 to 22. Chapters 14 and 16 may be covered on an optional basis. Some of the technical appen- dices may be omitted. Graduate and postgraduate students and researchers: This book is a handy refer- ence book on the major themes in econometrics. Supplements A comprehensive website contains the following supplementary material: –Data from the text, as well as additional large set data referenced in the book; the data will be periodically updated by the authors. –A Solutions Manual, written by Dawn Porter, providing answers to all of the questions and problems throughout the text. –A digital image library containing all of the graphs and figures from the text. For more information, please go to www.mhhe.com/gujarati5e guj75772_fm.qxd 05/09/2008 11:15 AM Page xix Acknowledgments Since the publication of the first edition of this book in 1978, we have received valuable advice, comments, criticism, and suggestions from a variety of people. In particular, we would like to acknowledge the help we have received from Michael McAleer of the University of Western Australia, Peter Kennedy of Simon Frazer University in Canada, Kenneth White, of the University of British Columbia, George K. Zestos, of Christopher Newport University, Virginia, and Paul Offner, of Georgetown University, Washington, D.C. We are also grateful to several people who have influenced us by their scholarship. We especially want to thank Arthur Goldberger of the University of Wisconsin, William Greene of New York University, and the late G. S. Maddala. We continue to be grateful to the following reviewers who provided valuable insight, criticism, and suggestions for previous editions of this text: Michael A. Grove at the University of Oregon, Harumi Ito at Brown University, Han Kim at South Dakota University, Phanindra V. Wunnava at Middlebury College, and Andrew Paizis of the City University of New York. Several authors have influenced the writing of this text. In particular, we are grateful to these authors: Chandan Mukherjee, director of the Centre for Development Studies, Trivandrum, India; Howard White and Marc Wuyts, both at the Institute of Social Studies in the Netherlands; Badi H. Baltagi, Texas A&M University; B. Bhaskara Rao, University of New South Wales, Australia; R. Carter Hill, Louisiana University; William E. Griffiths, University of New England; George G. Judge, University of California at Berkeley; Marno Verbeek, Center for Economic Studies, KU Leuven; Jeffrey Wooldridge, Michigan State University; Kerry Patterson, University of Reading, U.K.; Francis X. Diebold, Wharton School, University of Pennsylvania; Wojciech W. Charemza and Derek F. Deadman, both of the University of Leicester, U.K.; and Gary Koop, University of Glasgow. A number of very valuable comments and suggestions given by reviewers of the fourth edition have greatly improved this edition. We would like to thank the following: Valerie Bencivenga Gary Krueger University of Texas–Austin Macalester College Andrew Economopoulos Subal Kumbhakar Ursinus College Binghamton University Eric Eide Tae-Hwy Lee Brigham Young University University of California–Riverside Gary Ferrier Solaiman Miah University of Arkansas–Fayetteville West Virginia State University David Garman Fabio Milani Tufts University University of California–Irvine David Harris Helen Naughton Benedictine College University of Oregon Don Holley Solomon Smith Boise State University Langston University George Jakubson Kay Strong Cornell University Bowling Green State University Bruce Johnson Derek Tittle Centre College of Kentucky Georgia Institute of Technology Duke Kao Tiemen Woutersen Syracuse University Johns Hopkins University xix guj75772_fm.qxd 05/09/2008 11:15 AM Page xx xx Acknowledgments We would like to thank students and teachers all over the world who have not only used this book but have communicated with us about various aspects of the book. For their behind-the-scenes help at McGraw-Hill, we are grateful to Douglas Reiner, Noelle Fox, and Anne Hilbert. Finally, but not least important, Dr. Gujarati would like to thank his daughters, Joan and Diane, for their constant support and encouragement in the preparation of this and the pre- vious editions. Damodar N. Gujarati Dawn C. Porter guj75772_intro.qxd 23/08/2008 10:29 AM Page 1 Introduction I.1 What Is Econometrics? Literally interpreted, econometrics means “economic measurement.” Although measure- ment is an important part of econometrics, the scope of econometrics is much broader, as can be seen from the following quotations: Econometrics, the result of a certain outlook on the role of economics, consists of the applica- tion of mathematical statistics to economic data to lend empirical support to the models constructed by mathematical economics and to obtain numerical results.1... econometrics may be defined as the quantitative analysis of actual economic phenomena based on the concurrent development of theory and observation, related by appropriate methods of inference.2 Econometrics may be defined as the social science in which the tools of economic theory, mathematics, and statistical inference are applied to the analysis of economic phenomena.3 Econometrics is concerned with the empirical determination of economic laws.4 The art of the econometrician consists in finding the set of assumptions that are both suffi- ciently specific and sufficiently realistic to allow him to take the best possible advantage of the data available to him.5 Econometricians... are a positive help in trying to dispel the poor public image of economics (quantitative or otherwise) as a subject in which empty boxes are opened by assuming the existence of can-openers to reveal contents which any ten economists will interpret in 11 ways.6 The method of econometric research aims, essentially, at a conjunction of economic theory and actual measurements, using the theory and technique of statistical inference as a bridge pier.7 1 Gerhard Tintner, Methodology of Mathematical Economics and Econometrics, The University of Chicago Press, Chicago, 1968, p. 74. 2 P. A. Samuelson, T. C. Koopmans, and J. R. N. Stone, “Report of the Evaluative Committee for Econo- metrica,” Econometrica, vol. 22, no. 2, April 1954, pp. 141–146. 3 Arthur S. Goldberger, Econometric Theory, John Wiley & Sons, New York, 1964, p. 1. 4 H. Theil, Principles of Econometrics, John Wiley & Sons, New York, 1971, p. 1. 5 E. Malinvaud, Statistical Methods of Econometrics, Rand McNally, Chicago, 1966, p. 514. 6 Adrian C. Darnell and J. Lynne Evans, The Limits of Econometrics, Edward Elgar Publishing, Hants, England, 1990, p. 54. 7 T. Haavelmo, “The Probability Approach in Econometrics,” Supplement to Econometrica, vol. 12, 1944, preface p. iii. 1 guj75772_intro.qxd 23/08/2008 10:29 AM Page 2 2 Basic Econometrics I.2 Why a Separate Discipline? As the preceding definitions suggest, econometrics is an amalgam of economic theory, mathematical economics, economic statistics, and mathematical statistics. Yet the subject deserves to be studied in its own right for the following reasons. Economic theory makes statements or hypotheses that are mostly qualitative in nature. For example, microeconomic theory states that, other things remaining the same, a reduc- tion in the price of a commodity is expected to increase the quantity demanded of that com- modity. Thus, economic theory postulates a negative or inverse relationship between the price and quantity demanded of a commodity. But the theory itself does not provide any numerical measure of the relationship between the two; that is, it does not tell by how much the quantity will go up or down as a result of a certain change in the price of the commod- ity. It is the job of the econometrician to provide such numerical estimates. Stated differ- ently, econometrics gives empirical content to most economic theory. The main concern of mathematical economics is to express economic theory in mathe- matical form (equations) without regard to measurability or empirical verification of the theory. Econometrics, as noted previously, is mainly interested in the empirical verification of economic theory. As we shall see, the econometrician often uses the mathematical equations proposed by the mathematical economist but puts these equations in such a form that they lend themselves to empirical testing. And this conversion of mathematical into econometric equations requires a great deal of ingenuity and practical skill. Economic statistics is mainly concerned with collecting, processing, and presenting economic data in the form of charts and tables. These are the jobs of the economic statisti- cian. It is he or she who is primarily responsible for collecting data on gross national product (GNP), employment, unemployment, prices, and so on. The data thus collected constitute the raw data for econometric work. But the economic statistician does not go any further, not being concerned with using the collected data to test economic theories. Of course, one who does that becomes an econometrician. Although mathematical statistics provides many tools used in the trade, the econometri- cian often needs special methods in view of the unique nature of most economic data, namely, that the data are not generated as the result of a controlled experiment. The econo- metrician, like the meteorologist, generally depends on data that cannot be controlled directly. As Spanos correctly observes: In econometrics the modeler is often faced with observational as opposed to experimental data. This has two important implications for empirical modeling in econometrics. First, the modeler is required to master very different skills than those needed for analyzing experimen- tal data.... Second, the separation of the data collector and the data analyst requires the mod- eler to familiarize himself/herself thoroughly with the nature and structure of data in question.8 I.3 Methodology of Econometrics How do econometricians proceed in their analysis of an economic problem? That is, what is their methodology? Although there are several schools of thought on econometric methodology, we present here the traditional or classical methodology, which still domi- nates empirical research in economics and other social and behavioral sciences.9 8 Aris Spanos, Probability Theory and Statistical Inference: Econometric Modeling with Observational Data, Cambridge University Press, United Kingdom, 1999, p. 21. 9 For an enlightening, if advanced, discussion on econometric methodology, see David F. Hendry, Dynamic Econometrics, Oxford University Press, New York, 1995. See also Aris Spanos, op. cit. guj75772_intro.qxd 23/08/2008 10:29 AM Page 3 Introduction 3 Broadly speaking, traditional econometric methodology proceeds along the following lines: 1. Statement of theory or hypothesis. 2. Specification of the mathematical model of the theory. 3. Specification of the statistical, or econometric, model. 4. Obtaining the data. 5. Estimation of the parameters of the econometric model. 6. Hypothesis testing. 7. Forecasting or prediction. 8. Using the model for control or policy purposes. To illustrate the preceding steps, let us consider the well-known Keynesian theory of consumption. 1. Statement of Theory or Hypothesis Keynes stated: The fundamental psychological law... is that men [women] are disposed, as a rule and on average, to increase their consumption as their income increases, but not as much as the increase in their income.10 In short, Keynes postulated that the marginal propensity to consume (MPC), the rate of change of consumption for a unit (say, a dollar) change in income, is greater than zero but less than 1. 2. Specification of the Mathematical Model of Consumption Although Keynes postulated a positive relationship between consumption and income, he did not specify the precise form of the functional relationship between the two. For simplicity, a mathematical economist might suggest the following form of the Keynesian consumption function: Y = β1 + β2 X 0 < β2 < 1 (I.3.1) where Y = consumption expenditure and X = income, and where β1 and β2 , known as the parameters of the model, are, respectively, the intercept and slope coefficients. The slope coefficient β2 measures the MPC. Geometrically, Equation I.3.1 is as shown in Figure I.1. This equation, which states that consumption is linearly related to income, is an example of a mathematical model of the re