Introduction to Econometrics

[Pages:42]Introduction to Econometrics

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Introduction to Econometrics

FOURTH EDITION

James H. Stock

Harvard University

Mark W. Watson

Princeton University

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New York, NY

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Vice President, Business, Economics, and UK Courseware: Donna Battista Director of Portfolio Management: Adrienne D'Ambrosio Specialist Portfolio Manager: David Alexander Editorial Assistant: Nicole Nedwidek Vice President, Product Marketing: Roxanne McCarley Product Marketing Assistant: Marianela Silvestri Manager of Field Marketing, Business Publishing: Adam Goldstein Executive Field Marketing Manager: Carlie Marvel Vice President, Production and Digital Studio, Arts and Business: Etain O'Dea Director, Production and Digital Studio, Business and Economics: Ashley Santora Managing Producer, Business: Alison Kalil Content Producer: Christine Donovan Operations Specialist: Carol Melville

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About the cover: The cover shows a time series plot of 72 indicators of real economic activity in the United States beginning in 1959. The plot shows the growth of these variables since 1959 and their (roughly) synchronized downturns associated with recessions. These series are a subset of the 131-variable dataset used in Chapter 17 to construct dynamic factor model forecasts of future growth in real GDP.

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Library of Congress Cataloging-in-Publication Data Names: Stock, James H., author. | Watson, Mark W., author. Title: Introduction to econometrics / James H. Stock, Harvard University,

Mark W. Watson, Princeton University. Description: Fourth edition. | New York, NY : Pearson, [2019] | Series:

The Pearson series in economics | Includes bibliographical references and index. Identifiers: LCCN 2018035117 | ISBN 9780134461991 Subjects: LCSH: Econometrics. Classification: LCC HB139 .S765 2019 | DDC 330.01/5195--dc23 LC record available at

ISBN-10: 0-13-446199-1 ISBN-13: 978-0-13-446199-1

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Brief Contents

PART ONE Chapter 1 Chapter 2 Chapter 3

PART TWO Chapter 4 Chapter 5

Chapter 6 Chapter 7 Chapter 8 Chapter 9

PART THREE Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14

PART FOUR Chapter 15 Chapter 16 Chapter 17

PART FIVE Chapter 18 Chapter 19

Introduction and Review Economic Questions and Data 1 Review of Probability 13 Review of Statistics 61

Fundamentals of Regression Analysis Linear Regression with One Regressor 101 Regression with a Single Regressor: Hypothesis Tests and Confidence Intervals 136 Linear Regression with Multiple Regressors 169 Hypothesis Tests and Confidence Intervals in Multiple Regression 205 Nonlinear Regression Functions 235 Assessing Studies Based on Multiple Regression 288

Further Topics in Regression Analysis Regression with Panel Data 319 Regression with a Binary Dependent Variable 350 Instrumental Variables Regression 385 Experiments and Quasi-Experiments 432 Prediction with Many Regressors and Big Data 472

Regression Analysis of Economic Time Series Data Introduction to Time Series Regression and Forecasting 512 Estimation of Dynamic Causal Effects 567 Additional Topics in Time Series Regression 607

Regression Analysis of Economic Time Series Data The Theory of Linear Regression with One Regressor 645 The Theory of Multiple Regression 671

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Contents

Prefacexxvii

PART ONE CHAPTER 1

1.1

1.2 1.3

Introduction and Review

Economic Questions and Data 1

Economic Questions We Examine 1

Question #1: Does Reducing Class Size Improve Elementary School Education? 1 Question #2: Is There Racial Discrimination in the Market for Home Loans? 2 Question #3: How Much Do Cigarette Taxes Reduce Smoking? 3 Question #4: By How Much Will U.S. GDP Grow Next Year? 4 Quantitative Questions, Quantitative Answers 4

Causal Effects and Idealized Experiments 5

Estimation of Causal Effects 5 Prediction, Forecasting, and Causality 6

Data: Sources and Types 6

Experimental versus Observational Data 7 Cross-Sectional Data 7 Time Series Data 8 Panel Data 9

CHAPTER 2 2.1 2.2

2.3

Review of Probability 13

Random Variables and Probability Distributions 14

Probabilities, the Sample Space, and Random Variables 14 Probability Distribution of a Discrete Random Variable 14 Probability Distribution of a Continuous Random Variable 16

Expected Values, Mean, and Variance 18

The Expected Value of a Random Variable 18 The Standard Deviation and Variance 19 Mean and Variance of a Linear Function of a Random Variable 20 Other Measures of the Shape of a Distribution 21 Standardized Random Variables 23

Two Random Variables 23

Joint and Marginal Distributions 23 Conditional Distributions 24 Independence28 Covariance and Correlation 28 The Mean and Variance of Sums of Random Variables 29

vii

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viii

Contents

2.4 The Normal, Chi-Squared, Student t, and F Distributions 33

The Normal Distribution 33 The Chi-Squared Distribution 38 The Student t Distribution 38 The F Distribution 38

2.5 Random Sampling and the Distribution of the Sample Average 39

Random Sampling 39 The Sampling Distribution of the Sample Average 40

2.6 Large-Sample Approximations to Sampling Distributions 43

The Law of Large Numbers and Consistency 43 The Central Limit Theorem 44

APPENDIX 2.1 Derivation of Results in Key Concept 2.3 58 APPENDIX 2.2 The Conditional Mean as the Minimum Mean

Squared Error Predictor 59

CHAPTER 3 3.1 3.2

3.3 3.4 3.5 3.6

Review of Statistics 61

Estimation of the Population Mean 62

Estimators and Their Properties 62 Properties of Y64 The Importance of Random Sampling 65

Hypothesis Tests Concerning the Population Mean 66

Null and Alternative Hypotheses 67 The p-Value67 Calculating the p-Value When sY Is Known 68 The Sample Variance, Sample Standard Deviation, and Standard Error 69 Calculating the p-Value When sY Is Unknown 71 The t-Statistic 71 Hypothesis Testing with a Prespecified Significance Level 72 One-Sided Alternatives 74

Confidence Intervals for the Population Mean 75

Comparing Means from Different Populations 77

Hypothesis Tests for the Difference Between Two Means 77 Confidence Intervals for the Difference Between Two Population Means 78

Differences-of-Means Estimation of Causal Effects Using Experimental Data 79

The Causal Effect as a Difference of Conditional Expectations 79 Estimation of the Causal Effect Using Differences of Means 79

Using the t-Statistic When the Sample Size Is Small 81

The t-Statistic and the Student t Distribution 83 Use of the Student t Distribution in Practice 84

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