I E ntroductory conomEtrIcs S N L i I E ntroductory conomEtrIcs Intuition, Proof, and Practice Jeffrey S. Zax Stanford Economics and Finance An Imprint of Stanford University Press S Stanford, California N L iii Stanford University Press Stanford, California © 2011 by the Board of Trustees of the Leland Stanford Junior University. All rights reserved. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying and recording, or in any information storage or retrieval system without the prior written permission of Stanford University Press. Printed in the United States of America on acid-free, archival-quality paper. Library of Congress Cataloging-in-Publication Data Zax, Jeffrey S. Introductory econometrics: intuition, proof, and practice / Jeffrey S. Zax. p. cm. Includes bibliographical references and index. ISBN 978-0-8047-7262-4 (cloth : alk. paper) 1. Econometrics—Textbooks. I. Title. HB139.Z39 2011 330.01′5195—dc22 2010027083 S N Typeset by Newgen in 11/13 Times New Roman L iv To all the students who have trusted this book to help them understand; to Judy, Jacob, and Talya, who help me understand every day; and to Zvi Griliches, who helped us all understand. S N L v Brief Contents Contents ix List of Tables and Figures xv Preface xxi Chapter 1 What is a regression? 1 Chapter 2 the essential tool 35 Chapter 3 Covariance and Correlation 57 Chapter 4 fitting a Line 88 Chapter 5 from sample to Population 136 Chapter 6 Confidence intervals and Hypothesis tests 191 Chapter 7 inference in ordinary Least squares 232 Chapter 8 What if the Disturbances Have nonzero expectations or Different Variances? 281 Chapter 9 What if the Disturbances Are Correlated? 321 Chapter 10 What if the Disturbances and the explanatory Variables Are related? 363 Chapter 11 What if there is More than one x? 411 Chapter 12 Understanding and interpreting regression with two x’s 453 Chapter 13 Making regression More flexible 501 Chapter 14 More than two explanatory Variables 541 Chapter 15 Categorical Dependent Variables 582 Epilogue 627 Appendix 629 References 637 Index 639 S N vii vii Contents List of Tables and Figures xv Preface xxi Chapter 1 What is a regression? 1 1.0 What We Need to Know When We Finish This Chapter 2 1.1 Why Are We Doing This? 3 1.2 Education and Earnings 5 1.3 What Does a Regression Look Like? 6 1.4 Where Do We Begin? 6 1.5 Where’s the Explanation? 7 1.6 What Do We Look for in This Explanation? 9 1.7 How Do We Interpret the Explanation? 12 1.8 How Do We Evaluate the Explanation? 17 1.9 R2 and the F-statistic 19 1.10 Have We Put This Together in a Responsible Way? 20 1.11 Do Regressions Always Look Like This? 25 1.12 How to Read This Book 28 1.13 Conclusion 28 Exercises 29 Chapter 2 the essential tool 35 2.0 What We Need to Know When We Finish This Chapter 35 2.1 Is This Really a Math Course in Disguise? 37 2.2 Fun with Summations 38 2.3 Constants in Summations 41 2.4 Averages 43 S 2.5 Summations of Sums 44 N ix ix
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