173232298 A Guide To Modern Econometrics By Verbeek 1 10 3i1b61

A Guide to Modern Econometrics 2nd edition

Marno Verbeek Erasmus University Rotterdam

A Guide to Modern Econometrics

A Guide to Modern Econometrics 2nd edition

Marno Verbeek Erasmus University Rotterdam

Copyright  2004

John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England Telephone (+44) 1243 779777

Email (for orders and customer service enquiries): [email protected], or faxed to (+44) 1243 770620. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the Publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional should be sought. Other Wiley Editorial Offices John Wiley & Sons Inc., 111 River Street, Hoboken, NJ 07030, USA Jossey-Bass, 989 Market Street, San Francisco, CA 94103-1741, USA Wiley-VCH Verlag GmbH, Boschstr. 12, D-69469 Weinheim, John Wiley & Sons Australia Ltd, 33 Park Road, Milton, Queensland 4064, Australia John Wiley & Sons (Asia) Pte Ltd, 2 Clementi Loop #02-01, Jin Xing Distripark, Singapore 129809 John Wiley & Sons Canada Ltd, 22 Worcester Road, Etobicoke, Ontario, Canada M9W 1L1 Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. Library of Congress Catag-in-Publication Data Verbeek, Marno. A guide to modern econometrics / Marno Verbeek. – 2nd ed. p. cm. Includes bibliographical references and index. ISBN 0-470-85773-0 (pbk. : alk. paper) 1. Econometrics. 2. Regression analysis. I. Title. HB139.V465 2004 330 .01 5195 – dc22 2004004222 British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN 0-470-85773-0 Typeset in 10/12pt Times by Laserwords Private Limited, Chennai, India Printed and bound in Great Britain by TJ International, Padstow, Cornwall This book is printed on acid-free paper responsibly manufactured from sustainable forestry in which at least two trees are planted for each one used for paper production.

Contents Preface 1 Introduction 1.1 About Econometrics 1.2 The Structure of this Book 1.3 Illustrations and Exercises 2 An Introduction to Linear Regression 2.1 Ordinary Least Squares as an Algebraic Tool 2.1.1 Ordinary Least Squares 2.1.2 Simple Linear Regression 2.1.3 Example: Individual Wages 2.1.4 Matrix Notation 2.2 The Linear Regression Model 2.3 Small Sample Properties of the OLS Estimator 2.3.1 The Gauss–Markov Assumptions 2.3.2 Properties of the OLS Estimator 2.3.3 Example: Individual Wages (Continued) 2.4 Goodness-of-fit 2.5 Hypothesis Testing 2.5.1 A Simple t-test 2.5.2 Example: Individual Wages (Continued) 2.5.3 Testing One Linear Restriction 2.5.4 A t Test of Significance of Regression Coefficients 2.5.5 Example: Individual Wages (Continued) 2.5.6 The General Case 2.5.7 Size, Power and p-Values

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CONTENTS

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2.6 Asymptotic Properties of the OLS Estimator 2.6.1 Consistency 2.6.2 Asymptotic Normality 2.6.3 Small Samples and Asymptotic Theory 2.7 Illustration: The Capital Asset Pricing Model 2.7.1 The CAPM as a Regression Model 2.7.2 Estimating and Testing the CAPM 2.8 Multicollinearity 2.8.1 Example: Individual Wages (Continued) 2.9 Prediction Exercises

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3 Interpreting and Comparing Regression Models 3.1 Interpreting the Linear Model 3.2 Selecting the Set of Regressors 3.2.1 Misspecifying the Set of Regressors 3.2.2 Selecting Regressors 3.2.3 Comparing Non-nested Models 3.3 Misspecifying the Functional Form 3.3.1 Nonlinear Models 3.3.2 Testing the Functional Form 3.3.3 Testing for a Structural Break 3.4 Illustration: Explaining House Prices 3.5 Illustration: Explaining Individual Wages 3.5.1 Linear Models 3.5.2 Loglinear Models 3.5.3 The Effects of Gender 3.5.4 Some Words of Warning Exercises

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4 Heteroskedasticity and Autocorrelation 4.1 Consequences for the OLS Estimator 4.2 Deriving an Alternative Estimator 4.3 Heteroskedasticity 4.3.1 Introduction 4.3.2 Estimator Properties and Hypothesis Testing 4.3.3 When the Variances are Unknown 4.3.4 Heteroskedasticity-consistent Standard Errors for OLS 4.3.5 A Model with Two Unknown Variances 4.3.6 Multiplicative Heteroskedasticity 4.4 Testing for Heteroskedasticity 4.4.1 Testing Equality of Two Unknown Variances 4.4.2 Testing for Multiplicative Heteroskedasticity 4.4.3 The Breusch–Pagan Test 4.4.4 The White Test 4.4.5 Which Test?

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CONTENTS

4.5 Illustration: Explaining Labour Demand 4.6 Autocorrelation 4.6.1 First Order Autocorrelation 4.6.2 Unknown ρ 4.7 Testing for First Order Autocorrelation 4.7.1 Asymptotic Tests 4.7.2 The Durbin–Watson Test 4.8 Illustration: The Demand for Ice Cream 4.9 Alternative Autocorrelation Patterns 4.9.1 Higher Order Autocorrelation 4.9.2 Moving Average Errors 4.10 What to do When you Find Autocorrelation? 4.10.1 Misspecification 4.10.2 Heteroskedasticity-and-autocorrelation-consistent Standard Errors for OLS 4.11 Illustration: Risk Premia in Foreign Exchange Markets 4.11.1 Notation 4.11.2 Tests for Risk Premia in the One-month Market 4.11.3 Tests for Risk Premia Using Overlapping Samples Exercises 5 Endogeneity, Instrumental Variables and GMM 5.1 A Review of the Properties of the OLS Estimator 5.2 Cases Where the OLS Estimator Cannot be Saved 5.2.1 Autocorrelation with a Lagged Dependent Variable 5.2.2 An Example with Measurement Error 5.2.3 Simultaneity: the Keynesian Model 5.3 The Instrumental Variables Estimator 5.3.1 Estimation with a Single Endogenous Regressor and a Single Instrument 5.3.2 Back to the Keynesian Model 5.3.3 Back to the Measurement Error Problem 5.3.4 Multiple Endogenous Regressors 5.4 Illustration: Estimating the Returns to Schooling 5.5 The Generalized Instrumental Variables Estimator 5.5.1 Multiple Endogenous Regressors with an Arbitrary Number of Instruments 5.5.2 Two-stage Least Squares and the Keynesian Model Again 5.5.3 Specification Tests 5.5.4 Weak Instruments 5.6 The Generalized Method of Moments 5.6.1 Example 5.6.2 The Generalized Method of Moments 5.6.3 Some Simple Examples 5.7 Illustration: Estimating Intertemporal Asset Pricing Models

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