DAR ECONOMETRICS B y fXA~PLE • " • • • • • • I I I I Econometrics by Example Darnodar Gujarati © Damodar Gujarati 2011 All rights reserved No reproduction, copy or transmission of this publication may be made without written permission No portion of this publication may be reproduced, copied or transmitted save with written permission or in accordance with the provisions of the Copyright, Designs and Patents Act 1988, or under the terms of any licence permitting limited copying issued by the Copyright Licensing Agency, Saffron House, 6-10 Kirby Street, London EC1N 8TS Any person who does any unauthorized act in relation to this publication may be liable to criminal prosecution and civil claimsJor damage'S The author has asserted his right to be identifies as the author of th in accordance with the Copyright, Designs ai\QJPptents Act 198&,) First published 2011 by PALGRAVE MACMILLAN Palgrave Macmillan in the UK is an imprint of Macmillan Publishers' Limited, registered in England, company number 785998, of Houndmills, Basingstoke, Hampshire RG21 6XS Palgrave Macmillan in the US is a division of St Martin's Press LLC, 175 Fifth Avenue, New York, NY 10010 Palgrave Macmillan is the global academic imprint of the above companies and has companies and representatives throughout the world Palgrave® and Macmillan® are registered trademarks in the United States, the United Kingdom, Europe and other countries ISBN 978-0-230-29039-6 This book is printed on paper suitable for recycling and made from fully managed and sustained forest sources Logging, pulping and manufacturing processes are expected to conform to the environmental regulations of the country of origin A catalogue record for this book is available from the British Library A catalog record for this book is available from the Library of Congress 10 20 19 18 17 16 15 14 13 12 11 Printed in Great Britain by the MPG Books Group, Bodmin and King's Lynn Dedication For Joan Gujarati, Diane Gujarati-Chesnut, Charles Chesnut and my grandchildren "Tommy" and Laura Chesnut Short contents Preface Acknowledgments A personal message from the author List of tables List of figures xv xix xxi xxiii xxvii Part I The linear regression model: an overview Functional forms of regression models Qualitative explanatory variables regression models 25 47 Part II Regression diagnostic I: multicollinearity Regression diagnostic II: heteroscedasticity Regression diagnostic Ill: autocorrelation Regression diagnostic IV: model specification errors 68 82 97 114 Part III 10 11 12 The logit and probit models Multinomial regression models Ordinal regression models Limited dependent variable regression models Modeling count data: the Poisson and negative binomial regression models 142 156 170 181 193 Part IV 13 14 15 16 17 18 19 Stationary and nonstationary time series Cointegration and error correction models Asset price volatility: the ARCH and GARCH models Economic forecasting Panel data regression models Survival analysis Stochastic regressors and the method of instrumental variables 206 224 238 251 279 296 309 Appendices Data sets used in the text Statistical appendix 340 346 Index 366 Contents Preface Acknowledgments A personal message from the author List of tables List of figures Part I Chapter The linear regression model The linear regression model: an overview 1.1 1.2 1.3 1.4 1.5 1.6 1.8 1.9 1.10 Chapter xv xix xxi xxiii xxvii The linear regression model The nature and sources of data Estimation of the linear regression model The classical linear regression model (CLRM) 10 Variances and standard errors of OLS estimators Testing hypotheses about the true or population regression coefficients 11 R2: a measure of goodness offit of the estimated regression 13 An illustrative example: the determinants of hourly wages 14 Forecasting 19 The road ahead 19 21 Exercise Appendix: The method of maximum likelihood 22 Functional forms of regression models 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 Log-linear, double-log, or constant elasticity models Testing validity of linear restrictions Log-lin or growth models Lin-log models Reciprocal models Polynomial regression models Choice of the functional form Comparing linear and log-linear models Regression on standardized variables Measures of goodness of fit Summary and conclusions Exercises 25 25 29 30 34 36 37 40 40 41 43 45 45 x Contents ) Chapter Qualitative explanatory variables regression models 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 Part II Chapter 67 Regression diagnostic I: multicollinearity 68 Consequences of heteroscedasticity Abortion rates in the USA Detection of heteroscedasticity Remedial measures Summary and conclusions Exercises Regression diagnostic III: autocorrelation 6.1 6.2 6.3 6.4 6.5 Chapter Consequences of imperfect collinearity An example: married women's hours of work in the labor market Detection of multicollinearity Remedial measures The method of principal components (PC) Summary and conclusions Exercises Regression diagnostic II: heteroscedasticity 5.1 5.2 5.3 5.4 5.5 Chapter 47 49 50 53 55 58 61 64 65 Critical evaluation of the classical linear regression model 4.1 4.2 4.3 4.4 4.5 4.6 Chapter Wage function revisited Refinement of the wage function Another refinement of the wage function Functional form of the wage regression Use of dummy variables in structural change Use of dummy variables in seasonal data Expanded sales function Summary and conclusions Exercises 47 US consumption function, 1947-2000 Tests of autocorrelation Remedial measures Model evaluation Summary and conclusions Exercises Regression diagnostic IV: model specification errors 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 Omission of relevant variables Tests of omitted variables Inclusion of irrelevant or unnecessary variables Misspecification of the functional form of a regression model Errors of measurement Outliers, leverage and influence data Probability distribution of the error term Random or stochastic regresssors 69 71 71 74 76 78 79 82 82 83 86 89 94 96 97 97 99 104 109 112 113 114 114 118 121 122 124 125 128 129 ... Econometrics by Example Darnodar Gujarati © Damodar Gujarati 2011 All rights reserved No reproduction, copy or transmission... Copyright, Designs aiQJPptents Act 198&,) First published 2011 by PALGRAVE MACMILLAN Palgrave Macmillan in the UK is an imprint of Macmillan Publishers' Limited, registered in England, company... terms by considering several interesting examples, such as charitable giving, fashion sales and exchange rates, in depth This need has now been met with Econometrics by Example What has made econometrics