DAR ECONOMETRICS B y " fXA~PLE • I I I I • • • • • • Econometrics Example by 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. 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A catalog record for this book is available from the Library of Congress. 10 9 8 7 6 5 4 3 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 xv Acknowledgments xix A personal message from the author xxi List of tables xxiii List of figures xxvii Part I 1 The linear regression model: an overview 2 2 Functional forms of regression models 25 3 Qualitative explanatory variables regression models 47 Part II 4 Regression diagnostic I: multicollinearity 68 5 Regression diagnostic II: heteroscedasticity 82 6 Regression diagnostic Ill: autocorrelation 97 7 Regression diagnostic IV: model specification errors 114 Part III 8 The logit and probit models 142 9 Multinomial regression models 156 10 Ordinal regression models 170 11 Limited dependent variable regression models 181 12 Modeling count data: the Poisson and negative binomial regression models 193 Part IV 13 Stationary and nonstationary time series 206 14 Cointegration and error correction models 224 15 Asset price volatility: the ARCH and GARCH models 238 16 Economic forecasting 251 17 Panel data regression models 279 18 Survival analysis 296 19 Stochastic regressors and the method of instrumental variables 309 Appendices 1 Data sets used in the text 340 2 Statistical appendix 346 Index 366 Contents Preface xv Acknowledgments xix A personal message from the author xxi List of tables xxiii List of figures xxvii Part I The linear regression model 1 Chapter 1 The linear regression model: an overview 2 1.1 The linear regression model 2 1.2 The nature and sources of data 5 1.3 Estimation of the linear regression model 6 1.4 The classical linear regression model (CLRM) 8 1.5 Variances and standard errors of OLS estimators 10 1.6 Testing hypotheses about the true or population regression coefficients 11 1. 7 R2: a measure of goodness offit of the estimated regression 13 1.8 An illustrative example: the determinants of hourly wages 14 1.9 Forecasting 19 1.10 The road ahead 19 Exercise 21 Appendix: The method of maximum likelihood 22 Chapter 2 Functional forms of regression models 25 2.1 Log-linear, double-log, or constant elasticity models 25 2.2 Testing validity of linear restrictions 29 2.3 Log-lin or growth models 30 2.4 Lin-log models 34 2.5 Reciprocal models 36 2.6 Polynomial regression models 37 2.7 Choice of the functional form 40 2.8 Comparing linear and log-linear models 40 2.9 Regression on standardized variables 41 2.10 Measures of goodness of fit 43 2.11 Summary and conclusions 45 Exercises 45 x Contents ) Chapter 3 Qualitative explanatory variables regression models 47 3.1 Wage function revisited 47 3.2 Refinement of the wage function 49 3.3 Another refinement of the wage function 50 3.4 Functional form of the wage regression 53 3.5 Use of dummy variables in structural change 55 3.6 Use of dummy variables in seasonal data 58 3.7 Expanded sales function 61 3.8 Summary and conclusions 64 Exercises 65 Part II Critical evaluation of the classical linear regression model 67 Chapter 4 Regression diagnostic I: multicollinearity 68 4.1 Consequences of imperfect collinearity 69 4.2 An example: married women's hours of work in the labor market 71 4.3 Detection of multicollinearity 71 4.4 Remedial measures 74 4.5 The method of principal components (PC) 76 4.6 Summary and conclusions 78 Exercises 79 Chapter 5 Regression diagnostic II: heteroscedasticity 82 5.1 Consequences of heteroscedasticity 82 5.2 Abortion rates in the USA 83 5.3 Detection of heteroscedasticity 86 5.4 Remedial measures 89 5.5 Summary and conclusions 94 Exercises 96 Chapter 6 Regression diagnostic III: autocorrelation 97 6.1 US consumption function, 1947-2000 97 6.2 Tests of autocorrelation 99 6.3 Remedial measures 104 6.4 Model evaluation 109 6.5 Summary and conclusions 112 Exercises 113 Chapter 7 Regression diagnostic IV: model specification errors 114 7.1 Omission of relevant variables 114 7.2 Tests of omitted variables 118 7.3 Inclusion of irrelevant or unnecessary variables 121 7.4 Misspecification of the functional form of a regression model 122 7.5 Errors of measurement 124 7.6 Outliers, leverage and influence data 125 7.7 Probability distribution of the error term 128 7.8 Random or stochastic regresssors 129