Table Of Content“Th is innovative textbook continues to be an invaluable resource for all students of econometrics.”
Frank J. Fabozzi, EDHEC Business School, France
“Gujarati makes state-of-the-art econometric procedures accessible to readers with limited tech-
nical backgrounds. As usual, the writing is crisp and clear, making it a pleasure to read.”
Michael Grossman, City University of New York Graduate Center, USA
“Gujarati’s wonderful text provides a no-clutter way of learning intermediate econometrics with
solid real-world examples.”
Jin Suk Park, University of Durham, UK
“Th e clear writing, numerous examples and fi gures, clear summaries, and useful exercises make
Econometrics by Example the ideal text for learning econometrics. Moreover, it is also the perfect
reference for students who wish to apply econometrics in other courses and in their professional
lives.”
Michael J. Meese, US Military Academy, West Point, USA
“Th is comprehensive book covers the basic and the most important advanced statistical tech-
niques that economists and social scientists need to conduct empirical research. Th e techniques
are discussed in a sequence that demonstrates their connections, their strengths and weaknesses,
as well as their applicability and appropriateness for diff erent types of data. Th e discussions are
accessible and clear.”
Paul Solano, University of Delaware, USA
“Dr Gujarati’s lucid, simple and extraordinary style of exposition makes students learn critical
concepts quickly. His book is essential for econometrics classes all over the world.”
Kishore G. Kulkarni, Distinguished Professor of Economics and Editor, Indian Journal of
Economics and Business
This page intentionally left blank
ECONOMETRICS
BY EXAMPLE
DAMODAR GUJARATI
© Damodar Gujarati 2011, 2015
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 claims for damages.
The author has asserted his right to be identifi ed as the author of this work
in accordance with the Copyright, Designs and Patents Act 1988.
First edition 2011
Second edition 2015
Published by
PALGRAVE
Palgrave in the UK is an imprint of Macmillan Publishers Limited,
registered in England, company number 785998, of 4 Crinan Street,
London N1 9XW.
Palgrave Macmillan in the US is a division of St Martin’s Press LLC,
175 Fifth Avenue, New York, NY 10010.
Palgrave is a global imprint of the above companies and is represented
throughout the world.
Palgrave® and Macmillan® are registered trademarks in the United States,
the United Kingdom, Europe and other countries
ISBN 978–1–137–37501–8
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.
Printed in China
SHORT CONTENTS
Preface xiii
Acknowledgments xvii
A personal message from the author xx
List of tables xxii
List of fi gures xxix
Part I: Basics of linear regression
1 Th e linear regression model: an overview 2
2 Functional forms of regression models 28
3 Qualitative explanatory variables regression models 53
Part II : Regression diagnostics
4 Regression diagnostic I: multicollinearity 80
5 Regression diagnostic II: heteroscedasticity 96
6 Regression diagnostic III: autocorrelation 113
7 Regression diagnostic IV: model specifi cation errors 131
Part III : Topics in cross-section data
8 Th e logit and probit models 170
9 Multinomial regression models 190
10 Ordinal regression models 206
11 Limited dependent variable regression models 219
12 Modeling count data: the Poisson and negative binomial regression models 236
Part IV : Time series econometrics
13 Stationary and nonstationary time series 250
14 Cointegration and error correction models 269
15 Asset price volatility: the ARCH and GARCH models 283
16 Economic forecasting 296
Part V: Selected topics in econometrics
17 Panel data regression models 326
18 Survival analysis 344
19 Stochastic regressors and the method of instrumental variables 358
20 Beyond OLS: quantile regression 390
VI SHORT CONTENTS
21 Multivariate regression models 407
Appendices
1 Data sets used in the text 425
2 Statistical appendix 436
Index 460
CONTENTS
Preface xiii
Acknowledgments xvii
A personal message from the author xx
List of tables xxii
List of fi gures xxix
Part I: Basics of linear regression
1 Th e linear regression model: an overview 2
1.1 Th e linear regression model 2
1.2 Th e nature and sources of data 5
1.3 Estimation of the linear regression model 6
1.4 Th e 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 coeffi cients 11
1.7 R2: a measure of goodness of fi t of the estimated regression 13
1.8 An illustrative example: the determinants of hourly wages 14
1.9 Forecasting 19
1.10 Th e road ahead 19
Exercises 22
Appendix: Th e method of maximum likelihood (ML) 25
2 Functional forms of regression models 28
2.1 Log-linear, double log or constant elasticity models 28
2.2 Testing validity of linear restrictions 32
2.3 Log-lin or growth models 33
2.4 Lin-log models 36
2.5 Reciprocal models 38
2.6 Polynomial regression models 40
2.7 Choice of the functional form 42
2.8 Comparing linear and log-linear models 43
2.9 Regression on standardized variables 44
2.10 Regression through the origin: the zero-intercept model 46
2.11 Measures of goodness of fi t 49
2.12 Summary and conclusions 50
VIII CONTENTS
Exercises 51
3 Qualitative explanatory variables regression models 53
3.1 Wage function revisited 53
3.2 Refi nement of the wage function 55
3.3 Another refi nement of the wage function 56
3.4 Functional form of the wage regression 59
3.5 Use of dummy variables in structural change 61
3.6 Use of dummy variables in seasonal data 64
3.7 Expanded sales function 66
3.8 Piecewise linear regression 69
3.9 Summary and conclusions 73
Exercises 74
Part II: Regression diagnostics
4 Regression diagnostic I: multicollinearity 80
4.1 Consequences of imperfect collinearity 81
4.2 An example: married women’s hours of work in the labor market 84
4.3 Detection of multicollinearity 85
4.4 Remedial measures 87
4.5 Th e method of principal components (PC) 89
4.6 Summary and conclusions 92
Exercises 93
5 Regression diagnostic II: heteroscedasticity 96
5.1 Consequences of heteroscedasticity 96
5.2 Abortion rates in the USA 97
5.3 Detection of heteroscedasticity 100
5.4 Remedial measures 103
5.5 Summary and conclusions 110
Exercises 110
6 Regression diagnostic III: autocorrelation 113
6.1 US consumption function, 1947–2000 113
6.2 Tests of autocorrelation 115
6.3 Remedial measures 121
6.4 Model evaluation 126
6.5 Summary and conclusions 129
Exercises 129
7 Regression diagnostic IV: model specifi cation errors 131
7.1 Omission of relevant variables 131
7.2 Tests of omitted variables 135
7.3 Inclusion of irrelevant or unnecessary variables 138
7.4 Misspecifi cation of the functional form of a regression model 139
7.5 Errors of measurement 141
7.6 Outliers, leverage and infl uence data 142
7.7 Probability distribution of the error term 145
7.8 Random or stochastic regressors 147
CONTENTS IX
7.9 Th e simultaneity problem 147
7.10 Dynamic regression models 153
7.11 Summary and conclusions 162
Exercises 163
Appendix: Inconsistency of the OLS estimators of the
consumption function 167 I
Part III: Topics in cross-section data
8 Th e logit and probit models 170
8.1 An illustrative example: to smoke or not to smoke 170
8.2 Th e linear probability model (LPM) 171
8.3 Th e logit model 172
8.4 Th e language of the odds ratio (OR) 180
8.5 Th e probit model 181
8.6 Summary and conclusions 184
Exercises 185
9 Multinomial regression models 190
9.1 Th e nature of multinomial regression models 190
9.2 Multinomial logit model (MLM): school choice 192
9.3 Conditional logit model (CLM) 198
9.4 Mixed logit (MXL) 201
9.5 Summary and conclusions 201
Exercises 203
10 Ordinal regression models 206
10.1 Ordered multinomial models (OMM) 207
10.2 Estimation of ordered logit model (OLM) 207
10.3 An illustrative example: attitudes toward working mothers 209
10.4 Limitation of the proportional odds model 212
10.5 Summary and conclusions 215
Exercises 216
Appendix: Derivation of Eq. (10.4) 218
11 Limited dependent variable regression models 219
11.1 Censored regression models 220
11.2 Maximum likelihood (ML) estimation of the censored regression
model: the Tobit model 223
11.3 Truncated sample regression models 227
11.4 A concluding example 229
11.5 Summary and conclusions 232
Exercises 233
Appendix: Heckman’s (Heckit) selection-bias model 234
12 Modeling count data: the Poisson and negative binomial regression models 236
12.1 An illustrative example 236
12.2 Th e Poisson regression model (PRM) 238
12.3 Limitation of the Poisson regression model 242
12.4 Th e Negative Binomial Regression Model (NBRM) 244
