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Gujarati: Basic
Econometrics, Fourth
Front Matter Preface © The McGraw−Hill
Companies, 2004
As in the previous three editions, the primary objective of the fourth edition
of Basic Econometrics is to provide an elementary but comprehensive introduction
to econometrics without resorting to matrix algebra, calculus, or
statistics beyond the elementary level.
In this edition I have attempted to incorporate some of the developments
in the theory and practice of econometrics that have taken place since the
publication of the third edition in 1995. With the availability of sophisticated
and user-friendly statistical packages, such as Eviews, Limdep,
Microfit, Minitab, PcGive, SAS, Shazam, and Stata, it is now possible to discuss
several econometric techniques that could not be included in the previous
editions of the book. I have taken full advantage of these statistical
packages in illustrating several examples and exercises in this edition.
I was pleasantly surprised to find that my book is used not only by economics
and business students but also by students and researchers in several
other disciplines, such as politics, international relations, agriculture,
and health sciences. Students in these disciplines will find the expanded discussion
of several topics very useful.
The major changes in this edition are as follows:
1. In the introductory chapter, after discussing the steps involved in traditional
econometric methodology, I discuss the very important question of
how one chooses among competing econometric models.
2. In Chapter 1, I discuss very briefly the measurement scale of economic
variables. It is important to know whether the variables are ratio
Gujarati: Basic
Econometrics, Fourth
Front Matter Preface © The McGraw−Hill
Companies, 2004
scale, interval scale, ordinal scale, or nominal scale, for that will determine
the econometric technique that is appropriate in a given situation.
3. The appendices to Chapter 3 now include the large-sample properties
of OLS estimators, particularly the property of consistency.
4. The appendix to Chapter 5 now brings into one place the properties
and interrelationships among the four important probability distributions
that are heavily used in this book, namely, the normal, t, chi square, and F.
5. Chapter 6, on functional forms of regression models, now includes a
discussion of regression on standardized variables.
6. To make the book more accessible to the nonspecialist, I have moved
the discussion of the matrix approach to linear regression from old Chapter 9
to Appendix C. Appendix C is slightly expanded to include some advanced
material for the benefit of the more mathematically inclined students. The
new Chapter 9 now discusses dummy variable regression models.
7. Chapter 10, on multicollinearity, includes an extended discussion of
the famous Longley data, which shed considerable light on the nature and
scope of multicollinearity.
8. Chapter 11, on heteroscedasticity, now includes in the appendix an
intuitive discussion of White’s robust standard errors.
9. Chapter 12, on autocorrelation, now includes a discussion of the
Newey–West method of correcting the OLS standard errors to take into account
likely autocorrelation in the error term. The corrected standard errors
are known as HAC standard errors. This chapter also discusses briefly the
topic of forecasting with autocorrelated error terms.
10. Chapter 13, on econometric modeling, replaces old Chapters 13 and
14. This chapter has several new topics that the applied researcher will find
particularly useful. They include a compact discussion of model selection
criteria, such as the Akaike information criterion, the Schwarz information
criterion, Mallows’s C p criterion, and forecast chi square. The chapter also
discusses topics such as outliers, leverage, influence, recursive least squares,
and Chow’s prediction failure test. This chapter concludes with some cautionary
advice to the practitioner about econometric theory and econometric
11. Chapter 14, on nonlinear regression models, is new. Because of the
easy availability of statistical software, it is no longer difficult to estimate
regression models that are nonlinear in the parameters. Some econometric
models are intrinsically nonlinear in the parameters and need to be estimated
by iterative methods. This chapter discusses and illustrates some
comparatively simple methods of estimating nonlinear-in-parameter regression
12. Chapter 15, on qualitative response regression models, which replaces
old Chapter 16, on dummy dependent variable regression models,
provides a fairly extensive discussion of regression models that involve a
dependent variable that is qualitative in nature. The main focus is on logit
Gujarati: Basic
Econometrics, Fourth
Front Matter Preface © The McGraw−Hill
Companies, 2004
and probit models and their variations. The chapter also discusses the
Poisson regression model, which is used for modeling count data, such as the
number of patents received by a firm in a year; the number of telephone
calls received in a span of, say, 5 minutes; etc. This chapter has a brief discussion
of multinomial logit and probit models and duration models.
13. Chapter 16, on panel data regression models, is new. A panel data
combines features of both time series and cross-section data. Because of increasing
availability of panel data in the social sciences, panel data regression
models are being increasingly used by researchers in many fields. This
chapter provides a nontechnical discussion of the fixed effects and random
effects models that are commonly used in estimating regression models
based on panel data.
14. Chapter 17, on dynamic econometric models, has now a rather extended
discussion of the Granger causality test, which is routinely used (and
misused) in applied research. The Granger causality test is sensitive to the
number of lagged terms used in the model. It also assumes that the underlying
time series is stationary.
15. Except for new problems and minor extensions of the existing estimation
techniques, Chapters 18, 19, and 20 on simultaneous equation models
are basically unchanged. This reflects the fact that interest in such models
has dwindled over the years for a variety of reasons, including their poor
forecasting performance after the OPEC oil shocks of the 1970s.
16. Chapter 21 is a substantial revision of old Chapter 21. Several concepts
of time series econometrics are developed and illustrated in this chapter. The
main thrust of the chapter is on the nature and importance of stationary
time series. The chapter discusses several methods of finding out if a given
time series is stationary. Stationarity of a time series is crucial for the application
of various econometric techniques discussed in this book.
17. Chapter 22 is also a substantial revision of old Chapter 22. It discusses
the topic of economic forecasting based on the Box–Jenkins (ARIMA) and
vector autoregression (VAR) methodologies. It also discusses the topic of
measuring volatility in financial time series by the techniques of autoregressive
conditional heteroscedasticity (ARCH) and generalized autoregressive conditional
heteroscedasticity (GARCH).
18. Appendix A, on statistical concepts, has been slightly expanded. Appendix
C discusses the linear regression model using matrix algebra. This is
for the benefit of the more advanced students.
As in the previous editions, all the econometric techniques discussed in
this book are illustrated by examples, several of which are based on concrete
data from various disciplines. The end-of-chapter questions and problems
have several new examples and data sets. For the advanced reader,
there are several technical appendices to the various chapters that give
proofs of the various theorems and or formulas developed in the text.
Gujarati: Basic
Econometrics, Fourth
Front Matter Preface © The McGraw−Hill
Companies, 2004
Changes in this edition have considerably expanded the scope of the text. I
hope this gives the instructor substantial flexibility in choosing topics that
are appropriate to the intended audience. Here are suggestions about how
this book may be used.
One-semester course for the nonspecialist: Appendix A, Chapters 1
through 9, an overview of Chapters 10, 11, 12 (omitting all the proofs).
One-semester course for economics majors: Appendix A, Chapters 1
through 13.
Two-semester course for economics majors: Appendices A, B, C,
Chapters 1 to 22. Chapters 14 and 16 may be covered on an optional basis.
Some of the technical appendices may be omitted.
Graduate and postgraduate students and researchers: This book is a
handy reference book on the major themes in econometrics.
Data CD
Every text is packaged with a CD that contains the data from the text in
ASCII or text format and can be read by most software packages.
Student Solutions Manual
Free to instructors and salable to students is a Student Solutions Manual
(ISBN 0072427922) that contains detailed solutions to the 475 questions
and problems in the text.
Web Site
With this fourth edition we are pleased to provide Eviews Student Version
3.1 on a CD along with all of the data from the text. This software is
available from the publisher packaged with the text (ISBN: 0072565705).
Eviews Student Version is available separately from QMS. Go to for further information.
A comprehensive web site provides additional material to support the study
of econometrics. Go to
Since the publication of the first edition of this book in 1978, I have received
valuable advice, comments, criticism, and suggestions from a variety of
people. In particular, I would like to acknowledge the help I have received
Gujarati: Basic
Econometrics, Fourth
Front Matter Preface © The McGraw−Hill
Companies, 2004
from Michael McAleer of the University of Western Australia, Peter Kennedy
of Simon Frazer University in Canada, and Kenneth White, of the University
of British Columbia, George K. Zestos of Christopher Newport University,
Virginia, and Paul Offner, Georgetown University, Washington, D.C.
I am also grateful to several people who have influenced me by their
scholarship. I especially want to thank Arthur Goldberger of the University
of Wisconsin, William Greene of New York University, and the late G. S.
Maddala. For this fourth edition I am especially grateful to these reviewers
who provided their invaluable insight, criticism, and suggestions: Michael
A. Grove at the University of Oregon, Harumi Ito at Brown University, Han
Kim at South Dakota University, Phanindra V. Wunnava at Middlebury College,
and George K. Zestos of Christopher Newport University.
Several authors have influenced my writing. In particular, I am grateful to
these authors: Chandan Mukherjee, director of the Centre for Development
Studies, Trivandrum, India; Howard White and Marc Wuyts, both at the
Institute of Social Studies in the Netherlands; Badi H. Baltagi, Texas A&M
University; B. Bhaskara Rao, University of New South Wales, Australia;
R. Carter Hill, Louisiana University; William E. Griffiths, University of New
England; George G. Judge, University of California at Berkeley; Marno
Verbeek, Center for Economic Studies, KU Leuven; Jeffrey Wooldridge,
Michigan State University; Kerry Patterson, University of Reading, U.K.;
Francis X. Diebold, Wharton School, University of Pennsylvania; Wojciech W.
Charemza and Derek F. Deadman, both of the University of Leicester, U.K.;
Gary Koop, University of Glasgow.
I am very grateful to several of my colleagues at West Point for their support
and encouragement over the years. In particular, I am grateful to
Brigadier General Daniel Kaufman, Colonel Howard Russ, Lieutenant
Colonel Mike Meese, Lieutenant Colonel Casey Wardynski, Major David
Trybulla, Major Kevin Foster, Dean Dudley, and Dennis Smallwood.
I would like to thank students and teachers all over the world who have
not only used my book but have communicated with me about various aspects
of the book.
For their behind the scenes help at McGraw-Hill, I am grateful to Lucille
Sutton, Aric Bright, and Catherine R. Schultz.
George F. Watson, the copyeditor, has done a marvellous job in editing a
rather lengthy and demanding manuscript. For that, I am much obliged to
Finally, but not least important, I would like to thank my wife, Pushpa,
and my daughters, Joan and Diane, for their constant support and encouragement
in the preparation of this and the previous editions.
Damodar N. Gujarati
Gujarati: Basic
Econometrics, Fourth
Front Matter Introduction © The McGraw−Hill
Companies, 2004
Literally interpreted, econometrics means “economic measurement.” Although
measurement is an important part of econometrics, the scope of
econometrics is much broader, as can be seen from the following quotations:
Econometrics, the result of a certain outlook on the role of economics, consists of
the application of mathematical statistics to economic data to lend empirical support
to the models constructed by mathematical economics and to obtain
numerical results. 1
. . . econometrics may be defined as the quantitative analysis of actual economic
phenomena based on the concurrent development of theory and observation, related
by appropriate methods of inference. 2
Econometrics may be defined as the social science in which the tools of economic
theory, mathematics, and statistical inference are applied to the analysis of economic
phenomena. 3
Econometrics is concerned with the empirical determination of economic
laws. 4
1 Gerhard Tintner, Methodology of Mathematical Economics and Econometrics, The University
of Chicago Press, Chicago, 1968, p. 74.
2 P. A. Samuelson, T. C. Koopmans, and J. R. N. Stone, “Report of the Evaluative Committee
for Econometrica,” Econometrica, vol. 22, no. 2, April 1954, pp. 141–146.
3 Arthur S. Goldberger, Econometric Theory, John Wiley & Sons, New York, 1964, p. 1.
4 H. Theil, Principles of Econometrics, John Wiley & Sons, New York, 1971, p. 1.
Gujarati: Basic
Econometrics, Fourth
Front Matter Introduction © The McGraw−Hill
Companies, 2004
The art of the econometrician consists in finding the set of assumptions that are
both sufficiently specific and sufficiently realistic to allow him to take the best
possible advantage of the data available to him. 5
Econometricians ...are a positive help in trying to dispel the poor public image
of economics (quantitative or otherwise) as a subject in which empty boxes are
opened by assuming the existence of can-openers to reveal contents which any
ten economists will interpret in 11 ways. 6
The method of econometric research aims, essentially, at a conjunction of economic
theory and actual measurements, using the theory and technique of statistical
inference as a bridge pier. 7
As the preceding definitions suggest, econometrics is an amalgam of economic
theory, mathematical economics, economic statistics, and mathematical
statistics. Yet the subject deserves to be studied in its own right for
the following reasons.
Economic theory makes statements or hypotheses that are mostly qualitative
in nature. For example, microeconomic theory states that, other
things remaining the same, a reduction in the price of a commodity is expected
to increase the quantity demanded of that commodity. Thus, economic
theory postulates a negative or inverse relationship between the price
and quantity demanded of a commodity. But the theory itself does not provide
any numerical measure of the relationship between the two; that is, it
does not tell by how much the quantity will go up or down as a result of a
certain change in the price of the commodity. It is the job of the econometrician
to provide such numerical estimates. Stated differently, econometrics
gives empirical content to most economic theory.
The main concern of mathematical economics is to express economic
theory in mathematical form (equations) without regard to measurability or
empirical verification of the theory. Econometrics, as noted previously, is
mainly interested in the empirical verification of economic theory. As we
shall see, the econometrician often uses the mathematical equations proposed
by the mathematical economist but puts these equations in such a
form that they lend themselves to empirical testing. And this conversion of
mathematical into econometric equations requires a great deal of ingenuity
and practical skill.
Economic statistics is mainly concerned with collecting, processing, and
presenting economic data in the form of charts and tables. These are the
5 E. Malinvaud, Statistical Methods of Econometrics, Rand McNally, Chicago, 1966, p. 514.
6 Adrian C. Darnell and J. Lynne Evans, The Limits of Econometrics, Edward Elgar Publishing,
Hants, England, 1990, p. 54.
7 T. Haavelmo, “The Probability Approach in Econometrics,” Supplement to Econometrica,
vol. 12, 1944, preface p. iii.
Gujarati: Basic
Econometrics, Fourth
Front Matter Introduction © The McGraw−Hill
Companies, 2004
jobs of the economic statistician. It is he or she who is primarily responsible
for collecting data on gross national product (GNP), employment, unemployment,
prices, etc. The data thus collected constitute the raw data for
econometric work. But the economic statistician does not go any further,
not being concerned with using the collected data to test economic theories.
Of course, one who does that becomes an econometrician.
Although mathematical statistics provides many tools used in the trade,
the econometrician often needs special methods in view of the unique nature
of most economic data, namely, that the data are not generated as the
result of a controlled experiment. The econometrician, like the meteorologist,
generally depends on data that cannot be controlled directly. As Spanos
correctly observes:
In econometrics the modeler is often faced with observational as opposed to
experimental data. This has two important implications for empirical modeling
in econometrics. First, the modeler is required to master very different skills
than those needed for analyzing experimental data. . . . Second, the separation
of the data collector and the data analyst requires the modeler to familiarize
himself/herself thoroughly with the nature and structure of data in question. 8
How do econometricians proceed in their analysis of an economic problem?
That is, what is their methodology? Although there are several schools of
thought on econometric methodology, we present here the traditional or
classical methodology, which still dominates empirical research in economics
and other social and behavioral sciences. 9
Broadly speaking, traditional econometric methodology proceeds along
the following lines:
1. Statement of theory or hypothesis.
2. Specification of the mathematical model of the theory
3. Specification of the statistical, or econometric, model
4. Obtaining the data
5. Estimation of the parameters of the econometric model
6. Hypothesis testing
7. Forecasting or prediction
8. Using the model for control or policy purposes.
To illustrate the preceding steps, let us consider the well-known Keynesian
theory of consumption.
8 Aris Spanos, Probability Theory and Statistical Inference: Econometric Modeling with Observational
Data, Cambridge University Press, United Kingdom, 1999, p. 21.
9 For an enlightening, if advanced, discussion on econometric methodology, see David F.
Hendry, Dynamic Econometrics, Oxford University Press, New York, 1995. See also Aris
Spanos, op. cit.
Gujarati: Basic
Econometrics, Fourth
Front Matter Introduction © The McGraw−Hill
Companies, 2004
1. Statement of Theory or Hypothesis
Keynes stated:
The fundamental psychological law . . . is that men [women] are disposed, as a
rule and on average, to increase their consumption as their income increases, but
not as much as the increase in their income. 10
In short, Keynes postulated that the marginal propensity to consume
(MPC), the rate of change of consumption for a unit (say, a dollar) change
in income, is greater than zero but less than 1.
2. Specification of the Mathematical Model of Consumption
Although Keynes postulated a positive relationship between consumption
and income, he did not specify the precise form of the functional relationship
between the two. For simplicity, a mathematical economist might suggest
the following form of the Keynesian consumption function:
Y = β 1 + β 2 X 0 <β 2 < 1 (I.3.1)
where Y = consumption expenditure and X = income, and where β 1 and β 2 ,
known as the parameters of the model, are, respectively, the intercept and
slope coefficients.
The slope coefficient β 2 measures the MPC. Geometrically, Eq. (I.3.1) is as
shown in Figure I.1. This equation, which states that consumption is lin-
Consumption expenditure
β 2 = MPC
β 1
Keynesian consumption function.
10 John Maynard Keynes, The General Theory of Employment, Interest and Money, Harcourt
Brace Jovanovich, New York, 1936, p. 96.