Introduction ② The McG econometrics. Fourth INTRODUCTION 11 other consumption model (theory) might equally fit the data as well? Forex ample, Milton Friedman has developed a model of consumption, called the permanent income hypothesis. Robert Hall has also developed a model of onsumption, called the life-cycle permanent income hypothesis. 6 Could one or both of these models also fit the data in table l1? In short, the question facing a researcher in practice is how to choose among competing hypotheses or models of a given phenomenon, such as the consumption-income relationship. As Miller contends No encounter with data is step towards genuine confirmation unless the hyp sis does a better job of coping with the data than some natural rival.... w strengthens a hypothesis, here, is a victory that is, at the same time, a defeat for a How then does one choose among competing models or hypotheses? Here the advice given by Clive Granger is worth keeping in mind I would like to suggest that in the future, when you are presented with a new piece of theory or empirical model, you ask these questions (i)What purpose does it have? What economic decisions does it help with? (ii)Is there any evidence being presented that allows me to evaluate its qual ity compared to alternative theories or models? I think attention to such questions will strengthen economic research and As we progress through this book, we will come across several competing hypotheses trying to explain various economic phenomena. For example, students of economics are familiar with the concept of the production func- tion, which is basically a relationship between output and inputs(say, capi d and labor). In the literature, two of the best known are the Cobb-douglas and the constant elasticity of substitution production functions. Given the data on output and inputs, we will have to find out which of the two pro- duction functions, if any, fits the data well. The eight-step classical econometric methodology discussed above is neutral in the sense that it can be used to test any of these rival hypotheses Is it possible to develop a methodology that is comprehensive enough to include competing hypotheses? This is an involved and controversial topic Milton Friedman, A Theory of Consumption Function, Princeton University Press oR. Hall, "Stochastic Implications of the Life Cycle Permanent Income Hypothesis: Theory and Evidence, " Joumal of Political Economy, 1978, vol 86, pp.971-987. R. W. Miller, Fact and Method: Explanation, Confirm and Reality in the Natural and Social Sciences, Princeton University Press, Princeton, N.J., 1978, p. 176 cLive W.J. Granger, Empirical Modeling in Economics, Cambridge University Press, U.K 9,p.58
Gujarati: Basic Econometrics, Fourth Edition Front Matter Introduction © The McGraw−Hill Companies, 2004 INTRODUCTION 11 15Milton Friedman, A Theory of Consumption Function, Princeton University Press, Princeton, N.J., 1957. 16R. Hall, “Stochastic Implications of the Life Cycle Permanent Income Hypothesis: Theory and Evidence,” Journal of Political Economy, 1978, vol. 86, pp. 971–987. 17R. W. Miller, Fact and Method: Explanation, Confirmation, and Reality in the Natural and Social Sciences, Princeton University Press, Princeton, N.J., 1978, p. 176. 18Clive W. J. Granger, Empirical Modeling in Economics, Cambridge University Press, U.K., 1999, p. 58. other consumption model (theory) might equally fit the data as well? For example, Milton Friedman has developed a model of consumption, called the permanent income hypothesis. 15 Robert Hall has also developed a model of consumption, called the life-cycle permanent income hypothesis. 16 Could one or both of these models also fit the data in Table I.1? In short, the question facing a researcher in practice is how to choose among competing hypotheses or models of a given phenomenon, such as the consumption–income relationship. As Miller contends: No encounter with data is step towards genuine confirmation unless the hypothesis does a better job of coping with the data than some natural rival. . . . What strengthens a hypothesis, here, is a victory that is, at the same time, a defeat for a plausible rival.17 How then does one choose among competing models or hypotheses? Here the advice given by Clive Granger is worth keeping in mind:18 I would like to suggest that in the future, when you are presented with a new piece of theory or empirical model, you ask these questions: (i) What purpose does it have? What economic decisions does it help with? and; (ii) Is there any evidence being presented that allows me to evaluate its quality compared to alternative theories or models? I think attention to such questions will strengthen economic research and discussion. As we progress through this book, we will come across several competing hypotheses trying to explain various economic phenomena. For example, students of economics are familiar with the concept of the production function, which is basically a relationship between output and inputs (say, capital and labor). In the literature, two of the best known are the Cobb–Douglas and the constant elasticity of substitution production functions. Given the data on output and inputs, we will have to find out which of the two production functions, if any, fits the data well. The eight-step classical econometric methodology discussed above is neutral in the sense that it can be used to test any of these rival hypotheses. Is it possible to develop a methodology that is comprehensive enough to include competing hypotheses? This is an involved and controversial topic
Introduction ② The McG econometrics. Fourth 12 BASIC ECONOMETRICS Econometrics Theoretical Applied Classical Bayesian Classical Bar FIGURE L5 Categories of econometrics. We will discuss it in Chapter 13, after we have acquired the necessary econometric the 4 TYPES OF ECONOMETRICS As the classificatory scheme in Figure I5 suggests, econometrics may be divided into two broad categories: theoretical econometrics and applied econometrics. In each category, one can approach the subject in the clas sical or Bayesian tradition. In this book the emphasis is on the classical approach. For the Bayesian approach, the reader may consult the refer- ences given at the end of the chapter. Theoretical econometrics is concerned with the development of appro- priate methods for measuring economic relationships specified by econo- metric models. In this aspect, econometrics leans heavily on mathematical statistics. For example, one of the methods used extensively in this book is least squares. Theoretical econometrics must spell out the assumptions of this method, its properties, and what happens to these properties when one or more of the assumptions of the method are not fulfilled In applied econometrics we use the tools of theoretical econometrics to udy some special field(s)of economics and business, such as the produc tion function, investment function, demand and supply functions, portfolio ry, This book is concerned largely with the development of econometric methods, their assumptions, their uses, their limitations. These methods are illustrated with examples from various areas of economics and business. But this is not a book of applied econometrics in the sense that it delves deeply into any particular field of economic application. That job is best left to books written specifically for this purpose. References to some of these books are provided at the end of this book 1.5 MATHEMATICAL AND STATISTICAL PREREQUISITES lthough this book is written at an elementary level, the author assumes that the reader is familiar with the basic concepts of statistical estimation and hypothesis testing. However, a broad but nontechnical overview of the basic statistical concepts used in this book is provided in Appendix A for
Gujarati: Basic Econometrics, Fourth Edition Front Matter Introduction © The McGraw−Hill Companies, 2004 12 BASIC ECONOMETRICS Econometrics Theoretical Classical Bayesian Applied Classical Bayesian FIGURE I.5 Categories of econometrics. We will discuss it in Chapter 13, after we have acquired the necessary econometric theory. I.4 TYPES OF ECONOMETRICS As the classificatory scheme in Figure I.5 suggests, econometrics may be divided into two broad categories: theoretical econometrics and applied econometrics. In each category, one can approach the subject in the classical or Bayesian tradition. In this book the emphasis is on the classical approach. For the Bayesian approach, the reader may consult the references given at the end of the chapter. Theoretical econometrics is concerned with the development of appropriate methods for measuring economic relationships specified by econometric models. In this aspect, econometrics leans heavily on mathematical statistics. For example, one of the methods used extensively in this book is least squares. Theoretical econometrics must spell out the assumptions of this method, its properties, and what happens to these properties when one or more of the assumptions of the method are not fulfilled. In applied econometrics we use the tools of theoretical econometrics to study some special field(s) of economics and business, such as the production function, investment function, demand and supply functions, portfolio theory, etc. This book is concerned largely with the development of econometric methods, their assumptions, their uses, their limitations. These methods are illustrated with examples from various areas of economics and business. But this is not a book of applied econometrics in the sense that it delves deeply into any particular field of economic application. That job is best left to books written specifically for this purpose. References to some of these books are provided at the end of this book. I.5 MATHEMATICAL AND STATISTICAL PREREQUISITES Although this book is written at an elementary level, the author assumes that the reader is familiar with the basic concepts of statistical estimation and hypothesis testing. However, a broad but nontechnical overview of the basic statistical concepts used in this book is provided in Appendix A for
Introduction ② The McG econometrics. Fourth INTRODUCTIOn 13 the benefit of those who want to refresh their knowledge. Insofar as mathe- matics is concerned, a nodding acquaintance with the notions of differential calculus is desirable, although not essential. Although most graduate level books in econometrics make heavy use of matrix algebra, i want to make it clear that it is not needed to study this book. It is my strong belief that the fundamental ideas of econometrics can be conveyed without the use of matrix algebra. However, for the benefit of the mathematically inclined stu dent, Appendix C gives the summary of basic regression theory in matrix notation. For these students, Appendix B provides a succinct summary of the main results from matrix algebra L6 THE ROLE OF THE COMPUTER Regression analysis, the bread-and-butter tool of econometrics, these day is unthinkable without the computer and some access to statistical soft ware(Believe me, I grew up in the generation of the slide rule! Fortunately several excellent regression packages are commercially available, both for the mainframe and the microcomputer, and the list is growing by the day Regression software packages, such as ET, LIMDEP, SHAZAM, MICRO TSP, MINITAB, EVIEWS, SAS, SPSS, STATA, Microfit, PcGive, and BMD have most of the econometric techniques and tests discussed in this book. In this book, from time to time, the reader will be asked to conduct Monte Carlo experiments using one or more of the statistical packages Monte Carlo experiments are"fun"exercises that will enable the reader to appreciate the properties of several statistical methods discussed in this book. The details of the Monte Carlo experiments will be discussed at ap propriate places L7 SUGGESTIONS FOR FURTHER READING The topic of econometric methodology is vast and controversial. For those interested in this topic, I suggest the following books Neil de Marchi and Christopher Gilbert, eds, History and Methodology of Econometrics, Oxford University Press, New York, 1989. This collection of readings discusses some early work on econometric methodology and has an extended discussion of the British approach to econometrics relating to time series data, that is, data collected over a period of time Wojciech W Charemza and Derek F. Deadman, New Directions in Ecor metric Practice: General to Specific Modelling, Cointegration and Vector Auto- gression, 2d ed, Edward Elgar Publishing Ltd, Hants, England, 1997. The luthors of this book critique the traditional approach to econometrics and give a detailed exposition of new approaches to econometric methodology Adrian C. Darnell and J. Lynne Evans, The Limits of econometrics, Edward Elgar Publishers Ltd, Hants, England, 1990. The book provides a somewhat
Gujarati: Basic Econometrics, Fourth Edition Front Matter Introduction © The McGraw−Hill Companies, 2004 INTRODUCTION 13 the benefit of those who want to refresh their knowledge. Insofar as mathematics is concerned, a nodding acquaintance with the notions of differential calculus is desirable, although not essential. Although most graduate level books in econometrics make heavy use of matrix algebra, I want to make it clear that it is not needed to study this book. It is my strong belief that the fundamental ideas of econometrics can be conveyed without the use of matrix algebra. However, for the benefit of the mathematically inclined student, Appendix C gives the summary of basic regression theory in matrix notation. For these students, Appendix B provides a succinct summary of the main results from matrix algebra. I.6 THE ROLE OF THE COMPUTER Regression analysis, the bread-and-butter tool of econometrics, these days is unthinkable without the computer and some access to statistical software. (Believe me, I grew up in the generation of the slide rule!) Fortunately, several excellent regression packages are commercially available, both for the mainframe and the microcomputer, and the list is growing by the day. Regression software packages, such as ET, LIMDEP, SHAZAM, MICRO TSP, MINITAB, EVIEWS, SAS, SPSS, STATA, Microfit, PcGive, and BMD have most of the econometric techniques and tests discussed in this book. In this book, from time to time, the reader will be asked to conduct Monte Carlo experiments using one or more of the statistical packages. Monte Carlo experiments are “fun” exercises that will enable the reader to appreciate the properties of several statistical methods discussed in this book. The details of the Monte Carlo experiments will be discussed at appropriate places. I.7 SUGGESTIONS FOR FURTHER READING The topic of econometric methodology is vast and controversial. For those interested in this topic, I suggest the following books: Neil de Marchi and Christopher Gilbert, eds., History and Methodology of Econometrics, Oxford University Press, New York, 1989. This collection of readings discusses some early work on econometric methodology and has an extended discussion of the British approach to econometrics relating to time series data, that is, data collected over a period of time. Wojciech W. Charemza and Derek F. Deadman, New Directions in Econometric Practice: General to Specific Modelling, Cointegration and Vector Autogression, 2d ed., Edward Elgar Publishing Ltd., Hants, England, 1997. The authors of this book critique the traditional approach to econometrics and give a detailed exposition of new approaches to econometric methodology. Adrian C. Darnell and J. Lynne Evans, The Limits of Econometrics, Edward Elgar Publishers Ltd., Hants, England, 1990. The book provides a somewhat
Introduction ② The McG econometrics. Fourth 14 BASIC ECONOMETRICS balanced discussion of the various methodological approaches to economet- rics. with renewed allegiance to traditional econometric methodology. Mary S Morgan, The History of Econometric Ideas, Cambridge University Press, New York, 1990. The author provides an excellent historical perspe tive on the theory and practice of econometrics, with an in-depth discussion of the early contributions of Haavelmo(1990 Nobel Laureate in Economics) to econometrics. In the same spirit, David F Hendry and Mary S Morgan, The Foundation of Econometric Analysis, Cambridge University Press, U.K 1995 have collected seminal writings in econometrics to show the evolution of econometric ideas over time David Colander and Reuven Brenner, eds, Educating Economists, Univer- sity of Michigan Press, Ann Arbor, Michigan, 1992, present a critical, at times gnostic, view of economic teaching and practice. For Bayesian statistics and econometrics, the following books are very useful: John H. Dey, Data in Doubt, Basic Blackwell Ltd, Oxford University Press, England, 1985. Peter M. Lee, Bayesian Statistics: An Introduction Oxford University Press, England, 1989. Dale J. Porier, Intermediate Statis tics and Econometrics: A Comparative Approach, MIT Press, Cambridg Massachusetts, 1995. Arnold Zeller, An Introduction to Bayesian Inference in Econometrics, John Wiley Sons, New York, 1971, is an advanced reference
Gujarati: Basic Econometrics, Fourth Edition Front Matter Introduction © The McGraw−Hill Companies, 2004 14 BASIC ECONOMETRICS balanced discussion of the various methodological approaches to econometrics, with renewed allegiance to traditional econometric methodology. Mary S. Morgan, The History of Econometric Ideas, Cambridge University Press, New York, 1990. The author provides an excellent historical perspective on the theory and practice of econometrics, with an in-depth discussion of the early contributions of Haavelmo (1990 Nobel Laureate in Economics) to econometrics. In the same spirit, David F. Hendry and Mary S. Morgan, The Foundation of Econometric Analysis, Cambridge University Press, U.K., 1995, have collected seminal writings in econometrics to show the evolution of econometric ideas over time. David Colander and Reuven Brenner, eds., Educating Economists, University of Michigan Press, Ann Arbor, Michigan, 1992, present a critical, at times agnostic, view of economic teaching and practice. For Bayesian statistics and econometrics, the following books are very useful: John H. Dey, Data in Doubt, Basic Blackwell Ltd., Oxford University Press, England, 1985. Peter M. Lee, Bayesian Statistics: An Introduction, Oxford University Press, England, 1989. Dale J. Porier, Intermediate Statistics and Econometrics: A Comparative Approach, MIT Press, Cambridge, Massachusetts, 1995. Arnold Zeller, An Introduction to Bayesian Inference in Econometrics, John Wiley & Sons, New York, 1971, is an advanced reference book
Introduction ② The McG econometrics. Fourth PART ONE SINGLE-EQUATION REGRESSION MODELS Part I of this text introduces single-equation regression models. In these models, one variable, called the dependent variable, is expressed as a linear function of one or more other variables, called the explanatory variables In such models it is assumed implicitly that causal relationships, if any, between the dependent and explanatory variables flow in one direction only, namely, from the explanatory variables to the dependent variable n Chapter 1, we discuss the historical as well as the modern interpreta tion of the term regression and illustrate the difference between the two in terpretations with several examples drawn from economics and other fields n Chapter 2, we introduce some fundamental concepts of regression alysis with the aid of the two-variable linear regression model, a model in which the dependent variable is expressed as a linear function of only a single explanatory variable In Chapter 3, we continue to deal with the two-variable model and intro- duce what is known as the classical linear regression model, a model that makes several simplifying assumptions. With these assumptions, we intro- duce the method of ordinary least squares (OLS) to estimate the parameters of the two-variable regression model. The method of oLS is simple to apply yet it has some very desirable statistical properties In Chapter 4, we introduce the(two-variable)classical normal linear re- gression model, a model that assumes that the random dependent variable follows the normal probability distribution. With this assumption, the Ols estimators obtained in Chapter 3 possess some stronger statistical proper- ties than the nonnormal classical linear regression model-properties that enable us to engage in statistical inference, namely, hypothesis testing
Gujarati: Basic Econometrics, Fourth Edition I. Single−Equation Regression Models Introduction © The McGraw−Hill Companies, 2004 15 PARTONE SINGLE-EQUATION REGRESSION MODELS Part I of this text introduces single-equation regression models. In these models, one variable, called the dependent variable, is expressed as a linear function of one or more other variables, called the explanatory variables. In such models it is assumed implicitly that causal relationships, if any, between the dependent and explanatory variables flow in one direction only, namely, from the explanatory variables to the dependent variable. In Chapter 1, we discuss the historical as well as the modern interpretation of the term regression and illustrate the difference between the two interpretations with several examples drawn from economics and other fields. In Chapter 2, we introduce some fundamental concepts of regression analysis with the aid of the two-variable linear regression model, a model in which the dependent variable is expressed as a linear function of only a single explanatory variable. In Chapter 3, we continue to deal with the two-variable model and introduce what is known as the classical linear regression model, a model that makes several simplifying assumptions. With these assumptions, we introduce the method of ordinary least squares (OLS) to estimate the parameters of the two-variable regression model. The method of OLS is simple to apply, yet it has some very desirable statistical properties. In Chapter 4, we introduce the (two-variable) classical normal linear regression model, a model that assumes that the random dependent variable follows the normal probability distribution. With this assumption, the OLS estimators obtained in Chapter 3 possess some stronger statistical properties than the nonnormal classical linear regression model—properties that enable us to engage in statistical inference, namely, hypothesis testing