《计量经济学》课程教学资源（国外经典教科书）Gujarati - Basic Econometrics, Fourth Edition

Introduction ② The McG econometrics. Fourth INTRODUCTION L1 WHAT IS ECONOMETRICS? Literally interpreted, econometrics means "economic measurement. " Al though 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 sup- port to the models constructed by mathematical economics and to obtain numerical results I econometrics may be defined as the quantitative analysis of actual economic phenomena based on the concurrent development of theory and observation, re- lated by appropriate methods of inference. 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 eco- nomic phenomena Econometrics is concerned with the empirical determination of economic Gerhard Tintner, Methodology of Mathematical Economics and Econometrics, The Univer- sity of Chicago Press, Chicago, 1968, p. 74 2P. 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 H. Theil, Principles of Econometrics, John Wiley Sons, New York, 1971,P./.p.I

Gujarati: Basic Econometrics, Fourth Edition Front Matter Introduction © The McGraw−Hill Companies, 2004 1 INTRODUCTION I.1 WHAT IS ECONOMETRICS? Literally interpreted, econometrics means “economic measurement.” Al￾though 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 sup￾port 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, re￾lated 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 eco￾nomic phenomena.3 Econometrics is concerned with the empirical determination of economic laws.4 1 Gerhard Tintner, Methodology of Mathematical Economics and Econometrics, The Univer￾sity 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

Introduction ② The McG Econometrics. Fourth 2 BASIC ECONOMETRICS 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 pened by assuming the existence of can- openers to reveal contents which any ten economists will interpret in 11 ways. The method of econometric research aims, essentially, at a conjunction of eco- nomic theory and actual measurements, using the theory and technique of statis- L2 WHY A SEPARATE DISCIPLINE? As the preceding definitions suggest, econometrics is an amalgam of eco- nomic theory, mathematical economics, economic statistics, and mathe matical 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 quali ative in nature. For example, microeconomic theory states that, other things remaining the same, a reduction in the price of a commodity is ex pected to increase the quantity demanded of that commodity. Thus, eco- nomic theory postulates a negative or inverse relationship between the price and quantity demanded of a commodity. But the theory itself does not pro- vide 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 econome- rician to provide such numerical estimates. Stated differently, economet- rics gives empirical content to most economic theory lho he main concern of mathematical economics is to express economic eory 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 pro- posed 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 skil Economic statistics is mainly concerned with collecting, processing, and presenting economic data in the form of charts and tables. These are the ud, Statistical Methods of Econometrics, Rand McNally, Chicago, 1966, P. 514 Adrian C. Darnell and J. Lynne Evans, The Limits of Econometrics, Edward Elgar Publish ing, Hants, England, 1990, p. 54 T Haavelmo, "The Probability Approach in Econometrics, "Supplement to Econometrica, vol.12,1944,pr

Gujarati: Basic Econometrics, Fourth Edition Front Matter Introduction © The McGraw−Hill Companies, 2004 2 BASIC ECONOMETRICS 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 Publish￾ing, Hants, England, 1990, p. 54. 7 T. Haavelmo, “The Probability Approach in Econometrics,” Supplement to Econometrica, vol. 12, 1944, preface p. iii. 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 eco￾nomic theory and actual measurements, using the theory and technique of statis￾tical inference as a bridge pier.7 I.2 WHY A SEPARATE DISCIPLINE? As the preceding definitions suggest, econometrics is an amalgam of eco￾nomic theory, mathematical economics, economic statistics, and mathe￾matical 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 quali￾tative in nature. For example, microeconomic theory states that, other things remaining the same, a reduction in the price of a commodity is ex￾pected to increase the quantity demanded of that commodity. Thus, eco￾nomic theory postulates a negative or inverse relationship between the price and quantity demanded of a commodity. But the theory itself does not pro￾vide 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 econome￾trician to provide such numerical estimates. Stated differently, economet￾rics 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 pro￾posed 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

Introduction ② The McG econometrics. Fourth INTRODUCTIon 3 jobs of the economic statistician. It is he or she who is primarily responsible for collecting data on gross national product(GNP), employment, unem- ployment, 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 na- ture of most economic data, namely, that the data are not generated as the result of a controlled experiment. The econometrician, like the meteorolo- gist, 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. 3 METHODOLOGY OF ECONOMETRICS 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 eco- nomics 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 SAris Spanos, Probability Theory and Statistical Inference: Econometric Modeling with Obser vational Data, Cambridge University Press, United Kingdom, 1999, p. 21 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 Edition Front Matter Introduction © The McGraw−Hill Companies, 2004 INTRODUCTION 3 8 Aris Spanos, Probability Theory and Statistical Inference: Econometric Modeling with Obser￾vational 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. jobs of the economic statistician. It is he or she who is primarily responsible for collecting data on gross national product (GNP), employment, unem￾ployment, 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 na￾ture of most economic data, namely, that the data are not generated as the result of a controlled experiment. The econometrician, like the meteorolo￾gist, 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 I.3 METHODOLOGY OF ECONOMETRICS 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 eco￾nomics 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

Introduction ② The McG Econometrics. Fourth 4 BASIC ECONOMETRICS 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 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 relation- ship between the two. For simplicity, a mathematical economist might sug gest the following form of the Keynesian consumption function Y=B1+B2X0<B2<1 (I3.1) where Y= consumption expenditure and X= income, and where B1 and B2 known as the parameters of the model, are, respectively, the intercept and slope coefficients The slope coefficient B2 measures the MPC. Geometrically, Eq (I.3.1)is as shown in Figure I 1. This equation, which states that consumption is lin β2=MPC FIGURE L1 Keynesian consumption function John Maynard Keynes, The General Theory of Employment, Interest and Money, Harcourt

Gujarati: Basic Econometrics, Fourth Edition Front Matter Introduction © The McGraw−Hill Companies, 2004 4 BASIC ECONOMETRICSConsumption expenditure X Income 1 β2 = MPC β1 Y FIGURE I.1 Keynesian consumption function. 10John Maynard Keynes, The General Theory of Employment, Interest and Money, Harcourt Brace Jovanovich, New York, 1936, p. 96. 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 relation￾ship between the two. For simplicity, a mathematical economist might sug￾gest the following form of the Keynesian consumption function: Y = β1 + β2X 0 < β2 < 1 (I.3.1) where Y = consumption expenditure and X = income, and where β1 and β2, known as the parameters of the model, are, respectively, the intercept and slope coefficients. The slope coefficient β2 measures the MPC. Geometrically, Eq. (I.3.1) is as shown in Figure I.1. This equation, which states that consumption is lin-

Introduction ② The McG econometrics. Fourth INTRODUCTION 5 early related to income, is an example of a mathematical model of the rela tionship between consumption and income that is called the consumption function in economics. A model is simply a set of mathematical equations If the model has only one equation, as in the preceding example, it is called a single-equation model, whereas if it has more than one equation, it is known as a multiple-equation model (the latter will be considered later the book) In Eq(I.3. 1) the variable appearing on the left side of is called the dependent variable and the variable(s) on the right side are called the independent, or explanatory, variable(s). Thus, in the Keynesian consumption function, Eq (I.3. 1), consumption(expenditure)is the depen dent variable and income is the explanatory variable 3. Specification of the Econometric Model of Consumption The purely mathematical model of the consumption function given in Eq.(I.3. 1) is of limited interest to the econometrician, for it assumes that there is an exact or deterministic relationship between consumption and income. But relationships between economic variables are generally inexact Thus, if we were to obtain data on consumption expenditure and disposable (i.e, aftertax) income of a sample of, say, 500 American families and plot these data on a graph paper with consumption expenditure on the vertical axis and disposable income on the horizontal axis, we would not expect all 500 observations to lie exactly on the straight line of Eq(1.3.1) because, in ddition to income, other variables affect consumption expenditure. For ex- ample, size of family, ages of the members in the family, family religion, etc are likely to exert some influence on consumption. To allow for the inexact relationships between economic variables, the econometrician would modify the deterministic consumption function (1.3. 1) as follows Y=B1+B2X+u (I3.2) where u, known as the disturbance, or error, term, is a random(stochas- tic)variable that has well-defined probabilistic properties. The disturbance term u may well represent all those factors that affect consumption but are not taken into account explicitly Equation(1. 3. 2)is an example of an econometric model. More techni cally, it is an example of a linear regression model, which is the major concern of this book. The econometric consumption function hypothesizes that the dependent variable Y(consumption) is linearly related to the ex planatory variable X (income) but that the relationship between the two is not exact; it is subject to individual variation The econometric model of the consumption function can be depicted as hown in Figure 1.2

Gujarati: Basic Econometrics, Fourth Edition Front Matter Introduction © The McGraw−Hill Companies, 2004 INTRODUCTION 5 early related to income, is an example of a mathematical model of the rela￾tionship between consumption and income that is called the consumption function in economics. A model is simply a set of mathematical equations. If the model has only one equation, as in the preceding example, it is called a single-equation model, whereas if it has more than one equation, it is known as a multiple-equation model (the latter will be considered later in the book). In Eq. (I.3.1) the variable appearing on the left side of the equality sign is called the dependent variable and the variable(s) on the right side are called the independent, or explanatory, variable(s). Thus, in the Keynesian consumption function, Eq. (I.3.1), consumption (expenditure) is the depen￾dent variable and income is the explanatory variable. 3. Specification of the Econometric Model of Consumption The purely mathematical model of the consumption function given in Eq. (I.3.1) is of limited interest to the econometrician, for it assumes that there is an exact or deterministic relationship between consumption and income. But relationships between economic variables are generally inexact. Thus, if we were to obtain data on consumption expenditure and disposable (i.e., aftertax) income of a sample of, say, 500 American families and plot these data on a graph paper with consumption expenditure on the vertical axis and disposable income on the horizontal axis, we would not expect all 500 observations to lie exactly on the straight line of Eq. (I.3.1) because, in addition to income, other variables affect consumption expenditure. For ex￾ample, size of family, ages of the members in the family, family religion, etc., are likely to exert some influence on consumption. To allow for the inexact relationships between economic variables, the econometrician would modify the deterministic consumption function (I.3.1) as follows: Y = β1 + β2X + u (I.3.2) where u, known as the disturbance, or error, term, is a random (stochas￾tic) variable that has well-defined probabilistic properties. The disturbance term u may well represent all those factors that affect consumption but are not taken into account explicitly. Equation (I.3.2) is an example of an econometric model. More techni￾cally, it is an example of a linear regression model, which is the major concern of this book. The econometric consumption function hypothesizes that the dependent variable Y (consumption) is linearly related to the ex￾planatory variable X (income) but that the relationship between the two is not exact; it is subject to individual variation. The econometric model of the consumption function can be depicted as shown in Figure I.2