《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 FIGURE L2 Econometric model of the Keynesian consumption function To estimate the econometric model given in(I.3.2), that is, to obtain the numerical values of B, and B2, we need data. Although we will have more to ay about the crucial importance of data for economic analysis in the next chapter, for now let us look at the data given in Table I 1, which relate to TABLE L1 DATA ON Y(PERSONAL CONSUMPTION EXPENDITURE AND X (GROSS DOMESTIC PRODUCT, 1982-1996), BOTH IN 1992 BILLIONS OF DOLLARS 1982 081.5 4620.3 1983 4803.7 1987 8223 5649 1058 42198 62444 4486.0 6610.7 4595 6742.1 1996 4714.1 69284

Gujarati: Basic Econometrics, Fourth Edition Front Matter Introduction © The McGraw−Hill Companies, 2004 6 BASIC ECONOMETRICSConsumption expenditure X Y Income u FIGURE I.2 Econometric model of the Keynesian consumption function. 4. Obtaining Data To estimate the econometric model given in (I.3.2), that is, to obtain the numerical values of β1 and β2, we need data. Although we will have more to say about the crucial importance of data for economic analysis in the next chapter, for now let us look at the data given in Table I.1, which relate to TABLE I.1 DATA ON Y (PERSONAL CONSUMPTION EXPENDITURE) AND X (GROSS DOMESTIC PRODUCT, 1982–1996), BOTH IN 1992 BILLIONS OF DOLLARS Year Y X 1982 3081.5 4620.3 1983 3240.6 4803.7 1984 3407.6 5140.1 1985 3566.5 5323.5 1986 3708.7 5487.7 1987 3822.3 5649.5 1988 3972.7 5865.2 1989 4064.6 6062.0 1990 4132.2 6136.3 1991 4105.8 6079.4 1992 4219.8 6244.4 1993 4343.6 6389.6 1994 4486.0 6610.7 1995 4595.3 6742.1 1996 4714.1 6928.4 Source: Economic Report of the President, 1998, Table B–2, p. 282

Introduction ② The McG econometrics. Fourth INTRODUCTION 7 4000 5000 6000 7000 FIGURE 1.3 Personal consumption expenditure(Y) in relation to GDP(X), 1982-1996, both in billions of 1992 the U.s. economy for the period 1981-1996. The Y variable in this table is the aggregate(for the economy as a whole) personal consumption expen diture(PCe)and the X variable is gross domestic product(GDP), a measure of aggregate income, both measured in billions of 1992 dollars. Therefore, the data are in"real" terms: that is, they are measured in constant(1992) prices. The data are plotted in Figure 1.3(cf Figure 1. 2). For the time being neglect the line drawn in the figure 5. Estimation of the econometric model Now that we have the data, our next task is to estimate the parameters of the consumption function. The numerical estimates of the parameters give empirical content to the consumption function. The actual mechanics of es- timating the parameters will be discussed in Chapter 3. For now, note that the statistical technique of regression analysis is the main tool used to obtain the estimates. Using this technique and the data given in Table I1 we obtain the following estimates of B1 and B2, namely, -184.08 and 0.7064 hus, the estimated consumption function is: Y=-184.08+0.7064X (L3.3 The hat on the y indicates that it is an estimate. The estimated consump- tion function(i.e, regression line) is shown in Figure 1.3 As a matter of convention, a hat over a variable or parameter indicates that it is an esti mated valu

Gujarati: Basic Econometrics, Fourth Edition Front Matter Introduction © The McGraw−Hill Companies, 2004 INTRODUCTION 7 5000 6000 7000 GDP (X) 4000 3000 3500 4000 4500 PCE ( Y) 5000 FIGURE I.3 Personal consumption expenditure (Y) in relation to GDP (X), 1982–1996, both in billions of 1992 dollars. the U.S. economy for the period 1981–1996. The Y variable in this table is the aggregate (for the economy as a whole) personal consumption expen￾diture (PCE) and the X variable is gross domestic product (GDP), a measure of aggregate income, both measured in billions of 1992 dollars. Therefore, the data are in “real” terms; that is, they are measured in constant (1992) prices. The data are plotted in Figure I.3 (cf. Figure I.2). For the time being neglect the line drawn in the figure. 5. Estimation of the Econometric Model Now that we have the data, our next task is to estimate the parameters of the consumption function. The numerical estimates of the parameters give empirical content to the consumption function. The actual mechanics of es￾timating the parameters will be discussed in Chapter 3. For now, note that the statistical technique of regression analysis is the main tool used to obtain the estimates. Using this technique and the data given in Table I.1, we obtain the following estimates of β1 and β2, namely, −184.08 and 0.7064. Thus, the estimated consumption function is: Yˆ = −184.08 + 0.7064Xi (I.3.3) The hat on the Y indicates that it is an estimate.11 The estimated consump￾tion function (i.e., regression line) is shown in Figure I.3. 11As a matter of convention, a hat over a variable or parameter indicates that it is an esti￾mated value

Introduction ② The McG 8 BASIC ECONOMETRICS As Figure 1.3 shows, the regression line fits the data quite well in that the data points are very close to the regression line. From this figure we see that for the period 1982-1996 the slope coefficient (i.e, the MPC) was about 0.70, suggesting that for the sample period an increase in real income of I dollar led, on average, to an increase of about 70 cents in real consumption expenditure. We say on average because the relationship between con- sumption and income is inexact; as is clear from Figure 1. 3; not all the data points lie exactly on the regression line. In simple terms we can say that, ac cording to our data, the average, or mean, consumption expenditure went up by about 70 cents for a dollars increase in real income 6. Hypothesis Testing Assuming that the fitted model is a reasonably good approximation of reality, we have to develop suitable criteria to find out whether the esti- mates obtained in, say, Eq(1.3.3)are in accord with the expectations of the theory that is being tested. According to "positive economists like Milton Friedman, a theory or hypothesis that is not verifiable by appeal to empiri cal evidence may not be admissible as a part of scientific enquiry. As noted earlier, Keynes expected the MPC to be positive but less than 1 In our example we found the mPc to be about 0.70. But before we accept this finding as confirmation of Keynesian consumption theory, we must en- quire whether this estimate is sufficiently below unity to convince us that this is not a chance occurrence or peculiarity of the particular data we have used. In other words, is 0.70 statistically less than 1? If it is, it may support Keynes theory. Such confirmation or refutation of economic theories on the basis of sample evidence is based on a branch of statistical theory known as statis tical inference (hypothesis testing). Throughout this book we shall see how this inference process is actually conducted. 7. Forecasting or Prediction If the chosen model does not refute the hypothesis or theory under consid- eration, we may use it to predict the future value(s) of the dependent, or forecast, variable Yon the basis of known or expected future value(s)of the explanatory, or predictor;, variable X. To illustrate, suppose we want to predict the mean consumption expen diture for 1997. The GDP value for 1997 was 7269. 8 billion dollars. 4 Putting 1Do not worry now about how these values were obtained. As we show in Chap3, the statistical method of least squares has produced these estimates. Also, for now do not worry bout the negative value of the intercep See Milton Friedman, The Methodology of Positive Economics, " Essays in Positive Eco- the topic discussed in this section. As we will discuss in subsequent chapters, it is a good idea to save a portion of the data to find out how well the fitted model predicts the out-of-sam

Gujarati: Basic Econometrics, Fourth Edition Front Matter Introduction © The McGraw−Hill Companies, 2004 8 BASIC ECONOMETRICS As Figure I.3 shows, the regression line fits the data quite well in that the data points are very close to the regression line. From this figure we see that for the period 1982–1996 the slope coefficient (i.e., the MPC) was about 0.70, suggesting that for the sample period an increase in real income of 1 dollar led, on average, to an increase of about 70 cents in real consumption expenditure.12 We say on average because the relationship between con￾sumption and income is inexact; as is clear from Figure I.3; not all the data points lie exactly on the regression line. In simple terms we can say that, ac￾cording to our data, the average, or mean, consumption expenditure went up by about 70 cents for a dollar’s increase in real income. 6. Hypothesis Testing Assuming that the fitted model is a reasonably good approximation of reality, we have to develop suitable criteria to find out whether the esti￾mates obtained in, say, Eq. (I.3.3) are in accord with the expectations of the theory that is being tested. According to “positive” economists like Milton Friedman, a theory or hypothesis that is not verifiable by appeal to empiri￾cal evidence may not be admissible as a part of scientific enquiry.13 As noted earlier, Keynes expected the MPC to be positive but less than 1. In our example we found the MPC to be about 0.70. But before we accept this finding as confirmation of Keynesian consumption theory, we must en￾quire whether this estimate is sufficiently below unity to convince us that this is not a chance occurrence or peculiarity of the particular data we have used. In other words, is 0.70 statistically less than 1? If it is, it may support Keynes’ theory. Such confirmation or refutation of economic theories on the basis of sample evidence is based on a branch of statistical theory known as statis￾tical inference (hypothesis testing). Throughout this book we shall see how this inference process is actually conducted. 7. Forecasting or Prediction If the chosen model does not refute the hypothesis or theory under consid￾eration, we may use it to predict the future value(s) of the dependent, or forecast, variable Y on the basis of known or expected future value(s) of the explanatory, or predictor, variable X. To illustrate, suppose we want to predict the mean consumption expen￾diture for 1997. The GDP value for 1997 was 7269.8 billion dollars.14 Putting 12Do not worry now about how these values were obtained. As we show in Chap. 3, the statistical method of least squares has produced these estimates. Also, for now do not worry about the negative value of the intercept. 13See Milton Friedman, “The Methodology of Positive Economics,” Essays in Positive Eco￾nomics, University of Chicago Press, Chicago, 1953. 14Data on PCE and GDP were available for 1997 but we purposely left them out to illustrate the topic discussed in this section. As we will discuss in subsequent chapters, it is a good idea to save a portion of the data to find out how well the fitted model predicts the out-of-sample observations

Introduction ② The McG econometrics. Fourth INTROdUCtion 9 his gDP figure on the right-hand side of (1.3.3), we obtain: YI 1997=-184.0779+0.7064(72698) (I34) =4951.3167 or about 4951 billion dollars. Thus, given the value of the gDP, the mean, or average, forecast consumption expenditure is about 4951 billion dol- lars. The actual value of the consumption expenditure reported in 1997 was 4913.5 billion dollars. The estimated model(I.3.3)thus overpredicted the actual consumption expenditure by about 37. 82 billion dollars. We could say the forecast error is about 37. 82 billion dollars, which is about 0.76 percent of the actual GDP value for 1997. When we fully discuss the linear regression model in subsequent chapters, we will try to find out if such an error is"small"or"large. But what is important for now is to note that such forecast errors are inevitable given the statistical nature of our analy There is another use of the estimated model (1.3.3). Suppose the Pres dent decides to propose a reduction in the income tax. What will be the ef- fect of such a policy on income and thereby on consumption expenditure and ultimately on employment? Suppose that, as a result of the proposed policy change, investment ex- penditure increases. What will be the effect on the economy? As macroeco- nomic theory shows, the change in income following, say, a dollars worth of change in investment expenditure is given by the income multiplier M, which is defined M 1-MPC (I3.5) If we use the MPC of 0. 70 obtained in(1.3.3), this multiplier becomes about M=3.33. That is, an increase(decrease) of a dollar in investment will even- tually lead to more than a threefold increase(decrease)in income; note that it takes time for the multiplier to work The critical value in this computation is MPC, for the multiplier depends on it. And this estimate of the MPC can be obtained from regression model such as(1.3.3). Thus, a quantitative estimate of MPC provides valuable formation for policy purposes. Knowing MPC, one can predict the future course of income, consumption expenditure, and employment following a hange in the government's fiscal policies 8. Use of the Model for Control or Policy Purposes Suppose we have the estimated consumption function given in(I.3.3) Suppose further the government believes that consumer expenditure of about 4900(billions of 1992 dollars)will keep the unemployment rate at its

Gujarati: Basic Econometrics, Fourth Edition Front Matter Introduction © The McGraw−Hill Companies, 2004 INTRODUCTION 9 this GDP figure on the right-hand side of (I.3.3), we obtain: Yˆ 1997 = −184.0779 + 0.7064 (7269.8) = 4951.3167 (I.3.4) or about 4951 billion dollars. Thus, given the value of the GDP, the mean, or average, forecast consumption expenditure is about 4951 billion dol￾lars. The actual value of the consumption expenditure reported in 1997 was 4913.5 billion dollars. The estimated model (I.3.3) thus overpredicted the actual consumption expenditure by about 37.82 billion dollars. We could say the forecast error is about 37.82 billion dollars, which is about 0.76 percent of the actual GDP value for 1997. When we fully discuss the linear regression model in subsequent chapters, we will try to find out if such an error is “small” or “large.” But what is important for now is to note that such forecast errors are inevitable given the statistical nature of our analysis. There is another use of the estimated model (I.3.3). Suppose the Presi￾dent decides to propose a reduction in the income tax. What will be the ef￾fect of such a policy on income and thereby on consumption expenditure and ultimately on employment? Suppose that, as a result of the proposed policy change, investment ex￾penditure increases. What will be the effect on the economy? As macroeco￾nomic theory shows, the change in income following, say, a dollar’s worth of change in investment expenditure is given by the income multiplier M, which is defined as M = 1 1 − MPC (I.3.5) If we use the MPC of 0.70 obtained in (I.3.3), this multiplier becomes about M = 3.33. That is, an increase (decrease) of a dollar in investment will even￾tually lead to more than a threefold increase (decrease) in income; note that it takes time for the multiplier to work. The critical value in this computation is MPC, for the multiplier depends on it. And this estimate of the MPC can be obtained from regression models such as (I.3.3). Thus, a quantitative estimate of MPC provides valuable in￾formation for policy purposes. Knowing MPC, one can predict the future course of income, consumption expenditure, and employment following a change in the government’s fiscal policies. 8. Use of the Model for Control or Policy Purposes Suppose we have the estimated consumption function given in (I.3.3). Suppose further the government believes that consumer expenditure of about 4900 (billions of 1992 dollars) will keep the unemployment rate at its

Introduction ② The McG econometrics. Fourth 10 BASIC ECONOMETRICS Economic theory I Mathematical model of theory Econometric model of theory Data Estimation of econometric mode Hypothesis testing Forecasting or predictio Using the model for FIGURE L4 Anatomy of econometric modeling control or policy purposes current level of about 4.2 percent 2000). What level of income will guarantee the target amount of con ion expenditure? If the regression results given in(1. 3. 3)seem reasonable, simple arith metic will show that 4900=-184.0779+0.7064X (I3.6) which gives X=7197, approximately. That is, an income level of about 7197(billion) dollars, given an MPC of about 0.70, will produce an expendi ture of about 4900 billion dollars As these calculations suggest, an estimated model may be used for con ol, or policy, purposes. By appropriate fiscal and monetary policy mix, the government can manipulate the control variable X to produce the desired level of the target variable y Figure I 4 summarizes the anatomy of classical econometric modeling Choosing among Competing Models When a governmental agency (e. g, the U.S. Department of Commerce)col- lects economic data, such as that shown in Table I 1, it does not necessarily have any economic theory in mind. How then does one know that the data really support the Keynesian theory of consumption? Is it because the Keynesian consumption function (i. e, the regression line) shown in Fig ure 1. 3 is extremely close to the actual data points? Is it possible that an

Gujarati: Basic Econometrics, Fourth Edition Front Matter Introduction © The McGraw−Hill Companies, 2004 10 BASIC ECONOMETRICS Estimation of econometric model Econometric model of theory Economic theory Data Forecasting or prediction Using the model for control or policy purposes Hypothesis testing Mathematical model of theory FIGURE I.4 Anatomy of econometric modeling. current level of about 4.2 percent (early 2000). What level of income will guarantee the target amount of consumption expenditure? If the regression results given in (I.3.3) seem reasonable, simple arith￾metic will show that 4900 = −184.0779 + 0.7064X (I.3.6) which gives X = 7197, approximately. That is, an income level of about 7197 (billion) dollars, given an MPC of about 0.70, will produce an expendi￾ture of about 4900 billion dollars. As these calculations suggest, an estimated model may be used for con￾trol, or policy, purposes. By appropriate fiscal and monetary policy mix, the government can manipulate the control variable X to produce the desired level of the target variable Y. Figure I.4 summarizes the anatomy of classical econometric modeling. Choosing among Competing Models When a governmental agency (e.g., the U.S. Department of Commerce) col￾lects economic data, such as that shown in Table I.1, it does not necessarily have any economic theory in mind. How then does one know that the data really support the Keynesian theory of consumption? Is it because the Keynesian consumption function (i.e., the regression line) shown in Fig￾ure I.3 is extremely close to the actual data points? Is it possible that an-