I.1 WHAT IS ECONOMETRICS ?
Literally interpreted, economics means "economic measurement" Although measurement is an important part of econometric,the scope of econometrics is much broader ,as can be seen from the following quotations :
Econometrics , the result of certain outlook on the role of economics, consists of the application of mathematical statistics to economic data to lend empirical support to the model constructed by mathematical economic and to obtain numerical result. 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 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 economics phenomena . 3
Econometrics is concerned whit 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 HTheil, Principles of Econometrics , John Wiley & sons, New York,1971 ,p. 1 .
The art of 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 positive 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 measurement ,using the theory and technique of statistical inference as bridge pier.7
________________
5. E.Malinvaud. Statistical Methods of econometrics, Rand Mc , Chicago, 1966, p . 514.
6 Adrian C. Darnell and J. Lynne Evans, The Limits Of Econometrics, Edward Elgar Publishing, Hands , England,1990, p.54
7.T.Haavelmo "Theprobanility Approach in Economictrics "Supplement to Econometrica, vol.12.1944.preface p.iii
1.2 WHY A SEPARATE DISCIPLINE
As the preceding definitions suggest, econometric is an amalgam of economic theory, mathematical economics, economic statistic, and mathematical statistics. Yet the subject deserves to be studied in its own right for following reasons.
Economic theory makes statements or hypotheses 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 of the relationship between the two ; that is, it does not tell by how much the quantity will go up or down as 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 give empirical content to most economic theory.
The main concern of mathematical economics is to express economic theory in mathematical from (equations) without regard to measurability , or empirical verification of the theory. Econometric , as noted previously , is mainly interested in the empirical verification of the theory. As we shall see, the econometrician often uses the mathematical equations proposed by the mathematical economist but puts these equations in such a mathematical into econometric equation requires a great deal ingenuity and practical skill.
Economic statistics is mainly concerned whit collecting, processing, and presenting economic data in the from of charts tables. These are the job of the economic statistician . It is her or she who is primarily responsible for collection on gross national product ( GNP), Employment, unemployment,price,etc. The data thus coleted costitute the raw data for econometric work. But the economic statistician does not go any further, not being concerned whit using the collected data to test economic theories.
Although mathematical statistics provides many tool 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 the 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 modelling 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 data analyst requires the modeler to familiarize himself/herself thoroughly whit the nature and structure of data in question. 8
1.3 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 though t on econometric methodology, we present here the traditional or classical methodology, Which still dominates empirical research in the economic and other social and behavioral sciences. 9
Broadly speaking , traditional econometric methodology proceeds along the following lines :
_________________
8. Aris Spanos, Probability Theory and Statistical Inference : Econometric Modeling whit 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.
1. Statement of Theory or Hypothesis
Keynes Stated :
The fundamental psychological law. . . is that men [Women] are disposed, as a rule and average , to increase their consumption as their income increases, but not as much as the increase in their income.10
In short. Keynes postulate that the marginal propensity to consume (MPC) , the rate of change of consumption for unit (say, a dollar change income , is greater zero but less than 1.
2.Spescification of the Mathematical of Consumption
Literally interpreted, economics means "economic measurement" Although measurement is an important part of econometric,the scope of econometrics is much broader ,as can be seen from the following quotations :
Econometrics , the result of certain outlook on the role of economics, consists of the application of mathematical statistics to economic data to lend empirical support to the model constructed by mathematical economic and to obtain numerical result. 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 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 economics phenomena . 3
Econometrics is concerned whit 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 HTheil, Principles of Econometrics , John Wiley & sons, New York,1971 ,p. 1 .
The art of 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 positive 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 measurement ,using the theory and technique of statistical inference as bridge pier.7
________________
5. E.Malinvaud. Statistical Methods of econometrics, Rand Mc , Chicago, 1966, p . 514.
6 Adrian C. Darnell and J. Lynne Evans, The Limits Of Econometrics, Edward Elgar Publishing, Hands , England,1990, p.54
7.T.Haavelmo "Theprobanility Approach in Economictrics "Supplement to Econometrica, vol.12.1944.preface p.iii
1.2 WHY A SEPARATE DISCIPLINE
As the preceding definitions suggest, econometric is an amalgam of economic theory, mathematical economics, economic statistic, and mathematical statistics. Yet the subject deserves to be studied in its own right for following reasons.
Economic theory makes statements or hypotheses 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 of the relationship between the two ; that is, it does not tell by how much the quantity will go up or down as 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 give empirical content to most economic theory.
The main concern of mathematical economics is to express economic theory in mathematical from (equations) without regard to measurability , or empirical verification of the theory. Econometric , as noted previously , is mainly interested in the empirical verification of the theory. As we shall see, the econometrician often uses the mathematical equations proposed by the mathematical economist but puts these equations in such a mathematical into econometric equation requires a great deal ingenuity and practical skill.
Economic statistics is mainly concerned whit collecting, processing, and presenting economic data in the from of charts tables. These are the job of the economic statistician . It is her or she who is primarily responsible for collection on gross national product ( GNP), Employment, unemployment,price,etc. The data thus coleted costitute the raw data for econometric work. But the economic statistician does not go any further, not being concerned whit using the collected data to test economic theories.
Although mathematical statistics provides many tool 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 the 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 modelling 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 data analyst requires the modeler to familiarize himself/herself thoroughly whit the nature and structure of data in question. 8
1.3 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 though t on econometric methodology, we present here the traditional or classical methodology, Which still dominates empirical research in the economic and other social and behavioral sciences. 9
Broadly speaking , traditional econometric methodology proceeds along the following lines :
- Statement of theory or hypothesis
- Specification of the mathematical model of the theory
- Specification of the statistical , or econometric , model
- Obtaining the data
- Estimation of the parameters of the econometric model
- Hypothesis testing
- Forecasting or prediction
- Using the model for control or policy purposes
_________________
8. Aris Spanos, Probability Theory and Statistical Inference : Econometric Modeling whit 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.
1. Statement of Theory or Hypothesis
Keynes Stated :
The fundamental psychological law. . . is that men [Women] are disposed, as a rule and average , to increase their consumption as their income increases, but not as much as the increase in their income.10
In short. Keynes postulate that the marginal propensity to consume (MPC) , the rate of change of consumption for unit (say, a dollar change income , is greater zero but less than 1.
2.Spescification of the Mathematical of Consumption
Although Keynes postulate a positive relationship between consumption an income , he did not specify the precise form of the functional relationship between the two. For simplicity , a mathematical economist might suggest the following from the Keynesian Consumption function :
where Y = consumption expenditure and X = Income , where B1 and B2, known as the parameters of model, are, respectively, the intercept and slope coefficients.
The slope coefficients B2 measures the MPC. Geometrically ,Eq (I.3.1) is as shown in figure I.1 equation, which states that consumption is linearly related to income
____________________
FIGURE I.1 Keynes consumption.
10. John Maynard Keynes, The General Theory of Employment, Interest and Money, Harcourt Brace Jovanovich, New York,1936, p.96.
, is an example of a mathematical model of the relationship between consumption and income that is called the consumption function in economics . A model is simply a set of mathematical equations.
FIGURE I.1 Keynes consumption.
10. John Maynard Keynes, The General Theory of Employment, Interest and Money, Harcourt Brace Jovanovich, New York,1936, p.96.
, is an example of a mathematical model of the relationship 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 multiple -equation model ( the latter be considered later in the book).
In eq. (I.3.) te 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, Eq.(I.3.1),consumption (expenditure ) is the dependent variable and income is 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 there is an exact or deterministic relationship between consumption and income . But relationship between economic variables are generally inexact. Thus , if we were to obtain data on consumption expenditure and disposable (i.e., aftertax) income of sample of say ,500 American families and plot these data on a graph paper whit consumption expenditure on the vertical axis and disposable income on the horizontal axis , we would not expect all 500 observation to lie exactly on the straight line Eq.(I.3.1) because , in addition income , other variables affect consumption expenditure. For example, size of family, ages of the member s in family , family religion ,etc. , are likely to exert same influence on consumption.
To allow for the inexact relationship between variable , the econometrician would modifly the deterministic consumption function ( I..3.1) as follows :
The purely mathematical model of the consumption function given in Eq.(I.3.1) is of limited interest to the econometrician, for it assumes there is an exact or deterministic relationship between consumption and income . But relationship between economic variables are generally inexact. Thus , if we were to obtain data on consumption expenditure and disposable (i.e., aftertax) income of sample of say ,500 American families and plot these data on a graph paper whit consumption expenditure on the vertical axis and disposable income on the horizontal axis , we would not expect all 500 observation to lie exactly on the straight line Eq.(I.3.1) because , in addition income , other variables affect consumption expenditure. For example, size of family, ages of the member s in family , family religion ,etc. , are likely to exert same influence on consumption.
To allow for the inexact relationship between variable , the econometrician would modifly the deterministic consumption function ( I..3.1) as follows :
 |
( I.3.1)
Where u, known as the disturbance, or error, term, is a random ( stochastic ) variable that has well-defined
probabilistic properties. The disturbance tern 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 technically, it is an example of a linear regression model, which is the major concern of the book. The econometric consumption function hypothesize variable Y (consumption) is linearly related to the explanatory variable X ( income) but 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
4.Obataining Data
To estimate econometric model given in (I3.2), that is ,to obtain the numerical of B1 and B2 , we need data . Although we will have more 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
the U.S.economy for period 1981-1996. The Y Variable in this table is aggregate ( for economy as a whole ) personal consumption expenditure ( PC E ) and X variable gross domestic product ( GNP ), 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 potted 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 estimating the parameters will be discussed in Chapter 3. For now , not that the statistical technique of regression analysis is the main tool used to obtain the estimates. Using this technique and data the given Table I.1, we obtain the following estimates of B1 and B2 namely,-184.08 and 0.7064. Thus , the estimated consumption function is :
^Y = -184.08 + 0.7064 Xi ( I.3.3)
The that on the Y indicates that it is an is an estimate .11. The estimated consumption function ( o.e., regression line ) is shown in figure I.3
_____________
11 As a matter of convention , a hat a variable or parameter indicates that is estimated variable.
As Figure I.3 shows, the regression fine fits the data quite well in the that the data points are very close to regression line. From this figure we see that for 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 dollars led ,on average , to an increase of about 70 cent in real consumption expenditure.12. We say on average because the relationship between consumption and income is inexact; as is clear Figure I.3;not all the data points lie exactly on the regression line. In sample terms we can say that, according to our data. the average, or mean , consumption expenditure wen up by about 70 cents for a dollar's increase in real income.
6.Hypothesis Testing
Assuming that that the fitted model is a reasonably good approximation of reality, we have to develop suitable criteria to find out whether the estimates obtained in say , Eq.(i.3.3) are in accord whit 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 empirical 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 Keynes consumption theory, we must enquiry whether this estimate is sufficiently below unity to convince us that this not a change occurrence or peculiarity of the particular data we have used . In other word,is 0.70 statistically less than 1 ?If it is 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 statistical inference (hypothesis testing).throughout this book we shall see how this inference process is accually conducted.
7.Forecasting or Prediction
If the chosen model does not refute the hypothesis or theory under consideration,we may use it to predict the future value ( s ) of the dependent forecast,variable Y on the basis of known or expected future (s ) of the explanatory, or predictor, variable X.
To illustrate, suppose we want to the mean consumption expenditure for 1997. The GPD value for 1997was 7269.8 billion dollars.14
_____________________
12 .Do not worry now about how these values were obtained . As we show 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.
13. See Milton Friedman , "the Methodology of Positive Economics,"Essays In Positive Economics, University of Chicago Press , Chicago 1953.
14. Data on PCE and GPD were available for 1977 but we purposely left them out to illustrate the topic discussed in this section. As will discuss in subsequent chapters, it is a good idea to save a portion of the data to find out how well fitted model predicts out -of sample observation.
Putting this GPD figure the right side of (1.3.3 ), we obtain :
^Y = 184.0779 + 0.7064 ( 7269.8 )
= 4951.3167
or about 4951 billion dollars. Thus given the value of the GPD, the mean , or average ,forecast consumption expenditure is about 4951 bilion dolars. 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 forecast error is about 37.82 billion dollars. wich is about 0.76 percent of the actual GPD value for 1977. When we fully discuss the the linear regression model in subsequent chapters.,we will try to find out if such forecast error is "small" or "large".But what is important of now is to note that such forecast error are inevitable given the statistical nature of our analysis.
There is another use of the estimated model ( I.3.3 ), Suppose the president decides to propose a reduction in the income tax. What will be the effect 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 expenditure increases. What will be effect on the economy ?. As macroeconomic shows,the change in income following,say ,a dollar's whorth of change in investment expenditure is given by the income multiplier M,which is defined as
If we use the MPC of 0.70 obtained in (I3.3) , this multiplier about M =3.33. That an increase ( decrease ) of a dollar in investment will eventually lead to more than a threefold increase ( decrease ) in income; note that it take time for the multiplier to work.
The critical value in this computation is MPC, for multiplier dependent on it . And this estimate of the MPC can obtained from regression models such as (I3.3) Thus , a quantitative estimate o MPC provide valuable in formation for policy purposes . Knowing MPC , one can predict the future course of income. consumption expenditure , and employment following a change in 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 believe that consumer expenditure of about 4900 (billions dollars ) wil keep the unemployment rate its
FIGURE I.4 Anatomy of econometric modeling.
current level of about 4.2 (early 200 ) . What level of incame will guarantee the target amoun of consumption expenditure ?
If the regression results in ( I3.3) seem reasonable , simple arithmetic will show that
4900 = - 184.0779 + 0.7064 X ( I.3.6 )
Which gives X = 7197, approximately. That is , an income level of about 7179 ( billion ) dollars, given an MPC of about 0.70, will produce an expenditure about 4900 billion dollars.
As these calculation suggest, an estimated model may be used for control , 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 fiscal econometric modelling.
No comments:
Post a Comment