Econometrics ch1
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This document provides an introduction to econometrics. It defines econometrics as the application of statistical and mathematical tools to economic data and theory. The document outlines the methodology of econometrics, including specifying a theoretical model, collecting data, estimating model parameters, testing hypotheses, forecasting, and using models for policy purposes. It provides the example of estimating the parameters of Keynes' consumption function to illustrate these steps.
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Econometrics ch1
- 1. 405 ECONOMETRICS Chapter # 0: Introduction By: Domodar N. Gujarati Prof. M. El-SakkaProf. M. El-Sakka Dept of Economics: Kuwait UniversityDept of Economics: Kuwait University
- 2. WHAT IS ECONOMETRICS? • Econometrics means “Econometrics means “economic measurementeconomic measurement”. the scope of”. the scope of econometrics is much broader, as can be seen from the followingeconometrics is much broader, as can be seen from the following definitions:definitions: • ““Consists ofConsists of the application of mathematical statisticsthe application of mathematical statistics to economicto economic data to lend empirical support to the models constructed bydata to lend empirical support to the models constructed by mathematical economics and tomathematical economics and to obtain numerical resultsobtain numerical results” (Gerhard” (Gerhard 1968).1968). • ““Econometrics may be defined as the social science in which the toolsEconometrics may be defined as the social science in which the tools of economic theory, mathematics, and statistical inference areof economic theory, mathematics, and statistical inference are applied to theapplied to the analysis of economic phenomenaanalysis of economic phenomena” (Goldberger 1964).” (Goldberger 1964). • ““Econometrics is concerned with theEconometrics is concerned with the empirical determinationempirical determination ofof economic lawseconomic laws” (Theil 1971).” (Theil 1971).
- 3. WHY ECONOMETRICS IS A SEPARATE DISCIPLINE? • the subject deserves to be studied in its own right for the followingthe subject deserves to be studied in its own right for the following reasons:reasons: • Economic theory makesEconomic theory makes statements or hypothesesstatements or hypotheses that are mostlythat are mostly qualitativequalitative in nature (the law of demand), the law does not providein nature (the law of demand), the law does not provide anyany numericalnumerical measure of the relationship. This is the job of themeasure of the relationship. This is the job of the econometrician.econometrician. • The main concern ofThe main concern of mathematical economicsmathematical economics is to express economicis to express economic theory in mathematical form without regard totheory in mathematical form without regard to measurabilitymeasurability oror empirical verification of the theory. Econometrics is mainlyempirical verification of the theory. Econometrics is mainly interested in theinterested in the empirical verificationempirical verification of economic theory.of economic theory. • Economic statisticsEconomic statistics is mainly concerned with collecting, processing,is mainly concerned with collecting, processing, and presenting economic data in the form of charts and tables. Itand presenting economic data in the form of charts and tables. It doesdoes not go any furthernot go any further. The one who does that is the. The one who does that is the econometrician.econometrician.
- 4. METHODOLOGY OF ECONOMETRICS • Broadly speaking, traditional econometric methodology proceedsBroadly speaking, traditional econometric methodology proceeds along the following lines:along the following lines: 1. Statement of theory or1. Statement of theory or hypothesishypothesis.. 2. Specification of the2. Specification of the mathematical modelmathematical model of the theoryof the theory 3. Specification of the statistical, or3. Specification of the statistical, or econometriceconometric, model, model 4. Collecting the4. Collecting the datadata 5. Estimation of the5. Estimation of the parametersparameters of the econometric modelof the econometric model 6. Hypothesis6. Hypothesis testingtesting 7. Forecasting or7. Forecasting or predictionprediction 8. Using the model for control or8. Using the model for control or policy purposes.policy purposes. • To illustrate the preceding steps, let us consider the well-knownTo illustrate the preceding steps, let us consider the well-known Keynesian theory of consumption.Keynesian theory of consumption.
- 5. 1. Statement of Theory or Hypothesis1. Statement of Theory or Hypothesis • Keynes states that on average, consumers increase their consumption asKeynes states that on average, consumers increase their consumption as their income increases, but not as much as the increase in their incometheir income increases, but not as much as the increase in their income (MPC < 1).(MPC < 1). 2. Specification of the Mathematical Model of Consumption (single-2. Specification of the Mathematical Model of Consumption (single- equation model)equation model) Y = βY = β11 + β+ β22X 0 < βX 0 < β22 < 1< 1 (I.3.1)(I.3.1) Y = consumption expenditure and (Y = consumption expenditure and (dependent variable)dependent variable) X =X = income, (independent, or explanatory variable)income, (independent, or explanatory variable) ββ11 == the interceptthe intercept ββ22 == thethe slope coefficientslope coefficient • The slope coefficientThe slope coefficient ββ22 measures the MPC.measures the MPC.
- 7. 3.3. Specification of the Econometric Model of ConsumptionSpecification of the Econometric Model of Consumption • TheThe relationshipsrelationships between economic variables are generallybetween economic variables are generally inexactinexact. In. In addition to income, other variables affect consumption expenditure. Foraddition to income, other variables affect consumption expenditure. For example,example, size of family, ages of the members in the family, family religionsize of family, ages of the members in the family, family religion,, etc., are likely to exert some influence on consumption.etc., are likely to exert some influence on consumption. • To allow for theTo allow for the inexactinexact relationships between economic variables, (I.3.1) isrelationships between economic variables, (I.3.1) is modified as follows:modified as follows: • Y = βY = β11 + β+ β22X +X + uu (I.3.2)(I.3.2) • where u, known aswhere u, known as the disturbance, or error, termthe disturbance, or error, term,, is a random (is a random (stochasticstochastic)) variable that has well-definedvariable that has well-defined probabilistic propertiesprobabilistic properties. The disturbance term. The disturbance term u may well represent all those factors that affect consumption but are notu may well represent all those factors that affect consumption but are not taken into accounttaken into account explicitly.explicitly.
- 8. • (I.3.2) is an example of a linear regression model, i.e., it hypothesizes that(I.3.2) is an example of a linear regression model, i.e., it hypothesizes that YY is linearly related to Xis linearly related to X, but that the relationship between the two is, but that the relationship between the two is not exactnot exact;; it is subject to individual variation. The econometric model of (I.3.2) can beit is subject to individual variation. The econometric model of (I.3.2) can be depicted as shown in Figure I.2.depicted as shown in Figure I.2.
- 9. 4. Obtaining Data4. Obtaining Data • To obtain the numerical values ofTo obtain the numerical values of β1 and β2, we need data.β1 and β2, we need data. Look at TableLook at Table I.1, which relate to theI.1, which relate to the personal consumption expenditurepersonal consumption expenditure (PCE) and the(PCE) and the gross domestic product (GDP)gross domestic product (GDP). The data are in “real” terms.. The data are in “real” terms.
- 10. The data are plotted in Figure I.3
- 11. 5. Estimation of the Econometric Model5. Estimation of the Econometric Model • Regression analysisRegression analysis is the main tool used to obtain the estimates. Using thisis the main tool used to obtain the estimates. Using this technique and the data given in Table I.1, we obtain the following estimatestechnique and the data given in Table I.1, we obtain the following estimates ofof ββ11 andand ββ22, namely,, namely, −184.08−184.08 andand 0.70640.7064.. Thus, the estimated consumptionThus, the estimated consumption function is:function is: • Yˆ = −184.08 + 0.7064XYˆ = −184.08 + 0.7064Xii (I.3.3)(I.3.3) • The estimatedThe estimated regression line is shown in Figure I.3. Theregression line is shown in Figure I.3. The regression line fitsregression line fits the data quite well. Thethe data quite well. The slopeslope coefficient (i.e., the MPC) was aboutcoefficient (i.e., the MPC) was about 0.70,0.70, anan increase in real income of 1 dollar led,increase in real income of 1 dollar led, on average, to an increase of about 70on average, to an increase of about 70 cents in real consumptioncents in real consumption..
- 12. 6. Hypothesis Testing6. Hypothesis Testing • That is to find out whether the estimates obtained in, Eq. (I.3.3) are inThat is to find out whether the estimates obtained in, Eq. (I.3.3) are in accordaccord with the expectations of the theory that is being testedwith the expectations of the theory that is being tested. Keynes. Keynes expected theexpected the MPC to be positive but less than 1MPC to be positive but less than 1. In our example we found the. In our example we found the MPC to be aboutMPC to be about 0.70.0.70. But before we accept this finding as confirmation ofBut before we accept this finding as confirmation of Keynesian consumption theory, we must enquire whether this estimate isKeynesian consumption theory, we must enquire whether this estimate is sufficiently below unity. In other words, issufficiently below unity. In other words, is 0.70 statistically less than 1?0.70 statistically less than 1? If itIf it is, it may supportis, it may support Keynes’ theory.Keynes’ theory. • Such confirmation or refutation of economic theories on the basis of sampleSuch confirmation or refutation of economic theories on the basis of sample evidence is based on a branch of statistical theory known asevidence is based on a branch of statistical theory known as statisticalstatistical inference (hypothesis testing).inference (hypothesis testing).
- 13. 7. Forecasting or Prediction7. Forecasting or Prediction • To illustrate, suppose we want to predict the mean consumptionTo illustrate, suppose we want to predict the mean consumption expenditure for 1997. The GDP value for 1997 wasexpenditure for 1997. The GDP value for 1997 was 7269.87269.8 billion dollarsbillion dollars consumption would be:consumption would be: Yˆ1997 = −184.0779 + 0.7064 (7269.8)Yˆ1997 = −184.0779 + 0.7064 (7269.8) = 4951= 4951.3.3 (I.3.4)(I.3.4) • TheThe actual valueactual value of the consumption expenditure reportedof the consumption expenditure reported in 1997 wasin 1997 was 4913.54913.5 billion dollars. The estimated model (I.3.3) thusbillion dollars. The estimated model (I.3.3) thus over-predictedover-predicted thethe actual consumption expenditure by aboutactual consumption expenditure by about 37.8237.82 billion dollars. We couldbillion dollars. We could say thesay the forecast errorforecast error is aboutis about 37.837.8 billion dollars, which is aboutbillion dollars, which is about 0.760.76 percent of the actual GDP value for 1997.percent of the actual GDP value for 1997. • Now suppose the government decides to propose aNow suppose the government decides to propose a reduction in the incomereduction in the income taxtax. What will be the effect of such a policy on income and thereby on. What will be the effect of such a policy on income and thereby on consumption expenditure and ultimately on employment?consumption expenditure and ultimately on employment?
- 14. • Suppose that, as a result of the proposed policy change, investmentSuppose that, as a result of the proposed policy change, investment expenditure increasesexpenditure increases. What will be the effect on the economy? As. What will be the effect on the economy? As macroeconomic theory shows, the change in income following, a dollar’smacroeconomic theory shows, the change in income following, a dollar’s worth of change in investment expenditure is given by the incomeworth of change in investment expenditure is given by the income multipliermultiplier M,M, which is defined as:which is defined as: • M =M = 1/(1 − MPC)1/(1 − MPC) (I.3.5)(I.3.5) • The multiplier is aboutThe multiplier is about M = 3.33M = 3.33. That is, an increase (decrease) of a dollar. That is, an increase (decrease) of a dollar in investment will eventuallyin investment will eventually lead to more than a threefold increaselead to more than a threefold increase (decrease) in income; note that it takes time for the multiplier to work.(decrease) in income; note that it takes time for the multiplier to work. • The critical value in this computation isThe critical value in this computation is MPCMPC. Thus, a quantitative estimate. Thus, a quantitative estimate of MPC provides valuable informationof MPC provides valuable information for policy purposes.for policy purposes. Knowing MPC,Knowing MPC, one can predict the future course of income, consumption expenditure, andone can predict the future course of income, consumption expenditure, and employmentemployment following a change in the government’s fiscal policies.following a change in the government’s fiscal policies.
- 15. 8. Use of the Model for Control or Policy Purposes8. Use of the Model for Control or Policy Purposes • Suppose we have the estimated consumption function given in (I.3.3).Suppose we have the estimated consumption function given in (I.3.3). Suppose further the government believes that consumer expenditure ofSuppose further the government believes that consumer expenditure of aboutabout 49004900 will keep thewill keep the unemployment rate at its current level of aboutunemployment rate at its current level of about 4.2%4.2%. What level of income will guarantee the target amount of. What level of income will guarantee the target amount of consumption expenditure?consumption expenditure? • If the regression results given in (I.3.3) seem reasonable, simple arithmeticIf the regression results given in (I.3.3) seem reasonable, simple arithmetic will show that:will show that: • 4900 = −1844900 = −184.0779 + 0.7064X.0779 + 0.7064X (I.3.6)(I.3.6) • which giveswhich gives X = 7197X = 7197, approximately. That is, an income level of about, approximately. That is, an income level of about 71977197 (billion) dollars, given an MPC of about 0.70, will produce an expenditure(billion) dollars, given an MPC of about 0.70, will produce an expenditure of about 4900 billion dollars. As these calculations suggest, an estimatedof about 4900 billion dollars. As these calculations suggest, an estimated model may be used for control, or policy, purposes. By appropriate fiscalmodel may be used for control, or policy, purposes. By appropriate fiscal and monetary policy mix, the government can manipulate theand monetary policy mix, the government can manipulate the controlcontrol variable X to produce the desired level of the target variablevariable X to produce the desired level of the target variable Y.Y.
- 16. • Figure I.4 summarizes the anatomy of classical econometric modeling.Figure I.4 summarizes the anatomy of classical econometric modeling.
- 17. • Choosing among Competing ModelsChoosing among Competing Models • When a governmental agency (e.g., the U.S. Department of Commerce)When a governmental agency (e.g., the U.S. Department of Commerce) collects economic data, such as that shown in Table I.1, it does notcollects economic data, such as that shown in Table I.1, it does not necessarily have any economic theory in mindnecessarily have any economic theory in mind. How then does one know that. How then does one know that the data really support thethe data really support the KeynesianKeynesian theory of consumption? Is it becausetheory of consumption? Is it because the Keynesian consumption function (i.e., the regression line) shown inthe Keynesian consumption function (i.e., the regression line) shown in Figure I.3 is extremely close to the actual data points? Is it possible thatFigure I.3 is extremely close to the actual data points? Is it possible that another consumptionanother consumption model (theory) might equally fit the data as well? Formodel (theory) might equally fit the data as well? For example, Miltonexample, Milton FriedmanFriedman has developed a model of consumption, calledhas developed a model of consumption, called thethe permanent income hypothesispermanent income hypothesis. Robert. Robert HallHall has also developed a model ofhas also developed a model of consumption, called theconsumption, called the life-cycle permanent income hypothesislife-cycle permanent income hypothesis. Could one. Could one or both of these models also fit the data in Table I.1?or both of these models also fit the data in Table I.1? • In short, the question facing aIn short, the question facing a researcherresearcher in practice isin practice is how to choosehow to choose among competing hypotheses or models of a given phenomenon, such as theamong competing hypotheses or models of a given phenomenon, such as the consumption–income relationship.consumption–income relationship.
- 18. • The eight-step classical econometric methodology discussed above isThe eight-step classical econometric methodology discussed above is neutralneutral in the sense that it can be used to test any of these rival hypothesesin the sense that it can be used to test any of these rival hypotheses. Is it. Is it possible to develop a methodology that is comprehensive enough to includepossible to develop a methodology that is comprehensive enough to include competing hypotheses? This is an involved and controversial topic.competing hypotheses? This is an involved and controversial topic.