Unit I: Basic Regression Analysis Nature and Scope of Ec onometrics – Simple Regression Model: Specification, OLS Method, Assumptions of CLRM and Gauss Maro! "heorem, #$pothesis "e sting and Goodness of %it –E&tensions of Simple Regression Model: Regression through Origin, Scaling and 'nits ofMeasurement, %unctional %orms of Regression Model – Ma&imum Lielihood Estimation Nature and Scope of Econometrics Definition Gold(erger defines econometrics as )the social science in which the tools of economic theory, mathematics and statistical inference are applied to the analysis of economic phenomena*+ t is concerned -ith the empirical determination of economic relationships+ n econometric anal$sis -e formulate the economic theor$ in mathematical terms and is com(ined -ith empirical measurement of economic phenomena+ "he most important characteristic of econometric relationships is that the$ contain a random element -hich is ho-e!er ignored ($ economic theor$ and mathematica l economics -hich postulates e&act relationship (et-een the !arious economic magnitudes+ Econometrics Economic theory Mathematicaleconomics Statisticalmethods Methodology of econometrics Categories of econometrics unctions of econometri cs Measurement of economic relations n man$ cases -e can appl$ the !arious econometric techni.ues in order to o(tain estimate s of the indi!idual coefficients of the economic relationships, from -hich -e ma$ e!aluate other parameters of ec onomic theor$ + !erification of economic theory Econometrics aims primaril$ at the !erification of economic theories+ n this case -e can sa$ that the purpose of the research anal$sis ie o(taining empirical e!idence to test the e&planator$ po-er of economic theori es to decide ho- -ell the$ e&plai n the o(ser!ed (eha!ior of the economic units orecasting n formulating polic$ decisions it is essential to (e a(le to forecast the !alue of the economic magnitudes+ Such forecasts -ill ena(le the polic$ maers to /udge -hether it is necessar$ to tae an$ measure in order to influence the rele!ant economic !aria(le+ Regression analysis "he term regression -as introduced ($Francis Galton+Regression analy sisis concerned -ith the stud$ of the dependent variable, on one or more explanatory variables. Simple and multiple regressions f -e are stud$ing the dependence of a !aria(le on onl$ a single e&planator$ !aria(le, such a stud$ is no-n as simple, or t"o#$aria%le regression analysis&#o-e!er, if -e are stud$ing the dependence of one !aria(le on more than one e&planator$ !aria(le, it is no-n as multiple regression analysis& 'ypes of Data A time seriesis a set of o(ser!ations on the !alues that a !aria(le taes at different times+ Cross#sectio n dataare data on one or more !aria(les collected at the same point in time. n pooled data are elements of (oth time series and cross0section data '(E ME'()D ))RDINAR* +EAS' S,UARES "he method of ordinar$ least s.uares is attri(uted to Carl %riedrich Gauss, a German mathemati cian+A population regression cur!e is simpl$ the locus of the conditional means of the dependent !aria(le for the fi&ed !alues of the e&planator$ !aria(le1s2+ Leasts!"ares cri terion states that the Sample Regression %unction can (e fi&ed in such a -a$ that Ƹ3"i 4 5 1 Ƹ #i 6 3#i 2 4 is as small as possi(le, -here 3 "i 4 are the s.uared residuals+ Ma-imum +i.elihood Estimation A method of point estimation -ith some stronger theoretical properties than the method of OLS is the method of ma-imum li.elihood /M+0& "he method of ma-imum li.elihood1 as the name indicates, consists in estimating the unno-n parameters in such a manner that the pro(a(ilit$ of o(ser!ing the gi!en #7s is as high as possi(le+ "he ML estimator of $4 is Ƹ3"i 4 %n. "his estimator is (iased, -hereas the OLS estimator of $4 5 Ƹ3"i 4 %1n6 42, as -e ha!e seen, is un(iased+ #o-e!er as n increases indefinitel$ , the ML estimator of $4 is also un(iased+ 'nder the normalit$ assumption, the ML and OLS estimators of the intercept and slope parameters of the regression model are identical+ ML method is generall$ called a largesample method. ML method is of (roader application in that it can also (e applied to regression models that are nonlinear in the parameters+ 2auss Mar.o$ 'heorem Gi!en the assumptions of the classical linear regression model, the least0 s.uares estimators, in the class of un(iased linear estimators, ha!e minimum !ariance, that is, the$ are 8L'E+ "he OLS estimator 3 &4, is said to (e a (est linear un(iased estimator 18L'E2 of&4if the follo-ing hold: 3& t is linear1 that is, a linear function of a random !aria(le, such as the dependent !aria(le # in the regression model+ 4& t is un%iased1 that is, its a!erage or e&pected !alue,E1 3 &42, is e.ual to the true !alue,&4. 5& t has minimum $ariancein the class of all such linear un(iased estimators9 an un(iased estimator -ith the least !ariance is no-n as an efficient estimator&
