Economics Research

LECTURE 1 Research in Economics :The Econometric Approach

I.MEANING At the cost of over simplification we may say that in economics research means construction of an econometric model of the following type: Y=a +bX+ u………………. (1) Here Y is the dependent variable. X is the explanatory variable. (There can be more than one explanatory variable). u is a disturbance term. It is a random variable . Equation (1) is the regression model. (It can be nonlinear also).

II.OBJECTIVES This econometric model is used for three purposes: 1) Estimating the effect of X on Y. 2) Testing hypothesis /ses. 3) Forecasting. One need not pursue all objectives for the research. III. THE RESEARCH PROBLEM OF ECONOMICS We must understand the core of the research problem a researcher in Economics faces. For illustrating this problem, one can for convenience distinguish between Experimental Method (EM) and Correlation method (CM).In Economics the researcher is forced to use the CM. Yet, she wants to draw valid conclusions like EM. Let us consider an example. Let there be two groups of land. In one group irrigation facilities (called treatment in EM) are provided. The other group does not get the treatment .The first group is called experimental group. The second group is

called control group. Let us call yield of rice , per unit of land,say acre, Y. There is Y for experimental group .We call this YE. Similarly for control group we write YC . The averages are called YEA and YCA. .The question is: can we conclude, from the observation that YCA. is smaller than YEA , that irrigation facilities improve

yield? Unfortunately, we

cannot. The experimental group may turn out to have a higher proportion of skilled cultivators compared to the control group .Similarly there can be many other factors, many of which we may not have even thought about. Is there a solution to this problem? There is. It is called randomization. A truly revolutionary idea!

Ronald.

A.

Fisher

contributed

significantly

in

developing the statistical theory (Design of Experiments, 1935).Randomization involves two aspects. One is selecting the respondents or units of study or ‘subjects’ in such a manner that each unit has equal probability of getting selected. The second stage is assigning the units into control group and experimental group in a manner where each unit has equal probability of getting assigned in any one of the groups. Now if one finds a difference in the two groups then

the reason must the treatment alone and no other factor .This is the logic behind randomization. The conclusions about effect of treatment on the outcome are valid in this situation. Let us try to analyse the implications of randomization using the regression function. Let us write again: Yi=a +bXi + u………………. (1) We see that Y has three components .one is ‘a’. We will try to see what it represents .The second is the treatment effect bX. The third is ‘u’ .u is a random variable. This is the consequence of selecting Y in a random manner with each Y having the same probability of getting selected. We think that u is that component of Y which varies randomly because of the influence of the ‘other factors’. Let us push he analysis further .Let X take two values, namely, 0 and 1. X is 1 when treatment is given and 0 when it is not given .For Y in the experimental group X is 1.For control group it is 0.If we take only control group then we can write Yi=a + u …………(2) Now we can also add the Ys.

Thus we have ΣYi=n a + Σu Her n is the number of subjects studied If Σu=0 then, we have ΣYi=n a Or, ΣYi /n =a= YCA Or, average Y of control group is ‘a’, the intercept term . Moreover, u=Yi- YCA. .So Σu=0.Let us turn to the experimental group. A little thinking will show that a +bXi= YEA. As a result , bXi is the treatment effect, YEA - YCA .Therefore we can say that ‘b’, the slope coefficient , is the treatment effect coefficient .If b=0 then there is no effect of the treatment . We see that the regression function states that Observed Y= YCA+ Treatment Effect +Random Effect (of the ‘other factors’). What has randomization achieved so far? It has helped us to decompose Y into a systematic component and a random component. It ha also helped us to see that the sum total of random effect is zero only when we are speaking in terms of averages .This leads us to a very important principle of estimation , namely . the principle of least squares.

IV.ESTIMATION: THE PRINCIPLE OF LEAST SQUARES Let us call the difference between observed Y and Estimated Y an error, ‘e’ Thus ei = Yi-Yc. ……………………… (3) Here , Yi is observed Y and Yc is estimated Y. We square e and add to get Σe2= Σ(Yi-Yc.)2 We want minimize these sum of squares by choosing a Yc.. The first order condition is that 2 Σ(Yi-Yc.) =0 or , Σ(Yi-Yc.) =0……………….. (4) or, ΣY-n Yc=0 or, ΣY/n= Yc or, Yc is the mean or average . We minimize the sum of squares when we estimate Y as an average. We want Σ (Yi-Yc.) = Σ(ei.) =0.But note another fact. If from the regression model we want to measure impact of X on Y, then randomization ensures that the other factors are captured by u. It is also required that Σu=0.By the principle of analogy,

this implies Σe=0 for the observed sample estimation .This is fulfilled by the principle of least squares. V. FROM ‘EM’ TO ‘CM’ The economics researcher rarely has the luxury of using data generated by random experiments. Experiments can be immoral, costly and time consuming. Yet the attempt is to get valid results of the impact of X on Y like EM. Analysis based on non – experimental method can study co-variation and correlation. But correlation analysis does not go as far as EM in analyzing causality. To get further the regression model has to fulfill certain conditions which are fulfilled by experimental method .These assumptions are precisely the assumptions of Classical Linear Regression Model (CLRM).