Key Concepts of Econometrics

Lecture 2: Key Concepts of EconometricsPrepared bySouth Asian Network on Economic Modeling

ReferenceIntroductory Econometrics: Jeffrey M Wooldridge 1Types of Economic DataCross Sectional Data- consists of a sample of households, individuals, countries etc. Sample units are taken at a point in time.Obtained mainly by random sampling. Example-in LFS 2010 we have info. of a large number of households on different characteristics, all taken roughly in 2010.Commonly used econometric models e.g. OLS, Probit, Tobit etc. are used with CS data.2Types of Economic DataTime Series Data-collection of observations on a single variable or a number of variables over time. E.g. prices of stock over a period of time, CPI, GDP data. As economic data are not independent of time, specific treatment/modeling is required.Special tests (ADF, PPP) are required to such data.3Types of Economic DataPanel/Longitudinal Data-it consists of a time series for each cross-sectional unit. Example: cross-section of countries observed over a time span. Same cross-sectional units are followed here.Panel data has certain advantages and econometrically more sophisticated as we can control some unobserved characteristics.Random Effect and Fixed Effect are two types of models applied with panel. 4Panel Data ModelingPanel data have 2 common features: (i) sample of individuals/firms/countries (N) is typically large; (ii) number of time period (T) is generally short.Why use it?: (i) increased precision of regression estimates; (ii) control for individual fixed effects; (iii) to model temporal effects without aggregation bias.FE: yit=i+xit+uit includes an individual effect i (constant over time) and marginal effects for xit.RE: FE model is appropriate when differences between agents are parametric shifts in regression fx.

5Panel Data ModelingRE: If the cross-section is drawn from a larger population-it is more appropriate to consider individual specific terms as randomly distributed effects across the cross-section of agents.RE: yit=+xit+uit +i assuming i= +i where i is individual disturbance fixed over time.6Regression with Cross Section DataIn a bivariate linear regression model, we are mainly interested to explain y in terms of x.We can define it simply as:Y=0+1X+uHere, y is the dependent and x is the independent variable whereas u is the error/disturbance term, representing factors other than x that affect y. It is unobserved term.

7Regression with Cross Section DataUnder Ordinary Least Square estimation, y=0+1x+uUnder OLS, with the sample of observations of x and y, a fitted line can be defined as: yi^= 0^+1^xiThis is the predicted y when x=xi. The residual for ith obs. is the difference between the actual and the fitted: ui^=yi-yi^=yi- 0^-1^ xi89

Regression with Cross Section Datayyiy^=0^+1^xxui ^=residualyi^=fitted valueRegression with Cross Section Data0^ and 1^ are chosen to make the sum of squared residual (ui^2) smallest. Under OLS this SSR is minimized as shown in Figure.Ideal situation is that for each i ui^=0but every u is not 0 so no data points actually lie on the OLS. 1011^o is the estimated average value of y when x=0.^ 1 is the estimated change in the average value of y due to a unit change in x.With a logarithmic transformation of the variables, betas are the elasticities.Interpretation of OLS Estimates