Lecture 2: Key Concepts of Econometrics

1. Lecture 2: Key Concepts of Econometrics Prepared by South Asian Network on Economic Modeling Reference Introductory Econometrics: Jeffrey M Wooldridge

2. Types of Economic Data • Cross 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.

3. Types of Economic Data • Time 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.

4. Types of Economic Data • Panel/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.

5. Panel Data Modeling • Panel 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=αi+xit’β+uitincludes an individual effect αi (constant over time) and marginal effects β for xit. • RE: FE model is appropriate when differences between agents are parametric shifts in regression fx.

6. Panel Data Modeling • RE: 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=α+xit’β+uit+τi assuming αi= α+τiwhere τi is individual disturbance fixed over time.

7. Regression with Cross Section Data • In a bivariate linear regression model, we are mainly interested to explain y in terms of x. • We can define it simply as: Y=β0+β1X+u • Here, 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.

8. Regression with Cross Section Data • Under Ordinary Least Square estimation, y=β0+β1x+u • Under OLS, with the sample of observations of x and y, a fitted line can be defined as: yi^= β0^+β1^xi • This 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- β0^-β1^ xi

9. Regression with Cross Section Data y yi • • ui^=residual • y^=β0^+β1^x • • • yi^=fitted value x

10. Regression with Cross Section Data • β0^ andβ1^ are chosen to make the sum of squared residual (Σui^2) smallest. Under OLS this SSR is minimized as shown in Figure. • Ideal situation is that for each iui^=0…but every u is not 0 so no data points actually lie on the OLS.

11. Interpretation of OLS Estimates • ^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, beta’s are the elasticities.