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

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 Commonly used econometric models e.g. OLS, Probit, Tobit etc. are used with CS data. 2

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. 3

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. 4

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: y it =α i +x it ’ β+u it includes an individual effect α i (constant over time) and marginal effects β for x it. RE: FE model is appropriate when differences between agents are parametric shifts in regression fx. 5

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: y it =α+x it ’ β+u it +τ i assuming α i = α+τ i where τ i is individual disturbance fixed over time. 6

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=β 0 +β 1 X+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. 7

Regression with Cross Section Data Under Ordinary Least Square estimation, y=β 0 +β 1 x+u Under OLS, with the sample of observations of x and y, a fitted line can be defined as: yi^= β 0 ^ +β 1 ^ xi This is the predicted y when x=x i. The residual for ith obs. is the difference between the actual and the fitted: u i ^ =y i -y i ^ =y i - β 0 ^ -β 1 ^ x i 8

9 Regression with Cross Section Data y yiyi y ^ =β 0 ^+ β 1 ^ x x u i ^ =residual y i ^ =fitted value

Regression with Cross Section Data β 0 ^ and β 1 ^ are chosen to make the sum of squared residual (Σu i ^2 ) smallest. Under OLS this SSR is minimized as shown in Figure. Ideal situation is that for each i u i ^ =0…but every u is not 0 so no data points actually lie on the OLS. 10

11  ^ 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. Interpretation of OLS Estimates