Econometrics_Slide03.pdf

Introductory Econometrics ECON2206/ECON3209 S2, 2009 Slides03 Lecturer: Minxian Yang ie_Slides03 my, School of Economics, UNSW 1 3. Multiple Regression Model: Estimation (Ch3) 3. Multiple Regression Model: Estimation ? Lecture plan – Motivation and definitions – ZCM assumption – Estimation method: OLS – Mechanics of OLS – Underlying assumptions of multiple regression model – Expected values and variances of OLS estimators – Omitted and irrelevant variables – Gauss-Markov theorem ie_Slides03 my, School of Economics, UNSW 2 3. Multiple Regression Model: Estimation (Ch3) ? Motivation – Example 1. wage = β0 + β1educ + error, where error represents exper. ? exper is likely related to educ. ? The ceteris paribus effect of educ on wage cannot be properly estimated in this model. If exper is available, then we can “hold expr fixed” in wage = β0 + β1educ + β2exper + u, where wage is explained by both educ and expr. ? β1 and β2 measure ceteris paribus effects, properly estimable if u is not “related” to educ and expr. ie_Slides03 my, School of Economics, UNSW 3 3. Multiple Regression Model: Estimation (Ch3) ? Motivation – Example 2. (flexible functional form) wage = β0 + β1age + β2age2 +...+ u, where wage may increase initially and decrease eventually as age increases. – In general, regression models with multiple x’s have the following merits. They ? allow us to explicitly control for (hold fixed) many factors that affect the dependent variable, in order to draw ceteris paribus conclusions; ? provide better explanation of the dependent variable; ? provide flexible functional forms. ie_Slides03 my, School of Economics, UNSW 4 3. Multiple Regression Model: Estimation (Ch3) ? Multiple regression model – Definition y = β0 + β1x1 +...+ βkxk + u , ? y : dependent variable (observable) ? x1, ..., xk : independent variables (observable) ? β1, ..., βk : slope parameters, “partial effect”, (to be estimated) ? β0 : intercept parameter (to be estimated) ? u : error term or