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# ie_Slide033 - Introductory Econometrics ECON2206/ECON3209...

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Introductory Econometrics ECON2206/ECON3209 Slides03 Lecturer: Rachida Ouysse ie_Slides03 R. Ouysse, School of Economics, UNSW 1

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3. Multiple Regression Model: Estimation (Ch3) 3. Multiple Regression Model: Estimation Lecture plan (largely parallel to Ch2) – Motivation and definitions Motivation and definitions – ZCM assumption – Estimation method: OLS – Mechanics of OLS Underlying assumptions of multiple regression model – Underlying assumptions of multiple regression model – Expected values and variances of OLS estimators Omitted and irrelevant variables – Omitted and irrelevant variables – Gauss-Markov theorem ie_Slides03 R. Ouysse, School of Economics, UNSW 2
3. Multiple Regression Model: Estimation (Ch3) • Motivation – Example 1. (control observable factors) wage = β 0 + β 1 educ + error, where error represents (or contains) exper . exper is likely related to educ . The ceteris paribus effect of educ on wage cannot be properly estimated in this model. Why? If exper is available, then we can “hold expr fixed” in wage = β 0 + β 1 educ + β 2 exper + u, where wage is explained by both educ and expr . β 1 and β 2 measure ceteris paribus effects, properly estimable if u is not “related” to educ and expr . ie_Slides03 R. Ouysse, School of Economics, UNSW 3

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3. Multiple Regression Model: Estimation (Ch3) • Motivation – Example 2. (flexible functional form) wage = β 0 + β 1 age + β 2 age 2 +...+ 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 factors that affect the dependent variable, in order to draw ceteris paribus conclusions; • provide better explanation of the dependent variable by provide better explanation of the dependent variable by accommodating flexible functional forms. ie_Slides03 R. Ouysse, School of Economics, UNSW 4
3. Multiple Regression Model: Estimation (Ch3) Multiple regression model – Definition y = β 0 + β 1 x 1 +...+ β k x k + u , y : dependent variable (observable) x 1 , ..., x k : independent variables (observable) β 1 , ..., β k : slope parameters, “ partial effect ”, ( b i d) (to be estimated) β 0 : intercept parameter (to be estimated) t di t b ( b bl ) u : error term or disturbance (unobservable) k : the number of independent variables The disturbance u represents factors other than x ’s – The disturbance represents factors other than . – With the intercept β 0 , the unconditional mean of u can always be set to zero: E ( u ) = 0 always be set to zero: = 0 . ie_Slides03 R. Ouysse, School of Economics, UNSW 5

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3. Multiple Regression Model: Estimation (Ch3) Zero conditional mean assumption – The zero-conditional-mean (ZCM) assumption is E ( u | x 1 , ..., x k ) = 0 , for the multiple regression model.
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