ie_Slide02(1) - Introductory Econometrics ECON2206/ECON3209...

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Introductory Econometrics ECON2206/ECON3209 Slides02 Lecturer: Minxian Yang ie_Slides02 my, School of Economics, UNSW 1
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2. Simple Regression Model (Ch2) 2. Simple Regression Model • Lecture plan – Motivation and definitions – ZCM assumption – Estimation method: OLS – Units of measurement – Nonlinear relationships – Underlying assumptions of simple regression model – Expected values and variances of OLS estimators – Regression with STATA ie_Slides02 my, School of Economics, UNSW 2
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2. Simple Regression Model (Ch2) • Motivation – Example 1. Ceteris paribus effect of fertiliser on soybean yield yield = β 0 + β 1 ferti + u . – Example 2. Ceteris paribus effect of education on wage wage = β 0 + β 1 educ + u . – In general, y = β 0 + β 1 x + u, where u represents factors other than x that affect y . – We are interested in • explaining y in terms of x , • how y responds to changes in x, holding other factors fixed. ie_Slides02 my, School of Economics, UNSW 3
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2. Simple Regression Model (Ch2) • Simple regression model – Definition y = β 0 + β 1 x + u , y : dependent variable (observable) x : independent variable (observable) β 1 : slope parameter, “ partial effect ,” (to be estimated) β 0 : intercept parameter (to be estimated) u : error term or disturbance (unobservable) – The disturbance u represents all factors other than x . – With the intercept β 0 , the population average of u can always be set to zero (without losing anything) E ( u ) = 0 . y = β 0 + E ( u ) + β 1 x + u − E ( u ) ie_Slides02 my, School of Economics, UNSW 4
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2. Simple Regression Model (Ch2) • Zero conditional mean assumption – If other factors in u are held fixed (Δ u = 0), the ceteris paribus effect of x on y is β 1 : Δ y = β 1 Δ x . – But under what condition u can be held fixed while x changes? • As x and u are treated as random variables, u is fixed while x varying ” is described as the mean of u for any given x is the same (zero) ”. – The required condition is E ( u | x ) = E ( u ) = 0 , known as zero-conditional-mean (ZCM) assumption. ie_Slides02 my, School of Economics, UNSW 5 Δ = “change” X = X 1 X 2 X 3 ... E(u |X) = 0 0 0 0 y = β 0 + β 1 x + u y + Δ y = β 0 + β 1 ( x + Δ x ) + u + Δ u
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• Zero conditional mean assumption – Example 2. wage = β 0 + β 1 educ + u Suppose u represents ability . Then ZCM assumption amounts to E ( ability | educ ) = 0 , ie, the average ability is the same irrespective of the years of education. This is not true • if people choose the education level to suit their ability; • or if more ability is associated with less (or more) education. In practice, we do not know if ZCM holds and have to
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This note was uploaded on 06/12/2011 for the course ECONOMICS 3291 taught by Professor Professorsnamespublishedtheyarethesoleowners during the Three '11 term at University of New South Wales.

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ie_Slide02(1) - Introductory Econometrics ECON2206/ECON3209...

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