Econometrics_Slide02.pdf

Introductory Econometrics ECON2206/ECON3209 S2, 2009 Slides02 Lecturer: Minxian Yang ie_Slides02 my, School of Economics, UNSW 1 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 SHAZAM ie_Slides02 my, School of Economics, UNSW 2 2. Simple Regression Model (Ch2) ? Motivation – Example 1. Ceteris paribus effect of fertiliser on soybean yield yield = β0 + β1ferti + u . – Example 2. Ceteris paribus effect of education on wage wage = β0 + β1educ + u . – In general, y = β0 + β1x + 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. ie_Slides02 my, School of Economics, UNSW 3 2. Simple Regression Model (Ch2) ? Simple regression model – Definition y = β0 + β1x + u , ? y : dependent variable (observable) ? x : independent variable (observable) ? β1 : slope parameter, “partial effect,” (to be estimated) ? β0 : intercept parameter (to be estimated) ? u : error term or disturbance (unobservable) – The disturbance u represents all factors other than x. – With the intercept β0, the population average of u can always be set to zero (without losing anything) E(u) = 0 . ie_Slides02 my, School of Economics, UNSW 4 2. Simple Regression Model (Ch2) ? Zero conditional mean assumption – If other factors in u are held fixed (Δu = 0), the ceteris paribus effect of x on y is β1 : Δy = β1 Δx . – 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,