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Unformatted text preview: ECON 103, Lecture 7: Multiple regression model Maria Casanova February 2nd (version 0) Maria Casanova Lecture 7 Requirements for this lecture: Chapter 4 and chapter 6 of Stock and Watson Maria Casanova Lecture 7 0. Introduction Remember the example in lecture 6 where we modeled the relationship between wages ( Y ) and fitness ( X 1 ) using a univariate regression model: Y i = β + β 1 X 1 i + ε i By restricting our attention to the relationship between Y and X 1 we ignored some other potentially important determinants of wages such as age ( X 2 ). Omitting potentially relevant regressors can lead to an incorrect estimate of the population regression line (i.e. cause a bias in the OLS estimator ˆ β 1 ) in the presence of two conditions: 1 the omitted regressor ( X 2 ) is correlated with the regressor X 1 . 2 the omitted regressor ( X 2 ) affects the dependent variable Y . Maria Casanova Lecture 7 0. Introduction Figure: X 1 (fitness) is uncorrelated with X 2 (age) 1 2 3 4 5 6 7 8 9 10 500 1000 1500 fitness wage (highest) (lowest) X 1 = β = 1000 β 1 = 0 Maria Casanova Lecture 7 0. Introduction Figure: X 1 (fitness) is correlated with X 2 (age) 1 2 3 4 5 6 7 8 9 10 500 1000 1500 fitness wage (highest) (lowest) X 1 = β = 1000 β 1 = 0 Maria Casanova Lecture 7 0. Introduction Under conditions (1) and (2), the OLS estimator will have omitted variable bias , which means that the first least squares assumption does not hold, i.e. E ( ε i  X i ) 6 = 0 How do we address omitted variable bias? we can divide the data into smaller groups (e.g. run separate regressions of wage on fitness for individuals aged 2025, 2530, etc.) This can become unpractical as we add more regressors. Moreover, this estimate does not provide an overall measure of the effect on wages of increasing fitness holding age constant . The estimate of the effect on wages of changing fitness holding age constant can be obtained using the multiple regression model . Maria Casanova Lecture 7 1. Multiple regression model In the multiple regression model more than one variable affects the dependent variable....
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This note was uploaded on 03/15/2010 for the course ECON 103 taught by Professor Sandrablack during the Winter '07 term at UCLA.
 Winter '07
 SandraBlack
 Econometrics

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