Econ 281 Regression Analysis with Multiple Variables

Econ 281 Regression Analysis with Multiple Variables -...

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1 Regression Analysis with Multiple Independent Variables Introduction to Econometrics Econ 281

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2 Introduction Remember the error term u i It contains all other variables that effect our dependent variable Y We assumed that E(u i |X)=0 Let’s look at the variables contained in u i , their relationship to X and Y and E(u i |X) in more detail i i i u X Y + + = 1 0 β
3 Introduction Let’s say there is a variable (W) that is correlated with Y and/or X Three Scenarios W is correlated with X but uncorrelated with Y W is correlated with Y but uncorrelated with X W is correlated with both X and Y

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4 Scenario I W is correlated with X but uncorrelated with Y In this case W is not in the error term E(u i |X)=0 holds We have no problems
5 Scenario II W is correlated with Y but uncorrelated with X In this case W is part of the error term But since Corr(X,W)=0 it is usually the case that LSA#1 holds E(u i |X)=0 We have no problems

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6 Scenario III W is correlated with both X and Y In this case W is part of the error term Since Corr(X,W) 0 LSA#1 fails to hold E(u i |X) 0 What are the consequences for our estimation?
7 Omitted Variable Bias Assume that Scenario III takes place and the LSA#1 does not hold Part of the variation in Y and X comes from variable W OLS uses the variation in X to estimate the slope coefficient on X But part of the variation in X comes from W Wrong (biased) estimate of the slope coefficient

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8 Omitted Variable Bias: Example I Remember estimating the effect of the Education on wages What if high ability individuals obtain more education? Ability correlated with education 01 ii i wage Education u β = +⋅ +
9 Omitted Variable Bias: Example I Remember estimating the effect of the Education on wages What if high ability individuals get higher wages regardless of their education? Ability is part of the error term 01 ii i wage Education u β = +⋅ +

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10 Omitted Variable Bias: Example I LSA#1 violated! What is the effect on the estimate of the slope coefficient? Part of the variation in education is due to ability differences This part of the variation in education should not be used to estimate the effect of education on wages However, OLS uses all the variation in education to estimate
11 Omitted Variable Bias: Example I Estimate of the effect of education on wages is biased Omitted Variable Bias What is the direction of the bias? Higher ability leads to higher wages AND higher education OLS estimates of are too high 1 ˆ β

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12 Omitted Variable Bias: Example I The circles represent the variation in Education and ability The intersection is what causes bias in the estimates because Ability is omitted ABILITY EDUCATION
13 Omitted Variable Bias: Example II Remember estimating the effect of the Student- Teacher-Ratio (STR) on Test Scores What if students that are less proficient in English do worse on the test?

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Econ 281 Regression Analysis with Multiple Variables -...

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