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# handout12 - Econ 139 Introduction to Econometrics Andrew...

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Econ 139: Introduction to Econometrics Andrew Sweeting 1 1 Department of Economics Duke University Spring 2011 Econ 139 Handout 12 (Duke) Instrumental Variables Spring 2011 1 / 78

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Threats to Internal Validity Recall our de&nition of internal validity: A statistical analysis is internally valid if the statistical inferences about causal e/ects are valid for the population being studied. We know that internal validity hinges on two things: 1 The estimator of the causal e/ect should be consistent (and ideally unbiased) 2 Hypothesis tests should have the desired signi&cance level (i.e. you should be using the correct standard errors) Econ 139 Handout 12 (Duke) Instrumental Variables Spring 2011 2 ± 78
Threats to Internal Validity We will continue to focus on threats to consistency In the context of simple univariate OLS, we know that: b β 1 = β 1 + & X i & X ± u i & X i & X ± 2 Since b β 1 = β 1 + 1 n ( X i & X ) u i 1 n ( X i & X ) 2 p ! β 1 + σ Xu σ 2 X , we know that b β 1 will be inconsistent if Cov ( X , u ) 6 = 0 So when might this occur? Econ 139 Handout 12 (Duke) Instrumental Variables Spring 2011 3 / 78

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Some threats to internal validity Measurement error in the regressors Omitted (and unobserved) variables Simultaneous causality X causes Y , but Y in turn causes X Today we& ll starting talking about Instrumental Variables (IV), a method that can help to address these problems Econ 139 Handout 12 (Duke) Instrumental Variables Spring 2011 4 / 78
Simultaneous Causality Consider the test scores and student-teacher ratio example. We assumed that there was a causal relationship running from STR to TestScore (i.e. that lower STR &s caused higher TestScore through a better learning environment). But what if the school board responds to low average test scores by hiring more teachers (i.e., to lower STR ) for those school districts? STR i = γ 0 + γ 1 TestScore i + v i Then the causality runs both ways. But why is this a problem? It leads to correlation between STR and the error term. Let&s see why. Econ 139 Handout 12 (Duke) Instrumental Variables Spring 2011 5 / 78

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Simultaneous causality Suppose there&s an omitted factor that leads to low TestScore but is not directly correlated with STR . Because of the school board&s actions, it will also lead to a decrease in STR . In particular, a negative error ( u i ) in TestScore i = β 0 + β 1 STR i + u i reduces TestScore , which then reduces STR (because more teachers are hired), so there will be a positive correlation between STR and u , which violates OLS Assumption 1. The problem that some unobserved factor a/ects both the dependent variable and some of the regressors is called an endogeneity problem here u has a causal e/ect on both TestScore and STR Econ 139 Handout 12 (Duke) Instrumental Variables Spring 2011 6 ± 78
Simultaneous Causality The canonical example of simultaneous causality concerns demand (or supply) estimation.

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handout12 - Econ 139 Introduction to Econometrics Andrew...

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