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Unformatted text preview: Econ 139: Introduction to Econometrics Andrew Sweeting 1 Department of Economics Duke University Spring 2011 Econ 139 Handout 11 (Duke) Regression with Panel Data Spring 2011 1 / 73 Threats to Validity Now that we have introduced several empirical tools, it&s time to step back and ask: What makes a study that uses multiple regression reliable or unreliable? Speci¡cally, when can a regression model uncover a causal relationship and when will it fail to do so? S¢W break the question up into two parts Internal Validity and External Validity Econ 139 Handout 11 (Duke) Regression with Panel Data Spring 2011 2 / 73 Internal & External Validity A statistical analysis is internally valid if the statistical inferences about causal e/ects are valid for the population being studied. For example, your class size study is valid not just for schools in your sample, but also schools in the overall population of interest (elementary schools in CA). A statistical analysis is externally valid if its inferences and conclusions can be generalized from the population and setting studied to other populations and settings. Your class size study also applies to high schools in CA, elementary schools elsewhere, or both Econ 139 Handout 11 (Duke) Regression with Panel Data Spring 2011 3 ¡ 73 Threats to Internal Validity Threats to external validity tend to involve di/erences between the population studied and the population of interest and are covered at length in Chapter 9. We will focus on threats to internal validity and introduce some tools that can help handle such threats. Internal validity has two components: 1 The estimator of the causal e/ect should be unbiased or at least consistent. 2 Hypothesis tests should have the desired signi&cance level (i.e. you should be using the correct standard errors) Econ 139 Handout 11 (Duke) Regression with Panel Data Spring 2011 4 ¡ 73 Threats to Internal Validity Let&s focus on the ¡rst case. We know that we can represent b β 1 in a univariate regression as: b β 1 = β 1 + ∑ & X i & X ¡ u i ∑ & X i & X ¡ 2 Econ 139 Handout 11 (Duke) Regression with Panel Data Spring 2011 5 / 73 The OLS Assumptions The three key assumptions of OLS are OLS Assumption 1 Correct Speci&cation E ( u i j X i ) = 8 X i OLS Assumption 2 Simple random sample ( X i , Y i ) are iid draws from their joint distribution, and OLS Assumption 3 No extreme outliers u i and X i have nonzero & ¡nite fourth moments: < E & X 4 i ¡ < ∞ and 0 < E & u 4 i ¡ < ∞ Econ 139 Handout 11 (Duke) Regression with Panel Data Spring 2011 6 / 73 The most common concern is that A1 is violated If E [ u i j X i ] 6 = 0 then E [( X i & μ X ) u i ] 6 = 0 and we know that b β 1 will then be biased and inconsistent....
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This note was uploaded on 08/02/2011 for the course ECON 139 taught by Professor Alessandrotarozzi during the Spring '08 term at Duke.
 Spring '08
 ALESSANDROTAROZZI
 Econometrics

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