Lecture_8 - Assessing Studies Based on Multiple Regression...

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1 Assessing Studies Based on Multiple Regression Let’s step back and take a broader look at regression: Is there a systematic way to assess (critique) regression studies?

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2 Is there a systematic way to assess regression studies? Multiple regression has some key virtues: It provides an estimate of the effect on Y of arbitrary changes X . It resolves the problem of omitted variable bias, if an omitted variable can be measured and included. It can handle nonlinear relations (effects that vary with the X ’s) Still, OLS might yield a biased estimator of the true causal effect – it might not yield “valid” inferences…
3 A Framework for Assessing Statistical Studies: Internal and External Validity Internal validity : the statistical inferences about causal effects are valid for the population being studied. External validity : the statistical inferences can be generalized from the population and setting studied to other populations and settings, where the “setting” refers to the legal, policy, and physical environment and related salient features.

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4 Threats to External Validity of Multiple Regression Studies How far can we generalize class size results from California school districts? Differences in populations (heterogeneity: has to do with different slope coefficients in different populations; perhaps due to institutional differences; e.g. different treatment of bilingual education in the class size example)
5 Threats to Internal Validity of Multiple Regression Analysis (SW Section 9.2) Internal validity : the statistical inferences about causal effects are valid for the population being studied. Five threats to the internal validity of regression studies: 1. Omitted variable bias 2. Wrong functional form 3. Errors-in-variables bias 4. Sample selection bias 5. Simultaneous causality bias All of these imply that E ( u i | X 1 i ,…, X ki ) 0 – in which case OLS is biased and inconsistent.

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Potential solutions to omitted variable bias 1. If the variable can be measured, include it as an additional regressor in multiple regression; 2. Possibly, use panel data in which each entity (individual) is observed more than once; 3. If the variable cannot be measured, use instrumental variables regression ; 4. Run a randomized controlled experiment. Why does this work?
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Lecture_8 - Assessing Studies Based on Multiple Regression...

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