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Unformatted text preview: 91Assessing Studies Based on Multiple Regression (SW Chapter 9) Let’s step back and take a broader look at regression: •Is there a systematic way to assess (critique) regression studies? We know the strengths – but what are the pitfalls of multiple regression? •When we put all this together, what have we learned about the effect on test scores of class size reduction? 92Is there a systematic way to assess regression studies?Multiple regression has some key virtues: •It provides an estimate of the effect on Yof arbitrary changes ΔX. •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 biasedestimator of the true causaleffect – it might not yield “valid” inferences… 93A Framework for Assessing Statistical Studies:Internal and External Validity (SW Section 9.1) 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. 94Threats to External Validity of Multiple Regression Studies How far can we generalize class size results from California school districts? •Differences in populations oCalifornia in 2005? oMassachusetts in 2005? oMexico in 2005? •Differences in settings odifferent legal requirements concerning special education odifferent treatment of bilingual education odifferences in teacher characteristics 95Threats 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.Errorsinvariables bias 4.Sample selection bias 5.Simultaneous causality bias All of these imply that E(uiX1i,…,Xki) ≠0 – in which case OLS is biased and inconsistent.961. Omitted variable bias Omitted variable bias arises if an omitted variable is both: (i) a determinant of Yand (ii) correlated with at least one included regressor. We first discussed omitted variable bias in regression with a single X, but OV bias will arise when there are multiple X’s as well, if the omitted variable satisfies conditions (i) and (ii) above. 97Potential 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 datain 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?Remember – if Xis randomly assigned, then Xnecessarily will be distributed independently of u; thus E(uX= x) = 0. 98...
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 Spring '11
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 Regression Analysis, Massachusetts, variable bias

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