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Unformatted text preview: 12/2/2009 1 Applied Business Tools ECO 6416 Assessing Validity 1 Validity of Studies Based on Multiple Regression • Step back and take a broader look at regression: • Is there a systematic way to assess/critique regression studies? • strengths – • and pitfalls? 2 Is there a systematic way to assess regression studies? Multiple regression has some key virtues: • Under standard assumptions, the LS estimator of coefficients is o Unbiased o Consistent 3 o Efficient • It estimates the effect on Y of arbitrary changes Δ 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) • It provides a basis for statistical testing of hypotheses Is there a systematic way to assess regression studies? • When standard assumptions are violated, the LS estimator is no longer optimal. • Under heteroskedasticity or serial correlation, LS estimator of coefficients remains unbiased but is no longer efficient 4 • Estimated standard errors are biased, so LS no longer provides a suitable basis for hypothesis testing. • Robust standard errors can be employed to remedy hypothesis testing problems • When appropriate, GLS can be used to obtain an efficient estimator. Is there a systematic way to assess regression studies? Still more serious problems can arise, causing OLS to yield a biased estimator of the true causal effects of interest – So that OLS does not yield “valid” inferences… 5 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 6 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. 12/2/2009 2 Threats to External Validity of Multiple Regression Studies Recall the analysis of class size on test scores in California: How far can we generalize the results? • Differences in populations • Massachusetts? 7 • Mexico? • California in 2015? • Differences in settings • different legal requirements concerning special education • different treatment of bilingual education • differences in teacher characteristics Threats to Internal Validity of Multiple Regression Analysis Internal validity : the statistical inferences about causal effects are valid for the population being studied. Five threats to the internal validity of regression studies: 8 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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- Spring '08
- Regression Analysis, external validity, variable bias, Sample selection bias, Simultaneous causality bias