Lecture 8 Prof. Arkonac's Slides (Ch 6 - Ch 7.2 ) for ECO 4000

Lecture 8 Prof. Arkonac's Slides (Ch 6 - Ch 7.2 ) for ECO 4000

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Multiple Regression I (cont’) & II ECO 4000, Statistical Analysis for Economics and Finance Fall 2010 Lecture 8 Prof: Seyhan Erden Arkonac, PhD 1

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Where we stopped last time, and what will we do today? Regression when X is a binary (dummy) variable (i.e. X=0 or X=1) Heteroskedasticity and Homoskedasticity (variance of the error term is constant? Or not?) The theoretical foundation of the OLS (not in detail!) Omitted variable bias THE MULTIPLE REGRESSION MODEL 2
3 Districts with fewer English Learners have higher test scores Districts with lower percent EL ( PctEL ) have smaller classes Among districts with comparable PctEL , the effect of class size i small (recall overall “test score gap” = 7.4)

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4 Digression on causality and regression analysis What do we want to estimate? What is, precisely, a causal effect? The common-sense definition of causality isn’t precise enough for our purposes. In this course, we define a causal effect as the effect that is measured in an ideal randomized controlled experiment .
5 Ideal Randomized Controlled Experiment Ideal : subjects all follow the treatment protocol – perfect compliance, no errors in reporting, etc.! Randomized : subjects from the population of interest are randomly assigned to a treatment or control group (so there are no confounding factors) Controlled : having a control group permits measuring the differential effect of the treatment Experiment : the treatment is assigned as part of the experiment: the subjects have no choice, so there is no “reverse causality” in which subjects choose the treatment they think will work best.

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6 Back to class size: Conceive an ideal randomized controlled experiment for measuring the effect on Test Score of reducing STR How does our observational data differ from this ideal? The treatment is not randomly assigned Consider PctEL – percent English learners – in the district. It plausibly satisfies the two criteria for omitted variable bias: Z = PctEL is: 1. a determinant of Y ; and 2. correlated with the regressor X . The “control” and “treatment” groups differ in a systematic way – corr( STR , PctEL ) 0
7 Randomized controlled experiments: Randomization + control group means that any differences between the treatment and control groups are random – not systematically related to the treatment We can eliminate the difference in PctEL between the large (control) and small (treatment) groups by examining the effect of class size among districts with the same PctEL . If the only systematic difference between the large and small class size groups is in PctEL , then we are back to the randomized controlled experiment – within each PctEL group. This is one way to “control” for the effect of PctEL when estimating the effect of STR .

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8 Return to omitted variable bias Three ways to overcome omitted variable bias 1. Run a randomized controlled experiment in which treatment ( STR ) is randomly assigned: then PctEL is still a determinant of TestScore , but PctEL is uncorrelated with STR . ( But this is unrealistic in practice. ) 2.
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Lecture 8 Prof. Arkonac's Slides (Ch 6 - Ch 7.2 ) for ECO 4000

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