Lecture_13_Prof._Arkonac's_Slides_(_Ch_9)

Lecture_13_Prof._Arkonac's_Slides_(_Ch_9) - Nonlinear...

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Nonlinear Regression Functions Lecture 13 Prof: Seyhan Erden Arkonac, PhD Problem Set 5 is due NOW! Solutions will be posted tomorrow evening. Midterm Exam is on Tuesday Oct. 26 th Exam from last semester is posted as practice exam. 1
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2 A 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.
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3 Threats to External Validity of Multiple Regression Studies How far can we generalize class size results from California school districts? Differences in populations California in 2005? Massachusetts in 2005? Mexico in 2005? Differences in settings different legal requirements concerning special education different treatment of bilingual education differences in teacher characteristics
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4 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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5 1. Omitted variable bias Omitted variable bias arises if an omitted variable is both : (i) a determinant of Y and (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.
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6 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? Remember – if X is randomly assigned, then X necessarily will be distributed independently of u ; thus E ( u | X = x ) = 0.
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7 2. Wrong functional form Arises if the functional form is incorrect – for example, an interaction term is incorrectly omitted; then inferences on causal effects will be biased. Potential solutions to functional form misspecification 1. Continuous dependent variable: use the “appropriate” nonlinear specifications in X (logarithms, interactions, etc.) 2. Discrete ( example : binary) dependent variable: need an extension of multiple regression methods (“probit” or “logit” analysis for binary dependent variables).
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8 3. Errors-in-variables bias
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Lecture_13_Prof._Arkonac's_Slides_(_Ch_9) - Nonlinear...

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