PanelDataNotes-20

# PanelDataNotes-20 - Econometric Analysis of Panel Data...

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Unformatted text preview: Econometric Analysis of Panel Data William Greene Department of Economics Stern School of Business Econometric Analysis of Panel Data 20. Sample Selection and Attrition Dueling Selection Biases – From two emails, same day. “I am trying to find methods which can deal with data that is non-randomised and suffers data that is non-randomised and suffers from selection bias from selection bias .” “I explain the probability of answering questions using, among other independent variables, a variable which measures knowledge breadth. Knowledge breadth can be constructed only for those individuals that fill in a skill description in the company intranet. This is where the selection bias comes from. The Crucial Element Selection on the unobservables Selection into the sample is based on both observables and unobservables All the observables are accounted for Unobservables in the selection rule also appear in the model of interest (or are correlated with unobservables in the model of interest) “Selection Bias”=the bias due to not accounting for the unobservables that link the equations. A Sample Selection Model Linear model 2 step ML – Murphy & Topel Binary choice application Other models Canonical Sample Selection Model Regression Equation y* =x + Sample Selection Mechanism d* =z +u; d=1[d* > 0] (probit) y = y* if d = 1; not observed otherwise Is the sample 'nonrandomly selected?' E[y* |x,d=1] = x +E[ | x,d 1] ′ β ε ′ γ ′ β ε = = x +E[ | x,u z ] = x something if Cor[ ,u|x] A left out variable problem (again) Incidental truncation ′ ′ β ε- γ ′ β + ε ≠ Applications Labor Supply model: y*=wage-reservation wage d=labor force participation Attrition model: Clinical studies of medicines Survival bias in financial data Income studies – value of a college application Treatment effects Any survey data in which respondents self select to report Etc… Estimation of the Selection Model Two step least squares Inefficient Simple – exists in current software Simple to understand and widely used Full information maximum likelihood Efficient Simple – exists in current software Not so simple to understand – widely misunderstood Heckman’s Model ′ ε ′ ε σ ρ ′ ε = ′ ′ ε- i i i i i i i i i 2 i i i i i i i i i i i y * = + d * = + u ; d=1[d * > 0] (probit) y = y * if d = 1; not observed otherwise [ ,u ]~Bivariate Normal[0,0, , ,1] E[y * |x ,d= 1] = +E[ | x ,d 1] = +E[ | x ,u i i i i i x β z γ x β x z β γ ′ φ ′...
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## This note was uploaded on 01/05/2012 for the course B 55.9912 taught by Professor Willamgreene during the Fall '11 term at NYU.

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PanelDataNotes-20 - Econometric Analysis of Panel Data...

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