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Unformatted text preview: Applied Econometrics William Greene Department of Economics Stern School of Business Applied Econometrics 23. Sample Selection Samples and Populations Consistent estimation The sample is randomly drawn from the population Sample statistics converge to their population counterparts A presumption: The ‘population’ is the population of interest. Implication: If the sample is randomly drawn from a specific subpopulation, statistics converge to the characteristics of that subpopulation Nonrandom Sampling Simple nonrandom samples: Average incomes of airport travelers mean income in the population as a whole? Survivorship: Time series of returns on business performance. Mutual fund performance. (Past performance is no guarantee of future success. ) Attrition: Drug trials. Effect of erythropoetin on quality of life survey. Selfselection: Labor supply models Shere Hite’s (1976) “The Hite Report” ‘survey’ of sexual habits of Americans. “While her books are groundbreaking and important, they are based on flawed statistical methods and one must view their results with skepticism.” Heckman’s Canonical Model A behavioral model: Offered wage = o* = 'x+v (x age,experience,educ...) Reservation wage = r* = 'z + u (z = age, kids, family stuff) Labor force participation: LFP = 1 β = δ 2 2 v u if o* r*, 0 otherwise Prob(LFP=1) = ( 'x 'z)/ Desired Hours = H* = 'w + Actual Hours = H* if LFP = 1 unobserved if LFP = 0 ≥ Φ β δ σ + σ γ ε ε and u are correlated. and v might be correlated. What is E[H*  w,LFP = 1]? Not 'w. ε γ Standard Sample Selection Model i i i i i i i i i i i 2 i i i i i i i i d * 'z u d = 1(d * > 0) y * = 'x + y = y * when d = 1, unobserved otherwise (u ,v ) ~ Bivariate Normal[(0,0),(1, , )] E[y  y is observed] = E[yd=1] = 'x +E[  = α + β ε ρσ σ β ε i i i i i i i i i d 1] = 'x +E[  u 'z] ( 'z ) = 'x +( ) ( 'z) = 'x+ = β εα φ α β ρσ Φ α β θλ Incidental Truncation u1,u2~N[(0,0),(1,.71,1) Conditional distribution of u2u1 > 0. No longer ~ N[0,1] Unconditional distribution of u2 ~ N[0,1] Selection as a Specification Error E[y i x i ,y i observed] = β ’x i + θ λ i Regression of y i on x i omits λ i ....
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This note was uploaded on 06/20/2011 for the course ECON 803 taught by Professor Pp during the Spring '11 term at Thammasat University.
 Spring '11
 PP
 Econometrics

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