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Econometrics-I-23

# Econometrics-I-23 - Applied Econometrics William Greene...

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Applied Econometrics William Greene Department of Economics Stern School of Business

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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

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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. Self-selection:   Labor supply models Shere Hite’s (1976) “The Hite Report” ‘survey’ of sexual habits  of Americans. “While her books are ground-breaking 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

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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[y|d= 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 ε φ α β ρσ Φ α β θλ
Incidental Truncation u1,u2~N[(0,0),(1,.71,1) Conditional distribution of u2|u1 > 0. No longer ~ N[0,1] Unconditional distribution of u2 ~ N[0,1]

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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 .   λ i
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