Prob3_MLE - Prob 3 Labor Force Participation 1 0 10 Educi...

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Prob 3: Labor Force Participation a ) Y i Work i = 1 : 10 Educ i + 20 Exper i + 30 Exper 2 i + 40 > u i : , X i o > u i 0 : Otherwise Here, u i is an unobserved threshold for individual i, educ denotes educa- tion, exper denotes experience, and exper2 denotes the square of experience. where X i [ Educ i Exper i Exper 2 i 1 ] : 1 x 4 : :Assume: ( Y i X i u i ) is i.i.d. over i. X variables are bounded and exogenous X has full column rank o is in the interior of a compact set u i is i.i.d. N(0, ± 2) To interpret this equation, suppose that an individual works (Work = 1) if Ln ( Wage i ) exceed some reservation level, r i : b ) Work i = 1 , Ln ( Wages i ) > r i : Assume that wages for individual i are given as : c ) Ln( Wage i ) = ² 1 0 Educ i + ² 20 Exper i + ² 30 Exper 2 i + ² 40 + " i : Assume that all explanatory variables in (c) are independent of r i and of " i : With u i r i ± " i ; the model in (a) follows from (b-c). Viewing the work decision in this manner should suggest a priori signs for the coe¢ cients. and then turn to an empirical application of the work decision. 1) With u i having a standard normal density and with as its (cu- mulative) distribution function, explain why: Pr ( Y i 1 j X i X i o ) : 1
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2) For three individuals, suppose that Y 1 = 1 ; Y 2 = 0 ; Y 3 = 1 : Letting X 1 ; X 2 ; and X 3 be the observed vectors of explanatory variables for these three individuals, explain why the following joint probability statement is correct: Pr ( Y 1 = 1 ; Y 2 = 0 ; Y 3 = 1 j X 1 ; X 2 ; X 3 X 1 o ) [1 X 2 o X 3 o ) o ± ± 0 With N observations, show that in general the averaged log of the above joint
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This note was uploaded on 11/05/2010 for the course ECON 613 taught by Professor Chanshen during the Spring '10 term at Georgetown.

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Prob3_MLE - Prob 3 Labor Force Participation 1 0 10 Educi...

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