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/.... ( ) ( - ). ( ). (Tobn, 1958) -.. (Gronau, 1974) : - (Wlls & Rosen, 1979) (Heckman, 1979) (Hausman &Wse, 1977) Black ) (Card, 001) (Frazs, 1993) (Kenn, et. al.,1979) (Morett, 004) (Harmon, et. al., 000) (& Smth, 004 Belzl, ) (Heckman, et. al., 005) (Hamermesh & Donald, 004).(007 -. : ). (. (Nader & Mace, 003) ( ) " ".
......... - -. - ). ( ().. ). (. ( ) :.(- ) ( ) ( )..(Mncer, 1958) ) (Mncer, 1974) (- :... (Mnceran Earnngs Functon).(Heckman, et. al., 003)
/.... ( ) " ". n NPV 0 n = Y e 0 0 rt dt Y0 = r (1 e rn ) :. Y0 r ( ) NPV : S + n rt S = YS e S YS dt = r ( e rs e r ( S + n ) S Y S S :. NPV 0 = NPV S. rs Y S = Y 0e ln( Y S ) = ln( Y0 ) + rs (). ) () (). () ( ) 1. Schoolng Earnngs Functon
... ). ( -. " " - : ln( Y S ) = ln( Y 0 ) + rs + β X + β X = β X + u 0 + β 1S + β X + β 3 1 ( ) X S. u. " ". (u ) β1. " " S () :. () 1. Earnngs Profle. - (Mncer, 1974, 1979) :....(- :)... Psacharopoulos & ) :...(Laard, 1979
/ -.- - : ) - () ( /. "". 1. Sample Selecton. Self-selecton.. ) -. (. 5. Endogenet.. ( )... Dumm ). (Varable Technque (Treatment Effect).. ()
..... ""... "". ().. " ".... - ( )... ( ). ( ) ( ) (Cov( x, e) = 0 ).
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....- 0.5 0.4 φ ( z ) Φ ( z ) 0.7 0.3 0.6 0.5 0. 0.4 0.3 0.1 0. 0.1 0 0-3 - -1 0 1 3 Z () 1 0.9 0.8 0.5 0.4 0.3 0. 0.1 0 φ ( z) Φ ( z ) -3 - -1 0 1 3 Z () 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0. 0.1 0 ( x N ( β x, σ ) E[ x ] = β x β x x ) β x : σ : E[ x, > a] = β x + σ{[ φ(( a β x ) / σ )] [1 Φ(( a β x ) / σ )]} () () : E[ x, > a] = β x + σλ ( α ), () : α = ( a β x ) / σ λ = [ φ (( a β x ) / σ )] [1 Φ (( a β x ) / σ )] : E[ x ] dλ α = β + σ x d α x β = β + σ ( λ α λ ) = β (1 λ + α λ ) σ x () 1. Maddala (1983: 365) and Greene (1993: 687).
/. β.-- "".(Greene, 1993: 691) ). (.... " ".-.(Greene, 1993: 69) : 1. Censored Data. :... ( ).(Maddala, 1983: 166)
... a ). (. a : = β x + u ; = a = f f a > a. ( ) : β E( x ) = Pr ob( = Pr ob( a) E( a) a + Pr ob( x a) + Pr ob( > a) E( > a) E( > a) > a) E[ x ] = Φ( α ) a + (1 Φ( α )){ β x + σ [ φ ( α ) (1 Φ( α ))]} E x ] = Φ( α ) a + (1 Φ( α ))( β x + σλ ), [ : α ( a β x ) / σ λ = φ ( α ) (1 Φ ( α E[ =, )) x ] = β x () () : () : x () (Tobn, 1958) (Tobt).. (Probt). Index 3. Latent ).(Maddala, 1983: 151) :.. a = 0 ~ N( μ, σ ). : ( = f > 0, = 0 f 0 E( ) = Pr ob( = Pr ob( 0) E( 0) 0 + Pr ob( 0) + Pr ob( > 0) E( > 0) E( > 0) > 0) = Pr ob( > 0) E( > 0).(Greene, 1993: 69-3) :..
/ E[ x E[ x x ] = β x ] = Pr ob[ + E[ Pr ob[ + a x E[ > a] x, a] x, x Pr ob[ > a] x > a] > a] () -.-- -.. "" -.. ( ).... () ( ) = β x + u. : () 1. Self-selecton Data
... ( ) (). :. K 0 + β1s + β k k = = β xk + u ( β 1 ) ( x 1 ) S 1. :. ( ( ) ). (. ( : z () = γ w + e. e ~ N(0, σ ) (z ) w e z =1 () z. z = 0.... ( ). Greene, 1993: 709 x () ) : (
/ E[ s observed ] = E[ = β x = β x + E[ u + E[ u e > 0] > 0] = β x + ρσ uλ ( α e ) : α = γ w σ λ = φ( α ) Φ( α ) s e observed = z z > γ w e ; e e z > 0 = β x ] () : + ρσ λ ( α ) + v = β x + β λλ ( α e ) + v.. λ () :. ( λ ) E[ 0] () z > = β k λk ( ρσ u / σ e ) δ ( α e ) x k : δ ( α ) = λ + α e λ -. - ( S ) u e (). ( )..( S > 0 ) : (S) -. ) ( ) ( S ). (
... s = η z + e s observed f s > () 0 () () : ( u, e) ~ bn (0, 0, σ, σ, ρ ) u e : E[ s > 0] = β x + E[ u η z > 0] = β x = β x + ρσ uλ ( α e ) : α = η z σ λ = φ ( η z σ ) / Φ ( η z σ ) e e u + e s > 0 = β x + ρσ λ ( α ) + v + E[ u e, e e e > η z ] () : () - ) ( ). (. ( Cov( u, x) =0) ). (. ( ) ) ( ). (. ( ) ). (). (-
/ ).. " " (IQ-.. ) ( ) S = β S s + u + : ( = γ z Z e : Cov( S, u) 0; Cov( Z, u) = 0; Cov( Z, S) 0 β s S Cov( S, u) 0 :. = β ss + u = β s ( γ z Z + e ) + u = θ Z Z + v () β s : IV θz Cov(, Z) Cov( S, Z) Cov(, Z) Cov( u, Z) β = = = = β + S S γ Z Cov( Z, Z) Cov( Z, Z) Cov( S, Z) Cov( S, Z) (). u Z. Cov( Z, u) =0 β β Cov( Z, u) 0 IV s s ().(Wooldrdge, 00) (Doughert, 00:5) :.... Instrumental Varable (Doughert, 00:54). : ( : Cov ( Z, X ) 0 : ( Cov( Z, u) = 0. () (
.... IV β s = β s - s : observed = = β x S = γ Z + e z z 1. : > 0 = β x + β S s + β S s e + ρσ + β λ ( α ) + v λ λ ( α ) + v u e ().-.. :. : ( ) s observed = z > 0 = β x + β λ ( α ) + v ( ) λ λ : λ (). (Probt).( ) ( λ = φ α ) / Φ( α ) λˆ ( ) : 1. Doughert (00: 53) (Heckman). Gronau, ). (1974 (Maddala, 1983)....(Doughert, 00: 98) 3. Sample Selecton
/ s observed = z > 0 = β x + β ˆ λ ( α ) + v (. 0 ) ( λ () > 0 ) : E ( x ) = Pr( = 0) E ( = 0) + Pr( > 0) E ( > 0) = Φ β x + σφ x = Φ β x + σφ + v x φ Φ () :. :. : ( a ) 1 β x a β x f ( > = φ Φ () a) 1 σ σ σ : n 1 β x a β x L = Π φ 1 Φ = 1 σ σ σ n n 1 ln L = [ ln( π ) + ln σ ] ( β x ) () σ = 1 n a β x ln 1 Φ = 1 σ (σ β )...(Greene, 003, ch. ) :......(Greene, 1993: ch. 1) :..
... : (Greene, 1993: 696 ) 1 ( β x ) β x L = Π exp Π 1 Φ > 0 1 / (πσ ) = σ 0 σ 1 ( ) ln = ln( ) + ln + β x L π σ > 0 σ + = 0 β x ln 1 Φ σ (σ β ) σ β β = ( x x ) x Y 1 1 1 1 1 λ 0 1 σ ( x x ) x λ 1 1 1 0 (). 1 = β σ ( x 1x1) x LS 0λ0 : λ = φ /( 1 Φ ) β = LS Y 1( Y1 β x1) σ = N x 0 0 : > 0 x Y 1. = 0 λ x x 1 () (). (Newton-Raphson) -. (Far, 1977). ().(Maddala, 1983: 154 :..).(Greene, 1993: ch. 1) :..
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....! (/ / ) ( / ) - -.- () (E&S.S.) t / / -/ / / / / / () (End.) t / / -/ / / / -/ / () (S.S.) t / / -/ / / / -/ / (OLS) t / / -/ / / / -/ / (OLS) t / / -/ / / / -/ / : () () / / / / - - / / / / R - F Wald. : - ( )... -. ( - ). ( ) ( ). () () () (IT ).. : %). (:
/.. " " - -. ( ) ( ). ( ) "" - -.- () (E&S.S.) t / / -/ / / / -/ / () (End.) t / / -/ / / / -/ / () (S.S.) t / / -/ / / / -/ / (OLS) t / / -/ / / / -/ / () () / / - - / R - F Wald ) :. ( -. ( - ). ( ) ( ). () () ()
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... Hamermesh, Danel S. & Stephen G. Donald (004). The Effect of College Currculum on Earnngs: Accountng for Non-Ignorable Non-Response Bas. NBER Workng Paper No. 10809, September, Cambrdge, MA. Frazs, Harle (1993). Selecton Bas and the Degree Effect. Journal of Human Resources, Vol. 8, No. 3. (Summer, 1993), pp. 538-554. Harmon, C., H. Oosterbeek, & I. Walker (000). The Returns to Educaton: A Revew of Evdence. Issues and Defcences n the Lterature. London, Centre for Economcs of Educaton, LSE. Hausman, J. A., & D. A. Wse (1977). Socal Expermentaton, Truncated Dstrbutons, and Effcent Estmaton. Econometrca, 45(4):PP 919-938. Heckman, James J., Lance J. Lochner, & Petra E. Todd (005). Earnngs Functons, Rates of Return and Treatment Effects: The Mncer Equaton and Beond, Mmeo. Heckman, James J., et. al. (003). Fft Years of Mncer Earnngs Regressons. NBER, Workng Paper (973, Ma). Heckman, J. (1979). Sample Selecton Bas as a Specfcaton Error. Econometrca 47(1):PP 153-61. Kenn, L. W., L.F. Lee, G. S. Maddala, & R. P. Trost (1979). Returns to College Educaton: An Investgaton of Self-selecton Bas Based on the Project Talent Data. Int l Economc Revew, 0 (3):PP 775-789. Maddala, G. S. (1983). Lmted-Dependent and Qualtatve Varables n Econometrcs. Cambrdge, Cambrdge Unverst Press. Mncer, Jacob (1979). Human Captal and Earnngs. Economc Dmensons of Educaton. D. M. Wndham, Natonal Academ of Educaton:PP 1-31. Mncer, Jacob (1974). Schoolng, Experence, and Earnngs. New York, Columba Un. Press. Mncer, J. (1958). Investment n Human Captal and Personal Income Dstrbuton. J. Pol. Econom, 66(4, August):PP 81-30. Morett, Enrco (004). Estmatng the Socal Return to Hgher Educaton: Evdence from Longtudnal and Repeated Cross-sectonal Data. J. of Econometrcs 11:PP 175 1. Nader, A. and J. Mace (003). Educaton and Earnngs: A Multlevel Analss. Economcs of Educaton Rev. ():PP 143-56. Psacharopoulos, G. (1981). Returns to Educaton: An Updated Internatonal Comparson. In: The Economc Value of Educaton: Studes n the Economcs of Educaton. M. Blaug. Hants, Edward Elgar: PP 31-41. Psacharopoulos, G. and H. A. Patrnos (004).Returns to Investment n Educaton: A Further Update. Educaton Economcs 1():PP 111-134. Psacharopoulos, G. & Rchard Laard (1979). Human Captal and Earnngs: Brtsh Evdence and a Crtque. Reprnted n: (199) The Economc value of Educaton:
/ Studes n the Economcs of Educaton. M. Blaug. Hants, Edward Elgar Publcaton, Ltd.:PP 458-503. Tobn, J. (1958). Estmaton of Relatonshps for Lmted Dependent Varables. Econometrca 6:PP 4-36. Wlls, R. J. and S. Rosen (1979). Educaton and Self-Selecton. J. of Poltcal Econom 87 (5, part ): S7 -S36. Wooldrdge, J. M. (00). Econometrc Analss of Cross Secton and Panel Data. MIT Press.
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