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1 - / / / / : // : //: " ". ( ) ( ) ( ) ( :. ( ( C3, I, J, J3 :JEL :. e-mal: anader@ut.ac.r

2 () -. ( ) -. " " ). ( 1. Selectvt & Endogenet. (Expermental Research).. (Ex Post). " -"

3 /.... ( ) ( - ). ( ). (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).( : ). (. (Nader & Mace, 003) ( ) " ".

4 ). ( ().. ). (. ( ) :.(- ) ( ) ( )..(Mncer, 1958) ) (Mncer, 1974) (- :... (Mnceran Earnngs Functon).(Heckman, et. al., 003)

5 /.... ( ) " ". 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

6 ... ). ( -. " " - : 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

7 / : ) - () ( /. "". 1. Sample Selecton. Self-selecton.. ) -. (. 5. Endogenet.. ( )... Dumm ). (Varable Technque (Treatment Effect).. ()

8 ..... ""... "". ().. " " ( )... ( ). ( ) ( ) (Cov( x, e) = 0 ).

9 / :.- "".. (Ex Post) ). (. " " ( ). "".. "".. ().. "". 1. Truncated Data

10 φ ( z ) Φ ( z ) Z () φ ( z) Φ ( z ) Z () ( 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).

11 /. β.-- "".(Greene, 1993: 691) ). (.... " ".-.(Greene, 1993: 69) : 1. Censored Data. :... ( ).(Maddala, 1983: 166)

12 ... 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) :..

13 / 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

14 ... ( ) (). :. 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 = ( ). Greene, 1993: 709 x () ) : (

15 / 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 ). (

16 ... 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) ). (. ( ) ) ( ). (. ( ) ). (). (-

17 / ).. " " (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. () (

18 .... 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

19 / 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) :..

20 ... : (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 λ 0 1 σ ( x x ) x λ (). 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) :..

21 /. ( - ). ( ).. ( ).. ( ).. ( ) /. / /. / / ( ).. ) ( ). (

22 ... () / / / / / / () / / / / / /.- () / / / / / / () / / / / / / () / / / / / () / / / / / () / / / / / / / / / / : () (/) () / () () () () () - :. " ". [ () ).. (. «- -» (). ( ) ()... ( ) (OLS) ( ).. / ). ( - -

23 / -. ( ) ( ). ( ). " ". ( ). ( ). ( ) ( ).. 1. Sample-selecton.

24 ....! (/ / ) ( / ) () (E&S.S.) t / / -/ / / / / / () (End.) t / / -/ / / / -/ / () (S.S.) t / / -/ / / / -/ / (OLS) t / / -/ / / / -/ / (OLS) t / / -/ / / / -/ / : () () / / / / - - / / / / R - F Wald. : - ( ) ( - ). ( ) ( ). () () () (IT ).. : %). (:

25 /.. " " - -. ( ) ( ). ( ) "" () (E&S.S.) t / / -/ / / / -/ / () (End.) t / / -/ / / / -/ / () (S.S.) t / / -/ / / / -/ / (OLS) t / / -/ / / / -/ / () () / / - - / R - F Wald ) :. ( -. ( - ). ( ) ( ). () () ()

26 ..... ( ) " ".. ) - ( ( ) ( ( :. ( ( ) "... ( ) "".

27 / ).(). (-.....()...( ) ().( ).-....().( )......(). - :.().( ) :...()(). Belzl, Chrstan (007). The Return to Schoolng n Structural Dnamc Models: A Surve. European Economc Revew 51:PP Black, Dan A., & Jeffre A. Smth (004). How Robust s the Evdence on the Effects of College Qualt? Evdence from Matchng. J. of Econometrcs 11 (004):PP Card, D. (001).Estmatng the Return to Schoolng: Progress on Some Persstent Econometrc Problems. Econometrca Vol. 69 (5):PP Doughert, Chrstopher (00). Introducton to Econometrcs. Oxford, Oxford Un. Press. Far, R. (1977). A Note on Computaton of the Tobt Estmator. Econometrca, 45:PP Greene, W. H. (1993, 003). Econometrc Analss. New Jerse, Prentce-Hall, Inc. Gronau, R. (1974). Wage Comparsons: A Selectvt Bas. J. of Pol. Econom, 8(6):PP

28 ... 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 , September, Cambrdge, MA. Frazs, Harle (1993). Selecton Bas and the Degree Effect. Journal of Human Resources, Vol. 8, No. 3. (Summer, 1993), pp 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 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 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 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 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 Morett, Enrco (004). Estmatng the Socal Return to Hgher Educaton: Evdence from Longtudnal and Repeated Cross-sectonal Data. J. of Econometrcs 11:PP Nader, A. and J. Mace (003). Educaton and Earnngs: A Multlevel Analss. Economcs of Educaton Rev. ():PP 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 Psacharopoulos, G. and H. A. Patrnos (004).Returns to Investment n Educaton: A Further Update. Educaton Economcs 1():PP Psacharopoulos, G. & Rchard Laard (1979). Human Captal and Earnngs: Brtsh Evdence and a Crtque. Reprnted n: (199) The Economc value of Educaton:

29 / Studes n the Economcs of Educaton. M. Blaug. Hants, Edward Elgar Publcaton, Ltd.:PP Tobn, J. (1958). Estmaton of Relatonshps for Lmted Dependent Varables. Econometrca 6:PP 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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