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1 : 3 :2002 CHIP,,Roy,, ; :,,,,,,, CHIP2002,Roy,,,,,,,,,, :,,, (Becker and Tomes,1986),,,, 30 %, 60 % 3,,: ,: edu. cn ;, Clemson,: clemson. edu;, 2006 ( EFA060202) 42

2 2009 5,,,, :,,,,,,,, : ln y i = s S i + X i + u i (1), y, S, X, u s, Griliches (1977) :, s,, s,,,,ols,ols,,,,,,,,,,, ( Han and Mulligan, 2001),?,,, Altonji and Dunn (1996),,, (Quantile Regression),,, Valero2Gil and Tijerina2Guajardo (2002),,, Roy (1951),Willis and Rosen (1979) Willis (1986),,,,S : ln y i = si S i + X i + u i (2) (1), (2), s, si, si i S i,,,s = 1, S = 0,,, S i u i, si Card (1995) si : si = d i - k, d i,,, 43

3 : y 1 i y 0 i,,,() y 1 i S = 1 y 0 i S = 0, y 1 i S = 0 y 0 i S = 1,Treatment Effect ( Counterfactual Missing), si,, local treatment effect (LATE) matching marginal treatment effect (MTE) Bjgrklund and Moffitt (1987) Heckman and Vytlacil (1999, 2000) MTE Roy MTE Z, MTE i = E(ln y 1 i - ln y 0 i X = x, P( Z) = p), p MTE i,mte i P, (CHIP),12 77, ,, CHIP,,( ),(),, (), 6835, 1295,1403,, %51156 %,,,, 44,, : (), ;,,,,,,30 %70 %,, % %61114 %,,,, 25 %,,, 50 %,, 3000,, 3000 ;,,, 1, : () ( ) (,,,,,

4 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) (7155) (61294) ( ) (781780) (181686) (111996) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) (31512) (31378) (01741) (01749) : ), ( ) 21 Roy,,,, Roy :,Roy ;, Roy, ;,Roy, Roy, : S = 1 if S 3 > 0 0 if S 3 0, S 3,, Z : S 3 = Z+,,, : ln y 0 ln y 1 y : y = = 0 + u 0 = X+ u 0 = 1 + u 1 = X+ u 1, y 0 y 1,, X,, X,,,, y 0 y 1,,, y 0 if S 3 0 S = 0 y 1 if S 3 > 0 S = 1, Z X, S y 2002, ; ;; ;,, 205,, % 40 % 60 % 80 %, 4, 3,2 1 45

5 : (exclusion restrictions),,,,, :,,,;,,,, ;,,,, u 0 u 1 N 0 0 0, , : u 0 = = 0 +, 0 u = = 1 + 1, 0, 1 N (0,1), 0 1 u 0 u 1 S = 1, y 1, : E(ln y 1 S = 1) = E( X+ u 1 X+ E > - Z= <( - Z > - Z ) = X+ 1 Π ) 1 - ( - ZΠ ) Z+ > 0) = X+ 1 E( ( ZΠ ) (1) = X+ 1 v = ZΠ, : E(ln y 1 S = 1) = X+ 1 ( v),( v) = <( v)π( v) Inverse Mills Ratio, < ( v) ( v) y 1 S = 1,,, ( v), ( v) 46 : S = 0 if Z 0 1 if Z> 0 Probit,^,( v), (1), 1 Heckman S = 0,ln y 1 : E(ln y 1 S = 0) = E( X+ u 1 X+ E( u 1 < - Z+ < 0) = Z ) = X- 1 ( - v) (2),, : E(ln y 0 S = 0) = E( X+ u 0 (2) Z+ < 0) = X- 0 ( - v) (3) : E(ln y 0 S = 1) = E( X+ u 0 X+ 0 ( v) Z+ > 0) =,, : E(ln y 1 - ln y 0 S = 1) = E(ln y 1 S = 1) - E(ln y 0 S = 1) = X+ 1 ( v) - [ X- 0 ( - v) ] = X (- ) + ( 1-0 ) ( - v) : E(ln y 1 ( - v) - ln y 0 S = 0) = X (- ) - ( 1-0 ) Roy, : si = ln y i1 - ln y i0,,roy,,, X (- ),,,,,,y, (Partial ML), S = 1,y 1

6 OLS (01000) (0100) (01000) (01000) (01000) (01001) (01000) (01000) (01000) (01043) (01016) (01017) (01154) (01118) (01110) R OLS, OLS 2 S, p 1,S,, :,;2 1, ;3 2 2,,,,,, 2,,, 2 3,,,,,,,,,, 2, 01039,01037,01035,, 21Roy OLS,,,OLS, Roy,, Roy, X :,,, ;,,, Z,, 18,, (1) (3),^ ^^, 30 %, Roy, :,2007 : 1977., http :ΠΠwww. rankedu. comπ? dp2bbsthread html 47

7 : ^ 1 ^ 0 ^ 3 3, ( ), ;(),,(,,,, (Pr ( S = 1) ),,,,( Pr ( S = 0) ) 3,( v) ( - v) ^ 1 ^ 0,,( - v) 01338, 5 %,^ 1, ), ;, Roy ln y 1 = 1 Pr ( S = 1) ^ 1 ^ 0, E(ln y 0 S) E (ln y 1 S),,, y 0 Roy,y 1 4 Roy,30 % 70 %, (01007) (01537) (01233) (01363) (01015) (01000) (01001) (01549) (01000) (01224) (01037) (01988) (01074) (01600) ln y 0 = 1 Pr ( S = 0) (01001) (01002) (01044) (01007) (01000) (01000) (01003) (01000) (01002) (01005) (01007) (01012) (01003) (01002) (01060) (01000) (01000) (01000) (01261) (01000) (01463) (01000) (01002) (01001) ( v) (01469) ( - v) (01042) (01000) (01000) (01000) (01000) : (1) p ; (2)( v) ( - v) p H 0 := 0 ; (3)( - v) Pr ( S = 0), ^ 0 ( - v) ; (4) 48

8 Π ln y (01333) (01381) (01362) (01372) (01233) (01218) (01204) (01224) ln y (01285) (01296) (01346) (01346) (01177) (01139) (01145) (01149) ln y (01327) (01342) (01372) (01390) ln y (01316) (01337) (01388) (01391) :, 01269,01452, %, 60 %,,, 3 %6 %,, 2407, 5020 ;, Roy,,,, Roy,,,, : 5 ln y (01354) (01404) (01427) ln y (01302) (01336) (01360) (01160) (01135) (01138) :,, , E(ln y ,,,,,Roy,, 11 Roy, : - ln y 0 S = 1) = X (- ) + ( 1-0 ) ( v) : E(lny 1 - ln y 0 S = 0) = X (- ) - ( 1-0 ) (- v),, X (- ) (- ), X X,,,,,,,,,X,,,6 : 6,,,,,,Roy,,,,,,, 49

9 : (01139) (01147) (01141) (01083) : (01080) (01069),,,,, 21OLS Roy,Roy OLS,, OLS, : ln y 0 = 0 + X+ u 0,ln y 1 = X+ u 1,,S, < Roy,X (- ),,,Roy,,Roy, , 6000,,6000,6112 %,,565, ,3 %, ,1000,,, : = (- 50 )Π Roy, 40000, 1,, : 7132 %, 9186 %, % 47827, 6112 %,,,, :, ; 41,,,,,,,,,,,,,,,,, 30,,,,,,,377,,, 10,30 ; 20 ; 5, 7, ; ,

10 ,,,,,,,,,,,,, 2004 : :, 4 J1 Altonji and T. Dunn, 1996,The Effects of Family Characteristics on the Return to Education, The Review of Economics and Statistics, Vol. 78 (4) : A. Bjgrklund and R. Moffitt, 1987,The Estimation of Wage Gains and Welfare Gains in Self2Selection Models, The Review of Economics and Statistics, Vol. 69 (1) : G. Becker and N. Tomes, 1986,Human Capital and the Rise and Fall of Families, Journal of Labor Economics, Vol. 4 (3) : S1 S39. D. Card, 1995,Earnings, Schooling, and Ability Revisited, Research in Labor Economics, vol. 14 : P. Carneiro, J. Heckman, and E. Vytlacil, 2002,Estimating The Return to Education When It Varies Among Individuals,working paper at www. econ. upenn. eduπcgi2binπmeconπbinπserve. cgiπ Epirical E. Eide and M. Showalter, 1999,Factors Affecting the Transmission of Earnings across Generations : A Quantile Regression, The Journal of Human Resources, Vol. 34 (2) : D. Ginther, 2000,Alternative Estimates of the Effect of Schooling on Earnings, The Review of Economics and Statistics, Vol. 82 (1) : Z. Griliches, 1977,Estimating the Returns to Schooling : Some Econometric Problems, Econometrica, Vol. 45 (1) : J. Heckman and E. Vytlacil, Local Instrumental Variable and Latent Variable Models for Identifying and Bounding Treatment Effects, Proceedings of the National Academy of Sciences, Vol. 96 : J. Heckman and E. Vytlacil, 2000,Local Instrumental Variables, in C. Hsiao, K. Morimune, and J. Powells, (eds. ), Nonlinear Statistical Modeling : Proceedings of the Thirteenth International Symposium in Economic Theory and Econometrics : Essays in Honor of Takeshi Amemiya, ( Cambridge : Cambridge University Press, 2000) : S. Han and C. Mulligan, 2001,Human Capital, Heterogeneity and Estimated Degrees of Intergenerational Mobility,The Economic Journal, Vol. 111 (470) : P. Taubman, 1989,Role of Parental Income in Educational Attainment, The American Economic Review, Vol. 79 (2) : A. Roy, 1951,Some Thoughts on the Distribution of Earnings, Oxford Economics Paper, vol. 3 (2) : J. Valero2Gil and J. Tijerina2Guajardo, 2002,Effects of Education on the Intergenerational Transmission of Labor Income in Mexico, Eastern Economic Journal, Vol. 28 (3) : R. Willis and S. Rosen, 1979,Education and Self2Selection, The Journal of Political Economy, Vol. 87 (5) : S7 S36. R. Willis, 1986, Wage Determinants : A Survey and Reinterpretation of Human Capital Earnings Functions, in Handbook of Labor Economics, Vol. I, O. Ashenfelter and R. Layard (eds. )., North2Holland. Parental Income and Return to College Education in Urban China Yuan Cheng and Zhang Lei (School of Economics, Peking University ; School of Economics, Clemson University) Abstract: In this paper, we examine the influence of parental income on the return to college education in a framework of heterogeneous returns to education among individuals. The Roy model is employed to correct the ability bias and to estimate the potential incomes from obtaining a college education and a high school education for each individual. We use the 2002 CHIP data and find strong evidence that the return to college education increases with parental income. Based on these findings, we discuss the efficiency and sustainability of National College Loan Policy and the possible measures that government may take to increase the return to college education for students from low - income families. Key Words :Return to College ; Heterogeneity ; Selection Bias ; Intergenerational Transmission of Income ; College Loan JEL Classification :C300, I200, J300 (: ) (: ) 51

Marginal Person. Average Person. (Average Return of College Goers) Return, Cost. (Average Return in the Population) (Marginal Return)

Marginal Person. Average Person. (Average Return of College Goers) Return, Cost. (Average Return in the Population) (Marginal Return) 1 2 3 Marginal Person Average Person (Average Return of College Goers) Return, Cost (Average Return in the Population) 4 (Marginal Return) 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27