1. Selection Bias, Comparative Advantage and Heterogeneous Returns to Education: Evidence from China James J. Heckman (University of Chicago) Xuesong Li (Institute of Quantitative & Technical Economics, Chinese Academy of Social Sciences)

2. 2 1. Introduction 2. Models with and without Heterogeneity 3. Selection Bias and The Marginal Treatment Effect 4. Data Set and Empirical Results 5. Concluding Remarks

3. 3 1.Introduction Heterogeneity and missing counterfactual states are central features of micro data. This paper uses China’s micro data, to estimate the return to education for China considering both heterogeneity and selection bias.

4. 4 Our work builds on previous research by Heckman and Vytlacil (1999, 2001), and Carneiro (2002), which develops a semi parametric framework.

5. 5 2. Models with and without Heterogeneity A conventional model of the return to education without heterogeneity in returns: (1) I for individuals (i=1, 2,...,n), lnYi is log income, Si is schooling level or years of schooling, Xi is a vector of variables βis the rate of return to education, γis a vector of coefficients.

6. 6 OLS problem: omitted ability Ai, Three strategies: (1) IV. But It is also very hard to find satisfactory instruments. In fact, most commonly used instruments in the schooling literature are invalid because they are correlated with the omitted ability. (2) Fixed effect method: find a paired comparison such as a genetic twin or sibling with similar or identical ability. It needs enough information

7. 7. (3) Proxy variables for ability Many empirical analyses reveal that better family background and better family resources are usually associated with better environments which raise ability. In our empirical work we use parental income as a proxy for ability.

8. 8 A model with heterogeneous returns to education (in random coefficient form) (2) βi is the heterogeneous rate of return to education, which varies among individuals. Xi is a vector of variables including the proxy for ability. We focus on two schooling choices: (1) high school Si=0 (2) college Si=1

9. 9 The two potential selection outcomes

10. 10 Observed log earnings are: where (5) is the heterogeneous return to education for individual i. βi varies in the population, and the return to schooling is a random variable with a distribution.

11. 11 The mean of βi given X is: (6) Decision rule: (7) Si* is a latent variable denoting the net benefit of going to school Zi is an observed vector of variables.

12. 12 Pi = Pi (Zi) is the propensity score or probability of receiving treatment (going to college). P(Z) can be estimated by a logit or probit model. Usi is the unobserved heterogeneity for individual i in the treatment selection equation. Without loss of generality, we may assume that Usi ~ Unif [0,1]. The decision of whether to go to college (or not) for individual i is determined completely by the comparison of the observed heterogeneity Pi(Zi) with the unobserved heterogeneity Usi. The smaller the Usi, the more likely it is that the person goes to college.

13. 13 3. Selection Bias and The Marginal Treatment Effect (8) ATE is the average treatment effect (the effect of randomly assigning a person to schooling) (9)

14. 14 (10) Selection bias is the mean difference in the no-schooling (S = 0) unobservables between those who go to school and those who do not.

15. 15 TT (treatment on the treated), the effect of treatment on those who receive it (e.g. go to college) compared with what they would experience without treatment (i.e. do not go to college), defined as (11) Sorting effect is the mean gain of the unobservables for people who choose ‘1’.

16. 16 IV is not a consistent estimator In the presence of heterogeneity and selection bias. (12)

17. 17 Neither OLS nor IV is a consistent estimator of the mean return to education in the presence of heterogeneity and selection. Under certain assumptions, it is possible to identify the heterogeneous return to education with marginal treatment effect (MTE) via the method of local instrument variables (LIV), where MTE is:

18. 18 The MTE is the average willingness to pay (WTP) for lnY1i (compared to lnY0i ) given characteristics Xi and unobserved heterogeneity Usi. MTE can be estimated from the following relationship, where LIV can be estimated by semi parametric methods for derivatives (Heckman, 2001):

19. 19 All the other treatment variables can be unified using MTE:

20. 20 Where the weights are:

21. 21 Treatment on the untreated (TUT) is the effect of treatment on those who do not receive it (i.e. do not go to college) compared with what they would experience with the treatment (i.e. go to college)

22. 22 4. Data Set and Empirical Results Data Source: China Urban Household Income and Expenditure Survey (CUHIES) 2000 Conducted by the Urban Socio-Economic Survey Organization of the National Bureau of Statistics. Six provinces: Guangdong Liaoning Sichuan Shaanxi Zhejiang Beijing.

23. 23 Sample size: 4250 households. For each household, there is rich information on all household members, including head, spouse, children and parents. Age, sex, education level, employment status and enterprise ownership, occupation, years of work experience and total annual income are available for each household member. There are seven education levels in the sample: university, college, special technical school, senior high school, junior high school, primary school, and other.

24. 24 The used sample consists of 587 individuals, including 273 people with four-year college (or university) certificates and 314 people with only senior high school certificates.

25. 25 Table 2. Summary Statistics Variable All (n=587)Treated (n=273)Untreated (n=314) MeanStd. ErrMeanStd. ErrMeanStd. Err Log Wage8.860.869.120.778.640.88 Age26.254.7226.484.1426.065.16 Years of work experience6.414.925.834.476.915.23 4-Year college attendance0.470.501000 Male0.560.500.540.500.590.49 Lived in Guangdong Province (GD)0.180.390.190.390.180.38 Lived in Liaoning Province (LN)0.280.450.300.460.270.44 Lived in Shaanxi Province (SX)0.100.300.080.270.120.33 Lived in Sichuan Province (SC)0.160.370.150.360.170.38 Lived in Beijing (BJ)0.150.360.150.360.140.35 Lived in Zhejiang Province (ZJ)0.120.330.120.330.120.33 Worked in state owned enterprises (SOEs)0.620.490.720.450.540.50 Worked in collective-owned firms0.080.270.040.200.110.32 Worked in joint-venture or foreign owned firms0.180.390.190.400.170.38 Worked in private owned firms0.120.320.050.210.180.38 Worked in IND_CON sector*0.260.440.210.400.320.47 Worked in TRA_COM sector*0.030.170.030.170.030.18 Worked in HOU_RES sector*0.080.270.070.260.090.29 Worked in SPO_SOC sector*0.220.410.160.360.270.45 Worked in CUL_SCI sector*0.100.290.140.340.060.24 Worked in FIN_INS sector*0.110.320.090.280.130.34 Worked in GOVERN sector*0.030.160.040.200.020.13 Worked in OTHER sector*0.170.380.270.450.080.28 Years of father’s education11.363.3812.263.2610.573.28 Years of mother’s education9.902.9910.413.319.462.60 Parental income (in 1000 yuan)21.3916.5924.3615.8918.8116.78

26. 26 Variable OLSIV CoefficientStandard ErrorCoefficientStandard Error Intercept8.31890.14938.30400.1552 4-Year’s college attendance0.29290.06300.56090.1695 Years of work experience0.03800.01940.01960.0202 Experience squared-0.00160.0010-0.00070.0010 Parental income in 1000 yuan0.01170.00200.00980.0023 Male0.15370.06020.14390.0607 Lived in Guangdong Province0.75430.12550.79080.1267 Lived in Liaoning Province0.26930.10850.31420.1092 Lived in Sichuan Province0.22780.11810.27590.1192 Lived in Beijing0.72460.12410.77750.1256 Lived in Zhejiang Province0.62410.12970.67390.1314 Worked in state owned enterprises-0.36790.0855-0.38730.0868 Worked in collective-owned firms-0.47860.1288-0.58900.1298 Worked in private owned firms-0.46490.1179-0.53040.1179 Worked in IND_CON sector*-0.27930.0788-0.30480.0792 Worked in TRA_COM sector*-0.45120.1762-0.46450.1779 Worked in SPO_SOC sector*-0.28800.0900-0.31060.0905 Worked in FIN_INS sector*-0.32200.1050-0.33270.1061 Table 3. Estimated Mincer Model

27. 27 VariableCoefficientStandard Error Mean Marginal Effect Intercept-4.73700.7305- Years of father’s education0.10170.02970.0211 Years of mother’s education0.06050.03420.0126 Parental income in 1000 yuan0.01900.00690.0040 Born before 19642.00080.79690.4159 Born in 19641.72850.91890.3593 Born in 19653.34230.82570.6947 Born in 19663.18130.85520.6613 Born in 19671.84551.11260.3836 Born in 19682.90300.81610.6034 Born in 19692.25690.79410.4691 Born in 19701.50760.75340.3134 Born in 19713.07710.71380.6396 Born in 19722.64240.71830.5492 Born in 19732.53950.68090.5279 Born in 19742.77400.67530.5766 Born in 19752.79310.67630.5806 Born in 19762.86340.66690.5952 Born in 19772.58900.66720.5381 Born in 19782.55720.66560.5315 Born in 19791.36310.76360.2833 Table 4. Estimated Logit Model For Schooling

28. 28 Variable High SchoolCollege Std. Err. Years of work experience0.03600.02250.01410.0278 Experience squared-0.00130.0011-0.00090.0013 Parental income in 1000 yuan0.01880.00380.00770.0038 Male0.13650.07230.19130.0777 Lived in Guangdong Province0.57120.19610.88530.1590 Lived in Liaoning Province0.19010.12630.39290.1049 Lived in Sichuan Province0.26120.13640.22960.1081 Lived in Beijing0.71220.16950.79710.1301 Lived in Zhejiang Province0.69300.15510.54610.1744 Worked in state owned enterprises-0.33680.1188-0.44710.1093 Worked in collective-owned firms-0.60600.2065-0.58680.1771 Worked in private owned firms-0.42050.1511-0.62560.1677 Worked in IND_CON sector*-0.22970.0821-0.39780.0990 Worked in TRA_COM sector*-0.35270.1318-0.50400.1557 Worked in SPO_SOC sector*-0.37020.1282-0.30400.1202 Worked in FIN_INS sector*-0.33450.1560-0.35430.1331 Table 5. Estimated Coefficients from Local Linear Regression Guassian Kernel, bandwidth = 0.4

29. 29 ParametersEstimation OLS0.2929 IV*0.5609 ATE0.4336 TT0.5149 TUT0.3630 Bias-0.1407 Selection Bias-0.2220 Sorting Gain0.0813 * Using propensity score as instrument Table 6. Comparison of Different Parameters

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34. 34 A: with firms’ ownership dummies but not sectoral dummies B: with sectoral dummies but not ownership dummies C: no sectoral and ownership dummies

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36. 36 5. Concluding Remarks Neglecting heterogeneity and selection bias leads to biased and inconsistent estimates, such as those obtained using conventional OLS and IV parameters. We demonstrate the importance of proxying for ability in the wage equation to identify returns to education. Excluding the proxy leads to implausibly high estimates of the return to schooling.

37. 37 In 2000 the average return to four-year college attendance is 43% (on average, 11% annually) for young people in the urban areas of the six provinces. The results imply that, after more than twenty years of economic reform with market orientation, the average return to education in China has increased markedly compared with that of the 1980s and early 1990s.