Heterogeneity in the Economic Returns to Schooling among Chinese Rural-Urban Migrants, * NILS working paper series No 200

Transcription

1 Heterogeneity in the Economic Returns to Schooling among Chinese Rural-Urban Migrants, * NILS working paper series No 200 Rong Zhu

2 Heterogeneity in the Economic Returns to Schooling among Chinese Rural Urban Migrants, Rong Zhu Abstract This paper analyzes the returns to schooling among Chinese rural migrant using data from the 2002 and 2007 China Household Income Project. Our nonparametric estimates show substantial dispersion and heterogeneity in the schooling rates of return among migrant workers. While the returns to schooling for the overall sample have increased over time, this result is mainly driven by the substantial increase in female migrants schooling coefficients. The schooling rates of return are also found to increase with migrant workers education levels. Our birth cohort analysis shows that the patterns of the evolution of schooling returns during are still present even after considering the effects of changes in migrants age structure and in unobserved ability distribution during JEL classif ication: I20; J24; J31 Keywords: Heterogeneity; return to education; migrant workers I am grateful to the Editor, Yi Qian, an anonymous referee and Bryan He for helpful comments. The usual disclaimer applies. National Institute of Labour Studies, Flinders University, Adelaide, Australia. Address: rong.zhu@flinders.edu.au. 1

3 1 Introduction Rural urban migration has been one of the most significant changes in China s labor market since the economic reform launched in the late 1970s. With the loosening of government s administrative controls over domestic population flows and the widening earning disparities between rural and urban areas in the last two decades, the number of rural urban migrants in China has increased significantly from an estimate of 80 million in 1995 to around 132 million in 2006 (Meng and Zhang, 2001; Demurger et al., 2009). As the most important form of internal migration in China and probably the greatest migration ever taking place in human history, rural urban migration in China has produced profound effects on China s labor market and attracts the attention from both researchers and policy makers (Zhao, 2005; Demurger et al., 2009; Akay et al., 2012). China s unique Household Registration System (Hukou System) distinguishes its rural urban migration in China from the internal migration in other developing countries. 1 Implemented since the 1950s, the Hukou System was initially utilized as a civil status registration system to allocate housing and jobs, rationed food, necessities and other social welfare benefits. It was designed as an important state institution to control China s domestic population movement, under which people s access to consumer goods and job opportunities were closely linked their places of residence. This system made it very difficult for people to move from rural to urban areas (Wang and Zuo, 1999; Zhao, 1999). Since the late 1970s, the Household Responsibility System in rural China has led to the abandonment of the rationing system and brought greater freedom to rural workers in choosing occupations, which makes the rural urban migration become possible. In the meantime, the rapid development of highly labor intensive industrial sectors has created massive job opportunities in urban China and resulted in rising disparities in earnings between rural and urban areas. Consequently, the migration to urban areas becomes not only practical but also profitable for China s rural residents (Poncet, 2006; Liu, 2008). The labor flows from rural to urban areas have become a constant social phenomenon 1 See Zhao (2005) for the origin and evolution of the Hukou system and a survey of literature on rural-urban migration in China. 2

4 since the mid and late 1980s. While many reforms have been implemented, the Household Registration System still imposes many restrictions on the urban employment opportunities for migrant workers. China s urban labor market is featuring a segmentation between rural migrants and urban residents (Meng and Zhang, 2001). Without urban Hukou, rural migrants are usually regarded as second class workers by employers and government departments. They are usually not covered by the urban social security system such as the health insurance. Their jobs are not valued by urban residents, which are usually low skilled, hard and dangerous (Demurger et al., 2009). They typically work for longer hours than urban residents, but the earnings they receive are often far below those for urban residents. The situation is exacerbated by the difficulty in changing rural Hukou to urban Hukou as rural migrants are generally less educated and less skilled, in spite of the substantial amount of time migrant workers have spent working in urban areas (Wang and Zuo, 1999; Liu, 2005). While the rural migrants certainly deserve researchers attention, the economic studies on rural migrants labor market outcomes are relatively limited when compared with those studies of China s urban residents. This paper contributes to the existing literature by examining the returns to schooling among Chinese rural urban migrants. While literature abounds in investigating the returns to education among urban residents in China (Byron and Manaloto, 1990; Liu, 1998; Li, 2003; Zhang et al., 2005) and also among off farm workers in rural areas (Wei et al., 1999; de Brauw and Rozelle, 2008), how the education that migrant workers received in rural areas affects their earnings in China s cities has not been systematically examined. 2 In this paper, using the nationally representative rural urban survey data from the the 2002 and 2007 China Household Income Project, we examine the returns to education 2 The literature shows that the rates of return to schooling in urban China were generally below 4% in the 1980s (Byron and Manaloto, 1990; Liu, 1998), and they were much lower than the world average (10.1%) and Asian average (9.6%) reported in Psachaporoulos (1994). More recent studies find a trend of rising schooling returns among urban workers during China s economic transition (Li, 2003; Zhang et al., 2005). For example, using annual survey data of urban households collected by China s National Bureau of Statistics, Zhang et al. (2005) find that the average rate rose from 4.0% in 1988 to 6.7% in 1995 before reaching 10.2% in Other studies focus the estimation of returns to education in rural China, and the schooling rates of return are also found to be lower than estimates for other developing economies (Wei et al., 1999; de Brauw and Rozelle, 2008). 3

5 among Chinese rural migrants. This paper contributes to the existing literature in two main ways. First, this study provides the first systematic analysis of schooling rates of return among rural migrants, thus contributing to the literature understanding the effects of education on earnings in China. Second, using the nonparametric approach developed by Racine and Li (2004) and Li and Racine (2004), we contribute to the recent literature on individual level heterogeneity in returns to schooling (Harmon et al., 2003; Koop and Tobias, 2004). As discussed in Akay et al. (2012), rural migrants in China are a very heterogeneous group with varied migration histories and different labor market outcomes. It is highly likely that the returns to schooling are very heterogeneous among this complex group. With most developing economies in the process of urbanization, how education affects migrant workers earnings in the urban labor market deserves our special attention. Our nonparametric analysis shows that the returns to schooling are indeed very heterogeneous among migrant workers. While the returns to schooling for the overall sample have increased over time, we show that this result is mainly driven by the substantial increase in female migrants schooling coefficients, and the returns to education among male migrants have actually decreased over time. This finding can help explain why the average gender wage gap among migrant workers decreased from 27% in 2002 to 16% in The schooling rates of return are also found to increase with migrant workers education levels. While the wage issues among rural migrants have been an important concern in the existing literature (Meng and Zhang, 2001; Demurger et al., 2009; Magnani and Zhu, 2012), increasing migrants educational attainments seems not only a viable way to narrow down the gender wage differentials among migrant workers, but also a feasible way to increase migrants earnings so that the wage gaps between rural migrants and urban residents can also be reduced. We also find that the marginal returns to senior high school and above are higher than the returns to primary and junior high school education. When a rural individual choose urban employment over investment in education after finishing the nine year compulsory education, it involves a trade off between a significant loss of higher lifetime earning potential and the short run benefits of wage employment in urban China. Moreover, we find that the changes in schooling returns over time does not result from the 4

6 change in migrants age structure from 2002 to Our birth cohort analysis further shows that the evolution of schooling returns during cannot be attributable to the change in unobserved ability distribution of migrant workers between 2002 and The remainder of this paper is organized as follows. Section 2 describes a theoretical model that motivates this study. Section 3 is a description of the data. In Section 4, we describe the empirical approach taken. Section 5 presents the estimation results. Section 6 concludes. 2 Theoretical Motivation We use a simple static model formulated by Card (1995) and restated in Card (1999) to illustrate how the returns to education could vary at the individual level. The Becker type model of optimal schooling assumes that each individual faces a market opportunity locus that gives the levels of earnings and costs associated with schooling choices. Let W (S) denote the average wage an individual will receive if he or she acquires the schooling level S. The individual is assumed to choose S to maximize the utility function given by: U(S, W ) = log(w (S)) C(S) (1) where log(w (S)) represents the overall economic benefits from acquiring education level S and C is an increasing convex function in S which measures the costs of schooling. An optimal schooling choice meets the following first order condition: W (S) W (S) = C (S) (2) The left hand side measures the percentage change of wage resulting from one more year of education, and the right hand side denotes the marginal cost involved. When the marginal benefit and the cost are both linear functions of S, the two components could be simply specified as: W (S) W (S) = w i k 1 S (3) 5

7 C (S) = c i + k 2 S (4) where w i is a random variable corresponding to the factors that may affect one s return to schooling, and c i corresponds to the tastes for schooling, access to funds or other known or unknown factors affecting one s costs of schooling. k 1 and k 2 are two constants. k 1 can be positive or negative, which depends on whether the percentage change of wage from one more year of schooling decreases or increases with migrants education levels. k 2 is likely to be positive for Chinese rural migrants as it is well known that the marginal cost of education is generally higher among people receiving higher levels of education in rural China. The specifications in equation (3) and (4) imply that the optimal schooling choice is equal to Si =(w i c i )/(k 1 + k 2 ), which is linear in individual specific heterogeneity terms. Individual i s marginal return to schooling could be correspondingly obtained as: β i = W (S ) W (S ) = w i k 1 S = w i k 2 k 1 + k 2 + c i k 1 k 1 + k 2 (5) Since w i and c i are two random variables, the equilibrium of this static model entails a distribution of marginal returns to education across the migrants population. It is likely that the background factors (w i and c i ) might lead to dispersion in schooling coefficients. Even among people who share the same level of education, the private returns could differ because of the randomness of w i. The prediction of this simple model provides us the motivation to empirically investigate the differences in economic returns to schooling at the individual level. 3 Data and Descriptive Statistics The data used for this study is from the 2002 and 2007 China Household Income Project (CHIP2002 and CHIP2007), which respectively consist of three surveys of different types of households in China: rural household survey, urban household survey and the survey of rural urban migrant households living in urban areas but without urban Hukou. We 6

8 only use the two rural urban migrant survey in 2002 and 2007 for this study, which were conducted in 2003 and 2008 for the reference periods of 2002 and The 2002 survey covered 5,327 individuals from 12 provinces, while the 2007 data surveyed 8,446 individuals from nine provinces in China. 4 As we want to compare the heterogeneous returns to education among rural migrants over time, we restrict our attention to the seven provinces that appeared in both waves. As a result, the two final samples consist of observations from Guangdong and Jiangsu in the more developed coastal areas, and Henan, Sichuan, Hubei, Anhui and Chongqing from the less developed inland areas. This leaves us 3,417 observations from the 2002 sample and 6,624 observations from the 2007 sample. We restrict our attention to the rural migrants aged 16 60, and the sample sizes are reduced to 2,555 and 5,766 in 2002 and Following the literature (Demurger et al., 2009; Magnani and Zhu, 2012), only migrant workers with positive wage information are used. We respectively drop 439 and 676 observations with missing information on monthly income and working hours in the two surveys. Finally, any individuals with missing information on other variables summarized in Table 1 and 2 are also dropped. This leads to a further deletion of 17 and 242 observations in 2002 and Our final samples consist of 2,099 migrants in 2002 and 4,848 migrants in Table 1 presents the means and standard deviations of earnings and selected individual characteristics by gender and year. The monthly income of each migrant is the sum of reported earnings in all forms received from the migrant s main job in urban China (including regular wages, bonuses, subsidies and all other income from the work unit). Hourly 3 The 2002 rural urban migrants survey has been used by Magnani and Zhu (2012) to examine the gender wage differentials among Chinese rural migrants. 4 Among the 12 provinces (municipalities) in the 2002 survey, Beijing, Guangdong, Jiangsu and Liaoning are from China s coastal areas, and Anhui, Henan, Hubei, Shanxi, Chongqing, Gansu, Sichuan and Yunnan are from inland areas in China. Among the 9 provinces in the 2007 survey, Guangdong, Jiangsu, Shanghai, Zhejiang are from coastal areas, and Henan, Sichuan, Hubei, Anhui and Chongqing are from inland China. 5 When we focus on the rural migrants aged 16-60, we lose 17.8% (from 2,555 to 2,099) and 15.9% (from 5,766 to 4,848) of observations in 2002 and The major reason for the loss of observations is that those observations do not have complete information on wages. It is likely that rural migrants with no information on wages are systematically different from the migrant workers in our final sample. The limited information in the data does not allow us to find any valid instrumental variable that affects availability of the wage information but exerts no impact on earnings. Even when such instrument is available, the method that can simultaneously address the selection problem and non-parametrically estimate observation specific schooling coefficients is not available. As a result, I follow the previous studies estimating the returns to education in China (Liu, 1998; Li, 2003; Yang, 2005) and ignore this problem. 7

9 wages are calculated using monthly income and weekly working hours. To enhance earnings comparability, we deflate the earnings in 2007 with the province level consumer price index so that all income and wages are measured in 2002 yuan. Experience, the potential labor market experience, is calculated as age minus schooling minus six. 6 Table 1: Summary Statistics by Gender and Year Male Female Male Female Monthly income ( ) (417.97) ( ) (846.99) Weekly working hours Hourly wage Log(Hourly wage) Age Years of schooling (18.97) (18.51) (16.14) (16.40) (5.89) (1.79) (4.66) (3.61) (0.71) (0.58) (0.58) (0.54) (8.32) (7.68) (10.00) (9.16) (2.57) (2.96) (2.32) (2.38) Primary school or below (in %) (0.50) (0.49) (0.45) (0.45) Junior high school (in %) (0.49) (0.46) (0.50) (0.50) Senior high school or above (in %) (0.32) (0.28) (0.40) (0.39) Experience Male (in %) Married (in %) (9.37) (9.22) (10.81) (10.30) (0.29) (0.28) (0.49) (0.49) (0.29) (0.28) (0.49) (0.49) Ethnic minority (in %) (0.20) (0.19) (0.14) (0.11) Observations 1, ,951 1,891 N ote: Standard deviations are reported in parentheses. Income and wages are measured in 2002 yuan with earnings in 2007 deflated by province specific consumer price index. Earnings have increased substantially over the five year period. The monthly income for male migrant workers has increased from yuan in 2002 to yuan in As expected, the weekly working hours of rural migrants are much longer than the usual 6 A few negative values of Experience are recorded as zero. 8

10 Age Table 2: Average Years of Education for Selected Subgroups Male Female Male Female (2.23) (2.59) (2.16) (1.99) (2.38) (2.76) (2.30) (2.43) (3.22) (3.04) (2.51) (2.73) Employer ownership Employment status Public Private (2.84) (3.11) (2.49) (2.49) (2.53) (2.94) (2.29) (2.37) Self employed (2.46) (2.83) (2.22) (2.50) Wage earners (3.02) (2.70) (2.31) (2.27) Coastal (2.50) (2.89) (2.25) (2.21) Region Inland (2.56) (2.95) (2.33) (2.43) N ote: Standard deviations are reported in in parentheses. 40 working hours per week among urban residents. The hourly wage rates have increased by 62% (= ) and 73% (= ) respectively for males and females during the five year period. The gender wage gap was 27% (= ) in 2002 and it reduced to 16% (= ) in The five year period has also witnessed an increase in rural migrants education attainment. The average years of schooling have increased from 8.34 to 9.29 years for male migrants and from 7.36 to 9.10 years for female migrant workers. Also, the proportions of junior high school graduates and graduates from senior high school or above have significantly increased. The gender gap in completed years of schooling is also much lower in 2007 than in Migrants in the 2007 survey are found to be younger than those in the 2002 survey, as more proportions of young people are moving from rural areas to cities. As people in the 2007 survey are younger on average, the percentage of married migrants is lower than in the 2002 survey. In Table 2, we report the average years of completed schooling for selected subgroups. For almost every group, higher education levels are observed in 2007 than in 2002, and 9

11 male migrants receive more years of education than females. Ages are categorized into three subgroups: 16 30, and Newer labor market entrants generally spent more time on education than older ones. In terms of sectors, public sectors tend to employ more educated migrant workers than private sectors. Self employed rural migrants are found to have less years of schooling than wage earners. In addition, we group those surveyed provinces into two regions according to their geographic locations and economic resemblances in China: the more developed coastal regions and the less developed inland provinces. 7 From 2002 to 2007, we also see the increase in the attained years of schooling for both the richer coastal areas and the poorer inland regions in China. Cross region differences in average years of schooling, although still existent, are found to have narrowed down over time. 4 Empirical Methodology 4.1 Local Linear Kernel Estimation We use the local linear kernel method developed by Racine and Li (2004) and Li and Racine (2004) to do the estimation, which has an advantage over conventional kernel methods in its capability to smooth both categorical and continuous variables. The nonparametric method is more flexible and robust than parametric methods since functional form and distribution assumptions are avoided and interactions that may exist among all variables are also allowed. Furthermore, this method is able to generate an observation specific coefficient estimate for each covariate, which is crucial for assessing the individual heterogeneity in returns to schooling in this study. The model is specified as W i =F (X i, Y i )+ε i, where W i is the logarithmic hourly wage and F is the functional form to be estimated. X i and Y i represent the vectors of continuous variables (Schooling and Experience) and unordered discrete variables (M ale, Ethnic minority, Married and P rovince) respectively. Then we find γ (X j )=(α j, β (X j )) to 7 The coastal provinces are Guangdong and Jiangsu. All other provinces (Henan, Sichuan, Hubei, Anhui and Chongqing) are located in the inland regions of China. 10

12 minimize the following objective function: N ( Wi α j (X i X j ) β (X j ) ) 2 K( ĥ, λ) (6) i=1 where α j predicts W j and β (X j ) is the vector of the partial derivative of F (X j, Y j ) with respect to X. K(ĥ, λ) is the multivariate product kernel for mixed data types which is equal to s q=1 1 g( x qi x qj ĥ q ĥ q ) l q=1 m(y qi, y qj, λ q ). In the product kernel, g is the second-order Gaussian kernel and h q is the bandwidth for the qth component of X. m is the kernel function for an unordered discrete variable, which equals to 1 if y qi =y qj and λ q otherwise (0 λ q 1). 8 If the bandwidths selected for discrete variables are all equal to 0, the product kernel l q=1 m(y qi, y qj, λ q ) for discrete variables becomes an indicator function. As a result, the conventional frequency based kernel method is a special case of the nonparametric approach we use. The basic idea of this nonparametric approach is that when estimating the coefficient for individual j, more weights are assigned to individuals who share similar labor market characteristics to individual j, and less weights are assigned to individuals with less similar personal characteristics. After running the OLS regression of W i on (1, X i X j ) with weights K(ĥ, λ), the coefficients on continuous variables for individual j are obtained as: ( γ(x j ) = α j, β ) N (X j ) = K(ĥ, λ) 1 (X i X j ) i=1 X i X j (X i X j )(X i X j ) N K(ĥ, λ) 1 W i i=1 X i X j 1 (7) The selection of smoothing parameters (h, λ) is crucial in kernel estimation. In this analysis, we employ the popular least square cross-validation procedure (LSCV), which can select the asymptotically optimal bandwidths in the sense of minimizing asymptotic mean squared errors (Li and Racine, 2007). The objective function is given by 8 We do not have ordered discrete predictors in this analysis. If there is an ordered categorical variable Z i, Li and Racine (2004) suggests using the kernel function n(z i, z j, µ) which equals to 1 if z i =z j and µ zi zj otherwise (0 µ 1). 11

13 CV (h, λ)= 1 N N i=1 (W i F i (X i, Y i )) 2, where F i (X i, Y i ) is the leave-one-out estimator of F (X i, Y i ). (h, λ) are the vectors of parameters selected to minimize CV (h, λ). It should be noted that the nonparametric approach is used to uncovered observation specific return to schooling. It is different from the conditional quantile regression approach by Koenker and Bassett (1978), which could be applied to uncover the heterogeneous schooling coefficients at different parts of wage distribution, but can not be used to estimate the effect for each observation. 9 The nonparametric coefficient estimate of education can also be inconsistent without controlling unobserved ability. Due to the data limitation, we cannot find a good proxy for ability. A valid instrumental variable is also hardly available. However, the bias from ignoring individual abilities is somehow compensated by the bias in the opposite direction from disregarding measurement errors. Our nonparametric estimates are comparable with existing studies on returns to education among Chinese urban residents since they also tend not to control for the bias from unobserved ability (Liu, 1998; Li, 2003; Zhang et al., 2005) Stochastic Dominance Tests We use the stochastic dominance approach developed by Abadie (2002) to make distributional comparisons of the returns to schooling between different population subgroups of rural migrants and know which subgroup benefits more from additional education. Assuming that β i is the coefficient on education for migrant i, we want to compare the 9 We refer to Li and Racine (2004) for more details about the kernel method and Hayfield and Racine (2008) for how to implement this approach. For recent studies applying the nonparametric approach to examine heterogeneous economic effects, we refer to Henderson et al. (2012) and Delgado et al. (2013). 10 Similar to previous studies using the China Household Income Project data, the migrant data does not have sufficient information for addressing the unobserved ability bias. Previous studies tend to use the IV methods to correct the unobserved ability bias. However, in the presence of heterogeneous effects, IV regression could only recover the local average treatment effect of education on earnings for compliers, a subgroup of population whose education levels would otherwise be induced to change with the values of instrumental variables (Imbens and Angrist, 1994; Card, 1999). In a recent survey, Card (1999) summarizes the literature and suggests that the omitted variable bias is actually small. The examination of individual heterogeneity in the schooling coefficients without controlling for the unobserved ability in this paper is also in line with Harmon et al. (2003) and Koop and Tobias (2004). As discussed in both Harmon et al. (2003) and Koop and Tobias (2004), when the dispersion in schooling returns is the focal interest, the result need not be affected by the omitted ability bias. 12

14 estimate distributions between two groups: group A ({βi A } N A i=1 ) and group B ({βb i } N B ). Let F A (β) and F B (β) represent the cumulative distribution functions of {β A i } N A i=1 and {βb i } N B i=1 respectively. The two null hypotheses we want to test are: (1). Equality of distributions: F A (β)=f B (β) β B, where B denotes the union support for β A and β B ; (2). First order stochastic dominance: F A dominates F B if F A (β) F B (β) β B, with strict inequality for some β. When testing the two null hypotheses, β i is replaced with its nonparametric estimate β i. F A and F B are also replaced with their corresponding empirical distribution functions F A and F B. 11 As in McFadden (1989) and Abadie (2002), the two test statistics are defined as: T ED = ( N AN B ) 1 2 supβ B N A + N F A (β) F B (β) B (8) T F SD = ( N ( AN B ) 1 2 supβ B FA (β) N A + N F ) B (β) B (9) where T ED is the two sample Kolmogorov Smirnov statistic to test the hypothesis of equal distributions between group A and group B, and T F SD is the generalized Kolmogorov Smirnov statistic to test the null hypothesis of first order stochastic dominance of F A over F B. However, the asymptotic distributions of T ED and T F SD under the null are generally unknown since they depend on the underlying distribution of the data. Abadie (2002) suggests approximating the distributions of test statistics by resampling from the pooled samples and recomputing the test statistics. A four step bootstrap strategy is thus developed to make the inference about hypotheses possible: (i) Let T be the generic notation for T ED and T F SD. Calculate the statistic T for the original coefficient samples of { β A i } N A i=1 and { β B i } N B i=1 ; (ii) Resample (N A +N B ) observations with replacement from the pooled sample of 11 The empirical cumulative distribution function for group j is defined as F j ( β)= 1 N N i=1 I( β j i β j ), where I is the indicator function. 13 i=1

15 ({ β A i } N A i=1 ; { β B i } N B i=1 ), and divide the observations into two groups with sample sizes N A and N B. Use the two generated samples to obtain T r ; (iii) Repeat step (ii) R times (R=300 in this implementation); (iv) Obtain the p values of the tests by calculating the relative frequency of ( T r > T ), which is equal to 1 R R r=1 I( T r > T ). Reject the null hypothesis if the p value obtained is smaller than some significance level α, 0<α< Results 5.1 Nonparametric Estimation Results In this section, we present the nonparametric coefficient estimates of Schooling obtained using the basic explanatory variables (Experience, Male, Married, Ethnic Minority and Province). 12 A schooling coefficient is obtained for each migrant worker. we present the nonparametric mean estimate, the estimates corresponding to the 10th, 25th, 50th, 75th and 90th percentiles of the coefficient estimate distribution in Table 3 (labeled Q10, Q25, Q50, Q75 and Q90). Standard errors obtained with wild bootstrap that are robust to heteroskedasticity are reported. 13 As a comparison, we also display the estimates from the OLS regression of log hourly wages on the aforementioned control variables and squared Experience. The OLS estimates of returns to education displayed in Table 3 show that the average rate of schooling returns among rural migrants have increased from 3.82% in 2002 to 4.93% in The nonparametric mean estimates, which show that an additional year of 12 Previous studies exhibit different practices regarding whether the arguably endogenous ownership and industry variables should be included as controls. An argument against the inclusion of these variables is that there is previous evidence of positive selection into highly paying ownerships and industries by better educated workers in urban China (Zhao, 2002; Zhang et al., 2005). In Table 2, we also observe contrasted structures of average years of schooling in the employer ownership and industry categories. The inclusion of these job related variables that are themselves affected by the regressor of interest (Schooling) in the wage equation is a typical case of what Angrist and Pischke (2009) refer as bad control. The change in the schooling coefficients when using these additional controls may simply be an artifact of selection bias. Angrist and Pischke (2009) suggest that it would be better without controlling for them. With this in mind, the following discussions are all based on those baseline estimates. 13 Standard errors obtained with wild bootstrap are robust in the presence of heteroskedasticity, and wild bootstrap works well compared to other bootstrap methods even if there is no heteroskedasticity (Cameron and Trivedi, 2005). 14

16 schooling will lead to 4.78% increase in hourly wages in 2002 and 5.54% in 2007, suggest that OLS estimation has understated the effects of schooling on rural migrants wages. The rate of return for rural migrants in 2002 seems to be a lot lower than the estimates of around 10% for urban residents documented in Zhang et al. (2005) for the year The average schooling rate of return for each gender is also found to be much lower among rural migrants than among urban residents. We use the consistent model specification test developed by Hsiao et al. (2007) to test the specification of the linear models. The linear specification is rejected at conventional confidence levels for each sample. The simple linear specification we use may omit important interactions and nonlinear relationships among variables. Thus, it is rejected by the specification test for each sample. While misspecified, the linear specification still provides reasonable approximation to the nonparametric mean coefficients. OLS NP mean Q10 Q25 Q50 Q75 Q90 Table 3: Nonparametric Estimates of Returns to Education All Male Female All Male Female (0.0059) (0.0085) (0.0080) (0.0037) (0.0049) (0.0057) (0.0067) (0.0095) (0.0089) (0.0047) (0.0053) (0.0066) (0.0039) (0.0043) (0.0039) (0.0030) (0.0041) (0.0043) (0.0046) (0.0063) (0.0069) (0.0035) (0.0048) (0.0057) (0.0059) (0.0081) (0.0089) (0.0047) (0.0058) (0.0075) (0.0079) (0.0097) (0.0092) (0.0076) (0.0084) (0.0091) (0.0100) (0.0151) (0.0159) (0.0092) (0.0093) (0.0113) Observations 2,099 1, ,842 2,951 1,891 N ote: Huber White standard errors to correct heteroscedasticity of unknown form are reported in parentheses for the OLS estimates. Standard errors for the nonparametric estimates are obtained via bootstrapping with 300 replications. All the estimates are significant at the 5% level. Complementary to the formal statistical test, we also compare the parametric and nonparametric models in light of their ability to fit the sample. The within sample fitting measures we use, which are suggested in Hayfield and Racine (2008), are R 2, mean squared 15

17 error (M SE) and mean absolute error (M AE). Supposing that the dependent variable is W i and the predicted dependent variable is Ŵi, then R 2 is the squared correlation coefficient between W i and Ŵi, the mean squared error is defined as MSE= 1 N N i=1 [W i Ŵi] 2, and the mean absolute error is defined as MAE= 1 N N i=1 W i Ŵi. The results are displayed in Table 4. When switching from OLS estimation to nonparametric kernel regression, the R 2 increases from to for the 2002 sample and for the 2007 sample it rises from to The other two measures all show that the nonparametric approach fits the samples better in the sense of having smaller mean squared errors (MSE) and smaller mean absolute errors (M AE). This improvement in sample fitting shows the flexibility of the nonparametric method since it could relax functional form assumptions and allow for any nonlinearities and interactions in and among all variables. As the linear specification we use is misspecified as indicated by the model specification test, our following discussion of the returns to schooling among rural migrants will be based on the nonparametric estimates. Table 4: Model Comparison OLS NP OLS NP R M SE M AE The results displayed in Table 3 show considerable individual differences in education returns within each gender group in each year. For example, among the male migrant workers surveyed in CHIP2002, the schooling coefficient at the 75th percentile of their estimate distribution (6.76%) is more than twice as large as it is at the 25th percentile (2.74%). To provide a clearer and more comprehensive picture, we do the following. First, we check whether the schooling coefficient distributions we obtain can be characterized as normal distributions. For this purpose, we use two normality tests by Shapiro and Wilk (1965) and Shapiro and Francia (1972). Both the Shapiro Wilk test (p=0.000 for 2002; p=0.000 for 2007) and the Shapiro Francia test (p=0.000 for 2002; p=0.001 for 2007) show that the schooling coefficient estimate distribution for each year does not follow the normal 16

18 Kernel Density Schooling Coefficient Estimates Figure 1: Kernel Density Plots of Schooling Coefficient Estimates Returns to Schooling All migrants 2002 Male migrants 2002 Female migrants 2002 All migrants 2007 Male migrants 2007 Female migrants Percentile Figure 2: Heterogeneous Returns to Schooling among Chinese Rural Migrants in 2002 and

19 distribution. The kernel density plots of schooling coefficient estimates in Figure 1 confirm this finding. Second, for every combination of year and gender, we plot the coefficient estimate on schooling corresponding to each percentile of the estimates distribution in Figure 2. Heterogeneous impacts of schooling on wages are evident for each group we have examined. The statistics used to describe the schooling coefficient distributions (N P mean, Q10, Q25, Q50, Q75 and Q90) in Table 3 literally reveal three main patterns in the presence of heterogeneous effects of education on wages: (i) The schooling coefficients are larger in 2007 than in 2002 for the pooled sample (males and females); (ii) Women are more rewarded for an additional year of schooling in 2007 than 2002, while male migrants have higher schooling returns to 2002 than in2007; (iii) The schooling coefficients are larger for male migrants than for female migrants in 2002, while the coefficients are larger for females than for males in However, the comparison of a few statistical values of two schooling coefficient distributions does not come to the conclusion that there are ranking/ordering between the two distributions. Using a statistical test developed by Abadie (2002), we first test the null hypothesis of equal schooling coefficient distributions between gender and year subgroups. Once it has been determined that the coefficient distribution for one group is different from the another, we use the first order stochastic dominance test to check whether there are any orderings or rankings of schooling coefficient distributions between different subgroups. Table 5: Stochastic Dominance Tests ED FSD B 2007 A / B 2002 A B F 2007 / B F B M 2002 / B M B M 2002 / B F B F 2007 / B M N ote: Reported p values are obtained via bootstrapping with 300 replications. ED denotes equality of distributions. FSD denotes first order stochastic dominance. The test results are displayed in Table 5. We use B g y to denote the coefficient distribu- 18

20 tion for year y and group g, where y=2002, 2007 and g=f (female), M (male) and A (all). When testing stochastic dominance, BA 2007 / B 2002, A for example, means the null hypothesis is that the distribution of schooling coefficients for the 2007 sample first order stochastically dominates the coefficient distribution for the 2002 sample. The null hypothesis is rejected if the p value obtained is smaller than some significance level α (0<α<0.5). We can easily reject equality of distributions at conventional test levels for each case in Table 5. Significant differences or changes in schooling coefficients are found for every two subgroups that we have compared. In terms of rankings, we find strong evidence of first order stochastic dominance of one group over the other for each of the five cases. These ordering results for distributions are much stronger than what can be concluded from just literally comparing the few statistical values of schooling returns between different subgroups. For example, we find that people enjoyed higher returns to education in 2007 than in 2002 at the 10th, 25th, 50th, 75th and 90th percentiles as well as at the mean of the schooling coefficient distribution. The stochastic dominance test provides further evidence that for every point β A in the union support of BA 2002 and B 2007, A the proportion of people with schooling returns exceeding β A in 2007 is always at least as large as that in 2002, with strict inequality holding for some points. To make this point more clear, I graphically illustrate this ordering relation in Figure 3, in which the cumulative distribution of schooling coefficients for 2002 almost never lies below that for Similarly, we find that the schooling coefficient distribution for female migrants in 2007 dominates the corresponding coefficient distribution in 2002 in the first order sense, indicating a trend of rising returns to education among female rural migrants. However, we find that male migrants coefficient distribution in 2002 first order stochastically dominates males distribution of heterogeneous returns to education in 2007, which indicates that the returns to schooling for male migrant workers have diminished over time. Finally, while the returns to schooling among female migrant workers are lower than those among male migrants in 2002, we find that female migrants returns to education have superseded and first order stochastically dominated male migrants schooling coefficients in Female urban workers are generally found to enjoy higher returns to education than 19

21 Figure 3: Cumulative Distributions of Schooling Coefficients for 2002 and 2007 male workers during China s economic transition (Li, 2003; Zhang et al., 2005), however, it is not true for China s migrant workers. 5.2 Schooling Coefficients by Education Level In this section, we summarize the first, second and third quartile rates of schooling return (Q25, Q50 and Q75) for subgroups defined by education level, and the results are reported in Table 6. In terms of the results for each education level, we find that the schooling rates of return tend to be higher among rural migrants with higher education attainments. For example, the median value of the schooling coefficients for male migrants in 2007 is for individuals with primary school education or below. The value is for male migrants with junior high school education and for men with senior high school education or above. As discussed in the previous section, the comparison of a few statistical values from two estimate distributions does not necessarily mean that there is ordering/ranking between the two coefficient distributions. We use the stochastic dominance test to formally check whether the returns to education indeed increase with education levels in the presence of heterogeneous returns. The results are displayed in Table 7. 20

22 Table 6: Nonparametric Estimates of Returns to Education by Education Levels Male Migrants Female Migrants Q25 Q50 Q75 Q25 Q50 Q75 Q25 Q50 Q75 Q25 Q50 Q75 Education level: Primary school or below Junior high school Senior high school or above Note: All the estimates are significant at the 5% level. 21

23 Table 7: Stochastic Dominance Test Results for Education Levels Male Migrants Female Migrants ED FSD ED FSD ED FSD ED FSD Education level: Junior high school/primary school or below Senior high school or above/junior high school N ote: Reported p values are obtained via bootstrapping with 300 replications. ED denotes equality of distributions. FSD denotes first order stochastic dominance. When testing first order stochastic dominance, A/B means that the null hypothesis is that distribution A first-order stochastically dominates distribution B. 22

24 We can easily reject the equality of schooling coefficient distribution between different education levels for each gender and year. We find that an additional year of education will lead to higher wage levels among rural migrants with higher educational attainments. For example, the schooling coefficient distribution for male migrants with senior high school education or above first order stochastically dominates the coefficient distribution for male migrants with junior high school education in 2007 (p value=0.7238). The p value is for female migrants. Similar results are also found for year This result means that if the government can implement some policy aiming at increasing rural migrants education levels, their wages will increase in a more rapid way, which can help reduced the wage disparity between rural migrants and urban residents in China s urban labor market (Meng and Zhang, 2001; Demurger et al., 2009). The gender and year patterns in returns to education displayed in Table 6 can also explain the evolution of gender wage differentials among rural migrants during China s economic transition. As displayed in Table 1, the average gender wage differential among rural migrants was 27% (= ) in 2002, and the wage gap decreased to 16% (= ) in Table 1 also shows that in 2002, male migrants have about one more year of schooling than female migrants. As Table 4 and Table 6 show that male migrants are more rewarded for education than female migrants in 2002, the one more year of schooling will lead to greater gender wage differentials between the two genders. However, the patterns have changed in There are very small difference in the years of education between the two genders. In terms of education levels, there is even a smaller proportion of individuals with primary school education or below among female migrants than male migrants. As female migrants enjoy higher returns to education in 2007 than males, and this help narrow down the average gender wage gap among rural migrants from 27% in 2002 to 16% in In this sense, the increase in the rural migrants education attainments can not only decrease the wage gap between rural migrants and urban residents (Meng and Zhang, 2001; Demurger et al., 2009), but also reduce the gender wage differentials among Chinese rural urban migrants (Magnani and Zhu, 2012). The above analysis of returns to education among rural migrants assumes that an 23

25 individual has the same rate of return for different levels of education, although the rate of return can vary with individual. Now we consider the case where the returns to schooling can differ at different levels of education for the same individual. The interesting case we consider is whether years in senior high school make a difference to the schooling returns. 14 de Brauw and Giles (2008) show that there is a significant negative relationship between migrant opportunity and high school enrollment in China. If the returns to education for senior high school education are larger than the returns for primary school and junior high school education, the decision of a rural individual to migrate to and work in urban areas after finishing the 9 year compulsory education can lead to a significant loss of lifetime earning ability. For this purpose, we rerun the nonparametric regression with the same set of controls as in Equation (6) while focus on two new measures of schooling: Min{S i,9} and (S i 9)*T i, where Min{S i,9} denotes the smaller value between S i and 9, and T i is a dummy variable that equals to 1 if S i is greater than 9 and zero otherwise. As junior high school education generally requires 9 years to finish in China, Min{S i,9} measures the number of years receiving primary and junior high school education. (S i 9)*T i measures the numbers of years receiving education in senior high school or above. 15 We use β 1i and β 2i to denote the coefficients of Min{S i,9} and (S i 9)*T i for individual i, which respectively estimate the return to primary and junior high school education (β 1i ) and the return to senior high school education or above (β 2i ). Estimation results of the first, second and third quartile rates of schooling return (Q25, Q50 and Q75) are presented in Table 8. We find that the returns to an additional year of schooling are higher at senior high school and above than the returns at the primary school or junior high school. For all migrant workers, in 2002, the median schooling return is for junior high school and below, and is for senior high school and above. In 2007, the median value of β 1i is and the median of β 2i is The higher education returns for senior high school education and above show that when a rural individual choose urban employment 14 We thank the anonymous referee for this suggestion. 15 (S i 9)*T i equals to zero if an individual has not finished junior high school education, and it is equal to (S i 9) is an individual has received some education after junior high school. 24

26 over more investment in education after finishing the nine year compulsory education, it involves a trade off between a significant loss of higher lifetime earning potential and the short run benefits of wage employment in urban China. 5.3 Schooling Coefficients for Other Selected Subgroups In this section, we summarize the first, second and third quartile rates of schooling return (Q25, Q50 and Q75) for selected subgroups defined by age group, employer ownership and region in Table 9. The results found for the whole sample in Section 5.1 generally hold for each subgroup. We observe decreasing returns among male migrant workers from 2002 to 2007, while female migrants returns to education have increased over time. While female migrants schooling coefficients are lower than males in 2002, the returns are higher for female workers than male workers in 2007 for each subgroup Age The results for different age groups displayed in Table 9 shows that newer labor market entrants generally are more rewarded for their education than older migrant workers. The stochastic dominance test results in Table 10 confirm the evidence of higher returns to education among younger migrant workers in the presence of individual level heterogeneity. This result is consistent with our finding for different education levels, as younger workers generally have more years of schooling than older migrant workers under the background of China s constant expansion of public education (Hawkins, 2000; Hannum et al., 2008) Employer Ownership The public private sector differences in returns to education within each gender group of rural migrants are small, as shown in Table 9. In Table 10, we cannot reject the null hypotheses that the schooling coefficient distributions in the private and public sectors are equal distributions for each gender group in In 2007, we find some weak evidence that the schooling coefficients in private and public sectors are not equal at the 10% level. However, we do not find any rankings/orderings among the schooling coefficient 25