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Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. evaluations of the effects of labour market policies, studies of the functioning of the labour market and evaluations of the labour market effects of measures within the educational system. Besides research, IFAU also works on: spreading knowledge about the activities of the institute through publications, seminars, courses, workshops and conferences; creating a library of Swedish evaluational studies; influencing the collection of data and making data easily available to researchers all over the country.
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Terms of use:
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IFAU also provides funding for research projects within its areas of interest. There are two fixed dates for applications every year: April 1 and November 1.
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Since the researchers at IFAU are mainly economists, researchers from other disciplines are encouraged to apply for funding.
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IFAU is run by a Director-General. The authority has a traditional board, consisting of a chairman, the Director-General and eight other members. The tasks of the board are, among other things, to make decisions about external grants and give its views on the jameshudson@example.net. A reference group including representatives for employers and employees as well as the ministries and authorities concerned is also connected to the institute. young people in urban areas of six provinces of China. The effect of college on those who go is 13%. Our evidence, and simple least squares evidence, suggests that after 20-plus years of economic reform with market orientation, the return to education has increased substantially in China, compared to the returns measured in the 1980's and the early 1990's.

The Institute for Labour Market Policy Evaluation (IFAU) is a research institute under the Swedish Ministry of Industry, Employment and Communications, situated in Uppsala. IFAU's objective is to promote, support and carry out: evaluations of the effects of labour market policies, studies of the functioning of the labour market and evaluations of the labour market effects of measures within the educational system. Besides research, IFAU also works on: spreading knowledge about the activities of the institute through publications, seminars, courses, workshops and conferences; creating a library of Swedish evaluational studies; influencing the collection of data and making data easily available to researchers all over the country.

IFAU also provides funding for research projects within its areas of interest. There are two fixed dates for applications every year: April 1 and November 1. Since the researchers at IFAU are mainly economists, researchers from other disciplines are encouraged to apply for funding.

IFAU is run by a Director-General. The authority has a traditional board, consisting of a chairman, the Director-General and eight other members. The tasks of the board are, among other things, to make decisions about external grants and give its views on the jameshudson@example.net. A reference group including representatives for employers and employees as well as the ministries and authorities concerned is also connected to the institute. Papers published in the Working Paper Series should, according to the IFAU policy, have been discussed at seminars held at IFAU and at least one other academic forum, and have been read by one external and one internal referee. They need not, however, have undergone the standard scrutiny for publication in a scientific journal. The purpose of the Working Paper Series is to provide a factual basis for public policy and the public policy discussion. ISSN 1651 ISSN -1166 
Introduction
Heterogeneity and missing counterfactual states are central features of microdata. Due to unobserved heterogeneity, observationally identical people make different choices, earn different wages and hold different levels and compositions of asset portfolios. The evaluation problem for social programs arises from a missing data problem. We cannot observe the outcomes of all possible choices for the same person. If we observe wages for college graduates, we cannot observe the wages they would have earned if they had been high school graduates.
Introduction
Conventional approaches to selection and missing data problems do not account for heterogeneity in responses to schooling on which agents select into schooling. This paper uses newly released cross-sectional micro data from the China Urban Household Investment and Expenditure Survey (CUHIES 2000) , to estimate the return to education for China when responses to schooling differ among individuals and individuals select into schooling based their idiosyncratic returns. Our work draws on previous research by Heckman and Vytlacil (1999 , 2000 , Carneiro, Heckman and Vytlacil (2001) and Carneiro (2002) , which develops a semiparametric framework that accounts for heterogeneity and selection. 1 Our results reveal that the average treatment effect (ATE) of four year college attendance (the earnings gain arising from randomly selecting someone to go to college for four years), is 43% (the annual return is 10.8%) in 2000 for young people in urban areas of six provinces of China, whereas the OLS (Ordinary Least Squares) and IV (Instrumental Variables) estimators give 29% and 56% respectively (with estimated annual returns of 7.25% and 14% respectively). Heterogeneity in returns is substantial in the population. Estimated selection bias is an empirically important negative 22%. Like Carneiro, Heckman and Vytlacil (2001) , we find that there is comparative advantage in the labor market for schooling. The best college graduates are among the worst high school graduates. OLS gives a downward-biased estimate of ATE . IV produces an upward biased estimate of ATE . 1 The MTE is the central concept in this literature. It was introduced by Bjorklund and Moffitt (1987) . The marginal treatment effect is the average return to schooling for persons indifferent to going on to schooling at different levels of unobservable factors that determine schooling choices. Heckman and Vytlacil (1999 , 2000 show that all conventional treatment parameters are different weighted averages of this parameter.
Introduction
After more than twenty years of economic reform with market orientation, the average return to education in China measured by OLS or ATE has increased markedly when compared to those in the 1980's and early 1990's. (Chow 2001 presents estimates of OLS-generated rates of return in this period). Education markets have begun to function effectively in China, and skills are now being rewarded more adequately than they have been in the past.
Introduction
The paper is organized in the following way. Section 2 describes earnings models with and without heterogeneous returns to education. Section 3 defines selection bias, defines the marginal treatment effect and presents a semiparametric method for estimating it. Section 4 discusses our data and presents empirical results for China. Section 5 concludes.
Models with and without Heterogeneity
We first consider a conventional model of the return to education without heterogeneity in returns. We write the following common coefficient Mincer model:
Models with and without Heterogeneity
where i is a subscript for individuals ( n , , 2 ,
Models with and without Heterogeneity
S is schooling level or years of schooling, i X is a vector of variables such as an intercept, years of Mincer experience, Mincer experience squared, and dummy variables for sex, region, sector, and ownership of firm. i U is the residual term with
Models with and without Heterogeneity
, β is the rate of return to education, and γ is a vector of coefficients.
Models with and without Heterogeneity
One problem with OLS (Ordinary Least Squares) estimates of Equation (1) The specification we consider is more general than the model (1). We estimate a model with heterogeneous returns to education, which may be written in random coefficient form as
Models with and without Heterogeneity
where i β is the heterogeneous rate of return to education, which varies among individuals. i X is a vector of conditioning variables defined below. This model accounts for ability bias in a more general setting.
Models with and without Heterogeneity
In this paper we focus on two schooling choices: high school and college. We let 1 = i S denote four-year college graduates and 0 = i S for senior high school graduates (those not going to college). Clearly, there are more choices of schooling and our analysis is a simplification of reality, but is a natural starting point with ample precedents in the literature. There is considerable evidence in many contexts that returns to schooling are nonlinear in years of schooling so conventional log wage on years of schooling regression coefficients generate rates of return that are badly biased estimates of the return to college education. (Heckman, Lochner and Todd, 2003) .
Models with and without Heterogeneity
The two potential selection outcomes ) ln , (ln 
Models with and without Heterogeneity
such as a genetic twin or sibling with similar or identical ability. A third approach is to use proxy variables for ability and include them as regressors in i X .
Models with and without Heterogeneity
Many data sets do not have enough information to use the fixed effect method, and the method is critically dependent on additive separability of errors. Such comparisons may exacerbate measurement error problems. 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. (See Carneiro and Carneiro, 2002 ).
Models with and without Heterogeneity
An alternative method uses proxies for ability and includes them as the regressors. Many empirical analyses reveal that better family background and better family resources are usually associated with better environments that raise ability (Carneiro and Heckman, 2003) . We use parental income as a proxy for ability in our empirical work.
Models with and without Heterogeneity
In a cross section it is usually impossible to know both 
Models with and without Heterogeneity
. In the presence of heterogeneity and selection in general, we can no longer use conventional methods like OLS or Instrumental Variables (IV) to identify economically interesting parameters.
Models with and without Heterogeneity
Collecting results
Models with and without Heterogeneity
is the heterogeneous return to education for individual i . When 0 1 γ γ ≠ (i.e. there is an observed heterogeneity
Models with and without Heterogeneity
there is an unobserved heterogeneity term ) (
Models with and without Heterogeneity
β varies in the population, the return to schooling is a random variable with a distribution. In the first case where we condition on X, the distribution of returns is degenerate. In the second case it is not degenerate. The mean of i β given X is:
Models with and without Heterogeneity
Suppose individuals select going to college (or not) according to the following decision rule:
Models with and without Heterogeneity
where * i S is a latent variable denoting the net benefit of going to school and i Z is an observed vector of variables
Models with and without Heterogeneity
is the propensity score or probability of receiving treatment (going to college), which can be estimated by a logit or probit model. si U is the unobserved heterogeneity for individual i in the treatment selection equation.
Models with and without Heterogeneity
Without loss of generality we may assume that (See Heckman and Vytlacil, 1999 . According to Equations (3a), (3b) and (5),
Models with and without Heterogeneity
, is the causal effect of education. Using equations (3a), (3b) and (6), the probability limit of the ordinary least squares estimator can be written as:
Models with and without Heterogeneity
where ATE is the average treatment effect, (the effect of randomly assigning a person with characteristics X to schooling) defined as
Models with and without Heterogeneity
If agents know and act on some components of
Models with and without Heterogeneity
S is generally correlated with both i U 0 and i U 1 , and the second term in Equation (8) will be not zero, so OLS is biased for ATE .
Models with and without Heterogeneity
Note that Equation (8) can also be written as:
Models with and without Heterogeneity
where TT is treatment on the treated, the effect of treatment on those who receive it (e.g., goes to college) compared to what they would experience without treatment (i.e., do not go to college), defined as:
Models with and without Heterogeneity
The sorting effect 1 0 ( 1 )
Models with and without Heterogeneity
is the mean gain of the unobservables for people who choose "1".
Models with and without Heterogeneity
The selection bias 
Models with and without Heterogeneity
where
Models with and without Heterogeneity
is the propensity score. In the presence of both heterogeneity and selection bias,
Models with and without Heterogeneity
is dependent on S i , so the second term in Equation (12) will be not zero, thus
Models with and without Heterogeneity
is not a consistent estimator. Only in some very special circumstances, when 0
Models with and without Heterogeneity
unobserved heterogeneity nor selection bias exist) or when
Models with and without Heterogeneity
is unobserved heterogeneity but no selection bias), will the second term in Equation (12) be zero. In this case, IV is a consistent estimator for ( ) X β (Heckman, 1997 and Heckman and .
Models with and without Heterogeneity
Neither OLS nor IV is a consistent estimator of the mean return to education in the presence of heterogeneity and selection. However, under the assumptions presented in Heckman and Vytlacil (1999 , 2000 , Carneiro, Heckman and Vytlacil (2001) , Carneiro (2002) and Navarro-Lozano (2002) , it is possible to identify the heterogeneous return to education with marginal treatment effect ( MTE ) via the method of Local Instrument
Models with and without Heterogeneity
Variables ( LIV ), where MTE is:
Models with and without Heterogeneity
The MTE is the average willingness to pay (WTP ) for 
Models with and without Heterogeneity
For notational simplicity, we keep the conditioning on X implicit in what follows. Heckman and Vytlacil (1999 , 2000 and Carneiro (2002) establish that all the other treatment variables can be unified using MTE Where the weights are:
Models with and without Heterogeneity
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 to what they would experience with the treatment (i.e. go to college), which is defined as:
Models with and without Heterogeneity
. Table 1 provides the comparison of average resident income in urban areas among these provinces. The average resident incomes in the three provinces, Beijing, Guangdong and Zhejiang, are much higher than the average level of China, while they are a bit lower in the other three provinces, Sichuan, Liaoning and Shaanxi. The average income in the six provinces we use is 7627 yuan, which is higher than the average income of China, 6280 yuan.
Models with and without Heterogeneity
The sample size for the six provinces is 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.
Models with and without Heterogeneity
For our purposes, we combine all the children in the six provinces who are either college or university graduates or senior high school graduates. They are all working and earn positive wages in 2000. Our sample consists of 587 individuals, including 273 people with four-year college (or university) certificates and 314 people with only senior high school certificates. There are 331 males and 256 females in the sample. The summary statistics for the variables used in our analysis are reported in Table 2 , which reveals the individuals in the sample are mainly young adults with a mean age of 26.3. Thus ours is an analysis of wages early in the life cycle of new cohorts of Chinese workers. Table 3 presents OLS and IV estimates of the mean return to four-year college attendance. We use the probability of going to college as the instrument with the exclusions defined below. The OLS and IV estimates are 29% and 56% respectively for the young people in the urban areas of six provinces of China in 2000 (annualized 7.25% and 14%, respectively). The OLS estimates are much higher than the OLS estimates reported by Chow (2001) for an earlier period (1980's and early 1990's). The variables in the outcome equation include the years of Mincer experience, Mincer experience squared, our proxy of ability (we use parental income as the proxy in this paper) and some dummy variables such as the sex, the provinces of residence, the sector and the firm ownership in which he or she works. The propensity score is estimated by a logistic model, with coefficient estimates presented in Table 4 . 4 We use father's education, mother's education, parental income, and the year of birth as determinants of the probability of going to college. The last column of the table is the mean marginal effect for each explanatory variable. Figure 1 shows the density function for the estimated probability of college attendance (Pr( 1)) S = . Table 5 and Figure 2 give the results from our semiparametric estimation. We use parental income in the earnings function to control for ability. For details on the procedures used to generate these numbers see Carneiro, Heckman and Vytlacil (2001) , whom we follow. Table 5 contains the estimated coefficients for Equations (3a) and (3b) using local linear regression. Heckman, 2001 or Heckman and . It also suggests that the marginal participant in Chinese higher education earns less than the average participant. Table 6 presents a comparison among various treatment parameters. The average return to 4-year college attendance for a randomly selected person is 43% (11% annually) given by ATE . The effect of going to college 4 The general forms of the logistic model and the marginal effects derived from it are defined as:
Models with and without Heterogeneity
on those who go is 51%, so there is purposive sorting into schooling on the basis of gain (13% annual). The OLS estimator is downward biased for ATE with only a 29% return (7% annual). The inconsistent IV estimator is 56% and is upward biased due to heterogeneity and selection bias (Heckman and Vytlacil derive the exact bias). The Chinese data set show that OLS ATE IV > > . The estimated selection bias of -22% is very important in estimating the economic return to schooling for China. Persons who go to college would make poor high school graduates. Treatment on the treated ( TT ) and treatment on the untreated ( TUT ) are 51% and 36% respectively.
Models with and without Heterogeneity
Thus IV is upward biased for TT.
Models with and without Heterogeneity
The estimated sorting gain is large and positive, suggesting that the principle of comparative advantage is important. The "sorting gain" reported in Table 6 is defined as: This is also revealed in the Table 6 . There is substantial heterogeneity among individuals and there is a positive sorting gain and a negative selection bias.
Models with and without Heterogeneity
In order to test the importance of introducing a proxy for ability in the wage equation, we exclude parental income from the wage equation and re-estimate the marginal treatment effects. The results are displayed in Figure 4 . In this case, the MTE increases in s u and its average value is obviously much higher than that in Figure 2 . Therefore, neglecting ability (or its proxy) results in an upward bias for the marginal treatment effect and the estimated return to schooling.
Models with and without Heterogeneity
To explore the sensitivity of the estimates to various exclusions and inclusions, we present the estimates shown in Tables 7(a Our main specification conditions on sectoral choices including the ownership structure of the firm. As is well known, conditioning on sectoral choices in the wage equation is likely to lead to an understatement of the full return to schooling because one benefit of education is that it facilitates choice of sector. When we drop various firm ownership and sectoral indicator variables, estimated returns go up (see Table 7d for estimates deleting all sectoral choice and ownership variables). This is clear from Figure 5 . However, the effect of including or excluding these variables is very small on estimated marginal treatment effects. Failing to condition on ability (parental income) raises the estimated return to implausible levels and changes the shape of the estimated MTE.
Models with and without Heterogeneity
This evidence is consistent with the findings of Carneiro (2002).
Concluding Remarks
This paper uses newly available micro data to identify the returns to higher education in China. We demonstrate the importance of considering heterogeneity and selection bias. Neglecting these two factors 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.
Concluding Remarks
Excluding it leads to implausibly high estimates of the return to schooling. On the other hand, controlling for sectoral choices barely budges the estimates.
Concluding Remarks
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 returns to those going to college are even higher. These estimates are all higher than the conventional OLS estimates of the Mincer model, which in turn are higher than the OLS estimates reported for earlier time periods. They imply that, after 20-plus years of economic reform with market orientation, the average return to education in China has increased substantially when compared to those in the 1980's and early 1990's. 

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