The Causal Effect of Education on Wages: Evidence from China’s Rural Industry

Haizheng Li &

Aselia Urmanbetova

School of Economics Georgia Institute of Technology

Atlanta, GA 30332-0615 Phone: 404-894-3542 Fax: 404-894-1890

E-mail: haizheng.li@econ.gatech.edu

_______________________ * The corresponding author: Haizheng Li, School of Economics, Georgia Institute of Technology, Atlanta, GA 30332-0615, Phone: 404-894-3542, Fax: 404-894-1890, E-mail: haizheng.li@econ.gatech.edu

The Causal Effect of Education on Wages: Evidence from China’s Rural Industry

Abstract Estimating the causal effect of education on earnings continues to pose econometric challenges because of the unobserved ability heterogeneity and the possible attenuation bias caused by measurement errors. In this study, we used household survey data to investigate the effect of education on earnings in China’s rural industry by controlling for such biases. We identified a unique instrument based on the Chinese culture. In particular, because of the cultural preference for boys in rural China, the existence of brothers has a negative effect on the education attainment of a girl. However, such circumstances presumably have no effect on the girl’s inherent ability. Therefore, the sibling information can be used as an instrument to correct for the omitted ability bias. Moreover, we are able to assess the effect of measurement errors based on the information in the data. In addition to the regular 2SLS method, we also apply the more efficient GMM method in the estimation, and conduct statistical tests on the validity of family background variables as instruments. Based on the sample used, we find no significant attenuation bias in the OLS estimation, but the omitted ability bias appears to be substantial and overestimates the rate of return. While the OLS estimation gives a return of 7.1% for women, the results from Instrumental Variable estimations indicate that education has an insignificant effect on wages in China’s rural industry. J. E. L Code: I21, J31 Key Words: Returns to schooling, Measurement error, Omitted Ability Bias, China.

I. Introduction

The study of economic returns to education plays an important role in modern

labor economics. Recently, much of the research has been focused on the “ability bias”

in the Ordinary Least Squares (OLS) estimation. One direction of the research is to apply

Instrumental Variable (IV) estimation to control for the omitted ability bias by exploring

new instruments. For example, Ashenfelter and Zimmerman (1997) use parental

education; Butcher and Case (1994) use the presence of any sister within a family; and

Card (1995) uses geographic proximity to a four-year college as instruments.

However, many studies find that the OLS estimation also suffers from attenuation

bias caused by measurement errors, which are common in reporting years of schooling.

Griliches (1977), Angrist and Krueger (1991), and Ashenfelter and Kruger (1994)

suggest that the omitted ability biases in the OLS estimates are relatively small, but the

downward bias due to measurement errors could be sizeable. Since the omitted ability

bias causes an overestimation while measurement error causes an underestimation, an

OLS estimate of return to education can bias in either way, i.e., either overestimates or

underestimates the true return, depending on the relative magnitudes of these biases.

The question of the effect of education on earnings in China has drawn an

increasing interest among researchers.1 However, all existing studies on returns to

education in rural China rely on the OLS estimation. These studies offer a range of

estimated returns. For example, Gregory and Meng (1995) report a return of 1.1% based

on 529 workers from township and village enterprises (TVEs). Johnson and Chow

(1997) find a return of 4.02% using a sample of 1,626 workers. Meng (1998) finds a

1 See Li (2003) and references therein for list of studies investigating the effect of education in urban China.

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return of 1.8% for women and only 0.7% (and statistically insignificant) for men. Wei et

al (1999) report the highest return of 4.8%. There rates are very low compared with the

10.1% world average and the 9.6% Asian average (Psacharopoulos, 1994).

Since these studies are all based on the OLS method, the extent to which the

estimated returns to education in rural China are affected by possible attenuation and

omitted ability biases remains to be undetermined. The goal of this study is to investigate

these biases and to provide a more accurate picture of the effect of schooling in wage

determination in China’s rural industry. Additionally, the results are useful in assessing

the net bias in the reported OLS estimates.

In order to control for the omitted ability bias, we identify a novel instrument

based on the unique Chinese culture. Specifically, because of the strong cultural

preference for boys in a family, especially in rural China, the existence of brothers should

have a negative effect on the educational attainment of girls. However, based on a

standard natural experiment argument, such circumstances presumably have no effect on

the girls’ inherent ability. Thus sibling composition can be used as an instrument to

control for the omitted ability bias in estimating the casual effect of education on

earnings.

In today’s China more than 807.39 million people, or 63.91 percent of the total

population, live in the countryside.2 Since the start of economic reform in 1978, the

Chinese rural sector has undergone substantial transformations. A major change has been

2 “Major Figures of the 2000 Population Census,” National Bureau of Statistics of People’s Republic of China, March 28, 2001, available at: http://www.cpirc.org.cn/e5cendata1.htm.

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the rapid growth of township and village enterprises (TVEs) in rural areas. In 1995,

TVEs contributed 56% to overall national industry output.3

The economic reward to education has important implications on attracting

human capital to China’s rural industry. And the amount of human capital affects the

sustainability of the long term growth of the TVE sector. In addition, millions of farmers

move to urban areas to seek jobs every year. The return to schooling in rural areas will

also influence the migration decision of the relatively educated individuals. Therefore, an

accurate assessment of the effect of education in wage determination has important policy

implications for China’s rural industry and rural development.

In general, in order to control for the omitted ability heterogeneity and the

attenuation bias, IV estimation is applied as an alternative to the OLS method. Using

different instruments, we apply IV techniques, including the more efficient Generalized

Method of Moments (GMM) method, to estimate the return to education in China’s rural

industry. In addition, we conduct statistical tests on the validity of various instruments.

Based on our sample, we find that the attenuation bias from measurement error is

negligible. However, the omitted ability bias is substantial. The OLS estimation gives a

return of 7.1% for women, the results based on IV estimations, however, indicate an

insignificant effect of education on wages in China’s rural industry. In addition, our tests

reject parental education variables, which are commonly used in IV estimations, as valid

instruments. On the other hand, our results confirm that the existence of brothers has

negative effect on a girl’s education attainment. And statistical tests do not provide any

evidence against the use of this sibling variable as an instrument.

3 Ma, J. (January 1997), China’s Economic Reform in the 1990’s, available at: http://members.aol.com/junmanew/chap4.htm.

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The rest of the paper is organized as follows. Section II discusses the empirical

methods and data. In Section III we investigate measurement error and its attenuation

effect. Then we use parental education as instruments and test their validity in Section

IV. In Section V, we employ a new instrument based on sibling composition in a family

to estimate the return to education for female workers. Section VI concludes.

II. Empirical Methods and Data

The most commonly used empirical model for estimating returns to schooling is

the following Mincerian-type (Mincer, 1974) earnings function,

Log Yi = β0 + β1Si + β2Expi + β3Expi2 + εi,

where Yi is the earnings, Si is years of schooling, and Expi is years of labor market

experience. Additionally, various control variables are usually included such as gender,

ethnicity, etc. Based on human capital theory, wages are determined by human capital.

Schooling and on-the-job training are major types of human capital investment.

Generally, experience is used as a proxy for job-training investment. Wages will reach

their peak when human capital is at its largest. As years of experience increase, human

capital depreciation will eventually dominate accumulation and wage rates will decline.

Thus the wage-experience profile should follow an inverse U-shape in experience.

The Mincerian model is customarily estimated by the Ordinary Least Squares

(OLS) procedure. It is well known that the OLS estimation suffers from the omitted

variable bias caused by unobservable individual ability variables, which may affect an

individual’s wages as well as his/her schooling level. Since it is likely that an

individual’s ability and education attainment are positively correlated, the omitted ability

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bias will result in overestimating the return. In addition, recent studies find that reported

schooling levels commonly contain measurement errors. In the OLS estimation,

measurement error will cause attenuation bias and result in underestimation.

The omitted ability bias can be illustrated in a simple model. Based on the theory

of schooling choice, at the time t = 0 an individual chooses the level of schooling that

would maximize the present value of her or his life-time earnings:

PV(S,α ) = rSA

S

rt eScdteSy −− −∫ )(),( α

( ) ,)(/1),( )( rSSArrS eScreeSy −−−− −−= α

where S denotes schooling level, α is the ability factor, y(S,α ) refers to the average level

of earnings per year with the education of S, c(S) is the direct cost associated with

schooling level S when a person completes her or his schooling at t = S, A indicates

maximum working age, and r is the discount rate.

For any particular level of schooling, a person with greater ability is more likely

to attain it. That is, for a given S>0, *a≥α is required, where *α is a cut-off value of

ability and ),( *αSy ( )(1 SAre −−− ) = r )(Sc . With any given ability *a≥α , an individual

would prefer a higher level of schooling if additional schooling increases the value of the

present value of earnings. Such optimizing behavior creates a positive correlation

between ability and schooling. As a consequence, the OLS will overestimate the true

return because an individual’s ability is unobservable. To eliminate omitted ability bias

and the attenuation bias, IV estimation is commonly used. The challenge, however, is to

find a right instrument that is correlated with schooling but uncorrelated with the ability.

Depending on the relative magnitude of these biases, the resultant IV estimates could be

either larger or smaller than the original OLS estimates.

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The data set for this study is from the second wave of the Chinese Household

Income Project (CHIP) for 1995. We use the rural part of the survey, which contains

information on 34,739 individuals from 19 provinces.4 We restrict our sample to those

who engaged in non-agricultural work and report their actual working hours and monthly

income (wages and bonuses) from their work units.5 Since many rural people worked in

urban areas on a temporary basis through migration, it is possible that temporary migrants

might have reported their non-farming income earned in urban areas. Such a situation

may mix the rate of return to schooling in urban areas with the returns in rural areas, and

thus obscure the true education effect in rural industry. Therefore, in our sample we

eliminate those respondents who reported working in a city for at least one month.6 The

resultant sample consists of 1,182 workers, with 36.6% females. The average schooling

level is 8.28 years, which corresponds to the lower middle school level. Descriptive

statistics are reported in Table 1.

Previous studies on returns to education in rural China rely on either annual or

monthly income. A potential problem with using such measures of income is that the

actual working hours remain unaccounted for. Generally, in China hours worked are

directly related to educational attainment, for example, workers with less education work

longer hours. In our sample, the simple correlation between years of schooling and

monthly work hours is –0.12 and highly significant. Thus, those with less education earn

additional income through extra working hours. As a result, the OLS estimation suffers

4 The provinces covered in CHIP-1995 include: Beijing, Hebei, Shanxi, Liaoling, Jilin, Jianso, Zhejiang, Anhui, Jiangxi, Shangdong, Henan, Hubei, Guangdong, Sichuan, Guizhou, Yunnan, Shaanxi, and Gansu. 5 In CHIP-1995, the question defined such groups as those, “who were involved in non-agricultural activities for three months or more in 1995.” 6 We do not exclude those migrants who work in another rural area. We also dropped nine observations with reported monthly incomes above 5,000 yuan, which is about eight standard deviations away from the mean. These individuals could be enterprise owners and their reported wages may include profits.

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from the bias caused by omitted working hours. Since CHIP-1995 data provide

information on hours worked, we can calculate actual hourly wage rates to eliminate this

bias. The hourly wage rate is calculated using reported monthly income (including

wages, bonuses, etc, from the work unit) and average monthly work hours.7 In the

sample, the average hourly wage rate is 3.11 yuan.

For information on schooling, CHIP-1995 data provide both reported years of

schooling and educational degrees/levels received. Thus, we can also estimate the years

of schooling based on the degree received, and use it as a second measure of schooling to

investigate the effect of measurement errors. Finally, CHIP-1995 provides information

on non-agricultural experience. Based on the Mincer human capital model, experience is

a proxy of human capital acquired through job-training. Thus, for the industrial sector,

non-farming experience should be most relevant to the model. Some previous studies,

such as Johnson and Chow (1997) and Wei et al (1999), use experience estimated with

age and years of schooling. Such an estimate of work experience does not differentiate

between different types of work that a person may have performed over her or his

lifetime, and thus obscures the true effect of experience on earnings.

III. The Attenuation Bias

In the OLS procedure, if the attenuation bias dominates, then the resultant OLS

estimate will underestimate true returns; and if the omitted ability bias dominates, the

OLS will overestimate the true return. Many studies find that the attenuation bias is

larger than the ability bias. For instance, Card (1995) and Ashenfelter and Zimmerman

(1997) find that the use of IV estimation leads to estimates that are at least 15% above the

7 Monthly work hours = average work hours/day × average work days/week × 4.

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corresponding the OLS estimates. Using the urban part of CHIP-1995, Li and Luo

(2003) also find that IV estimation almost doubles the OLS returns.

Therefore, it is desirable to investigate these biases separately in order to estimate

their relative magnitudes. We first assess the extent of attenuation bias. To investigate

the effect of measurement error in schooling levels, a different measure of schooling is

generally needed. For example, Ashenfelter and Krueger (1994) obtain the second

education measure by asking twins to report on both their own and their twin’s schooling

level. In our sample, the second measure of years of schooling is estimated using the

reported education degrees received.8

Suppose S1=S+v1 and S2=S+v2, where S is the true schooling years, S1 is reported

schooling years, S2 is estimated schooling years, and vi (i=1, 2) are measurement errors

that are uncorrelated with S and with each other, the correlation between the two

measures of schooling, S1 and S2, is Var(S)/[Var(S1)⋅Var(S2)]0.5. This ratio is sometimes

called the “reliability ratio.” In this sample, the reliability ratio is 0.87, which indicates

that 13 percent of the measured variance in schooling is error. Based on this ratio, the

degree of measurement error is not very large in this sample.

For the reported years of schooling (S1): the mean is 8.28 years with a standard

error of 2.75 years; and for the estimated years of schooling (S2): the mean is 8.92 years

with a standard error of 2.94 years. In general, the estimated schooling measure S2

should be less accurate than the reported measure S1. Thus the measurement error in S2

8 Based on the Chinese education system structure, the corresponding number of years for different education levels are estimated as follows: 1) for college or above—16 years, 2) for professional school—15 years, 3) for middle level professional, technical or vocational school—12 years, 4) for upper middle school—also 12 years, 5) for lower middle school—9 years, 6) for 4 or more years of elementary education—5 years, 7) for 1-3 years of elementary education—2 years, and 8) for illiterate or semi-illiterate—0 years.

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has a higher variance. It can be shown that, for the true return to schooling β1,

plim(b1)=β1⋅[σu2/(σu

2+σv2)], where b1 is the OLS estimate when schooling is measured

with error, σv2 is the variance of the measurement error, and σu

2 is the variance of the

population error in regressing schooling on other regressors in the earnings equation.

Clearly, the higher is the variance of the measurement error, the larger is the attenuation

bias. Therefore, the schooling measure S2 should result in a larger attenuation bias than

S1. This is confirmed by the result reported in Table 2 (Columns I and II). The estimated

return of 0.71% based on S2 is much lower than 1.4% based on S1.

A simple approach to reduce attenuation bias is to use the average of the two

measures, Sa, to estimate the model.9 In general, if there are sizeable measurement errors

in both schooling measures, the variance of measurement errors in Sa should be smaller.

Thus when using Sa, the attenuation bias will be reduced. On the other hand, if

measurement errors are present only in S2 but not in S1, then the estimate based on Sa will

be attenuated and should be smaller than the estimate based on S1. The resulting estimate

using Sa is 1.1 %, larger than 0.71 % based on S2 and smaller than 1.4 % based on S1.

This result indicates that the degree of measurement error in S1 is small.

If the measurement error in two schooling measures is not correlated, we can

apply IV estimation to remove the attenuation bias by using one measure of schooling as

an instrument for the other one. Since the error in estimating years of schooling based on

the degree received is mostly from the Chinese education system (for example, the

number of years spent obtaining the same degree may vary among individuals, e.g., one

can spend varying years in obtaining a degree from a middle level professional school), it

9 For a new approach to assessing the effect of measurement error in estimating the effect of education, see a recent study by Kane, Rouse, and Staiger (1999).

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is reasonable to assume that the error in estimated years based on reported degrees is not

correlated with the error in reported years of schooling. When using S2 as instrument for

S1, the estimated return is 0.87 percent (Table 2, Column IV), lower than the OLS

estimate using S1. In contrast, when using S1 as an instrument for S2, the resulting IV

estimation gives a return of 1.5% (Column V, Table 2), higher than the OLS estimate

based on S2. This result is consistent with the finding that the measurement error in S1 is

small while in S2 is considerable, because if attenuation bias exists when using S1, the IV

estimation should result in a smaller estimate that the corresponding OLS estimate.

Based on the above results, we think that the measurement error in the reported

years of schooling is small, and thus the resulting downward bias is negligible.

Therefore, it is expected that the OLS estimation will overestimate the true education

effect because of the omitted ability bias, and that the corresponding IV estimates should

be lower. In the next section, we will investigate the magnitude of upward bias caused by

the ability heterogeneity.

IV. The Omitted Ability Bias and Parental Education

In order to correct for omitted ability bias, recent studies adopt the natural

experiment approach and use family background variables as instruments for schooling

level. Parental education is commonly used to control for unobserved ability (Card 1995,

and Ashenfelter and Zimmerman 1997). In our sample, there are 448 workers with

available information on parental education. For this subgroup, the average years of

schooling equals 9.1 and the average age is 23.3 years old. The average level of

education is 4.4 years for mothers and 6.8 years for fathers.

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It is unclear though whether parental education should be used as an instrument or

as a proxy for the unobserved ability variables. Existing studies use it in both ways. If

parental education is used as a proxy (as in Card 1995), it is assumed to be correlated

with an individual’s ability. In other words, parents’ education will influence the

productivity and earning ability of their children. In contrast, when parental education is

used as an instrument (as in Ashenfelter and Zimmerman 1997), it is assumed to be

uncorrelated with the ability of their children but correlated with their education.

If parental education variables are valid proxies for an individual’s ability, the

inclusion of such variables should reduce the upward bias. Table 3 reports the results for

men and women. Columns I and II are the OLS estimates. Notably, the OLS estimates

for men (3.6%) and women (6.8%) are much higher for this younger group. This is

consistent with the finding using CHIP-1995 urban data (Li, 2003), i.e., the return to

schooling is higher for younger people based on the OLS estimation. One explanation is

that, as economic reforms deepen, the return to education rises.

Column III and IV of Table 3 are estimates with the father’s and mother’s

education added as control variables. As expected, the inclusion of parental education

reduces the estimated returns. The decreases, however, are very small: from 3.6% to

3.2% for males and from 6.8% to 6.2% for females.

On the other hand, the results show that maternal and paternal education has

asymmetric effects on earnings. This causes some concern for using parental education

as a proxy for ability. More specifically, for females, the father’s education has a

significant negative effect, -0.047; while the mother’s education has a positive effect,

0.044. For men, although statistically insignificant, both the mother’s and father’s

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education have positive effect, but the difference in the coefficients is drastic, 0.0009 for

mother’s education vs. 0.018 for father’s. If the father’s and mother’s education are good

proxies for an individual’s inherited ability, their effects should be similar. Therefore,

such results cast doubt on the validity of using parental education as a proxy for the

ability of their children. The resulting decrease in estimated returns could be caused by

multicollinearity, as parental education is positively correlated with their Children’s

schooling level.

For this reason, we proceed to use parental education as instruments for schooling

level. The results are reported in Column V in Table 3.10 The IV estimate of the return is

9.6% but insignificant at 10% level. However, the test on over-identifying restrictions

strongly rejects the null (the F-statistic of 5.61 and corresponding P-value of 1.8%.).11

For this test, the null hypothesis is that, if a subset of instruments is valid and identifies

the model, the additional instruments are valid. Since both instruments (paternal and

maternal education) are chosen using the same logic, the rejection of the over-identifying

restrictions test causes serious concerns in using parental education as instrumental

variables. It is likely that both instruments are invalid.

It is possible that other specification problems cause the rejection of the over-

identification test. For example, other explanatory variables may be correlated with the

regression error. In this model, an individual’s non-farming working experience may be

positively correlated with unobserved ability, as is well known in the literature of labor

economics (Mroz 1987). In this regard, we also use an individual’s age and age squared

10 To increase the degree of freedom for IV estimation, we use the entire sample for the models. We also estimate models for Columns V and VI separately for men and women. The results are similar. 11 There are different ways to implement the test on over-identifying restrictions, such as a GMM based test or an auxiliary regression based test. Our test follows Basmann (1960).

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as instruments for experience variables. The new result is presented in Table 3 Column

VI. The estimated return hardly changes. However, the test on overidentifying

restrictions strongly rejects the null again; the F-statistic and its P-value are 6.03 and

1.5%, respectively. Since age variables are unlikely to be endogenous, this result

indicates that parental education is not a valid instrument for an individual’s ability. It is

possible that parental education will not only affect a child’s education level, but also

influence the way a child is raised, and thus affect the child’s ability.

These results suggest that based on the sample, the commonly used family

background variable—parental education—is neither a suitable proxy nor a valid

instrument for ability; and thus cannot be used to tackle the ability heterogeneity problem

in estimating the returns to education in China’s rural industry.

V. The Omitted Ability Bias and Sibling Composition

In order to find a good instrument to correct for the omitted ability bias, we turn

to the Chinese cultural background. In China, especially in rural areas, higher values and

preferences have been placed on having boys. Culturally, boys are considered to carry on

the family name and thus are preferred. Based on Zhang (1994), a family’s decision to

have more children is determined by the gender composition of existing children. For

example, the conditional probability of ceasing to have more children is 24.8% for an

average woman with two daughters. But if either of the daughters were instead a son, the

probability would increase to around 40%.

Economically, in rural China, there is no old-age security system. It is

traditionally a son’s responsibility to take care of his old parents. Thus, having boys is

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like having (legitimate) old-age insurance for parents. Therefore, daughters and sons

make different contributions to family income. Having a boy presents a higher

‘investment value’ for parents.

Therefore, if the parents’ strategy concerning their children’s educational

investment is to maximize their own expected lifetime income, boys are more likely to

get more education than girls. When a family faces financial constraints, girls may be

asked to leave school in order to save costs or even to work to support her brother’s

education. As a result, a girl’s education will be adversely affected by the presence of

brothers.

Based on the argument of natural experiment, the girl’s inherent ability

presumably should remain unaffected by the existence of brothers. Thus the information

on sibling composition can be used as an instrument. Sibling variables have been used to

study the causal effect of education in the United States. For example, Butcher and Case

(1994) use “the presence of any sisters” within a family as an instrumental variable for

schooling of female workers on the basis that gender composition of siblings in a family

has a significant effect on educational attainment but no effect on inherent ability.

On the other hand, following the same argument, a boy’s education generally

should not be affected by the existence of sisters, and the sibling instrument is not helpful

in estimating the return for men. Therefore, we only use the sibling variable as an

instrument to correct omitted ability bias for working women. In the sample, 64.3 % of

199 female respondents have one or more brothers, and the maximum number of brothers

is four. The correlation coefficient for woman’s education and the number of brothers is

–0.049, indicating that in general a girl’s education is negatively affected by brothers.

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We first use the number of brothers as an instrument to estimate the return for

women. The resulting estimate becomes 0.76% (statistically insignificant) (see Column

II, Table 4). The magnitude is much smaller than the OLS estimate of 7.1%. It appears

that the upward bias caused by omitted ability variables is substantial based on both

magnitude and statistical significance. The IV estimation shows an insignificant effect

(statistically and economically) of education on earnings for women in China’s rural

industry. The first stage result shows that an additional brother reduces the girl’s

education by 0.2 year.12 This is consistent with the argument that a girl’s education is

negatively affected by brothers.

Furthermore, for women, it is more likely that their non-farming experience is

correlated with their unobserved ability, because non-farming jobs are scarce in rural

areas and more capable people are more likely to get such jobs. Thus the non-farming

experience variables are probably endogenous too. For this reason, we again use age and

its squares as instruments for experience variables.

Moreover, it is generally desirable to have over-identifying instruments in an IV

estimation in order to test over-identifying restrictions and for the IV estimator to have

meaningful first and second moments (Kinal 1980). We use both the number of brothers

as well as its square as instruments for schooling. One explanation for including the

square term is that, as the number of brothers increases, the girl’s status in the family may

improve relatively. Thus, the influence of an extra brother on the girl’s education may

diminish.

12 The insignificance of the instrument at the first stage causes some concern. However, given the relative small sample, we believe that this is likely to be caused by the sample size.

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With this specification, the estimated return based on 2SLS becomes –0.062

(Column IV, Table 4) and is highly insignificant.13 According to the result in Column II,

we cannot reject that education does not have any effect on wages. Given extra

instruments we have in this specification, we can conduct the test on over-identifying

restrictions. The corresponding F-statistics is 0.0016 and it does not reject the null (the

corresponding P-value is 97%) that instruments based on sibling composition and age are

valid

Finally, it is known that 2SLS is not the most efficient IV estimation. For

instance, if the regression error is heteroskedastic, 2SLS will be inefficient. In general,

the Generalized Method of Moments (GMM) estimation is asymptotically more efficient

when the regression error is heteroskedastic and/or serially correlated. Since

heteroskedasticity is common in cross-section data, we apply the GMM procedure to

estimate model IV in Table 4. This estimate is obtained by using an optimal weighting

matrix in the quadratic criterion function (see Hansen 1982). The result, however, is not

very different from the previous 2SLS results; the GMM estimate is –0.06, and again

very statistically insignificant (Column V, Table 4). Since the GMM is asymptotically

more efficient, it appears that with the current sample size, the efficiency gain is small.

In the last section, we find that parental education is not a valid instrument.

Given that the sibling variable is a valid instrument, the validity of parental education as

instruments can be tested. We use number of brothers, and father’s and mother’s

education as instruments to estimate the model and to conduct over-identification test.

The results are reported in Column III of Table 4. The test generates an F-statistic of

13 The negative sign could be caused by sample size and the weak instrument of age for non-farming experience.

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2.57, and rejects the null hypothesis at 10% level (with the P-value 7.9%). This result

indicates again that parental education is not a valid instrument.

VI. Conclusions

This study is aimed at estimating the causal effect of education on wages in

China’s rural industry. The goal is to control for both attenuation bias and omitted ability

bias resulted in the simple OLS procedure. We first investigate the degree of

measurement error in the schooling measure and its attenuation effect; and then address

the omitted ability bias using different instruments to estimate the returns to schooling.

Our results show that, in the directly reported years of schooling, measurement

error is small and the attenuation bias from the OLS is negligible. This finding indicates

that the omitted ability bias dominates the OLS estimation, and the true return to

education should be lower than the OLS estimates. The results from the subsequent IV

estimations confirm this prediction. While the OLS estimation gives a return of 7.1% for

women, the results based on IV estimations indicate that education has an insignificant

effect on wages in China’s rural industry. Based on our sample, the omitted ability bias

is substantial.

These results are different from some recent studies using IV method in

estimating the effect of education. Their IV estimates are often substantially higher than

OLS estimates (Card 1995, Butcher and Case 1994, and Ashenfelter and Zimmerman

1997). Even using data from urban China, Li and Luo (2003) find that attenuation bias is

dominant over the omitted ability bias, and that overall IV estimation provides much

higher estimates than that from the OLS procedure. In their sample, however, the

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information of years of schooling is not reported directly and is estimated based on the

education degrees received. Thus their schooling measure are likely to contain

considerable error, which results in much higher attenuation bias. This is consistent with

the finding in this study that the estimated years of schooling based on the degrees

contain greater measurement error than the directly reported years of schooling. In fact,

for the existing OLS estimates of the return to schooling in rural China, the years of

schooling are all estimated based on the educational degree completed. Thus they should

suffer from both biases.

In recent studies, most instruments for schooling come from family background

variables (Rosenzweig and Wolpin, 2000). However, our tests consistently reject the use

of parental education as valid instruments based on the sample used. On the other hand,

the sibling instrument based on the Chinese cultural preference for having boys in a

family offers a good alternative for estimating return to education for women. Our

results confirm that the existence of brothers has negative effect on a girl’s education

attainment. And statistical tests do not provide any evidence against the use of sibling

variables as instruments.

The results from the sample give an extremely low (if any) return to education in

China’s rural industry. Based on the IV estimation, we cannot reject that education does

not have any positive effect on wages. It remains to be studied whether such a low

reward to schooling contributes to slowing down of the rural industry in China. In 1980s,

the average employment growth rate for TVE was 13%, but it decreased to almost half

19

(7%) in 1990-1995. Even more dramatically, in 1995-2000 TVE output experienced zero

average growth.14

In this study, we investigated the biases in the OLS estimation on the causal effect

of education on wages and attempts to provide a more accurate estimate of the true effect.

Clearly, the IV results depend on the assumption that sibling composition is not

correlated with an individual’s ability. In addition, the true return to education for male

workers remains to be investigated with a proper instrument in future researches.

14 China Statistical Yearbook of China 2002.

20

Reference

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Ashenfelter, Orley and Alan B. Krueger (1994), “Estimates of Economic Return to

Schooling for A New Sample of Twins,” Quarterly Journal of Economics, 113:253-284.

Ashenfelter, Orley and David Zimmerman (1997), “Estimating of Return to Schooling

from Sibling Data: Fathers, Sons and Brothers,” Review of Economics and Statistics, 79:1-9.

Basmann, R. L. (1960) “On Finite Sample Distributions of Generalized Classical Linear Identifiability Test Statistics,” Journal of the American Statistical Association, Vol. 55, No. 292, December, 650-659. Butcher, Kristin F. and Anne Case (1994), “The Effects of Sibling Composition on

Women’s Education and Earnings,” Quarterly Journal of Economics, 109: 443-450.

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Return to Schooling”, in: Louis N. Christofides, E. Kenneth Grant and Robert Swidinsky, eds., Aspects of Labour Market Behavior: Essays in Honor of John Vanderkamp (University of Toronto, Canada), 201-222.

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Hansen, Lars Peter (1982): "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Vol. 50, No. 4, July, 1029-1054. Johnson, Emily N. and Gregory C. Chow (1997), “Rates of Return to Schooling in

China,” Pacific Economic Review, 2: 2, 101-113. Kane, Thomas, Cecilia Elena Rouse, and Douglas Staiger (1999), “Estimating Returns to

Schooling When Schooling is Misreported,” Working Paper, #419, Industrial Relations Section, Princeton University.

Kinal, Terrence W. (1980) “The Existence of Moments of k-class Estimations,” Econometrica, Vol. 48, No. 1, January, 241-249.

21

Li, Haizheng and Yi Luo (2003), “Reporting Errors, Ability Heterogeneity, and Returns to Schooling in China?” Pacific Economic Review, Special Issue, edited by Orley C. Ashenfelter and Junsen Zhang, forthcoming, projected 2003.

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University Press for the National Bureau of Economic Research. Mroz, Thomas A (1987), "The Sensitivity of An Empirical Model of Married Women's

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22

Table 1. Descriptive Statistics Variable Mean Standard

DeviationMinimum

Value Maximum

Value Age 33.81 11.31 15 80Females 0.37 0.48 Ethnic Minority 0.023 0.15 Monthly Income 553.13 659.86 16 5,000Hourly Wage 3.11 3.95 0.08 31.25Reported Years of Schooling 8.28 2.75 0 16Estimated Years of Schooling 8.92 2.94 0 16Professional School or above 0.091 0.29 Upper Middle School 0.19 0.39 Lower Middle School 0.51 0.50 Elementary or Illiterate 0.20 0.40 Non-Farming Experience 5.81 6.51 0 38 Mother Education 4.39 3.04 0 15Father Education 6.80 2.74 0 14Number of Male Children 1.18 0.73 0 4Notes: 1. Estimated years of schooling are based on the reported education degrees received. 2. Because only a very small number of respondents received education beyond the

Upper Middle School level, all the higher levels were combined into “Professional School or College.”

23

Table 2. The Effect of Measurement Error

Column Variable

I

OLS

II

OLS

III

OLS

IV

2SLS Instrument:

estimated years of schooling

V

2SLS Instrument:

reported years of schooling

Reported Years of Schooling

0.014 (1.95)

0.0087 (0.99)

Estimated Years of Schooling

0.0071(1.01)

0.015(1.84)

Average Years of Schooling

0.011(1.49)

Non-Farming Experience

0.022 (2.67)

0.022(2.61)

0.022(2.63)

0.022 (2.67)

0.022(2.62)

Non-Farming Experience Sq.

-0.00049 (-1.54)

-0.00047(-1.49)

-0.00050(-1.51)

-0.00048 (-1.45)

-0.00047(-1.42)

Female

-0.14 (-3.16)

-0.14(-3.17)

-0.14(-3.14)

-0.15 (-3.26)

-0.14(-3.00)

Ethnic Minority

0.069 (0.29)

0.066(0.28)

0.066(0.28)

0.070 (0.50)

0.060(0.43)

Sample Size 1182 1182 1182 1182 1182F-value 7.02 6.52 6.76 6.53 7.00Adjusted R-squared

0.025 0.023 0.024 0.023 0.025

Notes: 1. The constant term is not reported. The heteroskedasticity robust t-statistics are in

parentheses. 2. Column I is based on the reported years of schooling; Column II is based on the

estimated years of schooling, and Column III is based on the average of the two schooling measures.

3. In Column IV, reported schooling level is used as a regressor and estimated schooling is used as an instrument; in Column V, estimated schooling level is used as a regressor and reported years of schooling is used as an instrument.

24

Table 3. Control Variable vs. Instrumental Variable Approach

Column Variable

I

OLS Males

II

OLS Females

III

OLS Males

(Control)

IV

OLS Females (Control)

V

2SLS IV estimation

VI

2SLS IV estimation

Years of Schooling

0.036 (2.16)

0.068(3.30)

0.032(1.79)

0.062(2.92)

0.096 (1.55)

0.099(1.58)

Non-Farming Experience

0.073 (4.08)

0.027(0.77)

0.073(4.08)

0.040(1.15)

0.066 (3.64)

0.13(3.58)

Non-Farming Experience Sq.

-0.0036 (-6.10)

0.00038(0.18)

-0.0035(-5.78)

-0.00039(-0.18)

-0.0031 (-3.28)

-0.0055(-3.78)

Female

-0.15 (-2.21)

-0.13(-1.85)

Father’s Education

0.00091(0.06)

-0.047(-2.30)

Mother’s Education

0.018(1.25)

0.044(2.21)

Sample Size 261 187 261 187 448 448Overidentifying Restriction Test

F = 5.61 P = 0.018

F = 6.03P = 0.015

F-value 5.85 3.49 3.85 3.46 Adjusted R-squared

0.053 0.039 0.052 0.062

Notes: 1. The constant term is not reported. The heteroskedasticity robust t-statistics are in

parentheses. 2. In Columns III and IV, parental education variables are used as control variables. 3. In Column V, parental education variables are used as instruments for years of

schooling, and in Column VI, parental education and age, age squared are used as instruments for years of schooling, non-farming experience, and non-farming experience squared.

25

Table 4. Male Sibling Variable as An Instrument for Female Sample

Column Variable

I

OLS

II

2SLS

III

2SLS

IV

2SLS

V

GMM

Years of Schooling

0.071 (3.03)

0.0076(0.20)

0.17(0.52)

-0.062 (-0.39)

-0.061(-0.47)

Non-Farming Experience

0.026 (0.66)

0.041(0.41)

0.0026(0.052)

0.22 (0.95)

0.22(1.12)

Non-Farming Experience Sq.

0.00051 (0.17)

-0.00088(-0.10)

0.0026(0.64)

-0.011 (-0.45)

-0.011(-0.50)

Sample Size 199 199 187 199 199Overidentifying Restriction Test

F = 2.57P = 0.079

F = 0.0016 P = 0.97

F-value 3.98 R-squared 0.057 Notes: 1. The constant term is not reported. 2. For the OLS models, the heteroskedasticity robust t-statistics are in parentheses. 3. In Column II, the instrumental variable for years of schooling is the number of

brothers. 4. In Column III, instrumental variables for years of schooling are the number of

brothers and parental education variables. 5. In Column IV, instrumental variables for years of schooling, non-farming experience,

and non-farming experience squared are the number of brothers and number of brothers squared, age, and age squared respectively.

6. In Column V, the GMM estimation converges after 3 iterations, and the specification is the same as the model in Column IV.