Human capital resources

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Human capital resources are a crucial part of an individual's capital holdings and comprise much of the total aggregate wealth in economically advanced nations. During the last few decades, much energy has been devoted to the analysis of human capital and its empirical regularities. The result has been the accumulation of a large amount of evidence supporting the importance of human capital to the structure and evolution of earnings, occupations, employment and unemployment, fertility, and economic growth and development (HUERTA). The importance of education in the process of economic growth and development has been increasingly recognized, leading to the resurgence of interest in studying the relationship between education and labour market outcomes and earnings ( RANASINGHE). Over the past decade there has been a rising interest in the study of the relationship between returns and schooling. And It is well known that workers who have received better education earn higher wages in the labor market. Hundreds of studies in virtually every country show earning gains of 5-15 percent or more per addition year of schooling”. (Psacharopoulos(1985)). Despite of this fact, many people believe that the earning gap between higher and lower educated workers cannot be reliably estimated by schooling since education levels are not random variables. Thus the earning difference may either be over-estimated or under estimated ( Griliches1977).

2.literature review

The standard human capital earning function to explain variation across individuals in the acquisition of earning power, as first derived by Mincer (1974) may be stated as follows:


actual earning of individual i in year t;

years of schooling, assumed to be constant in the post-school or labor market period;

years of potential labor market experience (defined as age - S- 5) of individual i in year t;

stochastic error term.

Following Mincer equation (1) may be derived for a given individual as follows.


N=number of years spent in work;

L= N+S= age at retirement;

potential earnings capacity of an individual with S years of schooling;

r= discount rate

t= 0,1,2,........,L time, in years

e=base of natural logarithms

The present value of earning for a person with S years of schooling is :

This model states that the logarithm of potential earnings is a linear function of the years spent in school.

However, schooling is only one mechanism, albeit an important one, for human capital accumulation. Other mechanism include on-the- job training, investment in health, migration and acquiring information about the labour market.

The model assumes that across all individuals there is equality of schooling quality, access and ability. The model also assumes that education results in equal work productivity. The reality is that individuals are not equal in ability; access to education is not equal. Institutions do vary in the quality of the education programs provided; and that some programs are likely to raise work productivity more than others. The other problematic assumption is during period of formal schooling no time spent in the employed labor force. Thus, the rate of return to schooling for those who, completed a higher level of schooling and diverted less of their available time to the labor market during their schooling years, will be biased downwards. The most critical assumption is that after schooling all time spent in the employed labor force. The advantage of this assumption is that when combined with the assumption that during schooling no time is spent working, replace variable actual experience with a proxy, potential experience. Mincer measures potential experience as Age-S-5. This measure commonly is known as the “Mincer Proxy”. This proxy result in an overestimation actual work experience of person exiting the workforce for child birth, prolonged illness, unemployment, military service, etc. It will thus impart bias on the coefficient estimates of other regressors in the wage equation (Preston 2001).

Obtaining accurate and credible measures of returns to schooling involves minimizing the upward bias caused by omitted variables, and the downward attenuation bias caused by measurement errors in schooling. A main drawback of Ordinary Least Squares (OLS) estimates of returns to education is that they suffer from omitted variables bias ( RANASINGHE). Simple OLS estimates are affected by two biases. First, ability bias may bias upwards the observed returns to schooling (e.g. because high-ability people find it easier to undertake education), or bias downwards the observed returns to schooling (e.g. if low-ability people compensate by completing more education). Second, measurement error might bias the OLS returns downwards (Leigh).

In terms of this problem, David Card thought that “A convincing analysis of the causal link between education and earnings requires an exogenous source (he refers to geographic differences in the accessibility of college) of variation in education choices. Using data from the Young Men Cohort of the National Longitudinal Survey, he found that men, lived in areas nearby 4-year college, have higher educational levels and earn higher wages. Even if he controlled for regional and family background factors, students, who grew up in an area without a college, will decrease the years of education because of facing a high cost of college education, this phenomenon particularly applies to low-income families”(David Card 1993).

As a matter of fact, econometricians used different instrumental variables for schooling. For some of the researchers, they chose family background variables like parents' education. While other econometricians use institutional factors of the schooling system as the instrumental variables. Back to David Card's survey which used geographic differences as the instrumental variable for schooling, the instrumental variables estimates of return to schooling are 25-60 percent higher than the OLS estimates. “The finding suggest that the cross-sectional earnings gap may under-estimate the return to schooling within some groups (Angrist and Krueger(1991a))

“this inferences are robust to minor changes in spection, nevertheless, they rely on the assumption that living near a college has no effect on earnings apart from the effect through education”(David Card1993)and he used the interaction of college proximity and low family background as the instrumental variable which gave rise to estimates in the same range as the simpler instrumental variable. While according to David Card, “none of these estimates is precise. They all point toward relatively high returns to schooling for children of poorly-educated parents. This pattern is consistent with differential access to funds leads to relative under-investment in schooling among children of lower-income families”(David Card 1993)

endogeneity(ability bias,measurement error,unobserved component)

Individuals behave like much like firms. Just as Firms produce so that marginal cost equals to marginal revenue, so individual investors purchase human capital up to point the marginal cost equals the present value of marginal gain. Human capital investment does not always take place at school. Nor is human capital investment always an indivisible type of decision in which people devote themself only to full time investment. Often investment opportunities come in smaller units: one can go to school part time, one can take an adult education course or one can train on the job while simultaneously working (Polachek 1993).

Individuals' earnings are a function of schooling, . This model uses the utility function . It is based on individual maximizing the present discounted value of income discounting the future at constant rate, and earning nothing while in school. The optimal level of schooling is determined implicitly by the first order condition, when marginal benefit of schooling is equal the marginal cost. Equation (1) establish notation of marginal benefit of schooling that influence an individual's optimal schooling choice, parameterising them as function of observable characteristic, X , and unobservable components

Equation (2) does the same for marginal cost with the suggestion of IV's in Z are available that affect schooling through the discount rate and not marginal benefit.

The assumption in (2) of marginal cost with an individual specific discount rate and a component that is increasing at a constant positive rate in the amount of schooling seems plausible, for example, individual can finance education internally from family saving first, then from federal subsidised sources, and finally from private sources. The parameter is a random coefficient to allow for individual differences in response to instrument.

Equating (1) and (2)and after substituting parameterisations of observables results in an explicit equation (3) for an individual's optimal schooling , where is observed years of schooling. The instruments is assumed not to decrease schooling (3)

Integrating (1) and substituting (where Y is the observed log wage) results in this equation for earning , where is a random coefficient.(4)

There are two types of “ability in this model. In the first, individual differences in earnings capacity, that do not interact with education, are embodied in the individual - specific earning equation intercept . If is independent of the IV, affecting the level of schooling through the discount rate; then, the instrument satisfies the exclusion restriction. Specifically, with the assumption that is independent on and, conditional on . This model provides theoretical motivation for two-stage least squares (2SLS) estimation, in which the first stage is estimated by (3) and the second stage by (4).

The second type of ability is the marginal benefit to a year of schooling captured in , which varies across individuals. Note that (4) is allowed to be linear in the endogenous schooling variable and not quadratic because in (1) is modelled as invariant to schooling level. The 2SLS point estimate of the schooling coefficient is a weighted average of the heterogeneous marginal benefit for those whose schooling choices are effected by the instrument, conditional on . The monotonicity Implied in (3) when allows results from IV estimates to be interpreted as a weighted average casual response, similar to the local average treatment effect derived for instrumenting a binary endogenous regressor (Kling 2001).

ability bias: in Griliches's paper 1977, he assumed the true eqution is “

where A is a measure of “ability” which we have ignored in our procedure.

Then as is well known,

Ebys= β + γbAS = β + γcov(AS)/varS

From this, Griliches (1977) pointed out that the simple least squares estimate of logwage on schooling is biased upward based on the assupmption of (i) “ability” has an independent positive effect on earnings above and beyond its effect on the amount of schooling (correctly measured) accumulated.(ii) there is a positive relationship between “ability” and “schooling”.(iii) ability is the only left-out variable .For example, assume a person has ability which may incresae his wage at any level of education, if he also has more years' of schooling, this indicates that there is a positive relationship between schooling and error return which shows that schooling is an endogenous variable. Econometricians often interpreted the phenomenon that people with higher test scores(on IQ or achievemrnt tests) tend to have more schooling and higher earnings as evidence of ability bias.

Measurement error:

due to the measurement error for schooling(for example, because of misreporting), E{Xtεt}≠0 which implies that the schooling is an endogenous variable. And this induces a downward bias in OLS estimates. Note that εt is error return and Xt is the true value plus measurement error. (Verbeek,M,2008)

Unobserved component:

if a person who has fewer years' of schooling while gets higher returns to schooling, then the unobserved component will has a negative relationship with schooling, which causes a downward bias in the OLS estimates. and OLS estimates

The data set is obtained from the National Longituinal Survery of Young Men (NL SYM) in America, which involves 3010 young men.In the survey,a category of individuals was followed from 1966 when their age were from 14 to 24 , and the data from them was obtained from interviews in continuous years.The labour market information in the analysis mainly focuses on 1976 .At this year, the average years of schooling among the sample is more than 13 years (almost three years more than the year of 1966 )and the maximum is 18 years. Average experience in 1976 is 8.86 years among the group of men who aged between 24 and 34 years old , and their average hourly raw wage is $5.77.Among these male youth, the average education years their fathers and mothers had were about 9.988 years and 10.336 years respectively.And their father and mother education class is between 1-9 with an average of 5.93.Some of the subject group's kww ,IQ scores and the marital status in 1976 had no record in this survey ,these may lead to biased estimates .The rest data is used to identify whether other variables(all of them are dummy variables) may or may not affect the schooling.These factors are whether the individuals are black,lived in a cosmopolitan area,lived in south(in 1966 and 1976) ,grew up near 2-year college,near 4-year college,near 4-year public college,near 4-year private college ,dads education imputed and mothers education imputed or not.At the same time ,the data set also inspect the infuluence of whom they lived with at the age of 14 (with both mom and dad, with single mom or with step parent ) and they had a library card at home or not at that time. And whether they enroled in 1976 was also taken into consideration. In order to be more specific , the squared experiences and age were employed as well. At the end ,the average log wage in 1976 were recorded as 6.26.

However, some data of a number of males' KWW scores and IQ scores has not been recorded ,so the data set at this part is bias. There are also other possible weaknesses.First,the data available is not recent records(maily in 1976).Second, the number of males available for the survey is limited .Furthermore, in this model ,individual schooling has to be treated as exogenous when using the data, there are may other “ability bias” which is not taken into account in this survey ,but there are no more relevant data records.

The process of OLS regression results:

Source | SS df MS Number of obs = 3010

-------------+------------------------------ F( 6, 3003) = 204.93

Model | 172.165616 6 28.6942693 Prob > F = 0.0000

Residual | 420.475997 3003 .140018647 R-squared = 0.2905

-------------+------------------------------ Adj R-squared = 0.2891

Total | 592.641613 3009 .196956335 Root MSE = .37419


lwage76 | Coef. Std. Err. t P>|t| [95% Conf. Interval]


ed76 | .074009 .0035054 21.11 0.000 .0671357 .0808823

exp76 | .0835958 .0066478 12.57 0.000 .0705612 .0966305

exp762 | -.0022409 .0003178 -7.05 0.000 -.0028641 -.0016177

black | -.1896316 .0176266 -10.76 0.000 -.2241929 -.1550702

smsa76 | .161423 .0155733 10.37 0.000 .1308876 .1919583

south76 | -.1248615 .0151182 -8.26 0.000 -.1545046 -.0952184

_cons | 4.733664 .0676026 70.02 0.000 4.601112 4.866217


What should be noted is that the R2= 0.2905,which means 29.05% of the dependent variable(log wage in 1976 ) are explained by the independent variables listed as above.The coefficient of ed76 is 0.074009,explaing that when add one year of education, the wage will correspondingly increase 7.4%.Draw from the table ,the standard error of the coefficient is 0.0035054.That is the standard deviation between the estimated coefficient of education in year 1976 and its true value .

4.IV and schooling/experience/ experience^2......

Since schooling is endogenous, one solution is to instrument it. Recall that a suitable instrument is required to meet two conditions: relevance and exogeniety. Relevance of the instrumental variable means that it is correlated with the number of years of schooling .The exogeniety condition requires that the instrumental variable is not correlated with the error terms in the income equation. See more information about instrumental variable in Wooldridge (2002).

According to variety of literatures reviewed from previous studies, mother's education has a significant effect on children's educational outcomes. Educating women can have a significant effect on the family environment and improvement of human development (UNDP 1996). Studies also have showed that mother's education can present greater human capital outcomes of child than that of fathers (Thomas, Schoeni and Strauss 1996). Moreover, a great number of evidences show that mother plays an important role in family. More specifically higher mother's education provides a better learning environment for her children. (Heckman and Hotz 1986).

In general, more educated mother can make better choices for children' education and health investment, and they are more likely to have a higher household income. As a result, children can be invested more resources with efficient outcome and consider future education years.(Pedro Carneiro, Costas Meghir and Matthias Parey 2006). In addition, more educated-mothers spend time with their children more effectively in terms of educating their children compared with those mothers who do less-schooled. (Jere R. Behrman 1997). Higher educated Mothers' attitudes and expectation also have an impact on their children's decision making for their years of schooling. All in all, according to the studies stated above, mother's education is correlated with children's years of schooling

In our model, we use mother's education, age and age squared as instrument for schooling, experience and experience squared.

5.Returns to schooling--- regression(interpret estimates,compare with OLS estimates,se,R2, accuracy)

If the chosen instruments are strong, 2SLS may be used to estimate a structural model with endogenous regressors. Based on the above materials ,here we use momed (mother education )as an instrument variable to the schooling(education in the year 1976),age as an instrument variable to the experience and accordingly age2 is the instrument variable to the experience2.In this essay ,we focus on schooling in the first place.

Thus the first stage equation is :

Table1-3 reveal a series of reduced form education ,eperience, and experience squared equations ,using momed ,age and age squared as instrument variable respectively.

ed76i=β0+β1black+β2smsa76+β3south76+β4momed+β5age76+β6 age762+εi

Table 1: Estimated reduced form equation for ed76


ed76 | Coef. Std. Err. t P>|t| [95% Conf. Interval]


black | -.9227132 .1115548 -8.27 0.000 -1.141445 -.7039817

smsa76 | .7584246 .0972873 7.80 0.000 .5676681 .9491812

south76 | -.3154385 .0953935 -3.31 0.001 -.5024817 -.1283953

momed | .3123484 .0152281 20.51 0.000.2824898 .3422069

age76 | .9683554 .282725 3.43 0.001 .4140011 1.52271

age762 | -.0168472 .0049072 -3.43 0.001 -.026469 -.0072255

_cons | -3.90578 4.032447 -0.97 0.333 -11.81242 4.000858


F = 144.58 R2= 0.2241 = 0.2226 s=2.3603

From P>|t|=0.000<0.05,so we reject H0 :β4=0; therefore momed is correlated with ed76(i.e. a valid instrument variable to ed76).

exp76i=β0+β1black+β2smsa76+β3south76+β4momed+β5age76+β6 age762+εi

Table 2: Estimated reduced form equation for exp76


exp76 | Coef. Std. Err. t P>|t| [95% Conf. Interval]


black | .9227132 .1115548 8.27 0.000 .7039817 1.141445

smsa76 | -.7584246 .0972873 -7.80 0.000 -.9491812 -.5676681

south76 | .3154385 .0953935 3.31 0.001 .1283953 .5024817

momed | -.3123484 .0152281 -20.51 0.000 -.3422069 -.2824898

age76 | .0316446 .282725 0.11 0.911 -.5227096 .5859989

age762 | .0168472 .0049072 3.43 0.001 .0072255 .026469

_cons | -2.09422 4.032447 -0.52 0.604 -10.00086 5.812417


F =1043.67 R2= 0.6759 =0.6752 s=2.3603

From P>|t|=0.911>0.05,so we accept H0 :β5=0; therefore age76 is not correlated with exp76(i.e. might not be a good instrument variable to exp76).Further discuss later.

exp762i=β0+β1black+β2smsa76+β3south76+β4momed+β5age76+β6 age762+εi

Table 3: Estimated reduced form equation for exp762


exp762 | Coef. Std. Err. t P>|t| [95% Conf. Interval]


black | 17.66364 2.366235 7.46 0.000 13.02404 22.30325

smsa76 | -16.24792 2.063602 -7.87 0.000 -20.29414 -12.20171

south76 | 8.470029 2.023431 4.19 0.000 4.502578 12.43748

momed | -6.037235 .3230095 -18.69 0.000 -6.670577 -5.403892

age76 | -53.62013 5.996997 -8.94 0.000 -65.37877 -41.8615

age762 | 1.275609 .1040881 12.26 0.000 1.071518 1.4797

_cons | 648.6118 85.5339 7.58 0.000 480.9009 816.3228


F =932.13 R2= 0.6506 =0.6499 s=50.0648

From P>|t|=0.000<0.05,so we reject H0 :β6=0; therefore age762 is correlated with exp762(i.e. a valid instrument variable to exp762).

Thus the second stage equation is :

Estimate the single structural equation:

lwage76=β0+β1IV+β2IV +β3IV +blackβ4 +smsa76β5 +south76β6 +εi

Table4:Structural Equation Estimated By 2SLS


lwage76 | Coef. Std. Err. z P>|z| [95% Conf. Interval]


ed76 | .0881026 .0081242 10.84 0.000 .0721796 .1040257

exp76 | .0722564 .0166378 4.34 0.000 .039647 .1048658

exp762 | -.0016559 .0008355 -1.98 0.047 -.0032934 -.0000183

black | -.1687674 .0206861 -8.16 0.000 -.2093114 -.1282235

smsa76 | .1489788 .0170494 8.74 0.000 .1155626 .1823949

south76 | -.1189172 .015619 -7.61 0.000 -.1495299 -.0883045

_cons | 4.59284 .1261431 36.41 0.000 4.345605 4.840076


Wald chi2(6) =1057.36 R2 =0.2834 s= 0.37561

lwage76=4.59284 + 0.0881026 + 0.0722564- 0.0016559- 0.1687674black + 0 .1489788smsa76 - 0.1189172 south76+εi

Based on the above data and information ,it is clear that mother's education has a strong positive effect on schooling(0.28 to 0 .34 years of schooling) .The application of mother's education as an exogenous determinant of schooling bring out the result that the return to schooling is at the range of 0.07 to 0.10.

Table5:Comparison Between OLS and 2SLS



lwage76| Coef. Std.Err. R2 Coef. Std.Err.z R2 -------------+----------------------------------------------------------------------------------------------------------

ed76 | .074009 .0035054 0.2905.0881026.0081242 /

Clearly ,the estimated return to education in year 1976 under the method of 2SLS is 1.4 % higher than the one under OLS method. However, the standared error resulted from the OLS method is more desirable ,which is 0.0046188 lower than the figure under 2SLS measurement.The inaccuracy of 2SLS is such that the difference might just be due to the sampling error.Another reason for such a bigger standard error is attributed to the low correlation between mother's education and year's of schooling, which have been demonstrated in terms of the extremely small R2=0.2241, in the reduced form.While the relative low correlation between age76 and experience in 1976 is because of high p-value=0.911 (much higher than 0.05) ,namely,accept the H0:age76 has no relation with experience.What is further ,if the more weakly the instrument and endogenous regressors are correlated ,the less efficient the measurement of 2SLS.The goodness-of-fit is not necessarily considered in the analysis in 2SLS. R2 are more frequently be applied in the OLS method(Verbeek.M ,2008).The goal of using 2SLS method is to gain a consistent estimator for the causal effect of schooling upon earnings via instrument variables rather than pursuing the goodness-of-fit .

After we run the model with 2SLS , we may use the Durbin and Wu-Hausman tests to further exam the adjusted model 's endogeneity .

Tests of endogeneity:

Ho: all variables are exogenous

HA:at least one variable is endogenous

Durbin (score) chi2(3) = 3.95689 (p = 0.2662)

Wu-Hausman F(3,3000) = 1.31631 (p = 0.2672)

The P-value in both tests are bigger than 0.05,therefore cannot dimiss Ho: all variables are exogenous.

Hausman's specification Test:

In order to make the 2SLS estimator to be preferred to the OLS estimator, the matrix Z must have columns that are strong instrumental variables. That is

1. E(zi|xi)≠0,which means that the instrument variables zi and endogenous xi are correlated for i=1,2,…K; and

2. E(zi|εi)=0, which means that the instrument variable zi and the disturbance εi are not correlated for all i


---- Coefficients ----

| (b) (B) (b-B) sqrt(diag(V_b-V_B))

| ivreg . Difference S.E.


ed76 | .0881026 .074009 .0140937 .007329

exp76 | .0722564 .0835958 -.0113395 .015252

exp762 | -.0016559 -.0022409 .000585 .0007727

black | -.1687674 -.1896316 .0208641 .0108267

smsa76 | .1489788 .161423 -.0124442 .0069393

south76 | -.1189172 -.1248615 .0059443 .0039234


b = consistent under Ho and Ha; obtained from ivregress

B = inconsistent under Ha, efficient under Ho; obtained from regress


Ho: difference in coefficients not systematic

HA: difference in coefficients is systematic

chi2(6) = (b-B)'[(V_b-V_B)^(-1)](b-B)= 3.91

Prob>chi2 = 0.6883

From the Hausman specification Test ,we cannot dimiss Ho: difference in coefficients not systematic because the chi2(6)=3.91<chi2(6)cv=12.53 , (P-value=0.6883>0.05).In other words, we cannot reject the null specification of OLS can be accepted against the alternative of 2SLS.

Future discussion about Generalized Method of Moments (GMM)

The main difference between 2SLS and GMM can be explained that 2SLS requires errors to be distributed independently and identically, while GMM estimation simply requires independence, since the weighting matrix w naturally weights observations. The GMM estimator can also be a robust to heteroskedasticity.

Instrumental variables (GMM) regression Number of obs = 3010

Wald chi2(6) = 1166.48

Prob > chi2 = 0.0000

R-squared = 0.2834

GMM weight matrix: Robust Root MSE = .37561


| Robust

lwage76 | Coef. Std. Err. z P>|z| [95% Conf. Interval]


ed76 | .0881026 .0083517 10.55 0.000 .0717337 .1044716

exp76 | .0722564 .016846 4.29 0.000 .0392389 .1052739

exp762 | -.0016558 .0008446 -1.96 0.050 -.0033112 -5.34e-07

black | -.1687674 .0209611 -8.05 0.000 -.2098504 -.1276845

smsa76 | .1489788 .0168824 8.82 0.000 .1158899 .1820676

south76 | -.1189172 .0158102 -7.52 0.000 -.1499047 -.0879297

_cons | 4.59284 .1266613 36.26 0.000 4.344589 4.841092


Instrumented: ed76 exp76 exp762

Instruments: black smsa76 south76 momed age76 age762

Overidentifying restrictions tests

Overidentifying restrictions tests can be examined whether the instruments are correlated with the errors or not under the condition of overidentification in which we have more instrumental variables than endogenous variables. The test allows us to examine whether the instrument variables are valid or not. Basically, if the results in Sargan-Hansen test of overidentifiying restrictions show the rejection of null hypothesis, we can safely doubt the validity of the instruments.(Christopher F Baum 2007)

Since in our model, we are in the condition of exactly identified, we may not run this test. We suggest that we can added more instrument variables such as father education, nearc4 and so on which have been mentioned in previous literatures



Our essay estimates the returns to schooling for men in a standard human-capital model, using 2SLS model from a large U.S. sample to address the endogeneity of schooling. From what we have studied above, there is a causal relation between schooling and returns based on the human capital investment theory, basically people who have received more educations earned higher wages. While some arguments asserted that earning cannot be simply estimated by education level result from wages level can be affected by individuals' abilities. A previous study of human capital stocks suggest that human capital stocks may be endogenous and various specification errors could result in OLS estimates of the wage equation either overestimating or underestimating the productive returns from human capital.(T. Paul Schultz 2003). In order to find out coefficient estimates of endogenous years of schooling affecting on wages, we used two stage least squares model instead of ordinary least square procedure to eliminate the possible endogenous bias. David Card have analysed return to schooling by using college proximity as instrument variable and reached the wildly accepted notion that people with higher education level would have higher wages(David Card 1993). Our essay chosen mother's education level as an instrument variable to estimate a structural model with endogenous regresssors.


[1] studies of the united states are reviewd in Rosen(1977), and Willis(1986). A survey of international studies is presented in Psacharopoulos(1985).

[2] Griliches(1977)

[3] David Card 1993

[4] Angrist and Krueger(1991a)


[6]Verbeek,M,2008, a guide to modern econometrics , chichester,3nd, new york; chichester: wiley p134-137

“estimates of the economic return to schooling from a new sample of twins” indicates that omitted ability variables do not bias the estimated return to schooling upward, but that measurement error does bias it downward” while because the schooling differences between twins are not random, it is possible that this estimate of using twins is bias. (Orley Ashenfelter and Alan Krueger's 1994)


Griliches,Z 1977, Estimating the Returns to Schooling: Some Econometric Problems, Econometrica, Vol. 45, No. 1 (Jan., 1977), pp. 1-22,

Kling, JR 2001,Interpreting Instrumental Variables Estimates of the Returns to Schooling."Journal of Business & Economic Statistics 19.3 (2001): 358.

Polacheck, SW& Siebert, WS 1993, The economics of earnings, Cambridge University Press, Cambridge

Preston, AC 2001,The structure and determination of wage relativities, Ashgare, Hampshire.

Christopher F Baum, September 2007, Instrumental variables: Overview and advances, Boston College and DIW Berlin, UKSUG 13, London