# Using Momthers Education As Instrumental Variable Education Essay

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Human capital resources are a crucial part of an individuals 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 labor 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". (Psacharopoulos1985). 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:

(1)

WHERE

= 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.

Let

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 :

(2) (3)

(4)

Since L=N+S

(5)

Mincer assumes that the annual earning of the better educated can adjust to equalise the discounted values of lifetime earning at different schooling levels.

Thus:

(6)

which shows that the discounted values for individuals with S and 0 years of schooling will be the same.

Rearrangement of equation (6) shows that the potential earnings capacity of a person with S years of schooling is equal to:

(7)

ln logarithms equation (7) becomes:

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 (Ashenfelter and Krueger(1992))

"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 intrumental 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)

## 3.Endogeneity

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.

, (2)

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= Î² + Î³bAS = Î² + Î³cov(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{XtÎµt}â‰ 0 which implies that the schooling is an endogenous variable. And this induces a downward bias in OLS estimates. Note that Îµt 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.

## 4.data and OLS estimates

## Data description

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 OLS estimation

We begin with runing the OLS model which can be used together with 2SLS model to run the Husman test and have a comparison with the 2SLS model.

From the results presented above, what should be noted is that the R2= 0.2905,which means 29.05% of the dependent variable(log wage in 1976 ) can be explained by the independent variables listed as above. In addition to that, 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 .

## 5.Instrumental variable and schooling

Based on the discussion in part 3, we know that schooling is endogenous and one of the solutions is to instrument it. Recall that a suitable instrument is required to meet two conditions: relevance and exogeniety. The relevance side of the instrumental variable means that the IV must be correlated with the number of years of schooling .While the exogeniety condition requires that the instrumental variable must not correlated with the error terms in the income equation. See more information about instrumental variable in Wooldridge (2002).

According to a variety of literatures reviewed from previous studies, mother's education to some extent affect children's education. 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 .

For experience and experience square, age and age square are obvious candidates and in our model, we use mother's education as instrument for schooling.

## 6.Estimates of Return to schooling

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

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 low corelation between exp76 and age also leads to the larger standard error of the 2SLSmethod. What is further ,if the more weakly the instrument and endogenous regressors are correlated ,the less efficient the measurement of 2SLS. In addition to that,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 of the variables 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 we cannot dimiss Ho: all variables are exogenous which means all the variables are exdogenous.

## 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

## 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.

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's education, nearc4 which have been mentioned in previous literatures.

## 7.Concluding to remarks

This essay evaluates the relation of the returns to schooling for men in U.S. within a standard human-capital model. From what we have studied above, there is a causal relation between schooling and returns based on the human capital investment theory, namely the more education a person have ,the higher the corresponding wages. While some scholars asserted that earning cannot be simply estimated by education level .In other words,wages level can be affected by other factors ,like individuals' abilities. One previous study of human capital stocks suggested that human capital stocks may be endogenous . Various specification errors will lead the OLS estimates in the wage equation either overestimating or underestimating in terms of the productive returns from human capital.(T. Paul Schultz 2003). In order to find out the effect of years of schooling on wages, we used two stage least squares(2SLS)model instead of ordinary least square(OLS) method to eliminate the potential 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). In our essay , we use mother education as an intrument variable to schooling and age to the experience and age2 to experience2.Via 2 Stage Least Squares method,we estimated the reduced form for the eductaion in 1976,we find mother education is correlated with our dependent variable and age2 is correlated with experience2,however, due to some reason,age is not an desirable intrument variable to experience from the first stage equation.Mother's education is an exogenous but weak determinant of schooling.Then we use Durbin and Wu- hausman test the adjusted model ,the result is what we expected that all variables are thus exogenous,E(Xi|Îµi)=0.Through the Hausman specification ,it turned out to be that OLS method can be accepted as the alternative of 2SLS method.From the comparison between OLS and 2SLS method ,both the coefficient and standard errors of educatin in 1976 are bigger in the latter measurement likely due to the sampling erroers. Only based on 2SLS and OLS methods,there are may be some defective in the test results .Due to the limited data, instrument variables, and the unknow relationship between instrument variables and error terms ,we need further discuss and do more research .