Does School Quality Matter? Returns to Education and the Characteristics of Public Schools in the United States

Arguments that rise in public school funding provides few significant benefits for pupils, contrast other evidences on the school quality. First, some studies have found significantly positive relationship between school quality and earnings.[1] Second, the development of black-white relative earnings during the past century has been attributed to growth in the relative black school quality. [2]
There are various explanations for such evidences. Researches on earnings and school quality are mainly centered on the correlation between school attributes (such as per capita expenditure) and the mean earnings of students in a school district. With the argument that family background variables have an impact on both education expenditures and labor market earnings, the correlation of school quality and earnings is likely specious. On the contrary, some can claim that test scores are a lacking measure of school performance, since earnings and test scores are not identical though they may be correlated. Those having an impact on following labor market achievement may have an insignificant effect on test scores.
This research deals with the analysis on the link between earnings and school quality for men born between 1920 and 1949 using samples from the 1980 census.
The findings imply a significant variation in the rate of return to education across individuals with varying states and times of birth. A great deal of these differences is related with the disparities in the school quality. Those who are educated in schools having lower student-teacher ratios and greater relative teacher wages have higher rates of return. Furthermore, returns are found to be related to higher teacher education. However, with school quality measure constant, there is no evidence that the returns to education are linked to income or levels of schooling of the parents' generation.
The focal point of the paper is the relation between school quality and the education rate of return. Increase in the earnings and schoolings relationship does not essentially boost mean earnings, for instance, earnings gained by more educated employees might be at the expense of the less educated. Meanwhile, variations in school quality have an impact on the mean education level and on the marginal return to additional school years. Furthermore, holding constant the permanent discrepancies among individuals born in different states, there is a significant positive school quality impact on both the mean school years and mean student earnings. Also by augmenting the years of completed education, as well as each school year return, changes in school quality have an effect on succeeding income. 

I. An Empirical Framework for Modeling Returns to Schooling

The goal here is to link the returns to education of individuals attended schools in various states to the public school system attributes. It is assumed that individuals are educated in their state of birth and private schooling is ignored.
The equation used for earnings is a linear combination of the effects of birth of state and region of residence, which allow the observed rates of return to schooling to differ due to variation in the return to education across various regional labor markets and due to variation in the rate of return to education gained by individuals in a certain state of birth and cohort in any labor market.[3] By including the relations between state of birth and schooling and another set of relations between region of residence and education, the state of birth-specific input to the return to education is determined by individuals who attended school in one state and transferred to another region. In addition, it was assumed that the state of birth components in the return to education relies on the public school quality, and also potentially on a series of state-specific constants, which is a linear function of the quality of education in a certain state during the period that a specific cohort went to school and the state of birth effects. In this condition, the latter absorbs any variations in the returns to education such as those from discrepancies in the distributions of ability across states.
The paper first estimates the mean rate of return to education for individuals of a specific cohort born in a particular state, while holding constant state of birth, state of residence, and any regional dissimilarity in the return to education. Afterwards, a second-step regression is used to link the estimated rates of return to the quality variables. The procedure has quite a few significant advantages:
1. It offers convenient cut of the data and the demonstration of the diversity in the returns to education and their connection to measures of school quality.
2. It aids the general models of the earnings function
3. The simple correction for the interstate movement of children can be included.
It also comes with certain a disadvantage. Particularly with the two-step procedure the cohorts should be defined quite generally to acquire reliable estimates of the state- and cohort-specific returns to education.

A. Functional Form
The linear schooling-(log) earnings relation is broadly used in applied studies of earnings. Such relation is more or less linear in pooled samples (of individuals coming from various states and birth cohorts) but is nonlinear for certain subsamples. Also, changes in the public school quality alter the returns to elementary or secondary education more (or less) than the returns to college. Hence, the return to education function condition should allow for curves at 12 years of schooling.
Simple evidence on these issues was attained through estimation of a set of unrestricted earnings-schooling models from narrowly defined subsamples of individuals in the 1980 census.
Three general results were obtained:
1.  For a specific cohort and state of birth group, the earnings-education relation is roughly log-linear for education level over the minimum threshold.
2. The threshold differs broadly across states and over time within states, for instance, it is fairly low for older cohorts and for individuals belonging in states having lower mean educational attainment.
3. There is a positive correlation between the mean educational attainment of a state of birth and cohort group and the threshold point in their return to education function. From this, and through additional estimation and comparison, a simple empirical relation was observed: across various cohorts and states of birth and various race groups, the threshold point correspond roughly to the grade level achieved by the lower 20 percent of the  education distribution of employees.
Due to the pattern of the nonparametric estimates of the return to education function for the bigger states, the rest of the paper focuses on estimating the return to education for years of education over the second percentile of the education distribution of an individual's state of birth and cohort. It is important to mention that the estimated rates of return to years of schooling over the threshold prove to be rather comparable to the estimated returns from a conventional log-linear earnings-schooling model.

II. Measures of the Quality of Public Schooling

Data on the public school system attributes in each state are available on a semi-yearly basis from 1918 to 1958 in the Biennial Survey of Education and yearly since 1960 in the Digest of Education Statistics. The Office of Education tabularizes the outputs of questionnaires submitted to the education state offices, concerning the statewide enrollment, revenues, number of teaching positions, length of school term, mean teacher wages, and other variables.
The available data provided information on three main attributes: enrolled student to teacher ratio in the state, the mean length of the school term, and mean yearly teacher wages. The three hypotheses made were:
1. The rise in term length raises the quantity of materials dealt in a school year, thus boosting the economic value of extra years of education.
2. The decline in the student-teacher ratio enhances the classroom instruction quality which leads to greater returns for each completed school year.
3. Higher teacher wages allows schools to draw in and retain more qualified and highly motivated teachers, which results to better classroom instruction and greater returns to education.
Previous authors, such as Morgan and Sirageldin (1968), Johnson and Stafford (1973), Wachtel (1976), and Rizzuto and Wachtel (1980), have applied total expenditures per student as an index of school quality. However, it seems that the schooling quality is more directly related to indexes of student-teacher ratios and teacher wages than to total expenditures per student. This finding was also implied in Welch (1966). Nonetheless, approximately 60 percent of total education spending is from teacher salaries. Since the per capita spending on teaching wages is just the ratio of the mean teacher salary to the student-teacher ratio,  the gap in teacher wages and student-teacher ratios account for a majority of the differences in total spending per student.
Also, with the geographic deviations in the cost of living and in the level of alternative salaries accessible to possible teachers, it appears unlikely that the level of teacher salaries is a proper index of teacher quality in different states. Therefore teacher salaries are normalized in each state by the level of mean state salaries. In addition, the changing scope of the social security salary index and with the need for index-linking unequal salary series, the trend in the mean relative teacher wages during the sample period is removed. In particular, the relative teacher salary in each state is divided by the national mean of this ratio in the same year. By doing so any time-series inconsistency in the mean value of relative teacher wages are eliminated, while the interstate variation in relative teacher wages is preserved at a point in time.
The three school quality measures are reported for three cohorts of students born:
a.       between 1920 and 1929;
b.      between 1930 and 1939;
c.       between 1940 and 1949.
The assumptions for the means are that each individual goes into public school for 12 years and that the number of annual birth in any cohort is constant. By assuming 12 years of schooling, the potential quality of the education accessible to individuals in a particular cohort and abstract from the likely endogeneity of school quality and mean schooling are measured. However, the quality measures are found to be nearly equal when the averages are estimated by means of individual-specific schooling years for the men in each group.
Further results indicate considerable difference in school quality across states, while there is a much lesser interstate difference in the school quality measures for the later cohorts. The latter mainly applies in the term length variable, which is observed in a narrow range for individuals born in the later cohort. Meanwhile, the trends in school quality during the sample period differ extensively across states.

III. Returns to Education by Cohort and State of Birth for White Men

Presented in this section are the estimates of the mean education rates of return for white men born in the 48 mainland states and the District of Columbia from 1920 to 1949. The samples are divided into three 10-year birth groups and estimated rates of return for 147 individual states and age groups were obtained

A. Rates of Return to Education by State and Cohort
The estimated education rates of return are derived from three age group-specific regressions fitted to separate data on log weekly earnings for 1979. The explanatory variables in each regression comprise a set of indicator variables for an individual's current state of residence and individual’s state of birth, and hold for possible experience and its square, marital status, and residence within a standard metropolitan statistical area (SMSA)). The models also include interactions among nine present region-of-residence dummies and completed schooling in order to manage the differences in the education rate of return across various labor markets. Lastly, the models contain state of birth-specific interactions with individual schooling. Such interactions are viewed as estimates for the education rate of return for individuals belonging to certain cohort and state. Regardless of having the estimates attained from highly parameterized models, having 158 explanatory variables in the regression equation for each group, the estimates are fairly accurate, with standard errors ranging from 0.1-0.3 percent in the majority of states. The resulting patterns indicate that the mean rates of return to education are much lower for older employees: 5.1 percent annually for age group of 50-59, in contrast to 7.4 percent for the age group of 30-39 in 1979. Meanwhile, the interstate distribution in returns (adjusted for sampling error) suggests an opposing trend, in which it is largest for the oldest group and smallest for the youngest.
Also, the estimated correlations imply that returns to education are significantly related to all three school quality measures. On the other hand, by dividing the states into three groups, according to student-teacher ratio, the output shows that returns are greater among states having lower student-teacher ratio provided that teacher wages are controlled for, and greater among states having higher relative teacher salary, holding the student-teacher ratio constant.
Another finding, as implied by the resulting sampling error, suggest that the inter-cohort variations in the returns to education are inaccurately estimated for some of the smaller states. Hence, further observations show that the rates of return to education increased more rapidly between the 1920-29 group and the 1940-49 group in states that had a greater decline in student-teacher ratios.

B. Rates of Return and the Quality of Schools
The models in this section rely on the interstate co-variation between rates of return to education and measured school quality in estimating the impact of the quality variables. The estimated coefficients suggest significantly greater returns for the later cohorts: roughly 1.2 percent per decade. All three variables, student-teacher ratio, term length, and the relative teacher salary are robustly correlated with education return. However, when the three quality variables are jointly included, the impact of term length and the student-teacher ratio is smaller and less accurately determined. This is most likely due to the multi-collinearity across the quality variables.
The sizes of the estimated school quality coefficients suggest a quantitatively significant school quality impact on the return to education. For instance, a reduction in the student-teacher ratio by 10 pupils is related to a 0.9 percent rise in the return to years of education beyond the threshold level. If the threshold is 8 years of education and is impervious to the variation in school quality, then the decrease in the student-teacher ratio will increase the earnings by 3.6 percent of high school graduates. Likewise, a 30 percent raise in relative teacher pay is expected to increase the rate of return to education by about 0.3 percent and the high school graduates earnings by 1.2 percent, given that the threshold level of schooling is constant at 8 years.
Regardless the joint significance of the quality variables, they have a rather small contribution in explaining the inter-cohort trend in returns to education. Models with consideration of state effects, in comparison to those without, show that the quality variables explain more of the inter-cohort trend in returns to education. However, the cohort dummies are highly significant, and their exclusion results to a considerable exaggeration of the quality effects.
Meanwhile, the larger mean rates of return for younger employees do not essentially imply true cohort effects. If relation between age and the return to education does exist, the estimated cohort dummies baffle cohort and age.
In addition to the results showing school quality variables explain somewhat little of the cohort effects, such findings indicate that majority of the higher return to education noticed for younger employees can be credited to age effects.
Lastly, in considering the estimated state effects, they are found to be largely significant. The output also implies that there is absence of several significant state-specific determinants of the return to education in the analysis. Assessment of the estimated state effects shows that returns to education are rather low for men from South and in the North Central/Northwest regions and rather high for those from Midwest and Northeast.
Such finding for white men born in the southern states is quite unexpected, given that the quality measures in the analysis pertains to the whole school system for each state. States that functioned in an unintegrated school systems prior to 1954 usually had lower student-teacher ratios, longer term lengths, and higher teacher pay in white schools than in black schools (Card and Krueger, 1992). Thus, the mean quality measures with regards to entire student enrollments understate the quality of the white schools in these states. Nonetheless, when a dummy variable for the segregated states is included in the model, the results are not in agreement with a simple mismeasurement hypothesis for the quality of white schools in the South and instead, they indicate that other measures of quality were considerably lower in the South or that other attributes of the southern states have an effect on the returns to education.

C. Other Characteristics of Schools and States
In each case in analyzing the impact of other school and state-level attributes on the returns to education, three basic school quality measures and state-specific fixed effects are included. An observation is that the estimated coefficients of the school quality variables are greatly unchanged by the inclusion of controls for other attributes, such as teacher and private school characteristics, mean income in the state, and educational accomplishment.
Meanwhile, several prior studies have observed a strong relationship between aspects of family background, such as parental schooling and earning, and the student performance on standardized tests. If these family background attributes are associated with school quality and if such characteristics eventually vary significantly within states, the estimates of the school quality effect may be perplexed by the impact of family background variables.
Finally, the estimated impacts of the three major school quality variables are impervious to the addition of such family background variables.

a. Teacher Characteristics
In assessing the role of teacher attributes on the returns to education, the portion of male teachers is considered since controlling for the level of teacher wages, one might predict the teaching staff quality to differ given the percentage of male teachers. Presumably, if female teachers were paid lower compared to identical males for the period of 1926-66, one can perceive the fraction of male teachers as an alternative for lower-quality teachers. On the other hand, the percentage of male teachers can be taken as an indicator of higher nonwage return or better working environment within the schools, which would potentially draw in relatively more men into teaching, provided that the relative wages are controlled for.
The findings suggest that a rise in the portion of male teachers in the state has a significant negative effect on students' return to schooling. Also, a rise in the percentage of male teachers (in 1966) is linked to a 0.8-percentage-point decline in the return to years of schooling beyond the threshold. Moreover, it is difficult to determine whether the percentage of male teachers affects the return to education because males are less efficient teachers, or via some other channel.
Meanwhile, the estimated coefficient of average teacher education is positive and statistically significant, while the estimated impact of teachers' experience is insignificant. On the other hand the student-teacher ratio and relative teacher salary remain in being significant indicators of the return to education when such teacher quality variables are added. Furthermore, the study’s estimated coefficients are barely influenced by the inclusion of the teacher quality variables. Lastly, the inclusion of controls for the mean education and experience of teachers scarcely alters the estimated coefficient of the percentage of male teachers.

b. Educational Distribution
In an another model the estimates of the high school and college completion rates per state of birth and cohort group are included as to control for portion of a given cohort. For instance, assuming that more schools are established in a state, this leads to a reduction in the travel time for pupils and in the student-teacher ratio.
Assuming further that individuals differ in their expected returns to education and that as more schools are constructed several students having lower expected returns to education remain in school longer. Hence, improvements in school quality can be considered to be correlated with lower returns to education, suggesting a negative correlation between the mean return rate to education and the percentage of individuals having higher education. In addition, mean educational attainment and measures of education quality are strongly and positively correlated. This indicates that if rates of return differ systematically across the population and if individuals having higher expected returns opt for further education, there exist a potential downward bias in the estimates of the impact of schooling quality on returns to education. This can be managed partially by including measures of the proportion of individuals at higher education levels in each cohort.
Moreover, high school graduation rate and the college graduation rate do not have a statistically significant impact on the return to education. Also, the former holds a negative coefficient, while the college graduation rate has a little, positive coefficient. These findings, however, offer no evidence that students enter themselves into various levels of schooling based on different expected returns to education.
Meanwhile, with regards to the impact of the dispersion in educational achievement in a state on the return to schooling, increases in school quality are linked with lower dispersion in the schooling distribution.

c. Private Schools
Although not all attends public school, the school quality measures are based on the public school system attributes in each state. For the period 1920 to 1960, the percentage of students attending private schools increased, however, this range of the fraction of private enrollments differs across states. The existence of private schools brings in two possible sources of unobserved difference in school quality:
1. Private schools may be relatively more effective than public schools
2. Private schools may possibly have different employment levels, teacher wages, and term lengths in comparison to public schools.
To deal with these issues, data on private school enrollments and student-teacher ratios by state and cohort are gathered. The student-teacher ratio data in private schools is constrained to Catholic schools.
The findings show that when student-teacher ratios, term length, and relative teacher wages in the public schools are held constant, the private school enrollment variable coefficient is numerically small and statistically insignificant. These imply that increases in private school enrollment do not by themselves impact returns to schooling.
Meanwhile, with the exemption of the term length variable, the school quality variables are statistically significant. On the contrary, the variables measuring family background attributes, student educational attainment, and private school attendance typically have small and insignificant effects.

d. Evidence for Black and White Men Born in the South
Regardless the limited evidence of family background effects in the return to schooling, the wide disparity in school quality for men belonging to different states and cohorts seemingly reveals gaps in salaries and preferences for schooling over time and across states. A possibly more appropriate test of the school quality effects is based on the earnings experiences of blacks, since swift school quality developments that happened from 1920 and 1960 for black schools of the segregated southern states present an arguably exogenous experiment for assessing the impacts of school quality.
The findings from assessing the impact of school quality on the returns to education for southern-born black and white men were employed in northern cities. Itseems to be qualitatively and quantitatively similar to those in the previous sections. This gives additional evidence for an underlying interpretation of the school quality effects in previous sections.

D. Adjustments for Mobility of Preschool and School-Age Children
So far, the analyses have implicitly assumed that an individual goes to the public school in his state of birth. Interstate mobility of preschool and school-age children poses a concern comparable to measurement error in the interpretation of the returns to schooling for those born in a particular state. It is practical to focus on a single cohort and to consider that individuals are enrolled in only one state.
The results of interstate mobility-adjusted model seem to have minor impact on the qualitative and quantitative conclusions of the previous section. This also implies somewhat low mobility rates of preschool and school-age children and the lack of a strong link between interstate mobility and the geographic pattern of the measured quality of schooling.

E. Log-Linear Specification
A log-linear specification is broadly used in the literature, and it is useful in verifying the sensitivity of the estimates to the functional form assumptions. However, regardless of specification, the school quality variables have statistically significant and considerable impacts on the return to schooling. Such findings imply that the connection between school quality and the return to schooling is not primarily sensitive to the specification used to estimate the return to education.

IV. The Effects of School Quality on Education and Earnings

On one hand the advantage of analyzing the relationship of school quality and the return to schooling is being able to control for overlooked differences across state of birth groups and cohorts.  Background factors that augment income of individuals of a certain group are absorbed by the cohort-specific state of birth impacts included in initial equation. On the other hand, the disadvantage of focusing on the return to schooling is that variations in school quality may just expand the earnings distribution with no increase in the mean income. It is even possible that changes in school quality modify the schooling distribution, and the slope of the earnings-schooling relation, without impact on the earnings distribution.
In exploring these concerns, there are two considerations:
1. Analysis on the effect of changes in school quality on the location and shape of the earnings-schooling relationship.
2. Presentation of simple reduced-form evidence on the relationship between school quality and the levels of education and earnings.
However in interpreting the result, it must be kept in mind that as opposed to the analysis of the returns to schooling, the influences of school quality on the distribution of education and on the levels of earnings cannot be determined in models having unrestricted cohort-specific state of birth effects..

A. Location and Shape of the Earnings-Education Relationship
Given the assumption that the educational distribution is not affected by a decline in class size, there are two considerations,
1.      The schooling level attained by those belonging in the second percentile of the education distribution rises as class size decreases.
2.      A decline in the student-teacher ratio is linked with a small and statistically insignificant upward shift in the intercepts of the earnings-education relationship.
A regression of the state of birth-specific intercepts of the earnings-schooling relation on state of birth effects, cohort effects, and the three school quality variables produces negative coefficients for the student-teacher ratio and for term length variable, and positive for the relative teacher salary. The coefficients for all three are small and statistically insignificant. Meanwhile, the quality variables are found to be jointly insignificant.
The finding reflects that a decline in the student-teacher ratio turns and shifts out the earnings-education relation, with an intersect point about the twelfth or thirteenth grade level. Indeed, narrowing the sample to those who have precisely 12 years of education, the school quality seems to have an insignificant impact on earnings, indicating that the intersection is around the twelfth grade. At a fixed education level, those with postsecondary schooling seem to gain from enhanced school quality, while individual having below high school education seem to earn less. On the other side, a rise in school quality increases levels of education, mainly in the lower tail of the education distribution. These returns to education compensate for the apparent losses due to the shift in the earnings-schooling function, leading those in the lower tail of the earnings distribution roughly as wealthy and those in the mid and upper parts of the earnings distribution wealthier.
            The result of the regression aimed to further analyze the impacts of changes in school quality on those belonging in the lower tail of the earnings distribution, showed little but generally positive and marginally significant impacts of higher school quality on earnings of the tenth and twenty-fifth percentiles.

B. Reduced-Form Estimates
In summarizing the school quality effect on average income, several simple reduced-form estimates of the school quality impact on log earnings and schooling were computed. These reduced-form models consist of measures of school quality, state of residence and state of birth effects, and demographic variables such as age, age squared, and marital status indicators and residence in an SMSA).
The results indicate that improvements in school quality are due to increases in both average income and mean years of schooling. Meanwhile, each of the quality variables is a significant determinant of earnings and mean education, when each are included individually. On the other hand, jointly, the pattern of coefficient estimates is comparable to that in previous sections: the student-teacher ratio and the relative teacher salary remain significant, and the term length variable is insignificant. For the model wherein (log weekly earning as the dependent variable) the exclusion of state of birth dummies yields greater school quality effects. Meanwhile the exclusion of current state of residence effects lowers the goodness of fit of the earnings model but has a small effect on the magnitude of the school quality coefficients.
According to the estimates of the majority of models, a decline in the student-teacher ratio by 10 pupils is expected to increase mean earnings by about 4 percent and increase mean schooling by 0.6 years. However, the 0.6-year rise in mean education is likely to be perceived to raise earnings by 3.2 percent.
Meanwhile, the total gain in earnings from a decline in the student-teacher ratio is somewhat 30 percent greater than would be predicted on the basis of the rise in mean schooling alone. While, the gain in earnings is approximately 40 percent greater than would be predicted basing on the increase in schooling alone.
Finally two conclusions can be drawn from the reduced-form relations between earnings, education, and school quality.
1. Improvements in school quality for the past century are due to rise in years of education and average salary.
2. Increases in earnings seem to show both a gain for the extra years of schooling and a rise in the return for each existing year of schooling.
Both results must be adjusted by inability to control for overlooked cohort-specific factors that may increase the earnings of those from states having better schools in the reduced-form models. Taking these considerations together with the evidence assembled on the returns to schooling, there is strong support for the conclusion that improvements in school quality lead to bigger earnings.

V. Conclusion and Discussion

Men who attended schools in states having better-quality school systems earn higher economic returns for their years of education. Even though the evidence is essentially non-experimental, the findings are perceived to be consistent with a causal interpretation of the role of school quality, since:
1. The findings were based on statistical models that hold constant any variations across state of birth and cohort groups in the total earning levels.
2. Differences in the rates of return to schooling gained by present residents in various regions of the country were controlled for.
3. Any permanent dissimilarity across states in the return to schooling gained by different cohorts of men and for variations in family background measures (schooling and parents' generation income) that may have an effect on subsequent labor market performance is also controlled for.
4. The reduced-form analysis verifies that improvements in school quality raise the mean student earnings.
Hence the school quality effects are not just redistributive, nor are they an artifact of shift in the distribution of educational attainments.
The findings emphasize the paradox that school quality seems to have a vital impact on labor market performance but is generally assumed to have no effect on standardized achievement tests. However, two current experimental studies of school attributes and test scores are consistent with positive school quality effects.
1. A study suggests that decline in the student-teacher ratio for elementary school pupils significantly raise test scores on reading and math exams (Finn and Achilles 1990).
2. Another randomized study shows that increasing the school term by offering additional instruction during the summer has a positive impact on disadvantaged students' test scores (Sipe, Grossman, and Milliner 1988).          
Even though more is needed to be done to resolve the available evidence, still, the success in the labor market is at least as significant measurement in assessing the performance of the schooling system as success on standardized tests. At the very least, the result of a positive relationship between school quality and the economic returns to schooling must have silenced those who claim that investments in the public school system have no advantages for the pupils.



Source:
David Card and Alan  Krueger, “Does School Quality Matter? Returns to Education and the Characteristics of Public Schools in the United States”, Journal of Political Economy, Vol. 100, No. 1. (February, 1992), pp. 1-40.



[1] Welch (1966); Morgan and Sirageldin (1968); Johnson and Stafford (1973); Wachtel (1976); Rizzuto and Wachtel (1980).
[2] Welch (1967, 1973a, 1973b); Freeman (1976); Smith and Welch (1989).
[3]


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