How To Determine The Effect Of College Quality On Future Earnings

Transcription

1 Does the College You Attend Affect Your Future Income? Maciej Misztal and Dominic Valentino Many studies examine the relationship between quality of higher education and future returns to income. Rising costs of attendance, especially at the private elite institutions, warrant a thorough inspection and analysis of the quality effects in higher education. A literature study is undertaken which examines various approaches to this questions, as well as procedures for overcoming selection biases and omitted variable bias. The brief look at the structure of higher education and credit constraints is also included. A discussion follows which relates the findings to other topics within the economics of education framework. The most significant relationship is found in private northeast schools where the returns to attending have been increasing and significantly larger then recent returns from public schools. However, due to relatively high tuition costs and other factors, we do not recommend that all necessarily attend such schools. We find that individuals should make their own decisions based on a cost-benefit analysis reliant on their beliefs on returns of education.

2 I. Introduction Throughout much of the 1970s the earnings premia associated with age and experience in the United States were relatively large. At the same time, the opposite was true for return on education; in fact, the return on a college education decreased over much of the 1970 s. In the 1980s however, the situation of earnings premia was reversed. The return to postsecondary education that began to grow in 1979 created incentives for high school graduates to attend postsecondary institutions in the 1980s: in 1979, 31.2% of high school graduates aged attended some form of college, while in 1988 this figure increased to 37.3% (Levy and Murnane 1992). Research pertaining to the understanding of the earnings premium associated with college attendance has lead to the composition of a relatively large amount of literature regarding the returns to income associated with colleges of various type and quality. The question of how quality of college has an effect on future income is of particular importance, especially if one considers the increase in cost to attending college that students have endured in recent years: Is a 200% increase in the average cost of attending college between 1981 and 2002 (Boehner and McKeon 2003) warranted by some type of increase in the return to attendance, when the consumer price index increased by less than 100% during that time period? The following page features an exhibit that illustrates the pace of college costs and the point that the cost of tuition increased by more than double that of inflation at the beginning of the new millennium. One set of postsecondary schools that has undergone the largest increases in cost of attendance consists of private colleges and universities. At present, the cost of attending an elite private institution 1 is estimated to be approximately $1,000 per week, 1 The actual cost students incur is usually less than the cost stated due to financial aid 1

3 compared to $630 and $250 per week for general private schools and public schools respectively (Morganthau and Nayyar, 1996). These institutions are considered to be amongst the best in terms of quality of education. Especially amongst the elite private schools in the nation, graduates are known to obtain the highest incomes and best positions in both the labor force and academia; this often anecdotal evidence seems to conclude that private schools have a positive effect on future income. However, there is a 2

4 problem of selection that occurs during the application and admission process for students and schools that causes problems for those attempting to accept this inference. The fact that the best students may and most likely do attend the higher quality schools may cause a regression model to overestimate the college effect in an earnings equation. In other words, the high quality students that attend an elite school like Harvard may not necessarily earn the income they do after they graduate from Harvard because there were extraordinary increases in that individual s human capital while they attended. It is more likely that this individual would have earned a high income regardless of the level of quality or type of school he or she attended. In order to partially compensate for this problem in statistical analyses, good research includes some measure of student quality in their regression models (Dale and Kruger 2002, Brewer et al 1999, James, Alsalam, Conaty and To 1989, Solmon and Wachtel 1973). Some researchers have even attempted to model students choices in an effort to reduce the error caused by selection (Dale and Kruger 2002, Brewer et al 1999). In order to have a clear understanding of present research, it is necessary to clearly identify the ways in which most studies classify different colleges and universities. One way mentioned already is by prestige or source of control, e.g. private elite. A popular technique for sorting colleges is by selectivity. Studies that use this method obtain information such as SAT scores of students admitted to each college and calculate an average score for each institution which they include in their regression analyses as a selectivity measure. Another prominent approach is sorting colleges and universities by quality. To determine the quality level of a school some studies use popular standards and rankings according to the Carnegie Commission for Higher 3

5 Education (Solmon and Wachtel 1973) or Barron's Profiles of American Colleges (Brewer et al 1995). Some have even considered the number of PhD holding instructors a measure of quality for colleges and universities, finding significant results for this quantification and the effect it has on future earnings (Alsalam, Conaty and To 1989, Lindahl and Regnér 2003). This paper intends to gain and present a better understanding of the role of college quality and other postsecondary institution characteristics in determining future income. Particular attention will be placed on the application of two types of models for student outcomes: models based on human capital perspectives and models based on signaling theory. The heart of our research and inspection of the topic lies in section II, titled Literature Review. This section examines a portion of the large amount of literature written on the signaling and human capital effect of various types of colleges and universities on future income. In section III, Discussion, an interpretation of these studies, their methods, results, and conclusions will be presented; this section will also present some ideas for the future of research for this subject. Additionally, a clearer viewpoint of the decision process of colleges and universities, as well as the student and his or her decision process within the framework of economic models will be included. Section IV, Conclusion, will summarize findings regarding the topic by highlighting significant research results. II. Literature Review Care must be taken in choosing regression models when studying college quality and future income. College selection is not simply a choice made by the student. The college must confirm this choice by accepting the student, which leads to inaccuracies in simple regressions. Secondly, the effect of an institution may be attributable to the higher 4

6 average quality of student rather then the actual return to education, as noted earlier. A number of methods are used to combat these and other misspecification problems. Many papers use an instrumental variables approach, in which an observable statistic uncorrelated with the rest of the model but correlated with a desired unobservable characteristic is used to measure the effect of the desired unobservable characteristic. However this approach is limited as the number of instrumental variables that may be used in one regression must be kept relatively small to remain effective. Also finding appropriate instruments for the variables that are correlated with the variable in question but uncorrelated with every other variable is difficult. The Brewer et al (1999) papers below use a multinomial logit approach which is used to control for characteristics of both groups as well cross-sectional effects. However, independence of irrelevant alternatives must be assumed. This assumption is dubious for education and these models quickly become unwieldy as more factors are taken into account. One of the earliest studies of the relationship between college quality and earnings was completed by Solmon and Wachtel (1973); they used the rankings (scale 1-8) as developed by the Carnegie Commission for Higher Education as a measure for college quality in determining the return it generates in the earnings of the sample of approximately 3700 World War II veterans who volunteered for pilot or navigator training. To avoid misrepresentation of the college effect, Solmon included a measure of student ability in his regression analysis. Without including measures for the socioeconomic status of students and individual ability, the analysis concluded that the quality of an institution had a positive and significant impact for the sample group. Once these measures were included in the model, the estimation of the impact of school quality 5

7 on earnings was not clear, i.e. the effect of college type was not statistically significant. Solmon does give the coefficients for his regression but no information regarding the statistical significance of each variable. Another notable paper, published by James Estelle et al in (1989), examines the effect of college quality on future earnings and finds significantly different results. The study considered the characteristics of colleges including expenditures per student, public versus private control, location, and PhD awarding institutions, to determine the effect on future earnings of a set of male students who graduate high school in 1972; to account for the selection that takes place between student and institution and the difference in students backgrounds, data obtained from school transcript records and the National Longitudinal Survey of the High School class of 1972 (NLS-72) concerning family background, prior achievement, SAT scores, parents education and employment status was included in the regression analysis of future income. The study concludes that the returns to college quality are small in general, regardless on the model variable chosen. Specifically, attending an institution that employs a high degree of selectivity in admission and a private elite college in the northeastern area (the northeastern private school effect ) of the country has both a positive and statistically significant effect on future income. An interesting finding in this study comes from the fact that when the authors examined private schools outside the northeast, there was a slightly negative, insignificant effect on future income. The chart on the following page gives the results for the coefficients of their regression. Note that the coefficient for characteristic of being a private east (PRIV E) school is positive and significant in each type of the model used, while the private 6

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9 school only coefficient (PRIV) is negative and insignificant in each case. A more recent article published in 1999 by Brewer et al attempts to obtain an understanding of the relationship between undergraduate attendance at a private elite college (grouped in 6 categories via Barron's Profiles of American Colleges) and labor market outcomes with a longitudinal analysis of the logarithm of students hourly wages/total earnings and type of institution attended. They model the relationship utilizing data from the NLS-72 and High School and Beyond (HSB) for a pool of 5,227 students who attended and graduated from a four-year college. In addition to the wage earning regression, the study attempts to estimate the relationship between the net cost of attendance individuals incur and their choice of college, so that some idea of the selectivity that occurs may corrected from the model. The results of the regression highlight a large return to attending an elite private institution when compared to the bottom quality public schools. The authors conclude that the return to attending a top quality and medium quality private school had increased between the early 1970 s and late 1980 s: the earnings premium (as a percentage of the bottom publics figure) associated with attending an elite private institution rose from 15% in 1986 for those who had graduated for 10 years to 37% for those out of college for 6 years in The return to attending a medium quality private school is slightly smaller than the elite return. One finding that seemed contrary to intuition was that the regression indicated weak evidence for the return to elite public institutions when compared to the bottom publics. The exhibit on the following page labeled Table 3 gives the earnings 8

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11 differentials 2 for each type of school examined. Focusing ones attention to the sub rows denoted with (2)s for each type school 3 it can be noted that the only large and positive increases in wage with respect to the bottom public type school are achieved by the top and middle quality private schools. Brewer et al (1998) also published a similar study that considered the effect of college quality and the likelihood of participating in graduate studies. The authors note that the consideration of the likelihood to attend graduate school is unique in that students attend graduate school to open their options for privileged careers (e.g. doctor, lawyer, professor) more so than to obtain an increase in potential for wages in the labor market, whereas undergraduate degrees are more often sought to obtain the latter. The analysis of the regression model on the data gives the conclusion that attendance at an elite private school has a positive and significant effect on the probability that a student will attend graduate school, and additionally there will be a greater chance that students attend a major research school. Linda Loury and David Garman (1995) published a study that explored the effect college performance and selectivity has on earnings. Their analysis focused a considerable amount of attention on determining the different effects for whites and blacks. Using data from NLS-72 and HSB, the regression the study employed used measures to account for variation caused by selection and other pre-college differences. The results of the study indicate that Blacks who did poorer on standardized tests but attended more selective schools were mismatched, having a smaller chance of graduating and subsequently a lower future income than whites and black who were more 2 These differentials are calculated in relation to the bottom public type schools return 3 These rows of differential correspond to calculations completed with a correction for selectivity 10

12 properly matched to their colleges. When comparing the results of the study to research examples that do not include measures for college performance in their models, the authors found that the results of the studies would most likely overstate the effect of selectivity for whites and understate the effect for blacks. Several interesting studies on the effects of college quality and earnings have been completed for countries outside North America. One of these studies, College Quality and the Japanese Labor Market, by Hiroshi Ono (2004), gives a consideration of the effect that college quality has on the earnings of male students in Japan. This study sheds light onto the role that colleges play in the unique Japanese labor market; competition for acceptance into the best schools in Japan is fierce. Unlike schools in the United States, the key determining factor for acceptance into colleges in Japan is not past performance (in high school) but college entrance exams. Students invest a great deal of effort and time preparing for these exams also known as examination hell. Prior to this study little work had been completed regarding the payoff to college quality in this competitive market. This is due mainly to the scarcity of data in Japan. Ono used data from the Stratification Mobility National Survey (SSM) to estimate the relationship for male workers between earnings and the endogenous variables of college quality (as measured by the mean entrance test score of each institution), individual ability, years of experience, tenure, etc. The regression analysis in the study pointed towards the conclusion that college quality in Japan has a positive and significant effect on earnings even after accounting or individual ability. The magnitude of this effect ranges from 2.5 percent to 15.6 percent. The author goes on to note that the variance in rewards may be used to explain the motivations for students willingness to participate in 11

13 examination hell, i.e. college prestige. However, further research is necessary. For more information on the changing nature of higher education a more general overview of the field was needed. Hoxby (1997) analyzes the development in the structure of higher education in the past 50 years and its effects on tuition. The work is relevant for this topic in that it finds that the market for education has become deregionalized and students are better matched into institutions by quality. The variance in quality of students within an institution decreased, while variance across institutions increased. The paper attributes this to better sorting capability. The paper also noted that tuition is growing compared to rates of return and inflation. A classic problem when measuring returns to education is accounting for person ability and experience. Most papers account at least peripherally for these effects using SAT scores or AFQT results. A simpler, more accurate, and traditional method to control for genetic and environmental ability is to use data from twins. Miller, Mulvey, and Martin (2001) build on two twin studies by respected researchers in the field of education. Behrman et al (1977) used WWII veteran twins and found that although the return to schooling was 8 percent, only 2.7 percent could be attributed to schooling as opposed to genetic factors and shared family environment. Ashenfelter and Krueger (1994) use more recent data to account for omitted variable bias and find that genetic and environmental variables have no effect on returns to schooling and that measurement error biases estimates downward. However their data set is relatively small. Miller et al (2001) use a data set almost eight times as large from Australia which is also likely to be more random and representative. Their study reports similar results to Behrman. However, these are general returns to education studies and have wider focus then simply 12

14 higher education. However, one would expect these results to be magnified with regards to higher education only. A twin study focusing exclusively on higher education was conducted by Behrman, Rosenzwig, and Taubman (1996). They use sets of female twins to control for environment and previous schools attended. They find that personal endowments do have a significant effect on the amount of schooling received and choice of school. Many quality-measuring variables of colleges had significant effects in raising income among female twins, including granting graduate degrees, private status, small enrollments, and well-paid professors. The returns on graduate degree granting status and well-paid faculty in particular are underestimated by studies without controls for personal endowment and previous schooling, according to the paper. Finally, the study shows females with higher wage endowments are less likely to attend postsecondary institutions. When they do attend, females are more likely to spend more and they are likely to devote more years to schooling, in comparison to less endowed females. The authors suggest the last point is particularly troublesome as it is compounded by the fact that public schools are likely to pool their funds into flagship universities, thereby making the rest of the schools, and the poorer students who are likelier to attend them, worse off. Monks (2000) calculates the effect of gender and race of the student on returns from higher education. The model uses only the most general controls for selectivity by accounting for income and academic ability (AFQT scores) as observable characteristics relevant to choice. The study disregards multinomial logit correction and instrumental variables as being too difficult to implement with this model. Instead it focuses on the robustness of its data set from National Longitudinal Survey of Youth modified to control 13

15 for specific school selection. The results find males earning significantly more then females and found a negative premium for white students, after controlling for student ability and income. The study claims that institution quality matters and that research institutions or graduate degree-granting institutions both have significant positive premiums over liberal arts colleges. Quality as measured by Barron s selectivity measure also had significant effects at two tiers. These effects are higher for females and nonwhites. Black and Smith (2004) use matching to overcome the selection problem. If students and colleges sort, then the effect of a high quality student in a low quality college and vice-versa (so called counter-factual) are not adequately measured. This is in addition to the regular problem of selection bias not being accounted for in classic linear regressions. The study measures the probability of attending a high quality university, in addition to actual attendance of the university as control variables. In other words, it contrasts the predicted placement of a student by their observed statistics with the actual attendance outcome. While this admittedly is not a complete solution, the paper seeks to determine the presence of the selection problem, net necessarily accurately quantify it. The study reports that there is a higher likelihood of high quality students being mismatched into low quality schools then vice versa, implying that studies which only look at top tier attendance are non-random and biased upwards. In addition, the effect of sorting in general is higher in a non-random selection of higher schools then in random selection of general schools. The statistically significant characteristics of college quality are faculty salaries, freshman retention rate and average SAT score, all of which increase future income. Unfortunately, the number of high quality students in low quality schools 14

16 was too low in the data set to enumerate statistically significant results, as evidenced by the high standard errors. However, the paper still purports that even its unreliable estimates are troubling enough to suggest that the standard linear regressions do not sufficiently account for the counterfactuals. The paper also notes a significant tradeoff between bias from choosing too many variables and overspecifing the model and a bias from leaving out many of the variables that justify matching and the results. Dale and Krueger (2002) solve the selection problem by limiting their data set in a particularly clever way. Rather then using a general spread of the population, they consider groups of students accepted into different levels of selective colleges. They compare those who attended the most selective of those schools with ones who went to less elite schools. Then a comparison was done accounting for SAT scores of the present university relative to average SAT score of schools applied and accepted. The difference between the two studies is said to be the unobserved characteristic of motivation removed from ability. This could be deciphered by the admissions committee but not through SAT scores, accounting for the disparity between scores and acceptance. Thus, using two studies, observed ability, unobserved ability, and total ability can all be measured with respect to income. By matching sets of students accepted and rejected by the same institutions the paper attempts to overcome selection bias. However, the paper admits that there is no possible control for other types of sorting. Namely, an unobserved motivation might yield higher utility and income from a less selective school. Such examples may be specific majors or programs that might be available in larger more general colleges but not elite institutions. In such cases there is a comparative advantage for such students to attend less selective schools then they would 15

17 otherwise. Also, more able persons is more likely to apply to more selective institutions. Comparing the SAT score of the individual to the average of the schools applied should control for this effect. The results find that students who were accepted to and rejected from comparable schools earn comparable earnings even if they attended less selective schools, as measured by average SAT score. In addition, the study concludes that more able students predominantly attend more selective schools, verifying the suggested errors of previous papers. Once again, these conclusions can be questioned on the basis that more able students who may know they have a greater comparative advantage going to a less selective school are more likely to attend a less selective school. In this case, causality cannot be implied, although the claim is made that this does invalidate the more selective school always leads to higher income rule. Also of interest is the relationship between spending, tuition and future income. All three are positively correlated with one another, although the relationship between student expenditure and future income is probably the most important and causal. However, the continuous rise in college tuition is speculated to have decreased the rate of return on education in the present relative to 30 years ago. Finally, students from disadvantaged backgrounds have the highest premium for attending selective colleges. Speculation suggest that the lack of increase of children from low income backgrounds attending elite schools is troubling and perhaps financial aid and admissions policies should take this into regard. A related topic examines the importance of costs with regards to students choice of college. Crucial to the questions asked above is the existence of a restriction imposed by lack of financial endowment on higher education attendance. If poorer students with 16

18 equal ability were unable to attend college, then all other results would be skewed, even when controlling for income. Carneiro and Heckman (2002) do a literature survey and run their own analysis, accounting for the difference between predicted college attendance in instrumental variable models and traditional OLS regressions. Although they go on to look at long term credit constraints, the affect of family income on nurturing ability, this is more controversial and falls out of scope of this paper. Short term credit constraints, the lack of financial endowment affecting the immediate decision of attending higher education, can be better estimated. They are found to be relatively low at four percent. Long (2004) uses a conditional logistic choice model to take advantage of the heterogeneity within higher education data while being able to control the characteristics of each student. They find that while a thousand dollar increase in general tuition created a 15 percent decrease in likelihood of enrollment in 1972, this number fell in By 1992 this figure no longer had statistical significance. However, a positive effect on college attendance that was significant only in 1992 was county unemployment rate. The likelihood of attending one college over another based on a $1000 tuition hike was a decrease of 53 percent in Again, by 1992 that statistic had fallen by two-thirds. The perceived relationship between school cost and quality on future income partially explains the above observations. The study also found that distance played a smaller part in the student decision in 1992 and that students were more likely to choose a school with an SAT median score higher then their own, suggesting they were taking on greater challenges. In summary, distance and tuition have decreased in relevance in regards to school choice between 72 and 92 while the effect of county unemployment increased. 17

19 (A table is amended to our paper summarizing the above findings.) III. Discussion The following section will discuss inferences, conjectures, and interpretation of the literature study in the last section. As generalizations are made and conjectures are posed, it is crucial to consider that although there may be other relevant studies that address these questions more directly and from other perspectives, the following section only considers the previous research cited and addresses dilemmas only from the context already presented in this paper. The emphasis is on better understanding the material already covered, and not necessarily approaching the following topics holistically. The basic effects of quality of education on income and the subsequent influence on choice of schools is a topic that is particularly able to be set into the framework of economics without many irrelevant assumptions and overly complex models. Much of this may be attributed to the long history of the field and attention of particularly phenomenal economists in the past. It seems this field relies on theories that are not only elegant and simple, but also useful under empirical scrutiny. First, people seem to act rationally in a way that does not rely on particularly individualized preferences, which is the crutch of economic theorists. The Homo Economicus has been criticized as unrealistic. Real persons empirically seem to be relatively bad judges of risk and therefore bad predictors of future outcomes. Even this excuse does not always satisfactorily account for the linchpin of rationality: consistency. However, the choice of college is only undertaken at most a couple of times by each person and is pursued with the specific goal of maximizing one s future returns. Such an investment seems to be well investigated by the individual. Time-based research shows that with the increase in availability of information about schools as well as the increases 18

20 in customization and specialization of even the largest campuses, persons seem to be better sorted then ever to schools with other persons of similar ability (Hoxby 1997). This verifies the validity and efficiency of a largely free-market system between schools and students. The pairing of appropriate students to the appropriate schools is more efficient then ever, despite the preponderances and complexity of unobservable characteristics within the students. Due to the decrease in variance of student ability within a particular school and the increase in variance throughout the field of higher education it is clear that schools are better specializing into their niche and that a greater variety of students can be accommodated by a plethora of schools. This is reassuring as the market for both school and students is growing increasingly global, and both groups can only expect to become more heterogeneous overall. Distance in particular is an increasingly irrelevant factor in school choice. Rather then a handful of local schools, a modern student may pick from across the entire country, or even the world. However, there are conceivable market failures in this system. Although this paper does not wish to breach the topic of student financing, which in itself is a welldeveloped and expansive field of study, it is inevitable that the issue of capacity to pay is raised. In addition to natural ability, the cost of education is a restriction on students, and the research shows that disadvantaged persons have a higher premium to the education they will be least able to afford(long 2004). However, the flexibility of financing is also increasing and the above research which claims that cost is becoming a non-factor in choice of school may be explained through such flexibility. The policy prescriptions for scholarships as well as policy advice for other topics addressed in this section are beyond 19

21 the scope of this paper and have also been addressed by researchers in the field many times over. This paper also does not want to directly address the effect of income or environment on development of ability (so-called long term credit constraints), also a strong field of study. Conversely, the research among twins as well as other attempts to control for socio-economic status do support the claim that it is ability that drives the choices of students and schools. Financial endowments inherent in each student have only a secondary effect through the-above-mentioned ability. Merit is the basis of future success as both the value added and signaling models claim. In the end, the superficial reliability of assumptions of theory may be overlooked if the model is useful. The primary characteristic for evaluating the validity of a model is predictive power. Although both the value-added and the signaling models of education have extrapolative clout and in many cases agree on outcomes, there is a slight difference between each which must be considered in any comparison between the two. Unfortunately, although the understanding of higher education s effect on future income is better understood now than at any time in the past, the separation between the two models is still muddled. Once again, it is worth noting that the evaluation of the models is not a clear purpose of any of the studies above, and that there are certainly studies that better address this issue. However, proponents of either model will find justification in this work. Followers of the signaling school will find validity in the fact that prestigious schools and more specifically the private schools within the Northeast United States having the greatest pulling power and greatest selectivity, despite the apparent lesser 20

22 return in future income per dollar of tuition. Although tuition is correlated with spending per student (Dale and Kruger, 2002), this ratio varies wildly and becomes much greater towards the top of the higher education spectrum. Signaling may also better explain the increased benefits of females and minority students, specifically African-Americans, attending a better school. A degree will be better able to overcome statistical prejudice, which majority males do not need to overcome (Becker 1957). One would expect there to be a greater return to this group as they have farther to go in terms of improvement of future wages to achieve parity. Even if they receive the same wages as their white male counterparts, they will have significantly higher returns to education because their base is less. The divergence in future incomes of various majors does not contradict with signaling, as different majors have different perceived difficulties even across schools. An employer would presume a philosophy degree is not equivalent in value to a physics degree. The continued existence of prestigious liberal arts colleges with high returns to education across fields lightly supports signaling as such an education is increasingly less directly relevant to modern lifestyles, yet maintains high returns in future wages (James et al, 1989). However, the fact that this return is decreasing compared to general schools (Monks 2002) does suggest value added theory. Finally, the aspects of the student population in each school which are relevant to future income, such as average SAT score of schools accepted, and to a lesser extent the average SAT score of the students attending the school, are statistics irrelevant to the performance of a student in school (Dale and Kruger, 2002). They imply that GPA and competition in college are less important than the competition to get in. For instance, 21

23 once in a school, a student may well free ride on the reputation of his peers, and only acquire a fraction of their human capital while receiving much of their returns from education based on the degree alone. They can rely on their SAT scores to get them into college, and then no longer need to strive. This seems to be especially true in light of the recent allegations of grade-inflation throughout top universities. Less selective schools show more evidence of a greater use of an individual s access to resources within a school to improve one s human capital affecting returns to education (Black, et al, 2004). Colloquially, the future incomes in less selective schools depend on a students ability to take advantage of resources within a school and differentiate herself from her peers. This is especially true in large state schools, and honors programs directly reflect that belief. This is clearly a contradiction of signaling theory. Supporters of the value-added human capital school will claim that persons better self-select into the schools which will benefit them most. This will explain the small but undeniably present faction of high-ability students attending schools that are statistically less prestigious then they would be expected to attend. The specific reasons for each student to make this decision have not been empirically justified but are abundant and readily available through anecdotal evidence and intuition (i.e. specialized major, program, professor). The value-added approach justifies the resultant future income that is comparable to that of better signaling schools. In addition, the direct correlation between money spent per student and future income is better explained if that money actually improves the productivity of the student. Likewise, the increasing specialization of schools and majors, and the overall move away from an all-encompassing liberal arts education may be interpreted as a striving towards greater efficiency in training students. 22

24 Finally, the aspects of quality in institutions which seem to make a statistically significant difference in future wages are value-adding resources, such as faculty income, degree granting status, research status, and small enrollment. As with most analysis using these two methods, actual data most likely reflect some of both models. Therefore, there is really is no first best solution to improve selection between students and schools. Any inference or suggestion about making the system more efficient by optimizing by one system or the other is severely compromised by the presence of externalities of education and the complexity of the situation. In addition, the system as it stands now seems to be very efficient in matching student s ability and their returns to scale. More specifically, the system maximizes individuals productivity based on inherent constraints not imposed by the education system. If income or family name played a large part in the choice of schools, then this could be a sign of inefficiency. It is also true that students may optimize their resource spending decision between preparing for selection and actual education once in school based on their belief in each theory. When developing their individual cost-benefit analyses, they may decide that greater resources must be spent in getting the most prestigious degree by weighing resource towards preparations for applying, e.g. SAT prep courses. Perhaps afterwards they would have fewer resources (or motivation) to devote once actually attending the school. This seems especially true outside the United States, as demonstrated explicitly in the case of Japan (Ono 2000). Someone placing more emphasis on the value added approach might choose to make the most of a less costly education, perhaps by attending a large subsidized state school in which they are able to take advantage of fast track and 23

25 individualized attention. It is clear that both approaches are rational and supported by the empirical evidence. The studies mostly agree that school choice must be made on an individualized basis, and there is no set rule for optimizing the selection process for all students. It is therefore promising that the information costs and transaction cost for researching this choice and applying to schools is decreasing with the advent of better communication and sorting technologies stemming from the digital age. Imagining the choices made by students and schools as under a game theory model, it is unclear who would move first. The average ability of the students is the most valuable asset of the schools in improving the variables that attract students. The students are drawn to the schools which seem to present that best return in the future, and these are tied to the quality of student already attending. Therefore there is a clear cycle with no beginning between the choice of the school and the choice of the student. Likewise, from a funding perspective the amount of tuition that can be demanded and future donations is largely reliant on the quality of student, and the quality of student is strongly affected by the amount spent per student. The amount spent must be tied to tuition. While both the students and schools optimize to each other, it is the schools overall which have the greatest flexibility, as each school gets to play the game repeatedly, unlike any student. Like the students, optimally they find a niche and may try to attract the highest quality student in that niche. However, it would seem to be too costly to try to improve a school too substantially and compete with schools already at a higher tier. Certainly at the highest tiers it is pragmatically too late to create any sort of an institution to compete with the endowments of the private or public schools already having such status. 24

26 Perhaps the most difficult challenge in this field of study, and the reason why more specific answers cannot be obtained in the discussion above, remains the problem of double and self-selection. Although the evidence is promising regarding the ability of test results, GPA, and other easily observed performance statistics to characterize the ability of a student, there is still a disparity between these indicators and actual acceptance patterns. This divergence can be attributed to the ability of schools to evaluate non-observable characteristics through interviews and essays. In addition, it is clear that there may be demographic or secondary characteristics or values that influence the choice of whom to accept, especially in private schools. Therefore the inability to better separate the choice of the student from the choice of the schools is troubling. Although probit and logit methods in econometrics are designed to solve this problem, they become exponentially more complicated as they become more detailed and there are still clear restrictions of the models. A separate discussion considers the finding that students who attend privately controlled and funded schools may have very different outcomes in terms of future income, depending on where their school is located. This northeastern private school effect is most likely a result of the prestigious schools in the area and not just the geography itself. Interest rises from this finding of geographical significance and future research is warranted. Studies that focus on a large number of students disaggregated to a state level would be beneficial to an understanding of this phenomenon. Using this type of analysis, there is a chance of explaining why some have found that elite public schools have no significant impact on students future incomes. For further clarity we pose this idea in the form of a question: does it seem reasonable to conclude that attending elite 25

27 public schools such as UC Berkeley and Pennsylvania State University does not give students a better chance at achieving a higher income than a local community college, or is the model used to come to this conclusion not applied at the appropriate level? The matter of the private northeastern effect leads into a consideration of the questions that motivated our paper: are the large increases in the average cost of tuition at all colleges and universities and the difference between the cost of attending a private college as opposed to a less expensive public college warranted. We consider the conclusion that Brewer et al (1999) arrive at: there has been an increase in the earnings premium associated with attending elite private schools and medium quality private schools when compared to the return of the low quality public schools. In simple terms this means that increases in cost of attendance may be justified at some private schools, but no evidence supports the same for public schools of any quality level. Also when considering the large difference in cost of attending private schools and publics schools, there may be some rationalization for the same reason. However, in light of the evidence that high quality students do well regardless of their school quality level (Dale and Kruger 2002), it seems more reasonable from a cost benefit analysis that these high quality students should consider some of the elite private schools less expensive counterparts. IV. Conclusion Reviewing the results of literature focusing on elite and highly selective institutions, it seems clear that the student who attends these universities will experience higher incomes. The answer to whether or not these institutions are the root cause for such income premia is not complete, but using measures to account for student ability it 26

28 seems that at least some of the premium associated must be due college effects and not just students characteristics or motivation. Looking over time, the cost of attending all types of postsecondary institutions has risen on average over the past 20 years (Boehner and McKeon 2003). It is interesting to note that evidence suggest increases in cost of post secondary school is justified only at select private institutions (Brewer et al 1999). We also examined a number of peripheral issues. With regards to cost of education affect on choice of college Carneiro and Heckman (2002) find there is only a minor credit constraint and Long (2004) confirms that the importance of cost and distance in the choice of whether and where to go to college has been decreasing overtime. We then sample various controls for selection bias and omitted variable bias. Behrman, Rosenzwig, and Taubman (1996) provides a traditional twin study that finds that college-quality matters in terms of granting graduate degrees, private status, small enrollments, and well-paid professors. Monks (2000) uses a traditional model with a specialized data set and finds that amongst schools, research and graduate degree granting institutions have higher returns, especially among minorities and females. Black and Smith (2004) use a matching method and contrast the predicted ability to attend a more selective school with actual attendance. It suggests that studies that only take into account better schools contain bias and that students attending lower then predicted schools make a difference in the data, although they themselves could not measure it. Dale and Krueger (2002) resolve this dilemma by contrasting schools the student was accepted into with actual school attended and finds that the former is a better predictor of future income then the latter. However, selection on the basis of comparative advantage admitted could skew results and so the causality cannot be concluded. 27

29 A discussion followed relating these results were affirmed to be consistent with the rational aspects of economic theory and market between students and schools was hypothesized as becoming more efficient and optimal. The conclusions of the research were also analyzed in light of the value added model and signaling theory. Also considered was the optimal course for school selection by student and the effect of student selection by schools on ability to attract students. References: Ashenfelter, O., & Krueger, A. B. (1994). Estimates of the Economic Return to Schooling From a New Sample of Twins. American Economic Review, 84 (5), Becker, Gary S The Economics of Discrimination. University of Chicago Press, IL. Behrman, J. R., Rosenzweig, M. R., & Taubman, P. (1996). College Choice and Wages: Estimates Using Data on Female Twins. Review of Economics and Statistics, 78 (4), Behrman, J., Taubman, P. and Wales, T. (1977). Controlling for and Measuring the Effects of Genetics and Family Environment in Equations for Schooling and Labor Market Success. In P. Taubman (ed.), Kinometrics: the Determinants of Socioeconomic Success within and between Families. Amsterdam: North-Holland, pp Black, Dan A. and Jeffrey Smith "How Robust is the Evidence on the Effects of College Quality? Evidence from Matching," University of Western Ontario, CIBC Human Capital and Productivity Project Working Papers 20033, University of Western Ontario, CIBC Human Capital and Productivity Project. Boehner, John A. and Howard P. McKeon. The College Cost Crisis Report Congressional Report. Brewer, Dominic J., Eric Eide, and Ronald G. Ehrenberg, "Does It Pay To Attend An Elite Private College? Cross Cohort Evidence on the Effects of College Quality on Earnings," Journal of Human Resources, Vol. 34(1), pp Brewer, Dominic J., Eric Eide, and Ronald G. Ehrenberg, "Does it Pay to Attend an Elite Private College? Evidence on the Effects of Undergraduate College Quality on Graduate School Attendance," Economics of Education Review, Elsevier, Vol. 17(4), pp