Human capital attainment, university quality, and entry-level wages for college transfer students.

Hilmer, Michael J.

1. Introduction

The U.S. higher education population is highly mobile. Tinto (1987) finds that roughly 35% of college graduates from the National Longitudinal Study of the High School Class of 1972 graduate from a different institution than the one they first attend. Recent evidence suggests that the percentage of college attendees choosing to transfer is on the rise. For instance, a U.S. Department of Education survey of 1992 college graduates finds that over half of the roughly 11,000 students interviewed had attended more than one institution during their college careers (National Center for Education Statistics 1996). Despite their obvious place in American higher education, very little is known about college transfer students. The economics of higher education literature has devoted much attention to the economic returns to college attendance and the causes and consequences of college dropouts. Within the vast literature, however, the transfer student has largely been neglected.

This is particularly regrettable, as transfer students present the researcher with additional, potentially valuable information that nontransfers do not. In particular, transfer students will have taken courses at more than one quality institution. This fact can possibly be exploited to provide insight into the role of human capital accumulation in determining a student's postgraduation earnings. A common problem in the economics of higher education literature is that the well-known positive return to the quality of university from which a student graduates is predicted by both human capital and screening theories (for a more detailed discussion, see Weiss 1995). Much of this confusion may be based on the fact that previous studies have focused only on graduation quality. While such an approach is accurate for nontransfers, it is not accurate for transfer students. Transfer students clearly complete courses at institutions that are of different qualities. The human capital theory has implications for the pre dicted returns to initial quality and tenure for transfer students, while the screening theory does not. Thus, the returns to initial quality and tenure may be used to generate some idea which model more accurately describes the role of educational attainment in determining a student's entry-level earnings.

This study is one of the first to separately examine the economic returns to college attendance for transfer students. In particular, I focus on the returns to quality and educational tenure at institutions other than the one from which a transfer student graduates and ask what implications such values have for human capital theory. A theoretical discussion describes how the educational experiences of college transfer students can be used to address the role of human capital accumulation in determining a college graduate's entry-level earnings. Specifically, to be consistent with human capital theory, the quality of all institutions attended should have positive effects on future earnings, while the length of time spent at each institution is uncertain. The longitudinal nature of the data set analyzed allows me to improve the efficiency of my estimates by employing panel data techniques. Using random effects generalized least squares (GLS), I find significant, positive, and statistically similar returns to b oth initial and graduation quality and insignificant effects for both initial and graduation tenure. In other words, by finding that both initial and graduation quality have significant positive effects on future earnings, the results can be considered consistent with the predictions of the human capital theory.

2. Theory

To frame the empirical work here, I start by developing a simple model of college choice. In choosing a college, the prospective student has thousands of options to consider. This choice set will differ for each student as it is limited to only those colleges to which he or she is able to gain admission. Each college presents the student with a different combination of quality and cost. A college is an efficient option if no other college offers a higher quality at a lower cost. The student limits his or her search to these efficient options. From this efficient set, the student chooses the level of quality and implicitly the particular university that results in the highest total utility. If this value exceeds that which could be received in the labor market, the student chooses to attend the university. If it is less, he or she forgoes college attendance and enters the labor market directly...

To formalize the student's college choice, assume there are two distinct periods representing the college and postcollege years. (1) The student's objective is to maximize the utility he or she receives from consumption in the two periods. Each student enters the first period with a fixed amount of family wealth, M, which is allocated between current consumption, [X.sub.1], and the cost of college attendance. Let Q represent the quality of university from which the student graduates and let C represent the cost per unit of quality. (2) Finally, if the student chooses not to exhaust his or her first period wealth, he or she saves the remainder, at interest rate r, for use in the second period.

The student is able to work for k years during the second period. A student's future earnings will depend on the quality of university he or she attends. (3) Let f(Q) represent the student's postgraduation earnings function. In addition to earned income, the student receives interest payments on any money saved during the first period. The sum of these two incomes is spent on second-period consumption, [X.sub.2].

The optimization problem facing the university-bound student is

subject to [Max.sub.[X.sub.1],[X.sub.2],Q] U([X.sub.1], [X.sub.2]) [X.sub.1] + CQ [less than or equal to] M [X.sub.2] = f(Q) * k(1 + r)[M - C(Q) - [X.sub.1]]. (1)

The solution to this optimization problem yields a familiar system of Kuhn-Tucker conditions. (4) These conditions indicate that a student chooses his or her optimal institution by equating the marginal return to college quality to the marginal cost. As the marginal benefit of college quality depends on the effect that college quality has on a student's future earnings, the specification of the earnings function is of primary importance to a student's decision. Consequently, the work here focuses on the role that college quality plays on a student's future earnings.

Unfortunately, the student's problem is not necessarily as simple as specified in Equation 1. Graduation from college is an uncertain event. Simply gaining admission and enrolling at a particular institution does not guarantee that a student will one day complete the requirements for a degree at that institution. On graduation from high school, neither colleges nor students are certain whether students have the ability and/or desire to persist to graduation. Thus, it is reasonable to assume that substantial mismatching exists between students and first-choice colleges. In a nontransfer world, students who decide to attend a particular institution must either persist to graduation at that institution or drop out without receiving a degree. In a transfer world, students who are initially overmatched and do not meet the requirements at their first-choice institutions can transfer to lower-quality institutions rather than dropping out. (5) Likewise, students who are initially undermatched and far exceed the requi rements at their first-choice institutions can transfer to higher-quality institutions.

Consider the difference between the earnings function for a student who transfers from his or her initial-quality institution to a different-quality institution. This student will not have one fixed quality, as specified in Equation 1, but rather he or she will have different qualities for all institutions attended. Let [Q.sup.G] represent the quality of university from which the student graduates and let [Q.sup.T] represent the quality of university from which the student transfers. In addition to the different qualities, the student will have different tenures at each of the different institutions. To account for this, let [[alpha].sup.T] the percentage of total credits spent at the initial institution. The postgraduation earnings function for a transfer student is then

f([Q.sup.G], [Q.sup.T], [[alpha].sup.T]), (2)

as presumably the qualities and tenures of all institutions will affect a student's future earnings.

An important question is how the different qualities and tenures at each institution affect a student's future earnings. By examining only the quality of university from which a student graduates, previous studies (Wales 1973; Solmon and Wachtel 1975; Wise 1975; James et al. 1989; Mueller 1988; Rumberger and Thomas 1993) have implicitly treated the transfer student's earning function as specified in Equation 1 rather than Equation 2. As such, they have ignored the potentially important effect that initial quality and tenure may have on postgraduation earnings.

The additional information to be gained by controlling for a transfer student's entire educational background may provide insight into important economic questions. For example, human capital attainment is a cornerstone of much of the economics of education literature. According to the human capital theory of Becker (1964), the oft-cited positive return to a college education (recent examples include Katz and Murphy 1992, Murphy and Welch 1992, and Kane and Rouse 1995) results from the increased human capital attained through college attendance. A natural extension of this argument is that students who attend higher-quality universities accrue higher levels of human capital and should receive higher wages on graduation (this argument is supported by Psacharopoulos 1974). Indeed, James et al. (1989), Rumberger and Thomas (1993), and many others find a positive return to the quality of university from which a student graduates. If human capital increases with college quality, then the quality of each institutio n attended should affect a student's future earnings and not just the quality of university from which the student graduates. This observation leads to testable hypotheses about the postgraduation earnings function of college transfer students.

For demonstration purposes, I will distinguish between three students who graduate from the same-quality institution: those who transfer from a lower-quality institution, those who transfer from a higher-quality institution, and those who do not transfer. Contrasting the expected returns to quality and tenure for these students will demonstrate how transfer students might provide additional insight into the role of human capital accumulation in determining a student's future earnings.

Consider first the expected return to quality. Human capital theory implies that higher-quality universities provide higher levels of human capital. Hence, the return to quality should always be positive, not only for the graduation institution but for all institutions attended. In other words, holding graduation quality constant, the higher the quality of institution initially attended by a transfer student, the more human capital the student should have accumulated. This should be true regardless of whether the transfer student increases or decreases quality. For example, consider students graduating from a university with a median SAT score (the quality measure used in this analysis) of 1000. A student who transfers up from a college with a median SAT score of 800 should have accumulated more human capital than a student who transfers up from a college with a median SAT score of 600. Likewise, a student transferring down from a college with a median SAT score of 1400 should have accumulated more human capi tal than a student transferring down from a college with a median SAT score of 1200. Consequently, under human capital theory, we would expect a positive return to initial quality ([Q.sup.T] > 0) for transfer students regardless of whether they transfer up or down in quality.

In addition to the different-quality levels themselves, the lengths of time a student spends at different-quality institutions should affect his or her human capital accumulation. Predicting the expected return to tenure is not straightforward, however. To see why, consider a transfer student who increases quality from his or her initial institution ([Q.sup.G] > [Q.sup.T]). As a first pass, one might predict that according to human capital theory such a student would be accumulating less human capital than a student who attended the graduation university continuously without transferring. It then would follow that the longer the student spent at the initial, lower-quality institution, the less human capital he or she would accumulate. Contrast this to a transfer student who decreases quality from his or her initial institution ([Q.sup.G] < [Q.sup.T]). According to simple human capital theory, such a student would be accumulating more human capital than nontransfers, and the longer the student spends at the in itial, higher-quality institution, the higher the accumulation. Thus, to be consistent with simple human capital theory, one might simply expect a positive return to the length of time spent at initial institutions for transfer students who decrease quality and a negative return to the length of time spent at initial institutions for transfer students who increase quality.

This simple interpretation ignores the important role that learning plays in human capital accumulation, however. If indeed students transfer because of an initial mismatching between their ability and/or motivation and that required at their initial institution, then the tenure at their initial institution may not have had uniform effects on human capital accumulation. The reason for this is that effective learning might depend on the quality of the match between a particular student and his or her classmates at a given school. As an example, consider a student who is far overmatched at his or her initial school. Being toward the bottom of the class, the level and pace of instruction might be high and fast enough to preclude effective learning. If so, the student might actually lag so far behind his or her classmates that he or she is able to learn less than if he or she were in a class with less talented peers even though that class would be taught at a lower level and slower pace. In such a case, transfer ring down to a lower-quality institution might actually facilitate better learning and more human capital accumulation. Under such a scenario, the simple predictions outlined previously would be inaccurate. Therefore, without being able to isolate the specific effects of classroom learning, the predicted effects of tenure at initial and graduation institutions is uncertain. (6)

3. Empirical Model

The empirical work here attempts to test the predictions of the theoretical discussion by estimating wage functions for a sample of college graduates. To motivate the empirical work, I start by writing a general form of the wage function to be estimated. A student's future earnings are assumed to be a function of his or her experiences during college as well as individual and family background characteristics that may affect his or her productivity level. Let the student's future earnings be

[Y.sub.i] = Y([Z.sub.i], [A.sub.i], [J.sub.i], [P.sub.i]), (3)

where [Y.sub.i] is the log annual earnings of student i, [Z.sub.i] is a vector of individual and family background characteristics, [A.sub.i] is a vector representing i's academic performance in college, [J.sub.i] is the postgraduation job market experience of i, and [P.sub.i] is a vector of variables representing the attendance path i followed while pursuing his or her degree.

Several aspects of a student's educational path are observable to a potential employer. As demonstrated in Equation 2, a transfer student will have some combination of initial and graduation quality as well as some percentage of time spent at his or her initial institution. To account for these values, the student's educational path is considered:

[P.sub.i] = P([Q.sup.G.sub.i],[Q.sup.T.sub.i][[alpha].sup.T.sub.i]), (4)

where [Q.sup.G.sub.i] is the quality of university from which i graduates, [Q.sup.T.sub.i] is the quality of university from which i transfers, and [[alpha].sup.T.sub.i] is the percentage of total credits i spends at initial institutions before transferring to the degree-granting institution. (7)

A general form of the wage function to be estimated is thus

[Y.sub.i] = [B.sub.0] + [B.sub.1][Q.sup.G.sub.i] + [B.sub.2][Q.sup.T.sub.i] + [B.sub.3][[alpha].sup.T.sub.i] + [delta][Z.sub.i] + [eta][A.sub.i] + [gamma][J.sub.i] + [[epsilon].sub.i], (5)

where the variables are defined as previously and [[epsilon].sub.i] is a normally distributed error term. Parameters to be estimated are [B.sub.1], [B.sub.2], [B.sub.3], [delta], [eta], and [gamma]. Moreover, to test the predictions of the theoretical model (i.e., [B.sub.1] > 0 and [B.sub.2] > 0), I want to estimate Equation 5 for the subset of four-year transfer students only, as they are the only subset for which both quality measures are available. (8)

The data set I analyze in this study has postgraduate earnings for multiple years. Therefore, I can improve the efficiency of my estimates by analyzing a panel data set. My estimating equation is then

[Y.sub.i] = [B.sub.0] + [B.sub.1][Q.sup.G.sub.i] + [B.sub.2][Q.sup.T.sub.i] + [B.sub.3][[alpha].sup.T.sub.i] + [delta][Z.sub.it] + [eta][A.sub.it] + [gamma][J.sub.it] + [u.sub.t] [[epsilon].sub.it], (6)

The dependent variable is the logarithm of annual earnings of individual i in time period t(t = 1994, 1997). The constant vectors [Q.sup.G.sub.i], [Q.sup.T.sub.i], [[alpha].sup.T.sub.i], and [A.sub.i] are as defined previously, and the panel variables [Z.sub.it] and [J.sub.it] are vectors of time-specific individual and family background characteristics and postgraduation job market experience of i in time period t. The error term in Equation 6 has two components, [u.sub.i] and [[epsilon].sub.it], both of which have zero mean. The component [u.sub.i] is individual specific and time invariant and generates correlation over time across the observations of a given individual. Because of this correlation, ordinary least squares (OLS) estimation of this equation is inefficient, and the OLS standard errors are inconsistent. I therefore estimate this model using a random effects GLS technique that incorporates this error structure into the estimation. (9) Specifically, random effects GLS estimation utilizes the corr elation over time for a given individual in the estimation of the standard errors.

4. Data

The data analyzed in this study are drawn from a relatively new longitudinal study conducted by the U.S. Department of Education. The Baccalaureate and Beyond (B&B; National Center for Education Statistics 1996) survey tracks the experiences of a cohort of recent college graduates who received the baccalaureate degree during the 1992-1993 academic year and were first interviewed as part of the National Postsecondary Student Aid Study. The base year survey interviewed roughly 10,000 students and collected extensive information on student's postsecondary educational and labor market experiences, including detailed financial aid information. The first follow-up was conducted in April 1994 and collected detailed information on the student's postgraduate education and early postbaccalaureate labor market experiences. The second follow-up took place in April 1997 and collected postgraduate education and labor market information similar to the previous follow-up.

This sampling design makes the B&B ideal for examining the economic returns to college attendance, as such studies require information on several different aspects of a student's college experiences, including field of study, college performance, and the institution attended. Further, because it derives from an initial sample of college graduates, it provides far larger sample sizes than alternative data sets that derive from initial samples of high school graduates. (10) This is because, in general, only about half of all high school graduates ever attend a four-year college, and among those four-year college attendees, less than half tend to persist to graduation.

The dependent variable in my earnings functions is the logarithm of annual earnings. I impose the restriction that annual earnings must be greater than $5000 and less than $500,000. Table 1 contains detailed information on the control variables used in this analysis. The university quality measure is the median SAT score of entering freshmen at a particular institution as reported in Barron's Profiles of American Colleges (1994). The independent variables of interest are binary measures for college major, which are collapsed into seven categories: business, engineering, science, social science, humanities, education, and other major. I use these broad aggregated major categories to avoid small sample sizes associated with more detailed classifications. (11)

The control variables include continuous measures for age at bachelor's degree graduation in 1993, family income in 1991 (measured in dollars), and the student's SAT score. (12) I also include binary variables for race/ethnicity (black, Hispanic, other), gender, marital status, completion of a postgraduate degree, part-time school enrollment, and a control for imputation of the SAT score from ACT data. The models also include indicators for missing values of the continuous variables, in which case the continuous variable is set to zero for that observation. The panel data models also include a year dummy for 1997.

Table 2 presents descriptive statistics for 1994 and 1997 annual earnings and work experience and college qualities and tenures. The first two columns present values for the focus groups of this study: four-year transfers who increase quality and four-year transfers who decrease quality, respectively. For comparison purposes, the final two columns present values for nontransfers and two-year transfers. (13) Allowing for modest inflation, average earnings for this sample of college graduates appear to be consistent with national data. According to the 1990 census of population and housing, the average annual earnings of 18- to 24-year-old college graduates employed year-round full-time in 1990 were $23,430 for males and $20,229 for females (U.S. Bureau of the Census 1992). (14) Comparing across attendance paths suggests little difference between the groups in both 1994 and 1997. Specifically, the average annual earnings of the four groups are within roughly $1000 of each other in both sampled years. Additional ly, in both years, four-year transfers who decrease quality have the highest average earnings, while nontransfers have the lowest. Finally, it does not appear that the differences in average earnings are due strictly to differences in work experience, as all four groups average nearly the same work experience.

Other factors might certainly influence early postgraduate earnings. For instance, there is a wide disparity in the average quality of university from which students graduate. On average, four-year transfers who increase quality graduate from the highest-quality universities, while four-year transfers who decrease quality graduate from the lowest. Given the positive relationship between quality and earnings (James et al. 1989; Rumberger and Thomas 1993), the higher average graduation quality for four-year transfers who increase quality may help explain why they receive higher average earnings than nontransfers. The difference between transfer and graduation quality for the two groups of four-year transfers is potentially revealing. As mentioned previously, a probable reason that a student chooses to transfer is a mismatching between his or her ability and/or motivation and the quality of institution initially attended. The entries in Table 2 suggest that this is indeed correct. Four-year transfers who decrea se quality graduate from institutions that average roughly 115 SAT points lower in quality than those they started at, while those who increase quality graduate from institutions that average roughly 100 SAT points higher in quality. Not surprisingly, students who transfer take longer to graduate than nontransfers. This may explain why nontransfers have more postgraduation work experience by the time of the final survey. Finally, four-year transfers who increase quality have the shortest average tenures at initial institutions, while two-year transfers have the longest. This latter fact corresponds to conventional wisdom that community college attendees are likely to work and take smaller course loads while attending. (15) This may help explain why, despite graduating from lower average-quality universities, two-year transfers have higher average entry-level earnings than nontransfers.

Turning to the values reflecting postsecondary experiences presented in Table 3, the only difference in average grades across the different attendance groups is that transfers who increase quality receive grades that average nearly .2 points (on a four-point scale) higher. This could be due to the fact that such students were presumably "overqualified" at their initial institutions, and therefore, having faced less competition, they likely received higher grades before transferring. In addition, there is a noticeable difference in college major choices, which may help account for the observed difference in average annual earnings. Four-year transfers who increase quality are by far the most likely to major in engineering. Studies of returns to college major have frequently documented that engineers observe the highest return to their degrees, which may provide additional explanation of their increased annual earnings in this sample. Likewise, nontransfers and downward transfers disproportionately choose relat ively low-paying social science majors, which may help explain why they are the two groups with the lowest average earnings. All three groups who initially attended four-year colleges are more likely than two-year transfers to have received postgraduate degrees by the date of the last interview. Finally, comparing individual and family background characteristics suggests that both two- and four-year transfers are more likely than nontransfers to be female. At the same time, four-year transfers who decrease quality and nontransfers are more likely to be black, while two-year transfers are more likely than the remaining groups to be Hispanic.

An important question for the current study is what factors might influence a student's decision to transfer. Comparing the entries in Table 3 across attendance paths for college graduates provides some insight into this question. Four-year transfers who increase quality have the lowest high school grades and test scores but the highest college grades (from Table 2) of all graduates who never attend a two-year college. This provides additional support for the mismatching story by suggesting that students who transfer up are those who have worse records on high school graduation but perform better at their initial institutions. Conversely, students who transfer down have better high school records but perform worse at their initial institutions than students who transfer up. Two-year transfers provide a different story. Those students have the lowest average family incomes and high school grades but the highest average test scores of all college graduates. This suggests that two-year transfers are primarily tw o types of students: (i) those who lack the financial resources to attend a four-year college for four years and (ii) those who are of high ability but perform poorly in high school and attend a two-year college to improve their academic records.

5. Results

The empirical work presented here focuses on estimating the wage functions given in Equations 5 and 6. Table 4 presents random effects GLS log annual earnings estimates. (16) The first column groups all graduates together without distinguishing between nontransfers and transfers and is included for the sake of comparing this sample with previous samples. This specification suggests that results for the current sample are consistent with previous findings. Specifically, for this sample, increasing graduation quality by 100 SAT points increases annual earnings by roughly 3.5%, which is similar to the estimates in James et al. (1989), Rumberger and Thomas (1993), and so on. A problem with the estimates in column 1 and with previous research using that specification is that it requires the estimated coefficients to be constant across attendance paths. To allow for cross-path differences, the final four columns estimate the returns to graduation quality separately for each of the attendance paths described previou sly. These results suggest that the return to graduation quality differs relatively little across attendance paths, as they all suggest that the return is somewhere between 2.5% and 3.5%.

As discussed previously, however, the econometric specification in Table 4 is likely inaccurate for university transfers, as it does not consider the effect of initial quality. Results from the correct specification (Eqn. 6) are presented in Table 5. The three columns in Table 5 present different possible specifications for university transfers. According to Equation 6, the most complete specification is presented in column 3. Before discussing the results, it is useful to recall the predictions from the previous theoretical discussion. To be consistent with human capital theory, both transfer and graduation quality should have significant positive effects on future earnings, while the effects of attendance tenure are uncertain. The random effects GLS estimates in column 3 suggest that the return to initial and graduation quality are both positive and statistically significant. Further, the estimated coefficients for a 100-SAT-point increase in quality are both roughly 1.8% (a simple t-test suggests that thos e returns are not statistically different from each other). The fact that both the transfer and the graduation SAT coefficient estimates are positive and significant could then be interpreted as consistent with human capital theory. Further, the insignificant estimated effects of attendance tenure are not surprising given the unclear predicted effects. Hence, it appears that the results presented in this paper are consistent with the human capital theory of educational attainment.

6. Conclusion

This paper examines the returns to quality and educational tenure for university transfer students. The results suggest that both transfer and graduation quality have significant positive effects on the postgraduation earnings of all university transfer students regardless of whether they increase or decrease quality. Further, the effects of tenure at initial institutions are estimated to be statistically insignificant. Such evidence is consistent with human capital theory, which predicts positive returns to quality for all institutions attended and uncertain returns to tenure at those different institutions.

Table 1

Descriptions of Variables Used in Analysis


Multiyear variables
 Annual earnings Continuous variable representing
 the student's self-reported annual
 earnings at the time of the 1994
 and 1997 interviews.

Work experience Continuous variable representing
 the student's self-reported years
 of work experience at the time of
 the 1994 and 1997 interviews.

Still attending Binary dummy variable indicating
 whether the student was attending
 college part time while continuing
 to work full time at the time of
 the 1994 and 1997 interviews.

Postgraduate degree Binary dummy variables indicating
 whether the student had received
 an advanced degree by the 1994
 and 1997 interview dates.

Constant variables Graduation Continuous variable representing
 SAT, transfer SAT the median SAT score of entering
 freshmen in 1996 at the university
 from which the student graduated
 and at the last university
 attended before transferring,
 respectively. Imputed (using
 Astin 1971) for institutions
 reporting only average ACT scores.

% Credits pretransfer Continuous variables representing
 the percentage of credits the
 student completed at institutions
 other than the student's
 graduation institution. Calculated
 from official transcripts.

College GPA Continuous variable representing a
 student's college grade-point
 average. Calculated from official
 transcripts.

Business, engineering, Binary dummy variables indicating
 science, social science, the major field in which the
 education, humanities, other student received his or her
 major bachelor's degree.

Male, white, black, Hispanic, Binary dummy variables indicating
 other race, married the student's sex and ethnicity
 and whether the student was
 married at the time of the 1994
 and 1997 interviews.

Age at graduation Continuous variable indicating the
 student's age at college
 graduation.

Family income Continuous variable representing
 the total family income from the
 1991 calendar year.
Table 2

Descriptive Statistics for Dependent and Transfer Control Variables

 Four-Year Transfers
 Increase Quality Decrease Quality

Labor market characteristics
 1997 annual earnings 33,716.17 34,140.41
 (16,581.36) (19,366.50)
 1997 work experience 3.5199 3.5529
 (1.0335) (1.0527)
 1994 annual earnings 24,290.90 24,592.51
 (13,706.32) (10,948.38)
 1994 work experience .9065 .9664
 (.4007) (.4163)
College characteristics
 Graduation SAT 1013.56 911.2
 (105.26) (99.88)
 Transfer SAT 916.64 1026.11
 (93.97) (107.58)
 % Credits pretransfer .2668 .323 1
 (.2230) (.2361)
Observations 873 709


 Nontransfers Two-Year Transfers

Labor market characteristics
 1997 annual earnings 33,083.94 33,328.46
 (18,949.43) (17,912.06)
 1997 work experience 3.4781 3.5864
 (1.0180) (.9830)
 1994 annual earnings 23,547.24 23,580.26
 (20,680.66) (18,313.99)
 1994 work experience .8731 .9163
 (.3830) (.4214)
College characteristics
 Graduation SAT 990.16 960.70
 (125.63) (103.75)
 Transfer SAT -- --
 -- --
 % Credits pretransfer -- .2760
 -- (.2173)
Observations 2830 1270

Standard deviations, where applicable, are in parentheses. Persons with
missing values for a variable are excluded from the calculation of those
means.
Table 3

Descriptive Statistics for Other Independent Variables

 Four-Year Transfers
 Increase Quality Decrease Quality

Personal college experiences
 Still attending .1924 .2200
 Postgraduate degree .1123 .1227
 Age of graduation 25.8305 27.2257
 (6.6032) (7.9589)
College GPA 2.9678 3.1746
 (.6658) (.6350)
Major
 Business .1306 .1410
 Engineering .0664 .0564
 Science .0928 .1044
 Social Science .1764 .1354
 Other Major .3036 .2807
 Humanities .0859 .0874
 Education .1443 .1946
Individual and family
 characteristics
 Male .4456 .4457
 White .8843 .8858
 Black .0378 .0564
 Hispanic .0424 .0296
 Other race .0355 .0282
 Family income 44,192.89 37,254.66
 (50,189.66) (42,613.38)
Observations 873 709


 Nontransfers Two-Year Transfers

Personal college experiences
 Still attending .1760 .1969
 Postgraduate degree .1205 .0969
 Age of graduation 23.0099 25.7969
 (4.5041) (6.5863)
College GPA 2.9457 2.9474
 (.6009) (.6802)
Major
 Business .1343 .1685
 Engineering .0922 .0819
 Science .1088 .0811
 Social Science .1739 .1362
 Other Major .2399 .2622
 Humanities .0961 .0709
 Education .1548 .1992
Individual and family
 characteristics
 Male .4710 .4299
 White .8678 .8872
 Black .0576 .0446
 Hispanic .0332 .0339
 Other race .0413 .0441
 Family income 49,831.51 36,386.27
 (51,484.10) (39,390.72)
Observations 2830 1270

Standard deviations, where applicable, are in parentheses. Persons with
missing values for a variable are excluded from the calculation of those
means.
Table 4

Random Effects GLS Log Earnings Estimates by Attendance Path

 Four-Year Transfers
 All Students Increase Quality Decrease Quality

Graduation SAT/100 .0335 ** .0350 ** .0226
 (.0044) (.0124) (.0148)
[R.sup.2] .3134 .3625 .3043
Observations 9681 1489 1213


 Nontransfers Two-Year Transfers

Graduation SAT/100 .0396 ** .0279 **
 (.0061) (.0100)
[R.sup.2] .3181 .3126
Observations 4791 2188

Dependent variable is the logarithm of a student's annual earnings at
the time of the 1994 and 1997 interviews. Standard errors are in
parentheses. Regressions also include family income, age at receipt of
bachelor's degree, and dummy variables indicating sex, race (white
omitted), marital status, graduate degree attainment, part-time
attendance, graduation SAT score imputed, and dummy variables that are
equal to one if values for a variable are missing (in which case those
variables are set to zero).

** Significant at the 5% level.
Table 5

Random Effects GLS Log Earnings Estimates for Four-Year Transfers

 1 2 3

Graduation SAT/100 .0260 ** .0221 ** .0187 *
 (.0085) (.0088) (.0099)
Transfer SAT/100 -- .0143 * .0178 *
 -- (.0084) (.0097)
% Credits pretransfer -- -- -.0385
 -- -- (.0499)
% Credits pretransfer * transfer up -- -- .0396
 -- -- (.0580)
[R.sup.2] .3241 .3257 .3259
Observations 2702 2702 2702

Dependent variable is the logarithm of a student's annual earnings at
the time of the 1994 and 1997 interviews. Standard error are in
parantheses. Regressions also include family income, age at receipt of
bachelor's degree, and dummy variables indicating sex, race (white
omitted), martical status, graduate degree attainment, part-time
attendance, graduation and transfer SAT score imputed, and dummy
variables that are equal to one if values for a variable are missing (in
which case those variables are set to zero).

(*), (**) Significant at the 10% and 5% levels, respectively.

Received April 2000; accepted August 2001.

(1.) This model is being developed for the purpose of framing the empirical work presented here. Thus, it is convenient to assume that the student's attendance decision is static during the first period. It is recognized that this decision may actually be dynamic in nature, as the student must decide each year whether to continue at his or her current institution or to transfer to a different institution. Expanding the model to reflect such possible dynamics does not change the basic results in which I am interested. For an example of a dynamic model, see Altonji (1993).

(2.) Attendance costs should be increasing in quality for two reasons. First, higher-quality institutions tend to charge higher fees. Second, because of the small number of high-quality universities, a student will have to move from home to attend one, so that the opportunity cost of attendance will be higher. The data set used in this analysis allows us to test this proposition as follows. Net costs are calculated as the difference between the self-reported total attendance costs (tuition, books, mom and board, and living expenses) and total financial aid (loans, scholarships, and so on) for each student during the 1982-1983 academic year. The average net costs for students by quartiles of university quality are $1915.94, $3320.33, $3688.33, and $4471.61. Moreover, a regression with net costs at the dependent variable indicates that university quality has a significantly positive effect on attendance costs. Specifically, a one-unit increase in the mean SAT score of entering freshmen increases attendance cost s by $8.55.

(3.) This is not a trivial assumption. However, empirical evidence abounds that graduation quality has a positive effect on future earnings. For example, see Wales (1973), Solmon and Wachtel (1975), Wise (1975), Mueller (t988), James et al. (1989), and Rumberger and Thomas (1993).

(4.) A complete discussion of the model is available from the author on request.

(5.) The concept that students may start attending a particular college to see whether they have the ability and/or desire to complete the requirements of a degree is often referred to as the "option value" of college attendance. For a detailed discussion, see Comay, Melnick, and Pollatschek (1973); Manski (1989); and Altonji (1993).

(6.) One might be able to attempt to isolate this effect if more detailed information on a student's performance in different classes at the different institutions were available. For instance, having detailed data on grades received at different institutions might be helpful as per the previous discussion, as grades of A at a lower-quality institution might actually imply more human capital accumulation than grades of C or D at a higher-quality institution. Unfortunately, the B&B survey collects only an overall grade-point average instead of grades received at different institutions. The survey does report major-specific and overall grade point average (GPA), but controlling for the difference between the two does not provide any additional information, which is not surprising, as it is not totally clear at which institutions students would have taken their different types of courses.

(7.) Transfer students can attend more than one different institution before transferring to their ultimate university. Four-year transfers in this sample attended an average of 1.36 before transferring, while two-year college graduates attended an average of 1.44 before transferring. To account for this, different formulations of the initial quality measure were tried (i.e., average previous quality, time-weighted average perviout quality, and so on). The results did not differ significantly for any of the specifications.

(8.) I would obviously like to be able to estimate the function for community college transfers. Unfortenately, most community colleges have open-door policies and therefore do not require applicants to take standardized qualifying exams. As such, no comparable measure of initial quality is available for such students.

(9.) Since some individuals contribute earnings in 1997 but not 1994, my panel is unbalanced.

(10.) Prominent alternative data sets are the High School and Beyond (HSB) and the National Longitudinal Study of the High School Class of 1972 (NLS-72). The HSB is a nationally representative longitudinal survey of 12,000 students who were high school seniors and nearly 15,000 students who were high school sophomores in 1980 (National Center for Education Statistics 1987). Among HSB seniors, only 1941 had received a baccalaureate degree by their last follow-up (1986), while among HSB sophomores, only 3304 bad received a baccalaureate degree by their last follow-up (1992). The NLS-72 is a nationally representative sample of students who were seniors in high school a decade earlier (National Center for Education Statistics 1980). Of the 12,841 students participating in all follow-ups, 4417 had received at least a bachelor's degree by 1986. Because of data limitations, the numbers of students in each sample that can actually be examined are much smaller. For example, Grogger and Eide's (1995) sample of HSB stud ents consists of 1087 college graduates, while James et al.'s (1989) sample of NLS-72 students contains only 2280 (1241 male) college graduates.

(11.) These broad classifications are consistent with those used in previous work (e.g., Grogger and Eide 1995). A detailed description of the specific B&B-defined fields included in each broad category is available on request.

(12.) The family income data come from financial aid application information, if available. Otherwise, the data come from one of the following sources: the parent interview, the student interview, the Pell file, or the student loan file. The SAT score is taken from data supplied by Educational Testing Service (ETS), who administers the SAT, and if those data are unavailable, it was taken from records at the student's college; if either of these methods failed to provide SAT data, then student self-reports were used. If an ACT score is available but an SAT score is not, then an SAT score was imputed from the ACT score using the scale provided in Astin (1971).

(13.) There are a small number of students who start at a four-year college, transfer to a two-year college, then transfer back to a four-year college. Because these few students generally spent very little time at their initial four-year institution and more time at the two-year institution, I classify these students as two-year transfers.

(14.) Among college graduates in this sample, the average annual earnings for males is $23,638.63, while the annual eamings for females is $20,917.88.

(15.) Within the sample, two-year transfers averaged nearly one-half year more pregraduation work experience than four-year transfers and nearly one full year more than nontransfers.

(16.) A common concern with this type of analysis is the potential for self-selection bias. For example, future earnings for four-year transfers who decrease quality are observed only for students who actually chose that path and not for students who chose other paths. Possible corrections for this type of empirical problem include instrumental variables (IV) and Lee (1983)-type 2 stage selection models. As is often the case in such situations, however, for the current problem it is difficult to find either appropriate instruments or first-stage identifying variables for the decision to transfer up or down. A possible cause of this difficulty is that, as mentioned previously, students primarily seem to choose to transfer because of student/ school mismatching and that many of the covariates included in the empirical analysis likely account for this factor. Hence, in this instance, it does not seem that selection bias is a significant concern. Results of corrections that were tried are available on request.

References

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Michael J. Hilmer *

* Department of Applied and Agricultural Economics, Virginia Polytechnic and State University, Blacksburg, VA 24602-0401, USA; E-mail mhilmer@vt.edu.

Special thanks go to Eric Eide, Dan Goldhaber, Mark Showalter, seminar participants at the Comell Higher Education Research Institute, and two anonymous referees. The usual disclaimers apply.