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The demand for community college education
Economics of Education Review VOL. 2, no. 4 (Fall 1982): 351-361
The Demand for Community College Education Joseph M. Sulock
This article describes a model of Community College (CC) enrollment which is tested using cross-sectional data for the 1969-70 academic year. The sample consists of 126 relatively homogeneous CCs divided into sixty-two separate markets. Tuition, income, proximity of four-year schools, and the age of a CC are found to have significant influences on enrollment. An estimate is made of the marginal cost to a CC of attracting more students by lowering tuition.
Public two-year colleges, hereafter called Community Colleges and abbreviated as “CCs,” have grown substantially in recent years. For example, between 1960 and 1975 the number of full-time equivalent students enrolled at CCs increased nearly 400 percent, compared to an increase of about 130 percent for full-time equivalent students enrolled at four-year colleges over the same period. In spite of the increased importance of CCs in American higher education, little is known about the responses that potential students have to changes in the economic incentives surrounding these institutions. Most demand for education studies have analyzed total collegiate enrollment. However, inferences which may be true for the demand for education in general may not hold true for the demand for CC education. Using cross-section data for the 1969- 70 academic year, this article investigates sources of variation in CC enrollment. DATA
DESCRIPTION
Public two-year schools can differ in a number of characteristics important to a potential enrollee. Does the school emphasize liberal arts or does it specialize in a specific area such as business, engineering, or vocational trades ? Does the school have a commuting or Joseph M. Sulock is an associate professor at the University of North Carolina at Asheville. He is indebted to Andy Bamett and two anonymous referees for many helpful suggestions. [Manuscript received June 26, 1981; revision accepted October 15, 1981.1
351
Economics
of Education
Review
on-campus environment? Can a student transfer from the CC to a four-year public college within the state? Are extracurricular activities available? The CCs chosen are similar in these characteristics. Each school’s curriculum is primarily liberal arts; the CCs have few extracurricular activities, a commuting environment, and their students can transfer to a four-year, in-state, public college. The sample consists of 126 CCs which we conceive to be operating in sixty-two different markets. ’ Of these, forty-one observations are based on the county as the statistical unit. These counties were part of a Standard Metropolitan Statistical Area (SMSA), but their pricing and admission policies favored in-county residents, and some of these CCs were geographically isolated from surrounding counties. Thus virtually all the students came from the counties in which the CCs were located, which suggests the county may be the relevant market area that these CCs face. The remaining twenty-one observations are based on an SMSA as the statistical unit. Thus we will treat all CCs lying within the SMSA as one school with branch campuses located throughout the area. Finer division, such as into counties, did not appear to be justified since pricing policies did not favor in-county residents in these cases. Additionally, an eligible student might be nearer to the CC of a neighboring county, negating the transportation cost advantage of incounty CCs. In these situations, the market area of a CC may well extend into state counties bordering the CC district.2 THE CC ATTENDANCE
DECISION
We hypothesize that the quantity of CC education demanded depends on the price of attending a CC, the price of attending a four-year school, the time cost of CC attendance, the income of purchasing agents, the amount of time a CC has been in existence, the perception of the monetary benefits from postsecondary education, and the proximity of four-year schools to high school graduates. Tuition is the usual measure of the price of education at a postsecondary institution. In a cross-sectional sample this may not be a useful proxy because tuition differences can reflect variations in
1. One hundred twenty-six CCs do not, of course, exhaust the number of public two-year schools in the United States. However, data limitations restricted the choice of schools. 2. At one stage of the empirical work a dummy variable was used to determine if the county and SMSA observations differed significantly. The coefficient on the SMSA dummy was insignificant, and the inclusion of this variable did not alter the coefficients on the other variables.
352
The Demand for Community
College Education
price and quality. Consequently, it is important that a cross-sectional sample contain schools with similar institutional appeal. The CCs in our sample are relatively homogeneous. As we previously mentioned, the CCs are similar in a number of characteristics important to a potential enrollee. It is likely, therefore, that tuition differences will capture variations in price. Conceptually the foregone earnings, denoted FE, of attending a CC is equal to wT, where w is the relevant wage rate and T is the amount of time a student spends on education. Based on Parson’s (1974) research, T is assumed to be 1,300 hours per academic year, and w is three-fourths of the hourly wage rate in manufacturing. This wage rate adjustment is made in order to consider the lower wages paid for part- time and summer employment. There is no a priori expectation about the impact on CC demand of a change in this variable, since price and income effects are generated which go in opposite directions (Hoenack and Weiler 1979: 94). We assume the relevant competing four-year institutions are the public and private colleges and universities situated within the state where the CC is located. The representation of the price of enrolling at these institutions will be TUI4,
1 = FTE,
2 TU14j
* FTEi
.
FTE, is the number of full-time equivalent students enrolled at all four-year institutions in state S; TUI4i is the in-state tuition at college i, and FTEi is the number of full-time equivalents at college j. The proximity of potential enrollees to postsecondary institutions should also influence the enrollment decision. However, the CCs in our sample are very centrally located since all student eligibles in an area of observation live within thirty miles of a two-year school.3 Thus there will be little variation in the transportation and living expenses associated with CC enrollment. But this is not the case with attendance at a four-year school. The potential enrollees in the sample differ substantially in their access to these institutions. Our measure of this cross-sectional variation will be the geographical proximity of four-year institutions to high school graduates. The index used to measure this will be Li = Cilei, where Ci is the percent of a state’s four-year schools located within thirty miles of area i,
3. The population density within thirty miles may affect CC enrollment. be a problem, however, since all CCs were located in SMSAs.
This is unlikely
to
353
Economics
of Education
Review
and ei is the percent of the student eligibles accounted for by this area.4 We also expect the amount of time a CC has been in existence to affect the demand for CC education. Differences in this may be important for the following reasons. First, decisionmakers operate in an environment of risk concerning product quality due to the existence of imperfect information. One would expect that over time more information about the quality of a school will be disseminated. The most important vehicle for the transmission of such knowledge may be students who have “tried” the product in the school’s earlier years (the idea of word-of-mouth advertising).’ Second, the passage of time may reduce the subjective resistance of some decisionmakers. When a CC begins operation, some purchasing agents may not consider that a two-year school is an acceptable alternative to prestigious four-year schools for their student eligibles, and others may not have considered postsecondary education as an alternative to labor force participation. Since we will be using linear-regression techniques, and it is reasonable that the passage of time will have a nonlinear effect on educational demand, the following variable was formed under the assumption that the marginal effects of time are dissipated after six years. (The 1.94 factor scales the variable to reach 1 at t = six years) .6 z
=
ln(t+l)
, t =
0,
l,...,
5
1.94
z =
1,
t>6-
It is expected that cross-sectional variation in the monetary rewards from education will influence CC demand. These rewards could vary because the wage rate for a unit of human capital differs, and individuals may have different capacities to produce human capital. However, if college-educated labor is sufficiently mobile, then cross-sectional differences in the pecuniary returns from education will occur because of the latter reason. Our measure of the perception by individuals of the investment component of education, de-
4. A similar index was used by Hopkins
(197 1).
5. It should be pointed out that WC are not talking about information concerning the existence of the CC and its curricula. Such knowledge is probably widely (though not completely) distributed at the time the CC begins operation. 6. The rationale
354
for this functional
form is discussed
in the Appendix.
The Demand
for Community
College Education
noted I, will be the difference between the income of families where the head has four years of college and the income of families where the head has only a high school diploma. Since the measure of the number of student eligibles will be the high school graduates of the two preceding years, ideally we would like the income of the parents of these graduates in order to represent the income of families which is independent of the hours that students work. Such information has not been found, and the proxy used will be the median income for the statistical unit, denoted y. The leading character in our study, the demand for CC education, will be measured by the number of full-time equivalent students enrolled at a CC, denoted FTE. The dependent variable will be FTE/E where E is the number of high school graduates for the previous two scholastic years.7 THE ESTIMATED
EQUATIONS
In order to obtain unbiased and consistent estimates using ordinary least-squares, it is necessary that none of the explanatory variables in the equation is correlated with the error term. In particular, if CCs can use higher tuition charges to increase the amount supplied, then TUIZ, the tuition at a CC, may change as demand changes. This possibility is unlikely for our sample. First, tuition is set prior to the academic year by CC administrators. While tuition may depend on anticipated enrollment, it is unlikely to vary with actual enrollment. In addition, none of the CCs used nonprice rationing to allocate spaces. This suggests that the demand function is identified, and the inclusion of a separate supply equation is unnecessary. The demand equation initially estimated was assumed to take the form LN (FTE/E)
= u. + al LN (TU12) + a2 LN (TUI4) + +
~24 L
+
as
Z
+
(16
LN (I) +
07
a3
LN (Y)
LN (FE)
(1)
Preliminary empirical work indicated R ’ between TUIZ and TU14 was .67.8 But such a high correlation was expected. Certainly “high”priced two-year schools will find it difficult to compete with “low”7. The study only includes students enrolled in a degree program. The number of FTEs will be measured by the number of full-time students plus two-sevenths of the number of parttime students. This has been the usual conversion ratio based on a study of Mushkin and McLoone (1965). 8. When equation
1 was estimated,
the coefficient
on TU14 was negative.
355
Economics
of Education
TABLE 1.
Review
OLS ESTIMATION
Variable
Estimated Coefficient
constant
-9.41
Standard Equation
LN (TU14)
OF EQUATIONS
-2.37
Enor
T-Stat.
2 3.74
2.07 (= 6,)
LN (AID)
2 AND 3.
-2.51
.55
(= 6,)
3.78
.75
-3.17
R3 = .29 Equation Constant
1.52
LN (TU14)
- 25
LN(Y) L
z LN (4 LN (FE)
(=ilbI
3 4.82
1
+a;)
1.00
.49
.33
.17
.88
.27
.I8
.36
-1.59
LN (AID)
.32
.19
-1.27 2.04 -1.89 3.27 .50
.36
1.04 (= a^*r$)
-4.40
.29
3.49
RZ = .62 Source: Fumis (1973), Gleam (1971) and U.S. Bureau of Census (1970). For additional detail consult Sulock (1976).
priced four-year institutions. Consequently, we would expect both types of schools will pursue roughly similar pricing policies. But tuition at a CC is also likely to depend on the amount of outside aid per enrollee-for example, gifts and government supportthat it receives.9 The more such aid, the lower priced the school can be. Thus we can write LN (TU12)
Substituting
= bO + bl LN (TU14) + bz LN (AID)
(2) into (1) yields the following
LN (FTE/E)
= (a0 + al b,)
reduced- form equation:
+ (al bl + az) LN (TUM) + as LN (Y)
+ a4 L + a5 Z + a6 LN (I) + al LN (FE) +
The estimates
of equations
(2)
(2) and (3) are summarized
(3)
at b2 LN (AID) in Table
1.
9. The reader will notice that we are assuming that the subsidy the CC receives is independent of the actual number of enrollees. Conversations with individuals familiar with CC
356
The Demand for Community ANALYSIS
OF REGRESSION
College Education
COEFFICIENTS
In order to obtain cii, the estimate of the ceteris parjbus effect of a CC’s tuition on its enrollment, we recognize that ci, b, is 1.04 and b, is -2.37. Thus the estimated CC price elasticity is - .44. This figure is lower than ones obtained by previous researchers. For example, conducted industrywide studCorazzini (1972) and Hopkins (1971) ies and obtained price elasticity estimates of -.20 and -.lO, respectively. But there are two reasons which explain our lower result. First, there are more substitutes for CCs than for postsecondary institutions in general. Second, potential CC enrollees may be of lower ability than potential enrollees at four-year institutions. This last point requires elaboration. The mean ACT score of the CC students in our sample was 17.3 compared to a mean score of 21.6 for students enrolled at the sample four-year schools. Now Bishop (1977: 295) found that the price elasticity of demand decreased as the ability of enrollees decreased. In fact, he obtained a price elasticity estimate of - .47, virtually identical to ours, for students of below average ability. The foregone earnings coefficient is negative and statistically significant at the 1 percent level. Evidently the price effect outweighs the income effect of a change in this variable. This result is consistent with the findings of Feldman and Hoenack (1969: 388) that an increase in the relevant wage rate reduces collegiate attendance for relatively lower quality students. It is interesting that our tuition and foregone earnings estimates are consistent with those obtained in studies analyzing various ability groups. Relatively little work has been done on the different impacts economic variables have on such groups. Our results suggest that such differences are important and worth additional study. There was no statistically significant relationship between CC enrollment and the expected earnings payoff. Perhaps our measure of this payoff is too imperfect. But perhaps potential CC enrollees have high discount rates. If, so, our test may not be powerful enough to detect the relatively small effect the expected earnings payoff has on CC demand. For example, if the elasticity parameter is .05, we have only a 7 percent chance of obtaining a coefficient significant at the 5 percent level. The results lend support to the hypothesis that a CC will grow over time. We can determine the rate of growth a CC might expect since it is well known that if Y = f (t ), then d(LnY)/dt will yield funding indicated that this subsidy is determined prior to the academic year. It certainly is likely that this subsidy is influenced by the anticipated number of students, hence the expected amount of educational demand. But as long as this subsidy is independent of the actual amount demanded, it can be regarded as predetermined.
357
Economics
of Education
TABLE
2.
Review
CC GROWTH
RATE
IMPLIED
Year of Operation
BY EQUATION
Growth
3.
Rate
0 0.31 0.18 0.13 0.10 0.08 0.07 0
the growth rate. These results are shown in Table 2.” This implies that CC demand will have increased 120 percent after six years of operation. That is, beginning its seventh year of operation, a CC’s demand will be 120 percent higher than the demand it experienced in its first year of operation, all other relevant things being the same. The coefficient on TU14 in_ equation 3 is not &, the tuition cross elasticity, but equals ciz + ci, b, . However, since ci, and b, are -.44 and 2.07 respectively, 8, is .66. L, the representation of the transportation and living costs associated with four-year enrollment, has the expected sign. The coefficient of L is an estimate of the rate of proportional change of CC demand associated with the absolute change in this variable. POLICY CONSIDERATIONS Our results imply that a tuition reduction will increase enrollment at a CC. For example, suppose there is a $100 reduction in tuition at a CC represented by the mean values of the dependent and independent variables. Such a tuition decrease would result in a 41 percent change in this variable from its mean value of $241, and would cause an 18 percent increase in quantity demanded. The increase in enrollment is estimated to be 1,3 10 FTEs. But what is the extra subsidy per student to a CC of achieving this enrollment change ? The total subsidy, TS, a CC requires is represented by TS
= AE
where AE is the expenditure
10. These predictions 6, 7.
358
were generated
l
FTE -
TUIP
l
FTE
per student.
by calculating
ALN (FTE/E)/At
fort
= 1, 2, 3,4,
5,
The Demand for Community Totally
differentiating
this equation
yields
dTS = AE dFTE + dAE FTE - FTEdTUW = dFTE (AE-TUIP)
College Education
- FTEdTUIP
- TUIZdFTE
+ dAEFTE
If the CC administration desires to maintain the expenditure student as enrollment increases, then dAE is zero. Consequently, additional subsidy per student can be expressed as dTS dFTE
=
(AE -TUIP)
-
FTE dFTE
dTUI2
per the
.
Assuming a $100 decrease in tuition, this expression yields a change in subsidy of $1,690 calculated at the mean values of AE, TUIZ, and FTE. The average subsidy is $ 1,O 10. The estimated coefficients on TU14 and L imply an interaction between two-year and four-year schools. This possibility is important to policymakers since CCs are generally acclaimed as “demoinstitutions. The epithet democratic is used because most cratic” have no admission requirements other than a high school diploma, and tuition is usually a nominal amount relative to that of a fouryear institution. This postsecondary education is supposedly able to reach lower income groups. The implication is that CCs will increase total collegiate enrollment (and presumably the total amount of education purchased). What is usually ignored is that CCs will include in their enrollment students who would otherwise have attended four-year schools. This study suggests that this interaction exists. Thus one of the functions of CCs, their operation as democratic institutions, does not appear to be fulfilled as effectively as total enrollment figures would suggest. A study attempting to estimate the magnitude of the effect that twoyear schools have on other postsecondary institutions seems worthwhile. Such information would certainly be valuable to policymakers interested in assessing the effectiveness of this role of CCs in American education.
REFERENCES Bishop, J./ 1977 THE EFFECT OF PUBLIC Journal of Human Resources
POLICIES ON TIIE DEMAND 12 (Summer): 285-307.
Campbell, R., and B.N. Siegel/ 1967 DEMAND FOR HIGHER EDUCATION Review 57 (June): 482-494.
IN THE UNITED
FOR HIGHER
STATES.
EDUCATION.
American
Economic
359
Economics
of Education
Review
Corazaini, J.A.. J. Dugan, and H.G. Grabowski/1972 DETERMINANTS AND DISTRIBUTIONAL ASPECTS OF ENROLLMENT HIGHER EDUCATION. Journal of Human Resources 7 (Winter): 39-59.
IN
U.S.
Feldman, P., and S.A. Hocnack/ 1969 PRIVATE DEMAND FOR HIGHER EDUCATION IN THE UNITED STATES. In Economics and Financing of Higher Education in the United States, 375-95 by U.S. Congress, Joint Economic Committee Washington, D.C.: U.S. Government Printing Office. Fumiss, W.T., ed./1973 AMERICAN UNIVERSITIES Council on Education.
AND
COLLEGES,
11th
ed.
Washington,
Galper, H., and R.M. Dunn/ 1969 A SHORT RUN DEMAND FUNCTION FOR HIGHER EDUCATION MI of Political Economy 77 September/October: 765-777. Gleaaer, E. J., Jr., ed./ 1971 AMERICAN JUNIOR COLLEGES, cation.
8th ed.
Washington,
D.C.:
EDUCATION:
A MARKET
Mushkin, S. J., and E.P. McLoone/ 1965 PUBLIC SPENDING FOR HIGHER EDUCATION Governments.
IN 1970.
Parsons, D.O./ 1974 THE COST OF SCHOOL TIME, FOREGONE EARNINGS MATION. Joumal of Political Economy 82 (March/April): Sulock, J. M./ 1976 A THEORETICAL AND EMPIRICAL ANALYSIS AT COMMUNITY COLLEGES. Ph.D. dissertation, U.S. Bureau of the Census/l970 U.S. CENSUS OF POPULATION: Office.
1970.
American
IN THE U.S.
American
Hoenack, !%A., and W.C. Weher/ 1979 THE DEMAND FOR HIGHER EDUCATION AND INSTITUTIONAL FORECASTING. Economic Inquiry 57, no. 1 (January): 89- 113. Hopkins, T.D.11971 THE PROVISION OF HIGHER dissertation, Yale University.
D.C.:
Council
on Edu-
ENROLLMENT
INTERPRETATION.
Chicago:
AND HUMAN 251-265.
Iour-
Council
Ph.D.
of State
CAPITAL
FOR-
OF THE DEMAND FOR EDUCATION University of Virginia.
Washington,
D.C.:
U.S.
Government
Printing
APPENDIX One might argue that our treatment of time (see the paragraph preceding footnote 6) is somewhat arbitrary since economic theory is of little assistance in such matters. However, by considering the “mean effects” of variations in time, we can determine the plausibility of this explanatory variable. 360
The Demand for Community
College Education
We began by decomposing the observations into three categories. An observation is placed into group 1 if the school has been in existence zero-three years; it is in group 2 if it has been open for foursix years, and in group 3 if more than six years. We let Dl equal unity when an observation corresponds to group 1, zero otherwise; let D3 take the value of unity when the observation is from group 3, zero otherwise; and let the excluded category be group 2. If our treatment of time is plausible, we expect Dl to be negative and D3 to be positive. We would also anticipate that the absolute value of the coefficient on Dl will be greater than the absolute value of the one on D3. The results on Dl and D3 were as follows: Est. Coeff.
Dl D3
-0.364 0.0010
S. E.
T-Stat.
0.155
2.34
0.155
0.006
Though the coefficient on D3 was not significant, the results do lend support to the intuitively appealing idea that there will be diminishing returns to the effects that “time” has on enrollment demand, and to our assumption that these effects are dissipated after six years.
361
The Demand for Community College Education Joseph M. Sulock
This article describes a model of Community College (CC) enrollment which is tested using cross-sectional data for the 1969-70 academic year. The sample consists of 126 relatively homogeneous CCs divided into sixty-two separate markets. Tuition, income, proximity of four-year schools, and the age of a CC are found to have significant influences on enrollment. An estimate is made of the marginal cost to a CC of attracting more students by lowering tuition.
Public two-year colleges, hereafter called Community Colleges and abbreviated as “CCs,” have grown substantially in recent years. For example, between 1960 and 1975 the number of full-time equivalent students enrolled at CCs increased nearly 400 percent, compared to an increase of about 130 percent for full-time equivalent students enrolled at four-year colleges over the same period. In spite of the increased importance of CCs in American higher education, little is known about the responses that potential students have to changes in the economic incentives surrounding these institutions. Most demand for education studies have analyzed total collegiate enrollment. However, inferences which may be true for the demand for education in general may not hold true for the demand for CC education. Using cross-section data for the 1969- 70 academic year, this article investigates sources of variation in CC enrollment. DATA
DESCRIPTION
Public two-year schools can differ in a number of characteristics important to a potential enrollee. Does the school emphasize liberal arts or does it specialize in a specific area such as business, engineering, or vocational trades ? Does the school have a commuting or Joseph M. Sulock is an associate professor at the University of North Carolina at Asheville. He is indebted to Andy Bamett and two anonymous referees for many helpful suggestions. [Manuscript received June 26, 1981; revision accepted October 15, 1981.1
351
Economics
of Education
Review
on-campus environment? Can a student transfer from the CC to a four-year public college within the state? Are extracurricular activities available? The CCs chosen are similar in these characteristics. Each school’s curriculum is primarily liberal arts; the CCs have few extracurricular activities, a commuting environment, and their students can transfer to a four-year, in-state, public college. The sample consists of 126 CCs which we conceive to be operating in sixty-two different markets. ’ Of these, forty-one observations are based on the county as the statistical unit. These counties were part of a Standard Metropolitan Statistical Area (SMSA), but their pricing and admission policies favored in-county residents, and some of these CCs were geographically isolated from surrounding counties. Thus virtually all the students came from the counties in which the CCs were located, which suggests the county may be the relevant market area that these CCs face. The remaining twenty-one observations are based on an SMSA as the statistical unit. Thus we will treat all CCs lying within the SMSA as one school with branch campuses located throughout the area. Finer division, such as into counties, did not appear to be justified since pricing policies did not favor in-county residents in these cases. Additionally, an eligible student might be nearer to the CC of a neighboring county, negating the transportation cost advantage of incounty CCs. In these situations, the market area of a CC may well extend into state counties bordering the CC district.2 THE CC ATTENDANCE
DECISION
We hypothesize that the quantity of CC education demanded depends on the price of attending a CC, the price of attending a four-year school, the time cost of CC attendance, the income of purchasing agents, the amount of time a CC has been in existence, the perception of the monetary benefits from postsecondary education, and the proximity of four-year schools to high school graduates. Tuition is the usual measure of the price of education at a postsecondary institution. In a cross-sectional sample this may not be a useful proxy because tuition differences can reflect variations in
1. One hundred twenty-six CCs do not, of course, exhaust the number of public two-year schools in the United States. However, data limitations restricted the choice of schools. 2. At one stage of the empirical work a dummy variable was used to determine if the county and SMSA observations differed significantly. The coefficient on the SMSA dummy was insignificant, and the inclusion of this variable did not alter the coefficients on the other variables.
352
The Demand for Community
College Education
price and quality. Consequently, it is important that a cross-sectional sample contain schools with similar institutional appeal. The CCs in our sample are relatively homogeneous. As we previously mentioned, the CCs are similar in a number of characteristics important to a potential enrollee. It is likely, therefore, that tuition differences will capture variations in price. Conceptually the foregone earnings, denoted FE, of attending a CC is equal to wT, where w is the relevant wage rate and T is the amount of time a student spends on education. Based on Parson’s (1974) research, T is assumed to be 1,300 hours per academic year, and w is three-fourths of the hourly wage rate in manufacturing. This wage rate adjustment is made in order to consider the lower wages paid for part- time and summer employment. There is no a priori expectation about the impact on CC demand of a change in this variable, since price and income effects are generated which go in opposite directions (Hoenack and Weiler 1979: 94). We assume the relevant competing four-year institutions are the public and private colleges and universities situated within the state where the CC is located. The representation of the price of enrolling at these institutions will be TUI4,
1 = FTE,
2 TU14j
* FTEi
.
FTE, is the number of full-time equivalent students enrolled at all four-year institutions in state S; TUI4i is the in-state tuition at college i, and FTEi is the number of full-time equivalents at college j. The proximity of potential enrollees to postsecondary institutions should also influence the enrollment decision. However, the CCs in our sample are very centrally located since all student eligibles in an area of observation live within thirty miles of a two-year school.3 Thus there will be little variation in the transportation and living expenses associated with CC enrollment. But this is not the case with attendance at a four-year school. The potential enrollees in the sample differ substantially in their access to these institutions. Our measure of this cross-sectional variation will be the geographical proximity of four-year institutions to high school graduates. The index used to measure this will be Li = Cilei, where Ci is the percent of a state’s four-year schools located within thirty miles of area i,
3. The population density within thirty miles may affect CC enrollment. be a problem, however, since all CCs were located in SMSAs.
This is unlikely
to
353
Economics
of Education
Review
and ei is the percent of the student eligibles accounted for by this area.4 We also expect the amount of time a CC has been in existence to affect the demand for CC education. Differences in this may be important for the following reasons. First, decisionmakers operate in an environment of risk concerning product quality due to the existence of imperfect information. One would expect that over time more information about the quality of a school will be disseminated. The most important vehicle for the transmission of such knowledge may be students who have “tried” the product in the school’s earlier years (the idea of word-of-mouth advertising).’ Second, the passage of time may reduce the subjective resistance of some decisionmakers. When a CC begins operation, some purchasing agents may not consider that a two-year school is an acceptable alternative to prestigious four-year schools for their student eligibles, and others may not have considered postsecondary education as an alternative to labor force participation. Since we will be using linear-regression techniques, and it is reasonable that the passage of time will have a nonlinear effect on educational demand, the following variable was formed under the assumption that the marginal effects of time are dissipated after six years. (The 1.94 factor scales the variable to reach 1 at t = six years) .6 z
=
ln(t+l)
, t =
0,
l,...,
5
1.94
z =
1,
t>6-
It is expected that cross-sectional variation in the monetary rewards from education will influence CC demand. These rewards could vary because the wage rate for a unit of human capital differs, and individuals may have different capacities to produce human capital. However, if college-educated labor is sufficiently mobile, then cross-sectional differences in the pecuniary returns from education will occur because of the latter reason. Our measure of the perception by individuals of the investment component of education, de-
4. A similar index was used by Hopkins
(197 1).
5. It should be pointed out that WC are not talking about information concerning the existence of the CC and its curricula. Such knowledge is probably widely (though not completely) distributed at the time the CC begins operation. 6. The rationale
354
for this functional
form is discussed
in the Appendix.
The Demand
for Community
College Education
noted I, will be the difference between the income of families where the head has four years of college and the income of families where the head has only a high school diploma. Since the measure of the number of student eligibles will be the high school graduates of the two preceding years, ideally we would like the income of the parents of these graduates in order to represent the income of families which is independent of the hours that students work. Such information has not been found, and the proxy used will be the median income for the statistical unit, denoted y. The leading character in our study, the demand for CC education, will be measured by the number of full-time equivalent students enrolled at a CC, denoted FTE. The dependent variable will be FTE/E where E is the number of high school graduates for the previous two scholastic years.7 THE ESTIMATED
EQUATIONS
In order to obtain unbiased and consistent estimates using ordinary least-squares, it is necessary that none of the explanatory variables in the equation is correlated with the error term. In particular, if CCs can use higher tuition charges to increase the amount supplied, then TUIZ, the tuition at a CC, may change as demand changes. This possibility is unlikely for our sample. First, tuition is set prior to the academic year by CC administrators. While tuition may depend on anticipated enrollment, it is unlikely to vary with actual enrollment. In addition, none of the CCs used nonprice rationing to allocate spaces. This suggests that the demand function is identified, and the inclusion of a separate supply equation is unnecessary. The demand equation initially estimated was assumed to take the form LN (FTE/E)
= u. + al LN (TU12) + a2 LN (TUI4) + +
~24 L
+
as
Z
+
(16
LN (I) +
07
a3
LN (Y)
LN (FE)
(1)
Preliminary empirical work indicated R ’ between TUIZ and TU14 was .67.8 But such a high correlation was expected. Certainly “high”priced two-year schools will find it difficult to compete with “low”7. The study only includes students enrolled in a degree program. The number of FTEs will be measured by the number of full-time students plus two-sevenths of the number of parttime students. This has been the usual conversion ratio based on a study of Mushkin and McLoone (1965). 8. When equation
1 was estimated,
the coefficient
on TU14 was negative.
355
Economics
of Education
TABLE 1.
Review
OLS ESTIMATION
Variable
Estimated Coefficient
constant
-9.41
Standard Equation
LN (TU14)
OF EQUATIONS
-2.37
Enor
T-Stat.
2 3.74
2.07 (= 6,)
LN (AID)
2 AND 3.
-2.51
.55
(= 6,)
3.78
.75
-3.17
R3 = .29 Equation Constant
1.52
LN (TU14)
- 25
LN(Y) L
z LN (4 LN (FE)
(=ilbI
3 4.82
1
+a;)
1.00
.49
.33
.17
.88
.27
.I8
.36
-1.59
LN (AID)
.32
.19
-1.27 2.04 -1.89 3.27 .50
.36
1.04 (= a^*r$)
-4.40
.29
3.49
RZ = .62 Source: Fumis (1973), Gleam (1971) and U.S. Bureau of Census (1970). For additional detail consult Sulock (1976).
priced four-year institutions. Consequently, we would expect both types of schools will pursue roughly similar pricing policies. But tuition at a CC is also likely to depend on the amount of outside aid per enrollee-for example, gifts and government supportthat it receives.9 The more such aid, the lower priced the school can be. Thus we can write LN (TU12)
Substituting
= bO + bl LN (TU14) + bz LN (AID)
(2) into (1) yields the following
LN (FTE/E)
= (a0 + al b,)
reduced- form equation:
+ (al bl + az) LN (TUM) + as LN (Y)
+ a4 L + a5 Z + a6 LN (I) + al LN (FE) +
The estimates
of equations
(2)
(2) and (3) are summarized
(3)
at b2 LN (AID) in Table
1.
9. The reader will notice that we are assuming that the subsidy the CC receives is independent of the actual number of enrollees. Conversations with individuals familiar with CC
356
The Demand for Community ANALYSIS
OF REGRESSION
College Education
COEFFICIENTS
In order to obtain cii, the estimate of the ceteris parjbus effect of a CC’s tuition on its enrollment, we recognize that ci, b, is 1.04 and b, is -2.37. Thus the estimated CC price elasticity is - .44. This figure is lower than ones obtained by previous researchers. For example, conducted industrywide studCorazzini (1972) and Hopkins (1971) ies and obtained price elasticity estimates of -.20 and -.lO, respectively. But there are two reasons which explain our lower result. First, there are more substitutes for CCs than for postsecondary institutions in general. Second, potential CC enrollees may be of lower ability than potential enrollees at four-year institutions. This last point requires elaboration. The mean ACT score of the CC students in our sample was 17.3 compared to a mean score of 21.6 for students enrolled at the sample four-year schools. Now Bishop (1977: 295) found that the price elasticity of demand decreased as the ability of enrollees decreased. In fact, he obtained a price elasticity estimate of - .47, virtually identical to ours, for students of below average ability. The foregone earnings coefficient is negative and statistically significant at the 1 percent level. Evidently the price effect outweighs the income effect of a change in this variable. This result is consistent with the findings of Feldman and Hoenack (1969: 388) that an increase in the relevant wage rate reduces collegiate attendance for relatively lower quality students. It is interesting that our tuition and foregone earnings estimates are consistent with those obtained in studies analyzing various ability groups. Relatively little work has been done on the different impacts economic variables have on such groups. Our results suggest that such differences are important and worth additional study. There was no statistically significant relationship between CC enrollment and the expected earnings payoff. Perhaps our measure of this payoff is too imperfect. But perhaps potential CC enrollees have high discount rates. If, so, our test may not be powerful enough to detect the relatively small effect the expected earnings payoff has on CC demand. For example, if the elasticity parameter is .05, we have only a 7 percent chance of obtaining a coefficient significant at the 5 percent level. The results lend support to the hypothesis that a CC will grow over time. We can determine the rate of growth a CC might expect since it is well known that if Y = f (t ), then d(LnY)/dt will yield funding indicated that this subsidy is determined prior to the academic year. It certainly is likely that this subsidy is influenced by the anticipated number of students, hence the expected amount of educational demand. But as long as this subsidy is independent of the actual amount demanded, it can be regarded as predetermined.
357
Economics
of Education
TABLE
2.
Review
CC GROWTH
RATE
IMPLIED
Year of Operation
BY EQUATION
Growth
3.
Rate
0 0.31 0.18 0.13 0.10 0.08 0.07 0
the growth rate. These results are shown in Table 2.” This implies that CC demand will have increased 120 percent after six years of operation. That is, beginning its seventh year of operation, a CC’s demand will be 120 percent higher than the demand it experienced in its first year of operation, all other relevant things being the same. The coefficient on TU14 in_ equation 3 is not &, the tuition cross elasticity, but equals ciz + ci, b, . However, since ci, and b, are -.44 and 2.07 respectively, 8, is .66. L, the representation of the transportation and living costs associated with four-year enrollment, has the expected sign. The coefficient of L is an estimate of the rate of proportional change of CC demand associated with the absolute change in this variable. POLICY CONSIDERATIONS Our results imply that a tuition reduction will increase enrollment at a CC. For example, suppose there is a $100 reduction in tuition at a CC represented by the mean values of the dependent and independent variables. Such a tuition decrease would result in a 41 percent change in this variable from its mean value of $241, and would cause an 18 percent increase in quantity demanded. The increase in enrollment is estimated to be 1,3 10 FTEs. But what is the extra subsidy per student to a CC of achieving this enrollment change ? The total subsidy, TS, a CC requires is represented by TS
= AE
where AE is the expenditure
10. These predictions 6, 7.
358
were generated
l
FTE -
TUIP
l
FTE
per student.
by calculating
ALN (FTE/E)/At
fort
= 1, 2, 3,4,
5,
The Demand for Community Totally
differentiating
this equation
yields
dTS = AE dFTE + dAE FTE - FTEdTUW = dFTE (AE-TUIP)
College Education
- FTEdTUIP
- TUIZdFTE
+ dAEFTE
If the CC administration desires to maintain the expenditure student as enrollment increases, then dAE is zero. Consequently, additional subsidy per student can be expressed as dTS dFTE
=
(AE -TUIP)
-
FTE dFTE
dTUI2
per the
.
Assuming a $100 decrease in tuition, this expression yields a change in subsidy of $1,690 calculated at the mean values of AE, TUIZ, and FTE. The average subsidy is $ 1,O 10. The estimated coefficients on TU14 and L imply an interaction between two-year and four-year schools. This possibility is important to policymakers since CCs are generally acclaimed as “demoinstitutions. The epithet democratic is used because most cratic” have no admission requirements other than a high school diploma, and tuition is usually a nominal amount relative to that of a fouryear institution. This postsecondary education is supposedly able to reach lower income groups. The implication is that CCs will increase total collegiate enrollment (and presumably the total amount of education purchased). What is usually ignored is that CCs will include in their enrollment students who would otherwise have attended four-year schools. This study suggests that this interaction exists. Thus one of the functions of CCs, their operation as democratic institutions, does not appear to be fulfilled as effectively as total enrollment figures would suggest. A study attempting to estimate the magnitude of the effect that twoyear schools have on other postsecondary institutions seems worthwhile. Such information would certainly be valuable to policymakers interested in assessing the effectiveness of this role of CCs in American education.
REFERENCES Bishop, J./ 1977 THE EFFECT OF PUBLIC Journal of Human Resources
POLICIES ON TIIE DEMAND 12 (Summer): 285-307.
Campbell, R., and B.N. Siegel/ 1967 DEMAND FOR HIGHER EDUCATION Review 57 (June): 482-494.
IN THE UNITED
FOR HIGHER
STATES.
EDUCATION.
American
Economic
359
Economics
of Education
Review
Corazaini, J.A.. J. Dugan, and H.G. Grabowski/1972 DETERMINANTS AND DISTRIBUTIONAL ASPECTS OF ENROLLMENT HIGHER EDUCATION. Journal of Human Resources 7 (Winter): 39-59.
IN
U.S.
Feldman, P., and S.A. Hocnack/ 1969 PRIVATE DEMAND FOR HIGHER EDUCATION IN THE UNITED STATES. In Economics and Financing of Higher Education in the United States, 375-95 by U.S. Congress, Joint Economic Committee Washington, D.C.: U.S. Government Printing Office. Fumiss, W.T., ed./1973 AMERICAN UNIVERSITIES Council on Education.
AND
COLLEGES,
11th
ed.
Washington,
Galper, H., and R.M. Dunn/ 1969 A SHORT RUN DEMAND FUNCTION FOR HIGHER EDUCATION MI of Political Economy 77 September/October: 765-777. Gleaaer, E. J., Jr., ed./ 1971 AMERICAN JUNIOR COLLEGES, cation.
8th ed.
Washington,
D.C.:
EDUCATION:
A MARKET
Mushkin, S. J., and E.P. McLoone/ 1965 PUBLIC SPENDING FOR HIGHER EDUCATION Governments.
IN 1970.
Parsons, D.O./ 1974 THE COST OF SCHOOL TIME, FOREGONE EARNINGS MATION. Joumal of Political Economy 82 (March/April): Sulock, J. M./ 1976 A THEORETICAL AND EMPIRICAL ANALYSIS AT COMMUNITY COLLEGES. Ph.D. dissertation, U.S. Bureau of the Census/l970 U.S. CENSUS OF POPULATION: Office.
1970.
American
IN THE U.S.
American
Hoenack, !%A., and W.C. Weher/ 1979 THE DEMAND FOR HIGHER EDUCATION AND INSTITUTIONAL FORECASTING. Economic Inquiry 57, no. 1 (January): 89- 113. Hopkins, T.D.11971 THE PROVISION OF HIGHER dissertation, Yale University.
D.C.:
Council
on Edu-
ENROLLMENT
INTERPRETATION.
Chicago:
AND HUMAN 251-265.
Iour-
Council
Ph.D.
of State
CAPITAL
FOR-
OF THE DEMAND FOR EDUCATION University of Virginia.
Washington,
D.C.:
U.S.
Government
Printing
APPENDIX One might argue that our treatment of time (see the paragraph preceding footnote 6) is somewhat arbitrary since economic theory is of little assistance in such matters. However, by considering the “mean effects” of variations in time, we can determine the plausibility of this explanatory variable. 360
The Demand for Community
College Education
We began by decomposing the observations into three categories. An observation is placed into group 1 if the school has been in existence zero-three years; it is in group 2 if it has been open for foursix years, and in group 3 if more than six years. We let Dl equal unity when an observation corresponds to group 1, zero otherwise; let D3 take the value of unity when the observation is from group 3, zero otherwise; and let the excluded category be group 2. If our treatment of time is plausible, we expect Dl to be negative and D3 to be positive. We would also anticipate that the absolute value of the coefficient on Dl will be greater than the absolute value of the one on D3. The results on Dl and D3 were as follows: Est. Coeff.
Dl D3
-0.364 0.0010
S. E.
T-Stat.
0.155
2.34
0.155
0.006
Though the coefficient on D3 was not significant, the results do lend support to the intuitively appealing idea that there will be diminishing returns to the effects that “time” has on enrollment demand, and to our assumption that these effects are dissipated after six years.
361