Cohort crowding: how resources affect collegiate attainment

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The available empirical evidence does not support the notion that relatively large cohorts ofcollege students are “absorbed” by neighboring states. In fact, it appears that the enrollmentbehavior of state residents is closely tied to in-state college opportunitie s, with elasticities veryclose to the estimates using the full panel of BA degree data in Table 2. 22In addition, it seems plausible that time to degree may tend to rise with cohort size. Ifcollege-age individuals in large cohorts faced fewer resources, they may find college lessattractive, and marginal students might delay college enrollment. 23 What is more, fewer resourcesmight translate into slower progress while in school. Empirically, calculations using the CurrentPopulation Survey suggest that increasing cohort size does increase the age at degree receipt,though the magnitude of this effect is by no means large enough to explain the overall effect oncompletion rates. One concern is that, in the institutional measures of degree attainment, increasesin time to degree will tend to bias estimates of the effect of cohort size on the number of BAsproduced per cohort; yet, such errors should be offsetting as time to degree expands and contractswith cohort size. 24 All in all, we doubt these inter-temporal substitution effects have much effecton our estimates.To sum up, while the institutional measures are not, conceptually what we would like tohave (they are period, rather than cohort measures and represent graduates from institutionswithin a state rather than graduates of the resident population in a state), our evidence suggeststhat regressions that use these measure will produce estimates of the effect of cohort size oncollege completion that are close to the ones we would have obtained from conceptually22 Focusing on just the flagships s chools, we do find that out-of-state enrollment tends to fall in theface of large cohorts; however this effect is small enough and the flagship schools represent a small enoughshare of total enrollment, that this pattern hardly shows up when we combine data on all colleges anduniversities.23 If shifts in population size occurred at fairly high frequency, individuals who are part ofparticularly large cohorts might find it optimal to postpone college for several years. However, this kind ofsubstitution is unlikely to be plausible in large scale as most of the movements in cohort size observedoccur at relatively low frequency. Moreover, such inter-temporal adjustment would likely reduce thenumber of years over which an individual would get the benefits of a college education, thus reducing thereturn to the degree.24 A simple example will illustrate. Suppose that the fraction of a cohort ultimately receiving a BAremains constant, but cohort size grows at a rate of 1% per year. Also suppose that, as a result on theincrease in cohort size, the age at which individuals typically receive their BA rises from 22 to 23 yearsover a 10-year period. During this period we would observe an approximate 10% increase in the size of thepopulation, but only a 9% increase in the size of the number of BAs. As a result, we would underestimate?ln(BA) / ? ln(Pop) by about 10% – or estimate crowd out when none exists. This example might make itseem as if the data we are using will lead us to overestimate crowd out effects. However, if one runs thisthough experiment in reverse, one sees that during periods of declining cohort size (and decreased time todegree), we will tend to overestimate ?ln(BA) / ? ln(Pop). Since the variables we use in our regressions areall deviations from year and state means, some states will be experiencing increases in cohort size (relativeto the mean), while others are experiencing decreases in cohort size and the bias introduced by the fact thatwe are using period rather than cohort measures will tend to cancel out.15
appropriate measures. Where there are discrepancies between the Census measures and theinstitutional measures, they are due to the effects of differences in the age of observation for thecorresponding measure of cohort size. These results are consistent with the interpretation that the“crowding” that matters occurs at the collegiate level.III. Higher Education Resources and Cohort SizeIn considering the supply-side adjustment of colleges and universities to the reductionsand expansions in cohort size, colleges and universities face the potential margins of adjustmentof price (tuition), quantity (enrollment) and resources per student.While price is usually a natural margin for adjustment to a demand shock, both the fact that forpublic institutions tuition covers such a small fraction of total costs, and the unusual link betweenpolitical actors at the state level and public colleges and universities undercuts this potentialchannel for adjustment to market forces. 25 In fact, the link between cohort size and tuitioncharged by public institutions is not positive. Instead, the evidence from regressions of the tuitioncharged to in-state students by public colleges and universities on cohort size points clearly in theother direction: a 10% increase in cohort size is associated with a 2.7% decrease in tuition at thestate comprehensive schools and 4.2% decrease at flagship institutions. As in previousspecifications, these regressions include state and year fixed effects. Since there were secularincreases in tuition at state schools over the period under study, the right way to think about theseresults is that they suggest that tuition rose less rapidly in states that experienced populationgrowth over the period in question. It is only among the non-research private institutions that wesee the expected positive link between tuition and cohort size. When state and localappropriations are included in the regressions, the effect of cohort size on tuition approaches zero,with increases in state appropriations having a substantial negative effect on tuition prices atpublic universities. These results suggest that state universities raise tuition to cover expenses as alast resort in adverse budgetary environments. 26Beyond tuition levels, we consider the relationship between all sources of revenue andcohort size in the regressions presented in Table 5. For total education expenditures, state25 For example, in 1999, the Virginia legislature instituted a 20-percent reduction in tuition atpublic colleges as part of the fulfillment of campaign promises of then Governor James Gilmore. Withrecent reductions in state tax revenues, states have turned to cutting appropriations and allowing publicinstitutions to increase tuition.26 When either state employment or state and local appropriations are included in the regressionthe effect of cohort size on tuition approaches zero, with increases in either state employment of stateappropriations having a substantial negative effect on tuition prices. These results would seem to confirmthat states tend to raise tuitions when state economies are in trouble.16
Page 5 and 6: Cohort Crowding: How Resources Affe
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Page 14: elative to cohort size) was more se
Page 17: Explaining the Divergence between R
Page 22: analysis is whether results we attr
Page 27 and 28: ReferencesBaker, Michael, Dwayne Be
Page 29 and 30: Figure 1: Public university adjustm
Page 31 and 32: Table 1: Distribution of revenues,
Page 33 and 34: Table 3: Regression of total enroll
Page 35 and 36: Table 5: Regressions of revenue var
Page 37 and 38: Table 7: Effects of cohort size on
Page 39 and 40: and “Opening Fall Enrollment.”
Page 41 and 42: Primary-secondary school quality me
Page 43 and 44: GeorgiaIdahoLn Inst BA degrees10.21
Page 45 and 46: NebraskaNevadaLn Inst BA degrees9.2
Page 47: TexasUtahLn Inst BA degrees11.16719

Cohort crowding: how resources affect collegiate attainment

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