Cohort crowding: how resources affect collegiate attainment
Cohort crowding: how resources affect collegiate attainment Cohort crowding: how resources affect collegiate attainment
Results Based on Census DataAn alternative way to measure the effect of cohort size on degree completion employsCensus micro data on BA completion rates, organized by state of birth and birth cohort, as therelevant demographic variable. 19 Using alternative data sources serves to underscore thereliability of our results while necessarily answering somewhat different questions. Table 4presents estimates of the effects of cohort size (measured in terms of year and state of birth) ondegree completion using Census data, along with estimates of the effects on degrees conferredusing the institutional data for comparison. Because the dependent variable for the Census-basedestimates is the cohort share (fraction with a BA) while for the institutional-based results it is thenumber of BAs, subtracting one from the latter results will put these two estimates on the samefooting. Regressions of the share of the population born in each state and year with a BA degreeon cohort size (this time measured with cohort size at the year of birth) show a substantial declinein college completion shares with changes in cohort size. The magnitude of the estimated declinewhen using the Census data is somewhat smaller than the magnitude of the decline when usingthe institutional data – that is -0.26 or -0.24 versus -0.34 or –0.29, but the differences between thepoint estimates are not qualitatively important, nor are they statistically significant. 20 However,while including state-specific trends in the specifications using institutional data tends tostrengthen the evidence for “crowding out,” doing so significantly weakens the evidence in thespecifications using Census data.models using the institutional data restriction attention to census years. Results from the analysis producedresults that are completely consistent with results based on all years of data19 Note that when we use Census micro data organized by state and year of birth to measure thecollege completion rates, the regression estimates with the dependent variable specified as a completionrate (ln [BA/N]) are not equal to the specification in levels (ln[BA])minus one. The reason is that that thedenominator in the measure of the completion rate, a measure of cohort size calculated from the micro data,is not identical to the population measure from Vital Statistics sources. What we observe in the data is anegative correlation between the error (the difference in the measures) and the measure of population fromthe Vital Statistics source. While the simple correlation between the population measure from the VitalStatistics and the population measure from the Census micro data is 0.996, a regression of the Censusmeasure on the Vital Statistics measure (both measured in logs), produces a coefficient of .952 (.0127). Theresult is that regression estimates using the Census micro data in levels will produce estimates suggesting alower elasticity of completion with respect to population than related estimates with the dependent variablespecified as a completion rate.20 These estimates are quite similar to those presented in Card and Lemieux (2000). Depending onthe specification and cohorts used in their regressions, they estimate a 10% increase in cohort size isassociated with a decline in college completion of between 0.4 and 0.8 percentage points for men andbetween 0.3 and 0.6 percentage points for women. To convert these estimates into elasticities, one needs todivide by the average fraction receiving a BA in these cohorts – somewhat more than 0.2 for men andsomewhat less than 0.2 for women. Using different samples, somewhat different specifications, and vitalstatistics rather than census data to determine cohort size, we obtain results quite similar to those reportedby Card and Lemieux.13
Explaining the Divergence between Results Using Census and Institutional DataPossible explanations for the large difference between the results based on theinstitutional data versus the Census data with the inclusion of state-specific trends include eitherdifferences in the timing of the cohort size variable or differences in the nature of the measuresused.In terms of the timing of the cohort-based measure, cohort size at birth is used in theCensus regressions and cohort size at the typical college enrollment age (age 18) is used in theinstitutional measures. Given our maintained hypothesis that the primary reason for theassociation between cohort size and college completion rates involves cohort crowding atcolleges and universities, the right measure of cohort size is the cohort size during the typicalcollege going years. Cohort size at birth can then be thought of as an error-ridden proxy forcohort size 18 to 22 years later. Indeed, the correlation between year-of-birth measures of cohortsize and measures of the same cohort at age 18 after removing state and year effects is 0.84.Removing state-specific trends drops the simple correlation to 0.37. Thus, relatively short-runfluctuations in the size of cohorts measured in the year of birth are relatively weakly related to thesize of the college-age population in a state 18 years later. The modest degree of cohort crowdingshown in columns (2) and (4) of Table 4 is consistent with the notion that, once state specifictrends are included in the specification, cohort size at birth is a relatively poor proxy for cohortsize at college attendance age.Nevertheless, there are a number of reasons why the institutional measure of BAproduction regressed on cohort size at age 18 might tend to exaggerate estimates of cohortcrowding. It would not be too surprising to find that being born into a large (state-specific) cohortwould tend to increase the odds that a person went out of state to attend college or temporarilypostponed going to college. In either case our estimates based on the institutional data, wouldoverstate the magnitude of the effect of cohort size on college completion (crowding). TheResidence and Migration survey, which has been conducted periodically by the Department ofEducation since the 1940s, provides some information on enrollment by state of residence andcollege. We estimate the elasticity of total enrollment at the state level with respect to population[0.61 (0.11)] and the elasticity of enrollment of state residents with respect to population [0.62(0.08)]. 21 If increased out-of-state enrollment were a substantial part of the response to cohortexpansion, we would see larger elasticities (closer to 1) for enrollment of state residents than fortotal enrollment in the state. Yet, the elasticities for these two measures are virtually identical.21 Estimating equations include state and year fixed effects; the addition of state-specific trendsdoes not materially affect these results.14
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- 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
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- Page 37 and 38: Table 7: Effects of cohort size on
- Page 39 and 40: and “Opening Fall Enrollment.”
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- 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
Results Based on Census DataAn alternative way to measure the effect of cohort size on degree completion employsCensus micro data on BA completion rates, organized by state of birth and birth cohort, as therelevant demographic variable. 19 Using alternative data sources serves to underscore thereliability of our results while necessarily answering somewhat different questions. Table 4presents estimates of the effects of cohort size (measured in terms of year and state of birth) ondegree completion using Census data, along with estimates of the effects on degrees conferredusing the institutional data for comparison. Because the dependent variable for the Census-basedestimates is the cohort share (fraction with a BA) while for the institutional-based results it is thenumber of BAs, subtracting one from the latter results will put these two estimates on the samefooting. Regressions of the share of the population born in each state and year with a BA degreeon cohort size (this time measured with cohort size at the year of birth) s<strong>how</strong> a substantial declinein college completion shares with changes in cohort size. The magnitude of the estimated declinewhen using the Census data is somewhat smaller than the magnitude of the decline when usingthe institutional data – that is -0.26 or -0.24 versus -0.34 or –0.29, but the differences between thepoint estimates are not qualitatively important, nor are they statistically significant. 20 However,while including state-specific trends in the specifications using institutional data tends tostrengthen the evidence for “<strong>crowding</strong> out,” doing so significantly weakens the evidence in thespecifications using Census data.models using the institutional data restriction attention to census years. Results from the analysis producedresults that are completely consistent with results based on all years of data19 Note that when we use Census micro data organized by state and year of birth to measure thecollege completion rates, the regression estimates with the dependent variable specified as a completionrate (ln [BA/N]) are not equal to the specification in levels (ln[BA])minus one. The reason is that that thedenominator in the measure of the completion rate, a measure of cohort size calculated from the micro data,is not identical to the population measure from Vital Statistics sources. What we observe in the data is anegative correlation between the error (the difference in the measures) and the measure of population fromthe Vital Statistics source. While the simple correlation between the population measure from the VitalStatistics and the population measure from the Census micro data is 0.996, a regression of the Censusmeasure on the Vital Statistics measure (both measured in logs), produces a coefficient of .952 (.0127). Theresult is that regression estimates using the Census micro data in levels will produce estimates suggesting alower elasticity of completion with respect to population than related estimates with the dependent variablespecified as a completion rate.20 These estimates are quite similar to those presented in Card and Lemieux (2000). Depending onthe specification and cohorts used in their regressions, they estimate a 10% increase in cohort size isassociated with a decline in college completion of between 0.4 and 0.8 percentage points for men andbetween 0.3 and 0.6 percentage points for women. To convert these estimates into elasticities, one needs todivide by the average fraction receiving a BA in these cohorts – somewhat more than 0.2 for men andsomewhat less than 0.2 for women. Using different samples, somewhat different specifications, and vitalstatistics rather than census data to determine cohort size, we obtain results quite similar to those reportedby Card and Lemieux.13
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