Abstract

Between 2000 and 2010, U.S. public colleges and universities experienced widespread and uneven changes in funding from state and local appropriations. We find that over this period annual decreases in statewide appropriations led to lower public enrollment and higher for-profit enrollment (with no effect on enrollment overall), as well as increased student borrowing. In an analysis of mechanisms, we detect effects on spending, tuition, and capacity in the public sector. Altogether, the results reveal that core institutional resources affect the types of schools that students attend and yield new evidence of substitution between the public and for-profit sectors.

1.  Introduction

The majority of postsecondary students attend public colleges and universities. The sector derives a large share of its revenue from public sources, and the least selective schools are, in general, the most reliant on state and local appropriations.1 However, this crucial source of funding has been shrinking in response to budgetary pressures unrelated to education policy or student demand (Kane, Orszag, and Gunter 2003; Kane et al. 2005; Bell 2008; GAO 2014).2 Consequently, prospective students have reportedly faced large increases in the cost of attendance and resource-related frictions, including oversized classes, cutbacks in educational support and other student services, and caps on enrollment in certain fields and overall. Meanwhile, enrollment at for-profit colleges and student borrowing have both surged.

Several recent studies shed light on the importance of institutional resources in shaping student outcomes (e.g., Bound and Turner 2007; Bound, Lovenheim, and Turner 2010; Long 2015; Deming and Walters 2018). Related work shows that students trade off supply-side factors, like quality and price, when choosing where to enroll (e.g., Cohodes and Goodman 2014; Bettinger et al. 2016; Angrist et al. 2017). A subset of this literature focuses on the processes that induce students to attend for-profit colleges (Cellini 2009; Darolia 2013; Cellini, Darolia, and Turner 2018), where, on average, education is more expensive, returns are relatively low, and other student outcomes are generally worse. The evidence thus far indicates that within specialized circumstances, for example, when locally competing schools are awarded funds to improve their facilities or are publicly sanctioned for bad student outcomes, students substitute between nonselective public and for-profit colleges.

Our study unifies these concepts and explores how core institutional resources affect the types of schools students attend, focusing on potential interactions between the public and for-profit sectors. In particular, the analysis estimates the effects of state and local appropriations to public colleges and universities on enrollment and borrowing between 2000 and 2010, a period over which annual changes in such funding varied in the median state (in terms of variability) between −8 percent and 10 percent.3 The empirical strategy leverages this uneven variation, where the unit of analysis is a state-year, and exploits the earlier timing of state budget processes relative to the beginning of the academic year (holding cohort size and unemployment constant and abstracting from permanent state differences and national phenomena).4 The main estimates represent the average sensitivity of enrollment and borrowing to total appropriations in a state and, as such, offer insight into how prospective students respond to shocks to core resources that support the general operations and functionality of academic institutions.5 We conclude with an examination of effects on the supply of public education.

The main analysis generates several findings. First, all else equal, the effect of a decrease in statewide appropriations on overall enrollment is indistinguishable from zero.6 Second, underneath this net zero, there are statistically significant declines in public attendance and increases in for-profit attendance, with no effect on private nonprofit attendance, such that the implied marginal rate of substitution (MRS) between the two active sectors is about 0.75.7 Among freshmen, effects are concentrated at community colleges (as opposed to four-year universities), consistent with the heavier reliance of such schools on appropriations and with the substitution occurring among less competitive students (for whom for-profit schools likely represent the closest substitutes). Finally, given the shift in attendance toward the higher-borrowing for-profit sector, we hypothesize that appropriations cuts could increase debt financing of education among students and their families, especially if the public sector also price adjusts in response. Indeed, the estimates reveal a corresponding increase in borrowing across the two sectors. Further, borrowing within the for-profit sector increases in lockstep with enrollment growth, reflecting the sector's consistently high borrowing rates.8

Our analysis concludes with suggestive evidence that appropriations immediately affect conditions in the public sector, which may induce students to attend for-profits. First, annual spending on student services (e.g., registrar and admissions activities) and on academic support (e.g., educational materials and curriculum development) appears to respond directly to changes in appropriations in aggregate as well as on a per-student basis, suggesting campuses have fewer resources on hand to serve both prospective and continuing students. (Interestingly, spending on instruction does not appear to respond.) Second, we find evidence of meaningful changes in price (both published prices and the net price students actually pay) and capacity (e.g., the share of faculty who are part-time, the share of freshmen from within the state).9 Lastly, although our data do not allow us to directly test whether public sector classes become oversubscribed, our results are certainly consistent with such a mechanism.

Substitution between public and for-profit schools likely has long-run consequences.10 Students attending for-profit institutions tend to experience greater financial strain, as evidenced by their relatively high student loan default rates and small earnings gains (Kane and Rouse 1995; Cellini and Chaudhary 2014; Looney and Yannelis 2015; Armona, Chakrabarti, and Lovenheim 2018; Cellini and Turner 2018).11 Students who attend for-profits are also viewed less favorably by employers than students who pursue similar programs at other schools and on par with students who pursue no postsecondary education at all (Darolia et al. 2015; Deming et al. 2016). Finally, corresponding increases in borrowing may negatively affect household formation and career choice (Gicheva 2016; Mezza et al. 2016; Dettling and Hsu 2018).

The paper most related to ours is Cellini (2009), which uses variation from local community college bond referenda in California to demonstrate that the for-profit and public sectors compete locally for students.12 We extend this work by considering a wider set of enrollment outcomes, borrowing, and supply-side metrics, yielding a more complete characterization of the effects of funding on student outcomes and potential mechanisms. In addition, our estimates are nationally representative and derive from a more prevalent source of funding. Nonetheless, as we show in the conclusion, the responsiveness implied by this study is strikingly similar to ours.

Finally, in contemporaneous work, Deming and Walters (2018) examine the effect of state appropriations on public postsecondary outcomes at the school level. Although their analysis differs from ours along several dimensions, they find complementary evidence of enrollment effects at schools that experience shocks and spillovers to private schools within the same county.13

The rest of the paper proceeds as follows: Section 2 motivates the research design; section 3 describes the empirical framework; section 4 estimates the effect of appropriations on attendance and borrowing; section 5 examines educational spending and other measures of the supply of education in the public sector; and section 6 contextualizes the findings and concludes.

2.  Institutional Background and Conceptual Framework

State and Local Appropriations to Public Colleges

Public colleges and universities are distinguished from other institutions of higher education both in how they are administered (generally by publicly elected or appointed officials) and how they are funded (with a relatively high reliance on revenue from federal, state, and local sources). In particular, they receive a large portion of their operating revenue from state and local appropriations (figure 1). From a college's perspective, variation in this revenue may not fully coincide with changes in spending needs. Although higher education is a sizable component of state and local budgets, legislatures face several challenges in coordinating higher education spending with their corresponding objectives and outcomes.

Figure 1.

Relative Importance of Major Sources of Revenue

Note: Share reflects mean across states, weighted by public enrollment in a state-year. Denominator excludes revenue from hospital and other auxiliary operations.

Figure 1.

Relative Importance of Major Sources of Revenue

Note: Share reflects mean across states, weighted by public enrollment in a state-year. Denominator excludes revenue from hospital and other auxiliary operations.

First, state budgets are typically set before students enroll in school or register for classes—often in the spring before the relevant academic year—and thus legislators must rely on projected rather than actual annual spending needs (NASBO 2015). To project these needs, governments commonly utilize a “base plus” calculation (the previous year's funding plus adjustments for cost-of-living and anticipated enrollment changes), a formula-based calculation that weights over higher educational priorities (e.g., number of students, facility maintenance, student outcomes), or a combination of these two methods (Bell 2008; SRI International 2012).14 Taken at face value, the former maintains year-to-year stability in revenue flow but does not accommodate changes in higher education policy objectives or priorities, whereas the latter can accommodate such changes but cannot deliver year-to-year stability. Neither formula can accommodate unpredictable changes in student demand.

Second, in recent years, appropriations have fallen short of what these calculations recommend (Jones 2006; SRI International 2012; Dougherty and Reddy 2013). Whereas the amount of funds governments allocate to a particular category of spending should, in theory, primarily reflect the estimated expenditure needs of that category, in practice, several other considerations—for example, projected government revenue (composed mostly of taxes and lottery receipts), other spending obligations (which vary with factors unlikely to be correlated with the demand for higher education, such as program generosity, legislative attitudes, cost inflation, pension performance), legislative priorities, and, oftentimes, balanced budget requirements or specific tax and expenditure limits—can enter into final determinations (Kane, Orszag, and Gunter 2003; Kane et al. 2005; GAO 2014).15 In contrast to other areas of public spending, public colleges and universities have their own source of revenue—tuition—that can be used to offset changes in appropriations. As a consequence, higher education is often treated as the “balance wheel” of state and local budgets (Delaney and Doyle 2011; Serna and Harris 2014).16 Indeed, studies examining previous business cycles found that appropriations for higher education were pro-cyclical, whereas demand was countercyclical (Betts and McFarland 1995; Humphreys 2000). Those examining more recent periods found that this spending, in addition to economic conditions, reflected competing budget priorities, such as Medicaid and K–12 education (e.g., Kane and Orszag 2003; GAO 2014).

Altogether, it seems plausible that, after accounting for time-varying factors related to educational demand that legislators can readily observe (e.g., local economic conditions, the size of the college-aged population, national phenomena), the remaining variation in statewide appropriations for higher education over time is exogenous to student outcomes. This residual variation identifies our effects.

Supply-Side Responses in the Public Sector

Assuming that a public college generally operates at its budget constraint and does not have the ability to borrow, a decline in appropriations must either be offset by an increase in another form of revenue or lead to a decrease in spending. Either of these responses may materialize in a manner that is visible to prospective students and influence their enrollment.17

Between 2000 and 2010, public colleges heavily increased their reliance on tuition, such that by 2010, tuition had overtaken appropriations as the largest single source of operating revenue (figure 1; GAO 2014).18 Public colleges have three general levers for raising tuition revenue when appropriations fall, each with empirical support. The most transparent method is increasing the published cost of attendance (i.e., the sticker price; Koshal and Koshal 2000).19 They can also increase the effective (or net) price of attendance by decreasing the generosity of aid packages awarded to matriculating students (Webber 2017). Finally, they can draw in more out-of-state or foreign students, who often face higher published and net prices (Jaquette and Curs 2015; Bound et al. 2016). Note that the first two levers affect prices, while the last primarily affects capacity.

Otherwise, unmet spending needs, even if temporary while prices adjust, imply resource crowding, for which there is considerable anecdotal evidence over our window of study (Mitchell, Leachman, and Masterson 2016).20 To take one salient example, California (which maintains a policy of college affordability and low tuition rates) has designated particular majors, or sometimes entire campuses, as “impacted” in years when funding has been too low to support student interest. In such instances, enrollment becomes restricted, admissions criteria are temporarily raised, and students are directed to take classes or apply elsewhere.

For-Profit Institutions between 2000 and 2010

Between 2000 and 2010, the for-profit sector was booming, accounting for almost 30 percent of the total increase in enrollment over the same period. However, the sector did not come under formal federal scrutiny until June 2010, when the Senate Committee on Health, Education, Labor, and Pensions (the HELP Committee) began a two-year, in-depth investigation of the causes and consequences of its run-up. We first describe these institutions and then summarize the regulatory environment over this period, with the latter drawing heavily from the HELP Committee's report on its investigation (United States Senate 2012).

For-profits typically operate unlike other higher education institutions along several dimensions (Turner 2006; Deming, Goldin, and Katz 2012; U.S. Department of Treasury 2012). Although their market for students resembles community colleges in that for-profit enrollments tend to swell when cohorts are large and local labor markets are weak, they are a distinct class of institution that has historically offered very specialized programs of study and served a fairly small portion of those enrolled, particularly among recent high school graduates. Courses at for-profits are often designed to accommodate the schedules of part-time and older students who juggle continued education with other work and family responsibilities. Further, the sector as a whole is nearly fully supported by federal student loan and grant programs.

The task of regulating for-profits over this period was spread across states, educational accrediting agencies, and the federal government, none of which was properly incentivized or properly equipped to scrutinize the sector's activities. For instance, even though the federal government provides the majority of funding for for-profits through its array of student aid programs, the punitive measures designed to prevent institutions from abusing these programs appear to have been avoided through clever bookkeeping. In fact, while states theoretically were in the best position to monitor and regulate the for-profit sector, as each school's operations were often contained within their boundaries and primarily served their constituents, they also seemingly had the least incentive. On the one hand, the federal government never set minimum requirements for state authorization of for-profits, therefore, for-profits created very little overhead for states beyond the cost of routine inspections that states themselves were responsible for defining and enforcing. On the other hand, states had to fund public colleges offering a competing product, and the staff and resources required to regulate for-profits posed additional costs. Against this backdrop, from the 1990s through the 2000s, “many states [took] a passive or minimal role in approving institutions, reviewing and addressing complaints from students and the public, and ensuring that colleges [were] in compliance with state consumer protection laws” (United States Senate 2012, p. 8), consistently charging minimal operating fees, staffing few auditors to review operations, or both.21 Over our period of study, there is very little evidence of state legislation altering either standards for (the approval or operation of) for-profits or the regulatory environment.22

How Appropriations Funding Could Influence Attendance Patterns across Sectors

There is evidence that, in specialized circumstances, for-profit schools compete with community colleges for students (e.g., Cellini 2009; Darolia 2013). Cellini (2009) describes a framework for this relationship, whereby for-profits readily and easily absorb excess student demand, and finds evidence that for-profit schools fully enter and exit in response to large changes in funding at community colleges. A similar framework can be applied to our setting.

Education is a normal good, and consumers have preferences over education in each sector, with imperfect substitutability between the two sectors. The for-profit sector offers a differentiated (e.g., lower-quality) product and elastically absorbs excess demand for education in the public sector. Enrollment within a given sector depends on the aggregate demand for education, conditions in each sector, and the MRS between them. A negative funding shock within the public sector will decrease the quality or increase the price of a public education, both of which will reduce the quantity demanded of public education and raise the quantity demanded of for-profit education. The magnitude of these changes reflects the size of the shock, the degree of substitutability between the sectors (which can vary with quality), and the relative price of education across sectors (which can vary with price).23

Figure 2 presents prima facie evidence that these relationships hold within our empirical setting. Year-over-year changes in appropriations and for-profit attendance within a state are negatively related, both overall and for relatively large changes in appropriations.

Figure 2.

Appropriations and For-profit Attendance

Notes: Graphs plot the year-over-year percent change in appropriations against year-over-year percent change in for-profit attendance for 50 U.S. states (2001—10). Right figure restricts to top and bottom 10% of appropriations changes, only. Outliers are removed for this exercise, but the relationship is similar upon their inclusion. Fit coefficients are −0.384 and −0.363, respectively.

Figure 2.

Appropriations and For-profit Attendance

Notes: Graphs plot the year-over-year percent change in appropriations against year-over-year percent change in for-profit attendance for 50 U.S. states (2001—10). Right figure restricts to top and bottom 10% of appropriations changes, only. Outliers are removed for this exercise, but the relationship is similar upon their inclusion. Fit coefficients are −0.384 and −0.363, respectively.

3.  Data and Empirical Framework

Data

The analysis sample is drawn from the U.S. Department of Education's Delta Cost Project database.24 The database harmonizes finance, enrollment, and staffing records collected by the federal government through a series of mandatory annual surveys of higher educational institutions that have been made publicly available in the Integrated Postsecondary Education Data System (IPEDS). The Delta Cost Project compiles these data and attempts to reconcile changes in accounting standards and reporting formats over time to be more useful for longitudinal analysis of enrollment and financing. The panel covers all reporting institutions for academic years 2000 through 2010, corresponding to over 10,000 unique institutional identifiers.25 Data are adjusted for reporting issues at the institution level before analysis at the state-academic year.26

Our key revenue measure is combined state and local appropriations received by public colleges and universities in a state-academic year. We construct an array of outcomes (i.e., enrollment [overall and by sector], spending, faculty, and tuition) aggregated to the same level. Enrollment is quantified using either full-time equivalents (FTEs) or the number of freshmen (first-time first-year) students.27 The analysis focuses on the FTE concept—which includes freshmen, continuing students, nonconventional students, and graduate students—primarily because of reporting inconsistencies over time at for-profit colleges.28 To explore dynamics within the public sector, we also examine freshmen enrollment at public schools, overall and by school type, focusing on community colleges and four-year flagship universities. Finally, we analyze freshmen migration for the subset of years in which such data are available in IPEDS.29

To measure borrowing, we leverage federal loan volume reports by institution and academic year for loans disbursed through the Federal Family Education Loan and Federal Direct Loan programs.30 Again, at the state-academic year level, we examine borrowing across all public and for-profit colleges, borrowing within the subset of schools at which at least two-thirds of enrollment is composed of in-state residents, and borrowing by sector (i.e., public, private for-profit, and, as part of our robustness checks, private nonprofit institutions) level.31

For the analysis of mechanisms, we construct four tuition measures derived from either published sticker prices or gross tuition revenue collected by institutions (a proxy for the prices students actually pay, inclusive of their scholarships), weighted by enrollment where noted. The analysis also considers staffing (i.e., full-time and part-time faculty, share of faculty part-time) and several spending categories (i.e., academic support, student services, instruction).

Finally, we include time-varying measures of cohort size and economic conditions. Cohort size is measured with intercensal state population estimates for either 17-year-olds in July of the previous year or 18- to 24-year-olds in July of the current year, depending on whether the outcome of interest pertains to freshmen or FTE students, respectively. Economic conditions are measured over the academic year of interest, by averaging Bureau of Labor Statistics state unemployment rates from June to May.

Table 1 presents summary statistics for which the unit of observation is a state-academic year. In general, more students attend public colleges and universities than both private nonprofit and for-profit colleges. Within the public sector, there are about three times as many community college freshmen. While more borrowed dollars each year accrue to students at public institutions, on a per student basis, borrowing is concentrated within the for-profit sector.

Table 1.
Descriptive Statistics
NMeanSD
Main Sample
Enrollment 
Overall FTE 550 264,287 293,697 
For-profit FTE 550 21,284 40,764 
Private not-for-profit FTE 550 57,007 75,918 
Public FTE 550 185,995 213,530 
Public freshmen 550 30,324 29,182 
Public flagship freshmen 550 4,813 3,374 
Public community college freshmen 550 12,427 14,373 
For-profit share of “demand-elastic” (for-profit + community college) FTE 550 20.4 12.8 
For-profit share of “budget-sensitive” (for-profit + public) FTE 550 8.0 7.3 
Faculty and Tuition 
Full-time faculty 550 8,556 8,261 
Part-time faculty 550 7,118 8,792 
Share of faculty that are part-time 550 41.0 10.3 
flagship sticker price (real$) 550 6,726 2,412 
Enrollment-weighted tuition (real$) 550 6,743 2,587 
Enrollment-weighted community college tuition price (real$) 550 3,730 1,419 
Enrollment-weighted sticker price (real$) 550 4,935 1,844 
Revenue, Borrowing, and Controls 
Appropriations (real$)    
Billions 550 1.62 2.01 
Per college-aged individual 550 2,870 911 
Grants (real$)    
Billions 550 0.36 0.48 
Per college-aged individual 550 600 282 
Borrowing, private nonprofit (billions real$) 550 0.367 0.525 
Borrowing, for-profit (billions real$) 550 0.212 0.526 
Borrowing, public (billions real$) 550 0.521 0.473 
Borrowing, public and for-profit (billions, real$) 550 0.733 0.818 
Borrowing, public and for-profit, >2/3 in-state-attendees (billions, real$) 550 0.595 0.710 
Unemployment rate 550 5.2 1.8 
Cohort    
College-aged population 550 575,987 642,486 
18-year-old population 550 83,632 92,780 
Freshmen Migration Sample 
(publicstay_in_state)/(for-profit+public) 204 78.8 10.9 
(flagshipin_state)/(flagship) 204 71.3 15.9 
Appropriations (billions real$) 204 1.53 1.99 
NMeanSD
Main Sample
Enrollment 
Overall FTE 550 264,287 293,697 
For-profit FTE 550 21,284 40,764 
Private not-for-profit FTE 550 57,007 75,918 
Public FTE 550 185,995 213,530 
Public freshmen 550 30,324 29,182 
Public flagship freshmen 550 4,813 3,374 
Public community college freshmen 550 12,427 14,373 
For-profit share of “demand-elastic” (for-profit + community college) FTE 550 20.4 12.8 
For-profit share of “budget-sensitive” (for-profit + public) FTE 550 8.0 7.3 
Faculty and Tuition 
Full-time faculty 550 8,556 8,261 
Part-time faculty 550 7,118 8,792 
Share of faculty that are part-time 550 41.0 10.3 
flagship sticker price (real$) 550 6,726 2,412 
Enrollment-weighted tuition (real$) 550 6,743 2,587 
Enrollment-weighted community college tuition price (real$) 550 3,730 1,419 
Enrollment-weighted sticker price (real$) 550 4,935 1,844 
Revenue, Borrowing, and Controls 
Appropriations (real$)    
Billions 550 1.62 2.01 
Per college-aged individual 550 2,870 911 
Grants (real$)    
Billions 550 0.36 0.48 
Per college-aged individual 550 600 282 
Borrowing, private nonprofit (billions real$) 550 0.367 0.525 
Borrowing, for-profit (billions real$) 550 0.212 0.526 
Borrowing, public (billions real$) 550 0.521 0.473 
Borrowing, public and for-profit (billions, real$) 550 0.733 0.818 
Borrowing, public and for-profit, >2/3 in-state-attendees (billions, real$) 550 0.595 0.710 
Unemployment rate 550 5.2 1.8 
Cohort    
College-aged population 550 575,987 642,486 
18-year-old population 550 83,632 92,780 
Freshmen Migration Sample 
(publicstay_in_state)/(for-profit+public) 204 78.8 10.9 
(flagshipin_state)/(flagship) 204 71.3 15.9 
Appropriations (billions real$) 204 1.53 1.99 

Notes: Unit of observation is a state-year. SD = standard deviation; FTE = full-time equivalent.

With respect to the funding variables, appropriations far outstrip revenue from grants and contracts. There is extremely wide variation in appropriations over the sample, primarily reflecting differences across states in budget and population size. For example, between 2000 and 2010, average annual appropriations to higher education in California were $12.6 billion (ranging from $11.7 billion to $13.6 billion), whereas in Vermont, they were about $75 million (ranging from $72 million to $81 million). For comparability across states, the analysis examines changes in a state over time, where there is still considerable variation within the data; for example, the median state, in terms of variability, experienced annual changes in appropriations ranging from −8 percent to 10 percent.

Empirical Framework

Throughout the analysis, the estimating equation is a generalized difference-in-differences:
yst=α+β×ln(appropriations)st+Xstθ+γt+γs+ɛst,
(1)
where yst is the outcome of interest (e.g., the natural log of for-profit enrollment) for state s in year t,32appropriationsst is aggregated state and local appropriations,33Xst represents our cohort and unemployment rate controls, and γt and γs are academic year and state effects, respectively. Standard errors are clustered at the state level.

The coefficient of interest is β such that, when y is ln(for-profit enrollment), the estimate represents the elasticity of for-profit enrollment with respect to appropriations. A log-log specification is useful in our empirical setting, which entails very large across- and within-state differences in many dimensions of the market for higher education—including average appropriations levels and the for-profit sector's market share—but lacks evidence to guide how responsiveness might vary along these dimensions. Alternative specifications examine enrollment as a share of either the college-aged population or the higher education market, which allows students in different market settings to be differentially responsive to appropriations-related innovations and may make it easier to interpret the magnitude of shifts between sectors.34

Our specification captures several aspects of the logic put forth in section 2. First, examining contemporaneous measures of appropriations and attendance exploits the early timing of state budget-setting relative to the academic year. Second, the inclusion of state and year effects identifies β from variation of funding within a state, abstracting from interstate differences in legislative priorities and budget-setting processes, as well as annual fluctuations in national college enrollment, pricing, and funding, respectively. Third, our controls absorb extraneous variation from cohort size and economic conditions, each plausibly correlated with educational demand and both of which may be used by legislators to project spending needs. For a causal interpretation of β, we must assume that any remaining year-to-year variation in appropriations within a state is exogenous to student enrollment decisions. The analysis of total postsecondary enrollment in the next section offers an indirect test of this exogeneity assumption, as evidence of a statistical relationship might suggest that students respond to appropriations in ways this framework will not fully capture (e.g., where to attend college geographically, the decision to attend college) or even that appropriations are systematically linked to an omitted variable that coincides with attendance.35 Validity is discussed more thoroughly after results are presented.

4.  Main Analysis: Effects on Attendance and Borrowing

Postsecondary Attendance

Table 2 presents attendance effects for the FTE and public freshmen enrollment concepts, respectively.36 The top panel is split into two: The left columns examine log outcomes, and the right columns, which are described at the end of this subsection, examine shares.

Table 2.
Effects of Appropriations on Attendance and Borrowing
Panel A: Enrollment (Any Academic Level)
(1)(2)(3)(4)(5)(6)(7)(8)
Full-time Equivalent (FTE) EnrollmentFTE as a Share of 18—24-Year-Old Population
Overall EnrollmentPublic EnrollmentFor-Profit EnrollmentPrivate Nonprofit EnrollmentOverall EnrollmentPublic EnrollmentFor-Profit EnrollmentPrivate Nonprofit Enrollment
Appropriations −0.006 0.029** −0.186*** −0.042 −0.171 0.930* −0.880 −0.221 
 (0.022) (0.012) (0.058) (0.048) (1.538) (0.531) (1.603) (0.296) 
Unemployment rate 0.010** 0.012*** 0.031 0.021 0.463* 0.329*** 0.072 0.062 
 (0.004) (0.003) (0.022) (0.014) (0.269) (0.099) (0.231) (0.057) 
18—24-year-olds 0.446* 0.296*** −0.137 0.628 −22.605 −23.689*** 9.183 −8.100*** 
 (0.225) (0.090) (0.675) (0.590) (14.741) (3.181) (13.823) (2.730) 
Panel B: Freshmen Enrollment 
 (1) Public Freshmen (2) Flagship Freshmen (3) Other Four-Year Freshmen (4) Community Freshmen     
Appropriations 0.048*** 0.016 0.010 0.155**     
 (0.015) (0.023) (0.021) (0.062)     
Unemployment rate 0.010** 0.003 −0.005 0.051***     
 (0.005) (0.008) (0.006) (0.018)     
18-year-olds 0.730*** 0.109 0.759*** 1.308***     
 (0.138) (0.139) (0.140) (0.319)     
Panel C: Borrowing 
 (1) Borrowing at Public Schools (2) Borrowing at For-Profit Schools (3) Borrowing at Public and For-Profit Schools (4) Borrowing at Public and For—Profit Schools with >2/3 In-State Attendance     
Appropriations −0.001 −0.180** −0.074** −0.103***     
 (0.027) (0.079) (0.036) (0.038)     
Unemployment rate 0.026*** 0.061** 0.028** 0.032***     
 (0.009) (0.030) (0.011) (0.010)     
18—24-year-olds −0.014 −1.332* 0.077 0.456     
 (0.236) (0.788) (0.367) (0.346)     
N 550     
Panel A: Enrollment (Any Academic Level)
(1)(2)(3)(4)(5)(6)(7)(8)
Full-time Equivalent (FTE) EnrollmentFTE as a Share of 18—24-Year-Old Population
Overall EnrollmentPublic EnrollmentFor-Profit EnrollmentPrivate Nonprofit EnrollmentOverall EnrollmentPublic EnrollmentFor-Profit EnrollmentPrivate Nonprofit Enrollment
Appropriations −0.006 0.029** −0.186*** −0.042 −0.171 0.930* −0.880 −0.221 
 (0.022) (0.012) (0.058) (0.048) (1.538) (0.531) (1.603) (0.296) 
Unemployment rate 0.010** 0.012*** 0.031 0.021 0.463* 0.329*** 0.072 0.062 
 (0.004) (0.003) (0.022) (0.014) (0.269) (0.099) (0.231) (0.057) 
18—24-year-olds 0.446* 0.296*** −0.137 0.628 −22.605 −23.689*** 9.183 −8.100*** 
 (0.225) (0.090) (0.675) (0.590) (14.741) (3.181) (13.823) (2.730) 
Panel B: Freshmen Enrollment 
 (1) Public Freshmen (2) Flagship Freshmen (3) Other Four-Year Freshmen (4) Community Freshmen     
Appropriations 0.048*** 0.016 0.010 0.155**     
 (0.015) (0.023) (0.021) (0.062)     
Unemployment rate 0.010** 0.003 −0.005 0.051***     
 (0.005) (0.008) (0.006) (0.018)     
18-year-olds 0.730*** 0.109 0.759*** 1.308***     
 (0.138) (0.139) (0.140) (0.319)     
Panel C: Borrowing 
 (1) Borrowing at Public Schools (2) Borrowing at For-Profit Schools (3) Borrowing at Public and For-Profit Schools (4) Borrowing at Public and For—Profit Schools with >2/3 In-State Attendance     
Appropriations −0.001 −0.180** −0.074** −0.103***     
 (0.027) (0.079) (0.036) (0.038)     
Unemployment rate 0.026*** 0.061** 0.028** 0.032***     
 (0.009) (0.030) (0.011) (0.010)     
18—24-year-olds −0.014 −1.332* 0.077 0.456     
 (0.236) (0.788) (0.367) (0.346)     
N 550     

Notes: Each column reports coefficients from an ordinary least squares regression, where the outcome of interest is denoted by the column header, and observations are at the state-year level. Appropriations and population are measured in natural logs, as are the left panel outcomes. In right panel, share refers to a number between 0 and 100. In top panel, overall enrollment includes all students enrolled at any public, for-profit, or private non-profit institution. All regressions include state and year effects and a constant. The estimation sample is all 50 states, academic years 2000-10 (inclusive). Data indicate there was no private nonprofit enrollment in Wyoming over the period and no for-profit borrowing in Mississippi in 2000. Standard errors clustered at state level in parentheses.

*Significant at the 10% level; **significant at the 5% level; ***significant at the 1% level.

We first examine overall enrollment, that is, combined enrollment at public, for-profit, and private nonprofit schools. The estimated effect is indistinguishable from zero (top panel, column 1), resulting in two key takeaways that, together, support a causal interpretation of the sector-specific estimates. First, potentially confounding margins of response that the framework does not capture do not appear to be operating. Second, the variation in appropriations relied upon for identification does not appear to be systematically linked to omitted factors that influence (overall) enrollment.37 (The positive and significant coefficients on unemployment rate and cohort reflect the important relationship between these two factors and educational demand.)

We next examine public enrollment and find, all else equal, the sector shrinks as appropriations wane (top panel, column 2). Next, we restrict attention to freshmen attendance in order to examine effects on entry and to unpack effects by level. (Because of potential effects on persistence and completion, the theoretical predictions for FTE enrollment within the sector are less clear.) In theory, under flush funding conditions, prospective students along the extensive margin might be absorbed into the public sector, and those along the intensive margin within the sector might “level up” to more competitive schools. The middle panel of table 2 reveals a similar effect among freshmen (column 1), which appears to be concentrated at community colleges (columns 2–4), suggesting that effects on public college entry more than offset any “leveling up” to more competitive schools. More generally, the results indicate that fluctuations in statewide appropriations alter the educational plans of significantly many students, particularly those who, in better funding conditions, would attend community colleges.

Note that throughout this analysis, the cohort and unemployment rate coefficients imply that public enrollment reflects the overall demand for education. The sector appears to be reasonably elastic to accommodate an excess of students owing to larger-than-usual populations or worse-than-usual economic conditions, even holding statewide funding constant. Within the sector, freshman enrollment at flagships does not vary significantly with either of these conditions, suggesting excess demand is primarily accommodated by less-competitive schools.

Given that appropriations do not appear to influence overall enrollment, the effect on public enrollment is presumably offset in the other educational sectors. Further, in light of the logic put forth in section 2, the offset is likely concentrated in the for-profit sector.38 Indeed, the estimates imply that a 10 percent drop in appropriations induces about a 2 percent increase in for-profit attendance (top panel, column 3), and, although the sign is negative, the effect of appropriations on private nonprofit enrollment is indistinguishable from zero (top panel, column 4).

This framework does not take into account the sector's size when quantifying its growth; thus, large elasticities implied by the estimates could reflect a very small sector and vice versa.39 The top right panel of table 2 presents results for a specification that scales enrollment by the college-aged population, which delivers estimates that describe changes in size and that also help visualize dynamics across sectors. While the coefficients again imply that the for-profit sector absorbs the large majority of appropriations-driven changes in public enrollment, the effects are less precisely estimated, potentially reflecting the differential responsiveness by sector to cohort size seen in the left panel.40 Indeed, online Appendix C scales for-profit enrollment by “educational demand” and indicates that the sector's market share grows by about one-half of a percentage point, given a 10-percent drop in appropriations to public schools.

Postsecondary Student Borrowing

Earlier, we theorized that a change in appropriations will affect the amount or quality of public education a student can consume at some fixed price, with table 2 indicating students may be willing to spend more to offset negative shocks to their educational consumption.41 This section examines corresponding effects on borrowing, first by sector and then in aggregate.42

The channels through which, to a first order approximation, variation in appropriations can affect borrowing differ by sector. While both the for-profit and the public sector could see effects stemming from a change in attendance, public institutions rely on appropriations for revenue, suggesting that the latter could also see effects from a corresponding change in tuition (the other main source of revenue). (In contrast, for-profit colleges rely heavily on the federal lending programs for revenue, with many reportedly offering a battery of services to facilitate student loan applications and receipt.) An appropriations-induced change in public sector borrowing will represent the net effect of these two empirically inseparable channels. The estimate is slightly negative but insignificant (table 2, panel C, column 1), suggestive of a tuition response.43

As noted above, within the for-profit sector, any appropriations-induced effect on borrowing would be driven by a change in attendance.44 The second column reveals, in response to a 10 percent appropriations cut, borrowing at for-profits increases about 2 percent, all else equal. Given that between 80 and 90 percent of for-profit students borrow for their education, this estimate is very much in line with the increase in for-profit enrollment in the top panel.

As a final exercise, we examine aggregate borrowing across the public and for-profit sectors, which yields an estimate of the net effect on students and families of revenue-induced shifts in the higher education landscape. Specifically, if borrowing increases represent a transfer of cost burden from state and local governments to families, this estimate approximates the size of that transfer. We find that a 10 percent cut in appropriations generates a 0.7 percent increase in borrowing.45 Because some institutions draw a large portion of their student body from outside the state, we also restrict attention to institutions where we would expect pricing and attendance decisions to be the most sensitive to state funding. We define these schools as those where over two-thirds of the student body are residents of that state, in comparison to schools that compete nationally or regionally for students, who would be less affected by state funding.46 In the final column, we see that a 10 percent cut in appropriations induces a 1 percent increase in borrowing within this class of institutions, almost 50 percent larger than our main specification.

Validity

This section examines the validity of the identifying assumption—appropriations are not systematically correlated with the error term—required for a causal interpretation of the estimates.

Table 3 provides suggestive evidence that our appropriations measure is not picking up an unobservable, excluded variable that is broadly driving changes in the educational landscape.47 Specifically, using the main equation, we estimate the effects of appropriations on (1) average SAT scores, a measure of academic achievement and college readiness that we would not expect to be affected by variations in the revenue available to public colleges but that would be affected by, for instance, large-scale reforms (or funding shortages) in publicly provided education; (2) borrowing in the private nonprofit sector, which represents between 30 and 40 percent of borrowing nationally over the period of study but which, as a whole, is unlikely to be revenue-sensitive to appropriations, either directly (as it does not receive any of its funding from appropriations) or indirectly (as we did not detect an effect on enrollment there); (3) economic conditions; and (4) related forms of institutional funding (state and local grants and contracts). The estimates are all statistically indistinguishable from zero.

Table 3.
Validity Checks, Omitted Variables
Estimated Effect of Appropriations on Other Outcomes
Average SAT score −11.680 
 (8.011) 
Borrowing at private non-profit schools −0.120 
 (0.073) 
Unemployment rate −1.110 
 (0.890) 
Grants −0.120 
 (0.179) 
N 550 
Estimated Effect of Appropriations on Other Outcomes
Average SAT score −11.680 
 (8.011) 
Borrowing at private non-profit schools −0.120 
 (0.073) 
Unemployment rate −1.110 
 (0.890) 
Grants −0.120 
 (0.179) 
N 550 

Notes: Each row reports the coefficient on appropriations from an ordinary least squares regression, where the outcome of interest is denoted by the row title, and observations are at the state-year level. Appropriations, borrowing, and population are measured in natural logs. All regressions include state and year effects, unemployment rate and population controls, and a constant. (Row 3 necessarily excludes the unemployment rate control.) The estimation sample is all 50 states, academic years 2000—10 (inclusive). Standard errors clustered at state level in parentheses.

Table 4 varies the specification. In particular, we (1) introduce other large state and local budget items (i.e., tax revenue, pension spending, and health care spending); (2) account for potential pro-cyclicality of appropriations owing to state balanced budget requirements, as some work has found that state government spending tracks the business cycle with a lag of about one year (Clemens and Miran 2012); (3) include lagged public enrollment; and (4) instead consider per student resource availability (i.e., appropriations scaled by public enrollment in a prior year). Estimates are generally robust to these changes and remain same-signed throughout. Notably, the inclusion of lagged public enrollment shrinks the public and freshmen enrollment coefficients by over one-third (though the latter maintains statistical significance). These results could mean that freshmen are more sensitive to annual funding than returning or graduate students or simply that public enrollment in the prior year is more strongly correlated with public enrollment in the current year.48 We further vary the specification in online Appendix D to show our results are not driven by state trends or other phenomena (e.g., the Great Recession, the rise in online education, support for higher education from the American Recovery and Reinvestment Act).

Table 4.
Validity Checks, Alternative Specifications
NPublic Enrollment (1)Public Freshmen (2)For-Profit Enrollment (3)Borrowing at For-Profit Schools (4)Borrowing at Public and For-Profit Schools (5)
Baseline 550 0.029** 0.048*** −0.186*** −0.180** −0.074** 
  (0.012) (0.015) (0.058) (0.079) (0.036) 
Including controls for state and local budget 550 0.028** 0.047*** −0.189*** −0.177** −0.070* 
  (0.012) (0.014) (0.060) (0.074) (0.038) 
Allowing for a lag in the business cycle 550 0.028** 0.045*** −0.167*** −0.159** −0.069* 
(i.e., URt−1 (0.013) (0.013) (0.056) (0.070) (0.037) 
Including lagged public enrollment 500 0.017 0.031** −0.168*** −0.118 −0.085** 
(i.e., log(public)t−1 (0.011) (0.013) (0.055) (0.084) (0.033) 
Scaling by lagged public enrollment 450 0.017 0.035*** −0.180*** −0.156** −0.107*** 
(i.e., log(appropriationst/publict−2 (0.014) (0.012) (0.062) (0.077) (0.025) 
NPublic Enrollment (1)Public Freshmen (2)For-Profit Enrollment (3)Borrowing at For-Profit Schools (4)Borrowing at Public and For-Profit Schools (5)
Baseline 550 0.029** 0.048*** −0.186*** −0.180** −0.074** 
  (0.012) (0.015) (0.058) (0.079) (0.036) 
Including controls for state and local budget 550 0.028** 0.047*** −0.189*** −0.177** −0.070* 
  (0.012) (0.014) (0.060) (0.074) (0.038) 
Allowing for a lag in the business cycle 550 0.028** 0.045*** −0.167*** −0.159** −0.069* 
(i.e., URt−1 (0.013) (0.013) (0.056) (0.070) (0.037) 
Including lagged public enrollment 500 0.017 0.031** −0.168*** −0.118 −0.085** 
(i.e., log(public)t−1 (0.011) (0.013) (0.055) (0.084) (0.033) 
Scaling by lagged public enrollment 450 0.017 0.035*** −0.180*** −0.156** −0.107*** 
(i.e., log(appropriationst/publict−2 (0.014) (0.012) (0.062) (0.077) (0.025) 

Notes: Each cell reports the coefficient on appropriations from an ordinary least squares regression, where the outcome of interest is denoted by the column header and the perturbation of the main estimating equation is denoted by the row title. Observations are at the state-year level. Appropriations, enrollment, borrowing, budgetary spending, and population are measured in natural logs. All regressions include state and year effects, controls for the unemployment rate and the age 18—24 population, and a constant. Controls for state budget include tax revenue, pension spending, and health and hospital spending. The estimation sample is all 50 states, academic years 2000—

*Significant at the 10% level; **significant at the 5% level; ***significant at the 1% level.

As a falsification test, we examine whether our key outcomes are correlated with future appropriations (table 5).49 The estimated effect of appropriations in t + 1 on values in t is generally indistinguishable from zero (panel 2), with the exception of the public enrollment outcomes, which we might expect to correlate to some degree with t + 1 appropriations owing to the funding formulas described earlier.50 Even so, the public enrollment coefficients are smaller in magnitude than in the baseline specification, particularly when public freshmen is the outcome of interest (though these differences are not statistically different). In the third panel, we amend our estimating equation to separately include both appropriations in t and in t + 1. The t + 1 coefficients shrink across the board, such that none is statistically different from zero. Further, those in columns 3 and 4 fully reverse in sign, and, although the coefficient in column 5 does not, it is just 10 percent of its panel 2 size. Finally, and perhaps most importantly, all of the coefficients on appropriations in t maintain their sign and are magnitudinally larger than those in t + 1. Altogether, appropriations in the next year do not appear to predict attendance and borrowing in the current year. This evidence helps affirm the timing implied by the specification.

Table 5.
Validity Checks, Falsification Exercise
The Effect of Next Year's Appropriations on Key Outcomes this Year
NPublic Enrollment (1)Public Freshmen (2)Borrowing at For-Profit Schools (3)Borrowing at Public and For-Profit Schools (4)(5)
Baseline (this year's appropriations) 
Appropriationst 550 0.029** 0.048*** −0.186*** −0.180** −0.074** 
  (0.012) (0.015) (0.058) (0.079) (0.036) 
Fully Replacing this Year's Appropriations with Next Year's 
Appropriationst+1 500 0.028*** 0.040** −0.102 −0.134 −0.048 
  (0.010) (0.017) (0.072) (0.091) (0.048) 
Including Both this Year's Appropriations and Next Year's 
Appropriationst 500 0.016 0.026 −0.331** −0.269 −0.053 
  (0.015) (0.017) (0.132) (0.263) (0.034) 
Appropriationst+1 500 0.015 0.020 0.160 0.079 −0.005 
  (0.009) (0.021) (0.130) (0.237) (0.046) 
The Effect of Next Year's Appropriations on Key Outcomes this Year
NPublic Enrollment (1)Public Freshmen (2)Borrowing at For-Profit Schools (3)Borrowing at Public and For-Profit Schools (4)(5)
Baseline (this year's appropriations) 
Appropriationst 550 0.029** 0.048*** −0.186*** −0.180** −0.074** 
  (0.012) (0.015) (0.058) (0.079) (0.036) 
Fully Replacing this Year's Appropriations with Next Year's 
Appropriationst+1 500 0.028*** 0.040** −0.102 −0.134 −0.048 
  (0.010) (0.017) (0.072) (0.091) (0.048) 
Including Both this Year's Appropriations and Next Year's 
Appropriationst 500 0.016 0.026 −0.331** −0.269 −0.053 
  (0.015) (0.017) (0.132) (0.263) (0.034) 
Appropriationst+1 500 0.015 0.020 0.160 0.079 −0.005 
  (0.009) (0.021) (0.130) (0.237) (0.046) 

Notes: Each cell reports the coefficient on appropriations from an ordinary least squares regression, where the outcome of interest is denoted by the column header and the perturbation of the main estimating equation is denoted by the row title. Observations are at the state-year level. Appropriations, enrollment, borrowing, and population are measured in natural logs. All regressions include state and year effects, controls for the unemployment rate and population, and a constant. The estimation sample is all 50 states, academic years 2000—10 (inclusive) in the first panel, and academic years 2000—09 (inclusive) in panels 2 and 3. Data indicate there was no for-profit borrowing in Mississippi in 2000. Standard errors clustered at state level in parentheses.

**Significant at the 5% level; ***significant at the 1% level.

We might be concerned that reverse causality is introducing bias into our analysis if, say, statewide appropriations for higher education are determined by enrollment in the public sector. However, when we take into account both the timing of appropriations determinations and our full set of results, it seems unlikely that reverse causality poses a threat to our design. First, appropriations for the coming academic year are generally set before all students have enrolled in school or registered for classes. This timing suggests that enrollment is unlikely to drive variation in appropriations within the same year, unless budgets can respond immediately and perfectly. It is more likely that, even in a scenario where statewide enrollment fully determines spending on higher education, legislators would need to rely on projections of enrollment. For such a relationship to pose a threat to our design, these projections would need to rely on factors other than the unemployment rate and cohort controls that we include. Furthermore, our extended results in this section are not consistent with enrollment driving appropriations. For one, the same basic pattern of results holds upon inclusion of lagged public enrollment (table 4). Further, attendance today does not appear to be explicitly connected to funding tomorrow (table 5). Even then, we would expect the placebo variables that correlate with public enrollment to also be correlated with appropriations, but they are not.

Finally, it is unlikely that reverse causality could generate our broader set of enrollment findings. For example, consider that the association between overall and public sector enrollment, conditional on our other control variables, is extremely significant and near 1. If enrollment changes within states are important and immediate determinants of appropriations changes, we would expect higher funding to not only be correlated with higher public sector enrollment but also higher enrollment overall. However, we find no effect on the latter.51 Following a similar line of reasoning, even though a variety of factors increase enrollment in both the public and for-profit sectors, it would have to be that the variation in public enrollment effectively driving appropriation changes is extremely negatively correlated with fluctuations in for-profit enrollment (such that they generally offset each other).52,53

In sum, if appropriations were simply responding to current enrollment, which would be inconsistent with the timing of budget-setting processes, then (1) we would not expect to pass the placebo tests (the placebo variables themselves are correlated with enrollment), (2) we would expect lagged enrollment to confound the relationship between current appropriations and our main outcomes, and (3) it would be difficult to generate our broader set of findings (i.e., no effect on overall enrollment, public enrollment changes offset by for-profit enrollment changes). With this body of evidence, reverse causality does not appear to pose a substantial threat to our design.

5.  Effects on the Supply of a Public Education

All else equal, public institutions have three broad ways to adjust their ledgers for a shortfall in appropriations: (1) reduce spending, (2) increase prices, or (3) decrease capacity (essentially an application of one or both of the others). Adjustments along any of these margins could induce substitution. The measures analyzed below are described in online Appendix E.

Panel A of table 6 examines direct measures of annual spending at public schools—spending on student services (e.g., registrar and admissions activities), spending on academic support (e.g., educational materials and curriculum development), and spending on instruction. Because aggregate expenditure is likely endogenous to enrollment, we also consider measures on a per student basis. We detect meaningful reductions in expenditure on student services and academic support, both in aggregate and on a per student basis, suggesting campuses have fewer resources to serve prospective and reenrolling students. Interestingly, annual spending on instruction does not appear to vary with appropriations.

Table 6.
Effects of Appropriations on Conditions in the Public Sector
Panel A: Spending
Per Student (1)Aggregate (2)
Academic support 0.137* 0.166** 
 (0.079) (0.071) 
Student services 0.153*** 0.182*** 
 (0.049) (0.043) 
Instruction 0.055 0.083 
 (0.075) (0.068) 
Panel B: Tuition 
Enrollment-weighted tuition collected per student at community colleges  −0.218*** 
  (0.039) 
Flagship sticker price  −0.131*** 
  (0.041) 
Enrollment-weighted average sticker price  −0.074* 
  (0.041) 
Enrollment-weighted tuition collected per student at public institutions  −0.112*** 
  (0.023) 
Panel C: Capacity 
Full-time faculty  0.017 
  (0.025) 
Part-time faculty  0.131 
  (0.157) 
Percent of faculty who are part-time  −2.270* 
  (1.323) 
Flagship composition  8.975*** 
  (3.036) 
N 550 
Panel A: Spending
Per Student (1)Aggregate (2)
Academic support 0.137* 0.166** 
 (0.079) (0.071) 
Student services 0.153*** 0.182*** 
 (0.049) (0.043) 
Instruction 0.055 0.083 
 (0.075) (0.068) 
Panel B: Tuition 
Enrollment-weighted tuition collected per student at community colleges  −0.218*** 
  (0.039) 
Flagship sticker price  −0.131*** 
  (0.041) 
Enrollment-weighted average sticker price  −0.074* 
  (0.041) 
Enrollment-weighted tuition collected per student at public institutions  −0.112*** 
  (0.023) 
Panel C: Capacity 
Full-time faculty  0.017 
  (0.025) 
Part-time faculty  0.131 
  (0.157) 
Percent of faculty who are part-time  −2.270* 
  (1.323) 
Flagship composition  8.975*** 
  (3.036) 
N 550 

Notes: Each cell reports the coefficient on appropriations from an ordinary least squares regression, where the outcome of interest is denoted by the row title. Observations are at the state-year level. Appropriations, faculty, tuition, spending, and population are measured in natural logs. All regressions include state and year effects, controls for the unemployment rate and the relevant population measure, and a constant. “Per student” in panel A refers to per full-time equivalent public attendee in that state-year. Enrollment-weighted tuition is derived by aggregating gross tuition and fees revenue (i.e., tuition and fees collected from the student plus scholarships applied to tuition and fees) from each institution to the state-year and dividing by aggregate full-time equivalent enrollment. The sticker price is the lowest of in-state and in-district sticker prices for tuition and fees reported by the school to the Department of Education, weighted by distribution of enrollment within a state-year where relevant. Flagship composition pertains to the share of flagship freshmen in a state-year from that state. The estimation sample is all 50 states, academic years 2000—10 (inclusive), except for flagship composition which is measured every other year beginning in 2004. Standard errors clustered at state level in parentheses.

*Significant at the 10% level; **significant at the 5% level; ***significant at the 1% level.

Panel B of table 6 examines potential tuition responses under four definitions of tuition.54 All are inversely related to appropriations and are broadly in line with Webber (2017). All else equal, in response to a 10 percent appropriations cut, the sticker price of flagship institutions increases around 1.5 percent, and the average sticker price increases 1 percent. Similarly, we estimate increases in tuition revenue per student, both at community colleges on the order of 2 percent, and at public institutions more broadly, on the order of 0.75 percent.55

Finally, to test for evidence of changes in capacity, panel C of table 6 examines the share of faculty who are part-time and the share of freshmen from within the state. We detect a very small correlation between appropriations and faculty composition—for a 10 percent cut in appropriations, the share of faculty teaching part-time increases by 0.25 percentage point (less than 1 percent of the mean). We also find evidence, consistent with Jaquette and Curs (2015) and Bound et al. (2016), that flagship universities enroll fewer in-state freshmen when funding is cut. Lastly, although we cannot directly evaluate whether public sector classes also become oversubscribed, our other results are consistent with this mechanism.

6.  Discussion and Conclusion

We find that the uneven fluctuations in state and local appropriations to higher education between 2000 and 2010 induced both statistically and economically meaningful changes in college attendance and student borrowing. Specifically, the results imply, over this window, a 10 percent cut in statewide appropriations generated a 2 percent rise in for-profit enrollment and a 0.3 percent decline in public enrollment (with no effect on overall enrollment). They also reveal a corresponding increase in student borrowing, driven by the for-profit sector. Altogether, our analysis indicates that core institutional resources affect the types of schools students attend and offers evidence of substitution between the public and for-profit sectors.

It is important from a policy standpoint to understand how students sort across postsecondary institutions and, more specific to our analysis, whether remote budgetary processes bear consequences for students’ attendance decisions and associated outcomes. Specifically, if substitution into for-profit colleges represents a concern, legislators may wish to design policies that sustain conditions in the public sector. (Alternatively, if it does not, state and local governments may wish to reduce their role in the provision of education, given the existence of an alternate sector that can accommodate excess demand.) We can use our estimates to approximate the degree of substitution between the for-profit and public sectors in response to a change in appropriations. In our sample, the average number of for-profit college students in a state-year is roughly 21,000, such that the point estimate implies around 375 extra students in the for-profit sector from a 10 percent cut in appropriations. The average number of public college students is about 186,000, so that a same-sized cut applied to our point estimate implies a loss of 515 students from the public sector. Together, these results suggest that public sector losses are largely offset by for-profit sector gains, with an MRS of about 0.75.

We can also benchmark the magnitude of our estimates against those in Cellini (2009), which found that an additional $100 million in community college revenue raised through local bond initiatives in California between 1995 and 2002—or an implied 21.8 percent increase in annual public funding—induced about 700 students per county to substitute from for-profits.56 Within our context, a 21.8 percent increase in appropriations implies a 4.05 percent decrease in for-profit enrollment, on a mean of 21,284 students. In other words, a proportionate increase in funding in our environment induces 863 students to substitute from for-profits. These magnitudes are strikingly close, particularly considering how the sector has grown over time and the wide variation in the postsecondary landscape across states.

Still, substitution between the two sectors need not warrant intervention if not for the established evidence on student outcomes across sectors, particularly with respect to their labor market experiences. As noted earlier, current estimates of the returns to education imply sizable income differentials, and students who attend for-profits tend to be viewed less favorably by employers than students who pursue similar programs at other schools and on par with students who pursue no postsecondary education at all. Moreover, we find corresponding effects on student borrowing, which some studies have found hampers household formation and future consumption. Finally, given the source of variation, the effects may also imply a transfer of college financing from state and local governments to the federal government.57

In an analysis of mechanisms, we find evidence that fluctuations in appropriations correspond with changes in tuition and resources in the public sector. Although the analysis is suggestive, we attempt to parse the role of tuition by wedding our estimated tuition and enrollment effects to an estimate describing how students sort across schools in response to price alone. Angrist et al. (2017) find that an additional $6,225 in grant aid at in-state public colleges and universities in Nebraska led to a 5.7 percentage point increase in enrollment, implying a 0.92 percentage point response per $1,000.58 Our estimates imply a 0.09 percentage point decrease in public enrollment (from the share specification) and a 0.74 or 1.12 percent increase in average public tuition (depending on the concept) in response to a 10 percent decrease in appropriations. The averages of these tuition concepts in our data—$4,935 and $6,743, respectively—imply a $36.52 and $75.52 price change. Applying Angrist et al.’s estimate to these changes, we would expect tuition effects alone to reduce enrollment in the public sector by between 0.03 and 0.07 percentage point, which, using the larger estimate, would explain 80 percent of our enrollment effect.

Because our estimation strategy relies on variation within states and years, the borrowing and attendance effects we identify are, by design, rather immediate responses to changes in appropriations funding. In reality, school pricing and spending decisions may take time to fully adjust to funding shocks, or students’ attendance and borrowing decisions may partially rely on school performance-based metrics that take time to adjust to funding.59 In the event that the demand-side response is more gradual—or more cumulative—than the one for which our estimation strategy allows, our estimates likely represent a lower-bound estimate of the full effects of a funding cut. Future work could explore the medium-run effects of appropriations cuts by studying persistence, degree completion, and earnings or could allow for a more dynamic treatment of the relationship between public sector funding and demand-side responses.

Finally, note that while the analysis uncovers a mechanism by which students were induced into for-profit colleges and borrowing amid the run-up in for-profit attendance and student debt—issues that challenge policy makers today—our results are not well suited to explain these secular phenomena. In particular, the estimates do not represent the effects of any longer-standing national trends favoring the rapid growth of the for-profit sector (Deming, Goldin, and Katz 2012)—for example, the rise of certifications, worker retraining programs, online education—or any permanent state-specific strategies to reduce schools’ reliance on appropriations. Further, calculations within our data reveal that aggregate real appropriations declined only 5 percent between 2000 and 2010, on net, which, according to our estimates, would imply a 1 percent increase in for-profit enrollment—just a tiny share of the sector's nearly 350 percent growth seen in our sample. Even accounting for enrollment growth over this period, the 30 percent decline in appropriations we see per public student implies just a 6 percent increase.60 Understanding the major explanatory factors behind the run-up is an important topic for future research to address.

Notes

1. 

On average, state and local appropriations represent over 40 percent of total revenue at community colleges and just under 20 percent at four-year colleges (USDOE 2016).

2. 

Between 2000 and 2010, real appropriations per student fell $3,000 (or 30 percent). Over that time, the share of state and local spending on public welfare, hospitals, and pensions grew from 23 percent to 26 percent, while the share directed toward public postsecondary schools shrank from 3 to 2 percent. Kane, Orszag, and Apostolov (2005) estimate that, between 1988 and 1998, rising state spending to meet Medicaid obligations could explain about 80 percent of the decline in spending on higher education. (Government spending figures derived from published State Higher Education Executive Officer Association reports and Bureau of Economic Analysis tables from the U.S. Census Bureau's Census of Governments.)

3. 

Even same-sized changes in appropriations could be experienced by schools and students unevenly, as, for example, tuition may be set by separate bodies within states or school systems that can have their own sets of objectives, political constraints, and philosophies regarding the affordability of college.

4. 

We aggregate appropriations distributed across the state because determinations within a state are often subject to institutional needs and goals within a state's higher education system and thus less-plausibly exogenously given. Moreover, we do not want our estimates to conflate between-school-within-sector substitution with cross-sector substitution. Nonetheless, we confirm that our main findings hold at the institution level as well.

5. 

A causal interpretation of these estimates requires that, within our framework, annual statewide appropriations are exogenous to students’ attendance and borrowing. Section 4 analyzes the validity of this assumption.

6. 

We focus on appropriations “cuts” or “decreases” (rather than “changes” or even “increases”) to tell a consistent story about how all of the mechanisms interact. The median annual change in appropriations is −1 percent.

7. 

Effects are similar excluding the Great Recession and recovery (i.e., 2008–10), during which the higher education landscape was atypical (Barr and Turner 2013; Delaney 2014). About 70 percent of the for-profit sector's rise took place before the Great Recession (see figure A.1, which is available in a separate online appendix that can be accessed on Education Finance and Policy's Web site at www.mitpressjournals.org/doi/suppl/10.1162/edfp_a_00281). The staggering growth has flattened out recently, as these institutions have come under increased scrutiny and threat of regulation.

8. 

The analysis focuses on Stafford Loan borrowing through the Federal Direct Loan and Federal Family Education Loan programs, which make up about 70 percent of annual educational borrowing over the period of study (Baum, Elliott, and Ma 2014). For program borrowing rates by sector, see table 350 in the 2010 Digest of Education Statistics, at nces.ed.gov/pubs2011/2011015.pdf.

9. 

There is considerable evidence that enrollment is sensitive to net college prices (Dynarski 2003; Kane 2003, 2007; Deming and Dynarski 2010; Chung 2012; Fack and Grenet 2015; Castleman and Long 2016).

10. 

Cellini (2012) provides an overview of the social welfare implications of such spillovers.

11. 

Lang and Weinstein (2013) compare the sectors across degree and program type and find that for-profit college students with certificates in business and health fields appear to fare worse than comparable public college students, but for-profit students with vocational certificates may fare better. The study also examines differentials for students with associate degrees, but many public students in associate programs continue on to pursue a bachelor of arts degree (BA), making the associate degree estimates more difficult to interpret. Nonetheless, across all degree and program types considered, the authors surmise, when relative pricing between the two sectors is taken into account, “the return on investment is undoubtedly lower at for-profits” (p. 240).

12. 

Cellini (2009) notes several unique features of this setting. Specifically, relative to other states, California's higher education system relies heavily on its community colleges, which charge the lowest tuition rates in the country and, as such, receive 95 percent of their funding from state and local sources. According to Department of Education fall enrollment counts, in 1998, community colleges enrolled 58 percent of California's postsecondary students (compared with a national average of 36 percent).

13. 

In contrast to our study, the analysis by Deming and Walters examines institution-level effects; a longer horizon (1990–2013) over which the policy environment (particularly with respect to for-profit colleges) varies greatly; state-sourced revenue (only); and within-county spillovers (aggregating for-profit and nonprofit private institutions into one category). Further, they exploit additional variation in schools’ reliance on state resources in 1990 to help overcome potential endogeneity from policy maker discretion in how funding is allocated across schools within a state. While the authors do find evidence of such discretion, it is not pertinent for our state-level design.

14. 

SRI International (2012) notes that a handful of states—New Hampshire, North Dakota, Oklahoma, Rhode Island, Vermont, and West Virginia—primarily set spending for higher education based on legislative priorities or policies.

15. 

Federal legislation applies “maintenance of effort” (MOE) provisions to some expenditure categories—for example, K–12 education or welfare (Alexander et al. 2010). These provisions require states to contribute a certain amount (or share) to a program as a condition of eligibility for federal funding. Until 2008, federal funding programs for higher education generally did not require a state match. Results excluding years for which MOE provisions for higher education would be most likely to influence state spending are available in the online appendix.

16. 

State and local governments also provide funding to public colleges through grants and contracts. Appropriations represent a large majority of an institution's budget and play a more substantial role in supporting general operating expenses (e.g., instruction), whereas grants and contracts are designated funds toward specific projects or programs (e.g., research activities, training programs, building expenses, student aid). Although revenue from grants and contracts also varies over time, it is a relatively small category of funding and our results are not sensitive to its inclusion as a control. The remaining revenue—which mostly comes from the federal government, internal operations, investments, and gifts—represents a fairly static, minority portion of overall funding.

17. 

Fortin (2005) offers cross-country evidence of these relationships in the United States and Canada between 1973 and 1999.

18. 

Calculations within our data reveal, in the average state, about 98 percent of the net decrease in appropriations revenue per student over this period was offset by tuition revenue.

19. 

Practically speaking, altering the sticker price is likely the least viable option. First, sticker prices are published in advance of the school year and thus cannot adjust to unexpected changes in educational demand. Second, there is variation in the discretion that state legislatures have to set these prices when they balance their budgets, as the process often involves several entities, each with their own objectives, political constraints, and philosophies regarding the affordability of college (Bell 2008; GAO 2014). In only a handful of states (fewer than ten) does the primary tuition-setting authority belong to a central entity, which may be the governor, legislature, or a statewide governing board; in most states, this authority rests with a local or system-level governing board (Carlson 2013). (Individual institutions also usually have a consultative role in the process. In some states, they propose rates in accordance with guidelines from governing boards or the state legislature after the state budget is finalized for the upcoming fiscal year.)

21. 

The exacerbated negative economic conditions associated with the Great Recession (e.g., swollen cohorts, constrained revenue from state and local governments) likely compounded existing pressures on states to allow for-profits to flourish. Indeed, Long (2015) examines this period directly and finds that a large portion of recessionary crowding occurred among nontraditional or lower-ability students. Nonetheless, within our design, we will demonstrate that our findings are not merely a business cycle phenomenon: appropriations are uncorrelated with unemployment rates and our core results are robust to the exclusion of the severe changes in economic conditions that occurred during the Great Recession.

22. 

The earliest state actions of record took place when for-profits were first coming under fire from the federal government and popular press. In 2008, both Alabama and Tennessee enacted policies aimed at preventing poorly performing for-profits from operating, with Alabama closing schools as early as that same year (Loonin and McLaughlin 2011). Results excluding 2008–10 are available in the online appendix.

23. 

Prices in the for-profit sector are unlikely to (fully) respond to contemporaneous changes in demand that result from a shock to the public sector, as for-profit tuition is mostly determined by the cost of instruction and the generosity of federal financial aid programs (Cellini 2009, 2010; Cellini and Goldin 2014).

25. 

Of these, approximately 20 percent identify as public, 30 percent as private nonprofit, and 50 percent as for-profit, largely reflecting their respective sizes as, for example, the average public school in any given year enrolls about an order of magnitude more students than the average for-profit college.

26. 

We linearly interpolate our key variables for missing and imputed institution-years, so that changes in our state aggregates do not reflect spotty institutional reporting. A total of 932 for-profit institution-years (out of over 31,000) are affected by this interpolation. We interpolate funding and enrollment for 198 and 269 public institution-years (out of over 20,000), respectively. Throughout, financial data are real adjusted to 2013 dollars using the Higher Education Cost Adjustment index, a specially prepared price index generated by the association of public colleges intended to track changes in the costs of inputs purchased by colleges.

27. 

We rely on fall enrollment counts of these figures, which is somewhat at odds with concerns raised in earlier work that for-profit attendance derived from fall enrollment may miss a considerable number of students attending less conventional and short programs (Deming, Goldin, and Katz 2012). A twelve-month FTE enrollment measure is only available in our sample beginning in 2004, missing a sizable portion of our period of study. Moreover, the less conventional students in this study are not the subject of our analysis, which investigates for-profit enrollees who, in a better funding environment, would have attended public schools and thus likely would have enrolled in the fall.

28. 

FTE enrollment may also include students in online programs, who, importantly for the analysis, need not reside in the same state as the institution they attend. Results are generally robust to the exclusion of the years in which online education was most prevalent, as well as the exclusion of Arizona, a state known for relatively lax for-profit regulation and home to the University of Phoenix (which has a very large online presence).

29. 

In even years, the IPEDS survey collects additional information from each reporting institution on freshmen state of residence. Using data from survey years 2004 to 2010, we link counts of fall-enrolling freshmen by state of residence and sector of institution attended to statewide appropriations, grants, and contracts revenue.

30. 

Data are available on the Department of Education Federal Student Aid (FSA) Web site at https://studentaid.ed.gov/sa/about/data-center/student/title-iv.

31. 

An indicator for a school having over two-thirds in-state enrollment was derived from IPEDS data identifying, for each institution in 2012, the percent of first-time undergraduate students who indicated on their college application a home residence in the same state as the institution. A crosswalk available from the National Student Clearinghouse was used to link IPEDS identifications (IDs) to FSA IDs, by which the borrowing data are classified. For FSA IDs that linked to non-unique IPEDS IDs, the average of the IPEDS variable determined its inclusion in the restricted borrowing measure. For any non-linked IDs, the institution's borrowing was included in the count.

32. 

The functional form of the outcome variable follows a consistent rule of thumb: Share variables are denoted as percent of 100 and are estimated in levels, while count variables are expressed in logarithms.

33. 

Following the literature (e.g., Fortin 2005; Bound and Turner 2007; Jaquette and Curs 2015; Bound et al. 2016), revenue is specified as a natural log. An alternative specification is presented at the end of the section.

34. 

An exploration of nonlinearity in treatment—whereby we calculate residuals from a regression of log appropriations on state and year effects, construct an indicator for residuals in the top or bottom percentile, and add an interaction between this indicator and log appropriations to our estimating equation—suggests stronger effects for especially large changes in appropriations (results not shown). The interaction term is generally right-signed but insignificant if the top and bottom fifth percentiles are used instead.

35. 

A test of geographical responsiveness is available in the online Appendix A and finds negligible effects of appropriations to public colleges in a freshman student's home state on the state in which he or she attends college, supporting our focus on within-state enrollment and our interpretation that marginal students substitute between public and for-profit sectors. Online Appendix B confirms that the public enrollment results hold at the institution level as well.

36. 

Online table A.3 presents results excluding the time-varying covariates and weighting by population. Excluding the covariates, coefficients are similar but standard errors are a bit larger, consistent with their inclusion increasing precision but not driving the variation or estimated effects. Weighting slightly reduces the precision of the estimates.

37. 

Still, it is possible that omitted factors that differentially affect attendance in one sector (e.g., for-profit marketing campaigns targeting low-wage employees)—if they are correlated with appropriations—might yield an estimate that overstates the true parameter of interest even if they induce negligible effects on overall enrollment.

38. 

Further, the average private nonprofit institution draws over 40 percent of its student body from outside the state.

39. 

The validity analysis introduces state time trends to absorb variation from systematic growth of a given sector.

40. 

In addition, the college-aged population source data are intercensal estimates (i.e., interpolations that attempt to adjust for moves and deaths) rather than annual counts. Although this measure can help absorb variation in appropriations that correlates with educational demand (as it may, for instance, be used to project spending needs), it is a noisy approximation of the true population susceptible to substitution, and thus may reduce statistical power when used to scale enrollment.

41. 

Specifically, the table reveals that, when appropriations decline, overall enrollment is unchanged and instead students substitute from the public sector into for-profit colleges, which tend to be costlier for students (Cellini 2012). In addition, at for-profit colleges, borrowing rates are twice as high, and average annual borrowing among student borrowers is 1.5 times higher. See https://nces.ed.gov/programs/digest/d12/tables/dt12_387.asp for more information.

42. 

Broadly, educational borrowing reflects a combination of the generosity of available lending programs, attendance rates, college pricing, and financial need. Our framework abstracts from national trends in the generosity of lending at any given time, as well as underlying economic conditions that correlate with, and thus act as a proxy for, financial need. Although these are important channels informing the rise in aggregate borrowing (which we leave for future work), any shifts in borrowing we detect generally reflect only annual changes in attendance rates and cost.

43. 

While public attendance rises with appropriations, the effect is concentrated at community colleges (where tuition and borrowing are relatively low). We later find evidence that public sector tuition decreases in this state of the world.

44. 

We prefer to interpret the Title IV borrowing increase at for-profit colleges within our full set of results, which would suggest that the rise in for-profit borrowing is primarily driven by students substituting between the two sectors. In theory, an alternative explanation is that for-profits are raising tuition at the same time that appropriations are falling, which in turn increases borrowing in the sector. In practice, for-profits have little scope to raise tuition in a manner that would increase Title IV borrowing, as tuition at those schools that are Title IV–eligible tends to reflect federal borrowing limits (Cellini and Goldin 2014). The validity checks at the end of this section indicate little evidence of a borrowing response at private nonprofits, where we also would not anticipate a change in tuition.

45. 

We estimate commensurate effects on federal Pell Grant awards and receipt (–0.090 [SE = 0.037] and −0.092 [SE = 0.041], respectively), which, as with the lending increases, could be driven by increased enrollment in for-profit colleges, which tend to be costlier and relatively well equipped to procure federal aid on behalf of their students (Cellini 2010; Cellini and Goldin 2014).

46. 

About 75 percent of schools in the sample meet this requirement. The share is higher—about 90 percent—among for-profits, and higher still—between 90 and 95 percent—among public institutions.

47. 

Table A.5 shows that state-level time-varying measures that may correlate with enrollment—that is, the lagged unemployment rate, contemporaneous and lagged log unemployment insurance claims, lagged high school graduates, log grants for higher education, and a series of postsecondary enrollment measures generated using the October Supplement of the Current Population Survey—generally do not vary with appropriations (conditional on state and year effects). A separate analysis of coarser data (available upon request) yields no evidence of an effect of appropriations on student characteristics (including socioeconomic status) or financial aid application rates.

48. 

Nonetheless, in the regression predicting public enrollment, the p-value on lagged public enrollment is 0.436, much larger than the p-value on appropriations (0.147).

49. 

The introduction of a full set of lag and lead appropriations terms also more generally corroborates the timing implied by the specification. Results available upon request.

50. 

Still, even though they are not statistically significant, the estimated coefficients are negative, leading to potential concern that the true effects are as well. Alternatively, this specification may omit a key variable—e.g., appropriations today—that is correlated with both appropriations tomorrow and our outcomes. If, in fact, appropriations today are correlated with appropriations tomorrow, the coefficients reported in the first row will reflect some of the relationship between appropriations today and outcomes today that we have already shown. Indeed, when we replace our left-hand side outcome with appropriations today, we recover a statistically significant coefficient of 0.792. (Note that were we to multiply each of our main estimates by this amount, we would obtain almost our exact coefficients in table 5.)

51. 

In other words, the main factors that drive public enrollment also drive overall enrollment (of which public enrollment is the majority). Yet, it appears that these factors are not driving the appropriations changes identifying our effects, which suggests little scope for reverse causality.

52. 

If our identifying variation is driven by fluctuations in public enrollment, it is worth suggestively exploring how this could be reconciled with our for-profit enrollment estimates. Given that the estimated effect of appropriations on public enrollment is 0.029, for reverse causality to be driving the for-profit result, the negative association between public and for-profit enrollment would have to be quite large. Yet, a regression of for-profit enrollment on public enrollment, conditional on our control variables, is insignificant. If we take a worst-case scenario—namely, if we assume that the bottom of the 95% confidence interval for this insignificant estimate is the true association between the two sectors—it is still not large enough (i.e., combining the two estimates to produce an implied effect on for-profit enrollment translates to an effect that is an order of magnitude smaller than our main estimate). Although a convenient theory could be that changes in the for-profit sector drive public enrollment, which in turn drives appropriations, it is not clear why only fluctuations from the for-profit sector would ultimately drive appropriations instead of the other (more prevalent) factors that influence public enrollment. If all of these factors drove public enrollment and, in turn, appropriations, the implied effects would not come close to explaining all the results.

53. 

As an additional suggestive exercise, because enrollment this year cannot mechanically induce appropriations last year, we instrument appropriations in a given year with appropriations in the previous year. (We note that the exclusion restriction—i.e., appropriations last year are only correlated with outcomes this year through appropriations this year—may not hold.) The coefficients from this approach are extremely similar to our main estimates (available upon request).

54. 

College price (at large research universities) is historically insensitive to cohort size (Bound and Turner 2007), which suggests that public tuition does not respond to changes in demand for education. If this is the case and we estimate tuition increases in an environment of changing funding, changes in price are likely to be driven by a supply-side factor, rather than a tertiary variable from the demand side.

55. 

Online Appendix F presents a more in-depth look at the elasticity of for-profit enrollment with respect to public sector tuition, leveraging additional variation from the extent to which a state can use public tuition to offset changes in other revenue. Results generally suggest a cross-price elasticity around 1.25. This estimate likely represents an upper bound of the true relationship, as, even assuming tuition responses in this section are well identified and driving the enrollment effect, a number of other supply-side mechanisms are likely also at play.

56. 

The bonds are reportedly spent over ten years, implying an additional $10 million per year (if the bond revenue is distributed equally over the horizon). In the 2001–02 year, the average revenue from state and local appropriations for a California community college was about $45.9 million (i.e., $5 billion total, according to the 2002 California Postsecondary Education Commission, divided by 109 community colleges in the state at the time).

57. 

Increased borrowing, together with increased default rates detected by other studies (e.g., Looney and Yannelis 2015), is consistent with such a transfer. In the analysis of variation, we also find evidence of effects on Pell Grants.

58. 

These calculations are illustrative, as there are important differences between the two settings, particularly with respect to the marginal student being examined. Angrist et al. (2017) estimate substitution into Nebraskan public colleges and universities among scholarship applicants, most of whom would otherwise attend a four-year college.

59. 

Indeed, the cumulative effect of appropriations changes on our main outcomes when we include two lagged terms is magnitudinally, but not statistically, larger than our main results (results not shown).

60. 

Technically, this calculation relies on the estimates from the scaled specification in table 4.

Acknowledgments

The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. Steve Ramos provided excellent research assistance. We thank Adam Isen, Geng Li, John Mondragon, Matea Pender, Peter Hinrichs, Jesse Rothstein, John Sabelhaus, Byron Lutz, David Jenkins, Andy Chang, Michael Palumbo, Michael Lovenheim, Donna Lormand, and participants at the 2015 Association for Education Finance and Policy Annual Conference, the 2015 Federal Reserve System Applied Microeconomics Conference, the 2016 Association for Public Policy Analysis and Management Fall Research Conference, and the 2016 National Tax Association Annual Conference for helpful comments and suggestions.

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