Accounting for the Rise in College Tuition Grey Gordon and Aaron Hedlund Indiana University and University of Missouri

NBER/CRIW October 17, 2015

Motivation

6000

(mean) nettuit_per_fte 7000 8000 9000

10000

Real net tuition per FTE at 4-year, non-profit colleges:

1985

1990

1995 2000 Academic Year

2005

What is causing net tuition to rise?

2010

Motivation

Many theories exist. Supply side: I

Baumol’s cost disease — costs increase, productivity does not.

I

Cuts in government aid — reductions passed on to student.

I

Bowen rule — “arms race of spending” (Ehrenberg 2002).

Demand side: I

Bennett hypothesis — colleges capture student aid rents.

I

College premium increases — rents captured.

Our goal: test these theories quantitatively.

Method We combine I

a mostly standard lifecycle model with

I

Epple, Romano, Sarpca, and Sieg (2013)’s model of colleges.

In this paper, only one college, a monopolist. Rent extraction is exaggerated. We feed in estimates or statutory law for exogenous processes: I

college costs,

I

college non-tuition revenue (including government aid),

I

borrowing limits, interest rates, and grants,

I

and the college earnings premium.

Results

Between 1987 and 2010, net tuition increased 78%. All theories together account for a tuition increase of 106%. Separately, holding else equal at 1987 values, I

The supply-side theories decrease tuition by 6%.

I

Changes in student aid cause tuition to increase by 102%.

I

The college earnings premium causes tuition increases of 24%.

“Optimistic” predictions if aid and college premium stop changing.

Model Youths are born with sY , a vector of parental income and ability. Youth problem (in college):  Yj (l, sY ) =

max

c+φ≥0,l 0 ≥l

u(c + φ) + β

πYj+1 (l 0 , sY )+ (1 − π)Es 0 |j,sY V (0, l 0 , tmax , s 0 , 0)

s.t. c + T (sY ) + φ ≤ |{z} e Y + ξEFC (sY ) + ζ(sY ) + bs + bu | {z } |{z} | {z } | {z } R&B

earn.

transfers

gov grant

ann. borrow

statutory limits on borrowing (ls0 , lu0 , ls , lu , bs , bu ) = f (l 0 , l)

Worker problem is a mostly standard lifecycle problem

Worker Problem



Model

The decision to enroll is made at time zero: max{Y1 (0, sy ) + q + α, Es|sY V (0, 0, 0, s, 0)} | {z } | {z } college

q ≡ college quality α ≡ preference shock

work

Model The college problem: max q(θ, I )

I ≥0,T (·)

s.t. E N + T N = F + C(N1 ) + I N Endogenous θ ≡ average ability I ≡ investment N1 ≡ freshmen N ≡ NPV of freshmen T ≡ average net tuition Exogenous E ≡ endowment (non-tuition revenue) F ≡ fixed cost C(·) ≡ college “custodial costs” We parametrize q(θ, I ) as χq θχθ I 1−χθ . Full college problem

Data and Estimation We use NLSY97, IPEDS/Delta Cost Project, and take estimates from the literature. Change in exogenous variables that form basis for our experiments: Exogenous variable log college premium student loan interest room and board average gov grant subsidized limit unsubsidized limit non-tuition revenue per student fixed cost of college (billions) marginal cost, relative change

Label λ i φ ζ¯ l¯s l¯u E F 2 2 C /C1987

Note that unsubsidized loans began in 1993.

1987 .46 4.7 3072 488 23994 0 17843 12 1

2010 .66 3.0 9129 1779 23000 40805 18418 30 4.7

Data and Estimation

We estimate a number of parameters inside the model: Param ξ χθ χq α

Description transfer size ability input quality level pref. shock

Value .208 .252 2.68 .003

Target avg tuition ρ(p.inc,enroll) enroll rate % with loans

Data 5788 .295 .379 35.7

Model 6100 .316 .325 42.7

and some others I didn’t show you earlier. To keep tuition down with the monopolist, need low transfers and more marginal students, which introduces bias. Nontargeted, 1987/2010

Results Net tuition, investment, and HS grad enrollment 0.5 35000

Net tuition (model) Net tuition (data) Investment (model)

30000

Investment (data)

0.45

Enrollment (model) Enrollment (data)

2010 dollars

0.4

20000 0.35 15000

0.3 10000

5000 1990

1995

2000

2005

Year

Unsubsidized loans began in 1993.

0.25 2010

Enrollment rate

25000

Results Net tuition, investment, and HS grad enrollment 0.5 35000

Net tuition (model) Net tuition (data) Investment (model)

30000

Investment (data)

0.45

Enrollment (model) Enrollment (data)

2010 dollars

0.4

20000 0.35 15000

0.3 10000

5000 1990

1995

2000

2005

Year

Possible explanations for exaggerated tuition:

0.25 2010

Enrollment rate

25000

Results Net tuition, investment, and HS grad enrollment 0.5 35000

Net tuition (model) Net tuition (data) Investment (model)

30000

Investment (data)

0.45

Enrollment (model) Enrollment (data)

2010 dollars

0.4

20000 0.35 15000

0.3 10000

5000 1990

1995

2000

Year

1) Tuition smoothing?

2005

0.25 2010

Enrollment rate

25000

Results Net tuition, investment, and HS grad enrollment 0.5 35000

Net tuition (model) Net tuition (data) Investment (model)

30000

Investment (data)

0.45

Enrollment (model) Enrollment (data)

2010 dollars

0.4

20000 0.35 15000

0.3 10000

5000 1990

1995

2000

2005

Year

2) Colleges learning about willingness to pay?

0.25 2010

Enrollment rate

25000

Results Net tuition, investment, and HS grad enrollment 0.5 35000

Net tuition (model) Net tuition (data) Investment (model)

30000

Investment (data)

0.45

Enrollment (model) Enrollment (data)

2010 dollars

0.4

20000 0.35 15000

0.3 10000

5000 1990

1995

2000

2005

Year

3) Earnings premium forecast errors?

0.25 2010

Enrollment rate

25000

Results Statistic College costs College endowment Borrowing limits Interest rates Non-tuition cost Grants College premium Mean net tuition Enrollment rate % taking out loans Ability of graduates Investment Ex-ante utility

1987

Experiment * * * * * *

$6100 0.33 42.7 0.76 $21550 -40.98

* $7583 0.29 50.5 0.78 $22793 -40.99

$12345 0.27 100.00 0.80 $27338 -40.97

$5762 0.48 51.1 0.66 $20034 -40.78

2010 * * * * * * * $12559 0.48 100.00 0.74 $26837 -40.36

Monopolist extracts almost all rent: look at utility and borrowing.

Results Statistic College costs College endowment Borrowing limits Interest rates Non-tuition cost Grants College premium Mean net tuition Enrollment rate % taking out loans Ability of graduates Investment Ex-ante utility

1987

Experiment * * * * * *

$6100 0.33 42.7 0.76 $21550 -40.98

* $7583 0.29 50.5 0.78 $22793 -40.99

$12345 0.27 100.00 0.80 $27338 -40.97

$5762 0.48 51.1 0.66 $20034 -40.78

So, Bennett hypothesis moves tuition drastically.

2010 * * * * * * * $12559 0.48 100.00 0.74 $26837 -40.36

Results Statistic College costs College endowment Borrowing limits Interest rates Non-tuition cost Grants College premium Mean net tuition Enrollment rate % taking out loans Ability of graduates Investment Ex-ante utility

1987

Experiment * * * * * *

$6100 0.33 42.7 0.76 $21550 -40.98

* $7583 0.29 50.5 0.78 $22793 -40.99

$12345 0.27 100.00 0.80 $27338 -40.97

$5762 0.48 51.1 0.66 $20034 -40.78

2010 * * * * * * * $12559 0.48 100.00 0.74 $26837 -40.36

Increased costs cause more enrollment, lower ability, lower tuition.

Results

Micro evidence on pass-through rate from FSLP: I

Turner (2014): 12% (Pell).

I

Long (2004): up to 30% (Hope Scholarship GA).

I

Lucca, Nadauld, and Shen (2015): up to 65% (broad msr.).

I

Cellini and Goldin (2014): for-profit 78% higher tuition at FSLP-eligible schools.

For us, rough aggregate pass-through rates: I

Grants: 85% = (12559-11454)/(1779-488).

I

Borrowing Limits: 13% = (12559-9949)/(.5*40805-900)

Results

How can increased college costs result in lower tuition?

College costs

Intuition: I

Cost increase driven by F .

I

Tuition for current students is maxed out.

I

Reduce average cost by increasing enrollment, which lowers tuition by a composition effect.

The form of the cost increase matters for Baumol cost disease. The estimation does allow for implicit substitution of students. Baumol might explain tuition increases for individual colleges.

Conclusion

In an Epple et al. type model with a college monopolist, I

existing theories can explain the full tuition increase,

I

demand-side theories can explain the increase on their own,

I

and supply-side theories work in the wrong direction.

In future research, need multiple colleges to I

discipline market power,

I

reduce bias in parameter estimates,

I

allow for welfare implications, and

I

determine drivers of tuition by school type.

Results Second order effects can be large. Tuition cdf 1

1987 College costs fixed College endowment fixed 0.8

Borrowing limits fixed

Cumulative frequency

Interest rates fixed Non-tuition cost fixed 0.6

Grants fixed College premium fixed 2010

0.4

0.2

0 2000

4000

6000

8000

10000

12000

14000

16000

2010 dollars

Grants, borrowing limits drastically increase tuition at bottom tail.

Results Tuition function in 1987

12000

10000

Tuition

8000

6000

4000

2000 0 0.2 0.4 Ability

250000 0.6

200000 150000

0.8

100000 1

50000 0

Back

Parental income

Results Tuition function in 2010

22000

20000

Tuition

18000

16000

14000

12000

10000 0 0.2 0.4 Ability

250000 0.6

200000 150000

0.8

100000 1

50000 0

Back

Parental income

Results Enrollment comparison between 1987 and 2010 Pr(attend)>=.5 in 1987 and 2010 Pr(attend)>=.5 only in 2010 200000

Pr(attend)>=.5 only in 1987 Pr(attend)<.5 in 1987 and 2010

Parental income

150000

100000

50000

0 0

0.2

0.4

0.6

0.8

1

Ability

High ability, middle income priced out in 1987, not 2010.

Back

Model Unsimplified college problem: max q(θ, I )

I ≥0,T (·)

s.t. E + T = F + C + I α(sY ) = Prob(enroll|sY , T (sY ), q(θ, I )) θ = E(xα)/E(α) C = Nc (N1 J) T = NI (E(T α)) E = NI (E E(α)) I = NI (I E(α)) where E(x) the expectation over newborns, Pis JY −1 Nf (x) := j=0 (1 + r )−j f (π j x) computes a net present value, and I is the identity function. Back

Data and Estimation College cost function estimates: Estimated aggregate cost function 2010

Total cost (billions of 2010 dollars)

30

2005

25

20

15

2000 1995 1990 1987

1.8

1.85

1.9

FTE students / age 18 population

Back

Results Loans

Consumption

1987,attain=2

35000

70000

1987,attain=5

30000

60000

2010 dollars

2010 dollars

2010,attain=2

25000

2010,attain=5

50000

20000 15000

40000

10000

30000

0 20

30

40

50

60

70

80

90

Population with loans Fraction of workers

1 0.8 0.6 0.4 0.2 0 20

30

40

50

60

70

80

90

20000 20

Fraction of workers with loans

5000

30

40

50

60

70

80

90

Default or bad standing population 0.5 0.4 0.3 0.2 0.1 0 20

30

40

50

60

70

80

90

≈ 50% never default. Debt overhang for those who dropped out.

Model Workers, conditional on not defaulting: V R (a, l, t, s) =

max u(c) + βEs 0 |s V (a0 , l 0 , t 0 , s 0 , f 0 = 0)

c≥0,a0 ≥a

s.t. c + a0 /(1 + r (a0 )) + p(l, t) ≤ e(s)(1 − τ ) + a l 0 = (l − p(l, t))(1 + i), t 0 = max{t − 1, 0} s ≡ characteristics (age, years of completed college). a0 , a ≡ private credit r (a0 ) ≡ interest on credit (borrowing ⇒ 12.7%, saving ⇒ 2%). l 0 , l, t ≡ student loans and years remaining before loan paid off. p(l, t) ≡ prescribed student loan payment (“on-time payment”). τ ≡ tax (experiments are revenue neutral). V ≡ value from best of repaying and defaulting next period. Default problem is similar, but p(l, t) replaced by γe(s)(1 − τ ), principal l increases upon default, and duration t gets reset to tmax . Back

Data and Estimation

Avg. net tuition Enrollment rate Graduation rate % taking out loans Corr(p.income,enroll) Investment per student Avg. annual loan size College grad ability Corr(ability,enroll) Back

Model 1987 $6100 0.325 0.554 42.7 0.316 $21550 $4663 0.764 0.632

Tuition function (1987)

Data 1987 $5788* 0.379* 0.554* 35.7* $20251 $7144 -

Tuition function (2010)

Model Final SS $12559 0.483 0.554 100.0 0.276 $26837 $6873 0.735 0.782

Data 2010 $10293 0.414 0.594 52.9 0.295* $23750 $8414 0.716 0.522

Enrollment patterns

Data and Estimation The FTE-weighted averages of these measures over time: Trends of key aggregates 25000

0.55

20000

2010 dollars

15000

Net tuition Investment Endowment

0.45

Custodial cost Enrollment (FTE)

10000

Enrollment (HS grad)

0.4 5000

0 1990

1995

2000

2005

0.35 2010

Enrollment rate

0.5

Data and Estimation We estimate the custodial cost function following a similar procedure to Epple, Romano, and Sieg (2006): Estimated aggregate cost function 2010

Total cost (billions of 2010 dollars)

30

2005

25

20

15

2000 1995 1990 1987

1.8

1.85

FTE students / age 18 population

1.9

Results

Consider the FOC of the college problem absent preference shocks: T (sY ) = C 0 (N) + I − E +

qθ (θ, I ) (θ − x(sY )) qI (θ, I )

Direct effect: C 0 ↑⇒ T ↑, so tuition increases. Indirect effect: F + C (·) increases, placing pressure on budget constraint, causing I to fail. So, tuition falls. Back

Literature Nonexhaustive literature roughly divided into strands: Cost disease: Baumol (1967), Archibald and Feldman (2008) Government approp.: Heller (1999), Chakrabarty et al. (2012), Koshal and Koshal (2000), Titus et al. (2010), Cunningham et al. (2001) Bennett: McPherson and Shapiro (1991), Singell and Stone (2007), Rizzo and Ehrenberg (2004), Turner (2012,2014), Long (2004,2006), Cellini and Goldin (2014), Lucca et al. (2015), Frederick, Schmidt, and Davis (2012) College premium: Autor, Katz, and Kearney (2008), Katz and Murphy (1992), Goldin and Katz (2007), Card and Lemieux (2001), Andrews et al. (2012), Hoekstra (2009) Structural higher ed.: Abbott et al. (2013), Athreya and Eberly (2013), Ionescu and Simpson (2015), Ionescu (2011), Garriga and Keightley (2010), Keane and Wolpin (2001), Fillmore (2014), Fu (2014), Jones and Yang (2015), Epple, Romano, and Sieg (2006), Epple, Romano, Sarpca, and Sieg (2013).