slides 20min trend

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Accounting for the Rise in College Tuition

Grey Gordon and Aaron Hedlund Indiana University and University of Missouri

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Motivation

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

6000

7000

8000

9000

10000

(me

a

n

)

n

e

tt

u

it

_

p

e

r_

ft

e

1985 1990 1995 2000 2005 2010 Academic Year

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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.

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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,

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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 theoriesdecrease tuition by 6%.

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

I The college earnings premium causes tuition increases of 24%.

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Model

Youths are born withsY, a vector of parental income and ability.

Youth problem (in college):

Yj(l,sY) = max

c+φ≥0,l0_≥lu(c+φ) +β

πYj+1(l0,sY)+

(1−π)Es0_|j_,_sYV(0,l0,t_max,s0,0)

s.t. c +T(sY) + φ

|{z}

R&B

≤ eY

|{z}

earn.

+ξEFC(sY)

| {z }

transfers

+ ζ(sY)

| {z }

gov grant

+ bs+bu

| {z }

ann. borrow statutory limits on borrowing

(l_s0,l_u0,ls,lu,bs,bu) =f(l0,l)

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Model

The decision to enroll is made at time zero:

max{Y1(0,sy) +q+α

| {z }

college

,Es|sYV(0,0,0,s,0)

| {z }

work

}

q≡college quality

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Model

The college problem:

max

I≥0,T(·)q(θ,I)

s.t. EN +TN =F +C(N1) +IN

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 parametrizeq(θ,I) asχqθχθI1−χθ.

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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 Label 1987 2010

log college premium λ .46 .66

student loan interest i 4.7 3.0

room and board φ 3072 9129

average gov grant ζ¯ 488 1779

subsidized limit l¯s 23994 23000

unsubsidized limit ¯lu 0 40805

non-tuition revenue per student E 17843 18418

fixed cost of college (billions) F 12 30

marginal cost, relative change C2/C₁₉₈₇2 1 4.7

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Data and Estimation

We estimate a number of parameters inside the model:

Param Description Value Target Data Model

ξ transfer size .208 avg tuition 5788 6100

χθ ability input .252 ρ(p.inc,enroll) .295 .316

χq quality level 2.68 enroll rate .379 .325

α pref. shock .003 % with loans 35.7 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.

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Results

1990 1995 2000 2005 2010

0.25 0.3 0.35 0.4 0.45 0.5 Enrollment rate

1990 1995 2000 2005 2010

5000 10000 15000 20000 25000 30000 35000 Year 2010 dollars

Net tuition, investment, and HS grad enrollment

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

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Results

1990 1995 2000 2005 2010

0.25 0.3 0.35 0.4 0.45 0.5 Enrollment rate

1990 1995 2000 2005 2010

5000 10000 15000 20000 25000 30000 35000 Year 2010 dollars

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Results

1990 1995 2000 2005 20100.25

0.3 0.35 0.4 0.45 0.5

Enrollment rate

1990 1995 2000 2005 2010

5000 10000 15000 20000 25000 30000 35000

Year

2010 dollars

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Results

1990 1995 2000 2005 20100.25

0.3 0.35 0.4 0.45 0.5

Enrollment rate

1990 1995 2000 2005 2010

5000 10000 15000 20000 25000 30000 35000

Year

2010 dollars

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Results

1990 1995 2000 2005 20100.25

0.3 0.35 0.4 0.45 0.5

Enrollment rate

1990 1995 2000 2005 2010

5000 10000 15000 20000 25000 30000 35000

Year

2010 dollars

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Results

Statistic 1987 Experiment 2010

College costs * *

College endowment * *

Borrowing limits * *

Interest rates * *

Non-tuition cost * *

Grants * *

College premium * *

Mean net tuition $6100 $7583 $12345 $5762 $12559

Enrollment rate 0.33 0.29 0.27 0.48 0.48

% taking out loans 42.7 50.5 100.00 51.1 100.00

Ability of graduates 0.76 0.78 0.80 0.66 0.74

Investment $21550 $22793 $27338 $20034 $26837

Ex-ante utility -40.98 -40.99 -40.97 -40.78 -40.36

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Results

College costs * *

Interest rates * *

Grants * *

College premium * *

Mean net tuition $6100 $7583 $12345 $5762 $12559

Enrollment rate 0.33 0.29 0.27 0.48 0.48

% taking out loans 42.7 50.5 100.00 51.1 100.00

Investment $21550 $22793 $27338 $20034 $26837

Ex-ante utility -40.98 -40.99 -40.97 -40.78 -40.36

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Results

College costs * *

Interest rates * *

Grants * *

College premium * *

Mean net tuition $6100 $7583 $12345 $5762 $12559

Enrollment rate 0.33 0.29 0.27 0.48 0.48

% taking out loans 42.7 50.5 100.00 51.1 100.00

Investment $21550 $22793 $27338 $20034 $26837

Ex-ante utility -40.98 -40.99 -40.97 -40.78 -40.36

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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).

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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.

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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

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Results

Second order effects can be large.

2000 4000 6000 8000 10000 12000 14000 16000 0

0.2 0.4 0.6 0.8 1

2010 dollars

Cumulative frequency

Tuition cdf

1987

College costs fixed College endowment fixed Borrowing limits fixed Interest rates fixed Non-tuition cost fixed Grants fixed College premium fixed 2010

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Results

Ability

Parental income 2000

4000 6000

Tuition

8000 10000 12000

150000 200000

250000

100000 0.2

0

0 1 0.8 0.6 0.4

50000 Tuition function in 1987

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Results

1 0.8 0.6 Ability

0.4 0.2 0

0 10000

200000 250000 12000

14000

Parental income 150000 100000

Tuition

16000 20000 22000

Tuition function in 2010

50000 18000

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Results

0 0.2 0.4 0.6 0.8 1

0 50000 100000 150000 200000

Ability

Parental income

Enrollment comparison between 1987 and 2010

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

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

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Model

Unsimplified college problem:

max

I≥0,T(·)q(θ,I)

s.t. E+T =F +C+I

α(sY) =Prob(enroll|sY,T(sY),q(θ,I)) θ=E(xα)/E(α)

C=Nc(N1J)

T =NI(E(Tα))

E =NI(EE(α))

I =NI(IE(α))

whereE(x) is the expectation over newborns,

Nf(x) :=P_jJY₌₀−1(1 +r)−jf(πjx) computes a net present value,

andI is the identity function.

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Data and Estimation

College cost function estimates:

1.8 1.85 1.9

15 20 25 30

FTE students / age 18 population

Total cost (billions of 2010 dollars)

Estimated aggregate cost function

1987

1990 1995 2000

2005

2010

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Results

20 30 40 50 60 70 80 90 0 5000 10000 15000 20000 25000 30000 35000 2010 dollars Loans 1987,attain=2 1987,attain=5 2010,attain=2 2010,attain=5

20 30 40 50 60 70 80 90 20000 30000 40000 50000 60000 70000 2010 dollars Consumption

20 30 40 50 60 70 80 90 0 0.2 0.4 0.6 0.8 1

Fraction of workers

Population with loans

20 30 40 50 60 70 80 90 0 0.1 0.2 0.3 0.4 0.5

Fraction of workers with loans

Default or bad standing population

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Model

Workers, conditional on not defaulting:

VR(a,l,t,s) = max

c≥0,a0_≥au(c) +βEs0|sV(a 0

,l0,t0,s0,f0 = 0)

s.t. c+a0/(1 +r(a0)) +p(l,t)≤e(s)(1−τ) +a

l0 = (l−p(l,t))(1 +i), t0 = 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%).

l0,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, butp(l,t) replaced by γe(s)(1−τ),

principall increases upon default, and durationt gets reset totmax.

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Data and Estimation

Model Data Model Data

1987 1987 Final SS 2010

Avg. net tuition $6100 $5788* $12559 $10293

Enrollment rate 0.325 0.379* 0.483 0.414

Graduation rate 0.554 0.554* 0.554 0.594

% taking out loans 42.7 35.7* 100.0 52.9

Corr(p.income,enroll) 0.316 - 0.276 0.295*

Investment per student $21550 $20251 $26837 $23750

Avg. annual loan size $4663 $7144 $6873 $8414

College grad ability 0.764 - 0.735 0.716

Corr(ability,enroll) 0.632 - 0.782 0.522

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Data and Estimation

The FTE-weighted averages of these measures over time:

1990 1995 2000 2005 2010

0 5000 10000 15000 20000 25000

2010 dollars

1990 1995 2000 2005 2010

0.35 0.4 0.45 0.5 0.55

Enrollment rate

Trends of key aggregates

Net tuition

Investment

Endowment

Custodial cost

Enrollment (FTE)

Enrollment (HS grad)

Note thatE moves little,I and T increase gradually, andC

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Data and Estimation

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

1.8 1.85 1.9

15 20 25 30

FTE students / age 18 population

Total cost (billions of 2010 dollars)

Estimated aggregate cost function

1987

1990 1995 2000

2005

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Results

Consider the FOC of the college problem absent preference shocks:

T(sY) =C0(N) +I−E+

qθ(θ,I) qI(θ,I)

(θ−x(sY))

Direct effect: C0 ↑⇒T ↑, so tuition increases.

Indirect effect: F +C(·) increases, placing pressure on budget

constraint, causingI to fail. So, tuition falls.

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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),