tuition fees and students’ e ort at universityfferri/nueva_carpeta/research/bbf_16_july.pdf ·...

Tuition Fees and Students’ Effort at University(Work in progress)

Pilar Beneito, Jose E. Bosca and Javier FerriUniversity of Valencia

II Workshop AnaecoValencia

6-8 July 2016

II Workshop Anaeco Tuition fees & students’ effort 6-8 July 2016 1 / 34

Outline

Introduction: tuition fees rise.

Theoretical setting: a model of students’ effort.

Empirical setting:I Data: University of Valencia.I Identification strategy.I Estimation results.

Final comments.


Introduction: tuition fees rise

Many developed countries have witnessed in the last decades a significant

expansion in the number of students participating in higher education.

Higher education systems vary across advanced countries in many aspects,

but most of them share a common feature: higher education is heavily

subsidised.

Although subsidising higher education is theoretically justified (positive

externalities of education) a debate is open as regards who should bear a

higher burden of the total cost of studying at university :

I Greenaway and Haynes (The Economic Journal, 2003): beneficiaries ofhigher education in the UK should make a greater contribution to thefinancing of the higher education system =⇒ in the UK tuition feesincreased from £1,000 per annum in 1998/99, to £3,000 in 2006/07and to £6,000-£9,000 in 2012/13 (accompanied by the possibility ofdefering the payment of fees by taking income contingent loans).



In countries like Spain raising tuition fees has not been an issue under

political discussion for many years.

However, the devasting effects of the Great Recession in Spain made the

government to approve a reduction of the subsidy to higher education.

In Spain, Law 14/2012 seeks to ’rationalise’ public expenditure shifting a

higher part of the costs of education onto the beneficiaries, i.e. the students:

I From the 2012-13 academic year on, university tuition fees coverbetween 15 and 25 percent of the total cost of education in thefirst-time registration, between 30 and 40 in the second-timeregistration, between 65 and 75 if a student makes a third-timeregistration and between 90 and 100 percent in the fourth-time orsuccessive registrations.



UVEG: Cost per credit in 2011-12 (in euros) and increase in 2012-13 (in %)

1st Reg. 2nd Reg. 3rd Reg. 4th Reg.

Economics and Business 13.07 22.87 28.75 28.75

(% increase in 2012-13) (33.3%) (33.3%) (127.3%) (203.1%)

Medicine 18.48 32.34 40.66 40.66

(% increase in 2012-13) (33.3%) (33.3%) (127.3%) (203.1%)

The cost of a first or second registration for a module in the degrees of

Economics, Business or Medicine at the University of Valencia (UVEG)

increased more than 33 percent in 2012-13 with respect to previous

academic year.

More pronnounced was the fee rise for third or fourth registrations (127 and

203 percent, respectively).



Some literature about the possible effects of increasing tuition fees:

I Tuition fees and enrollment: Hubner (Economics of Education Review,2012); Coelli (Canadian Journal of Economics, 2009).

I Tuition fees and drop-outs: Garibaldi, Giavazzi, Ichino and Rettore(The Review of Economics and Statistics, 2012); Bradley and Migali(WP, 2015, Lancaster University).

I Financial rewards and students achievement: Leuven, Oosterbeek andvan der Klaauw (Journal of the European Economic Association,2010); Camerer and Hogarth (Journal of Risk and Uncertainty, 1999).

I Tuition fees and student behaviour:F Bolli and Johnes (Journal of Education and Work, 2015): tuition fees

rise modifies students’ allocation of study time between classes andhome.

F Ketel et al. (The Economic Journal, 2016): psychological costs offailing their studies may be lower for students that pay low tuition feesfor their study.



What we do?

I We focus on the following question: do students ’smart-up’ whentuition fees rise?

I A positive answer implies a higher efficiency in the use of ’subsidised’education resources.

I To investigate the causal effect of tuition fees on students’ effort andacademic achievement:

F Theoretical setting: a simple theoretical model of students’ effort andtuition fees.

F Empirical setting: using data from the University of Valencia, we applydiff-in-diff (DID) regressions.

I (We don’t consider enrollment and/or drop-out decisions).


Theoretical setting


Theoretical setting

A representative student starts at university at period t0 where she is going

to be until t0 + nu =⇒ We do not consider enrolment decision.

Anyone entering university pays tuition fees (tf ) and gets a degree after nuperiods=⇒ We do not model drop-outs.

At the end of year t0 + nu the student takes an exam.I If she passes, then she gets a First Class (FC) certificate.I If she fails she pays a monetary penalty and obtains a Second Class

(SC) certificate.

Given inherent ability, the probability of getting a FC degree is a positive

function of the student’s effort, s.


Theoretical setting

In order to choose her optimal effort level, our student maximizes the

expected present value of utility which depends on a constant flow of

consumption (c) and leisure (l).

Present value of consumption equalizes present value of income=⇒No

posibility for bequest.

There are two possible cases (which will depend on student’s effort, s):

I (1) the student gets a FC degree ⇒Probability Prob (FC)I (2) the student gets a SC degree ⇒Probability 1-Prob (FC)


Theoretical setting

And the present value of consumption under these two cases:

I c1 = y0 + sβ + b− tf ⇒Probability Prob (FC)I c2 = y0 + sβ − (2tf + d)⇒Probability 1-Prob (FC)

where:

I y0 is the lifetime income if not-graduate;I sβ is the premium for getting a degree;I β measures the responsiveness of lifetime income to effort;I b is the premium lifetime income for a FC degree (=0 for a SC degree);I tf stands for the tuition fees involved in a FC degree ;I d is the ’extra’ penalty in fees for a SC certificate.

The monetary cost of getting a SC degree is more than double that of a FC

(the student has to pay again for the tuition fees plus a penalty for not

succeeding to get a FC certificate).

At university the student reveals her effort in obtaining the degree, which

remains constant for the whole working life (nw − nu periods).


Theoretical setting

The probability of succeding in getting a FC degree is assumed to follow a

sigmoid function (”S” shape curve) of effort, s.

In particular, we assume a generalized logistic function, bounded at 1,with

location parameter µ (and scale parameter assumed to be 1 and omitted in

notation):

Prob(FC) = F(µ, s) =1

1 + e−(s−µ)

Parameter µ is the midpoint of the function.

Changes in µ ⇒ shift the function. These are changes in ability and/or

inherent difficulty of studies.

Thus, µ can be interpreted as an ’ability/difficulty’ parameter: an increase in

ability reduces µ; an increase in difficulty of studies increases µ.


Plot 1: Probability of getting a FC certificate for µ = 3, 5, 7.

0 1 2 3 4 5 6 7 8 9 10

Effort index

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Pro

babili

ty o

f gettin

g a

FC

degre

e

P = [1 3]

P = [1 5]

P = [1 7]


Theoretical setting

Leisure is a negative function of effort⇒ l = h− s, where h is total time

available and split between leisure and time effort.

Preference for leisure (=1-preference for consumption): parameter 1− α.

Then the optimization problem of the student takes the form

maxs

E[U(c, l)] = F(µ, s)(

y0 + sβ + b− tf)α

(h− s)1−α +

(1− F(µ, s))(

y0 + sβ − (2tf + d))α

(h− s)1−α

s.t.

F(µ, s) =1

1 + e−(s−µ)

0 6 s 6 h

Parameters: µ, y0, β, b, h, α, d and tf .


Theoretical setting

The first order condition takes the form:

[Fs(µ, s)cα

1 + α cα−11 βsβ−1F(µ, s)

−Fs(µ, s)cα2 + α cα−1

2 βsβ−1 (1− F(µ, s))

](h− s)1−α

− (1− α) (h− s)−α [F(µ, s)cα1 + (1− F(µ, s)) cα

2 ] = 0

This equation does not admit an analytical solution.

Hence we rely on a numerical solution.


Theoretical model: parameter set-up

First, we normalize total time available and backup lifetime income

h = y0 = 10.Next, we obtain tf and d consistent with y0, using information on the actual

cost of tuition fees at UVEG and assuming a temporal disccount rate

γ = 0.8.β is set such that a university degree implies a reward of 15% with respecto

to y0 (regardeless of it being a FC or a SC degree).

We assume that getting a First Class certificate almost doubles the income

with respect to a Second Class degree, and so we set b = y0.

Finally, we set α such that, for a student with µ = 6.5, the model solution

replicates the probability of passing in the first registration that we observe

in the data for Economics & Business at UVEG.

Table T1. Parameter values

y0 h β b α γ tf d µ f10 10 0.15 10 0.61 0.8 0.53 0.30 6.5 1


Theoretical model: solution

Table T2. Model solution

Student’s effort Prob FC degree

Benchmark 6.54 48.4y0 = 10→ 9 6.70 52.6β = 0.15→ 0 6.61 50.3b = 10→ 11 6.68 52.0α = 0.61→ 0.63 6.69 52.2tf = 0.53→ 0.7 6.62 50.5d = 0.3→ 0.4 6.57 49.3µ = 6.5→ 6.0 6.30 57.6

Higher effort and probability of getting a FC degree: the lower the

non-graduate income; the lower the income responsiveness to effort at

university; the higher the income premium for a FC degree; the lower the

preferences for leisure; the higher tuition fees; the higher the step penalty for

failing to obtain a FC certificate;

Lower effort and higher probability of getting a FC degree:I the higher innate ability.


Theoretical model: solution

Plot 1: Heterogeneity in the response to tuition fees

(Different response of Prob(FC) to tuition fees’ rise depending on ability).

2.5 3 3.5 4 4.5 5.5 6 6.5 7 7.55

Ability parameter (µ)

0

1

2

3

4

5

6

Ch

an

ge

in

Pro

b o

f g

ett

ing

a F

C d

eg

ree

High ability Low ability


Empirical setting


Data: University of Valencia

Data: students of Economics, Business, and Medicine, at the University of

Valencia, from 2010 to 2014 (5 years).

Economics and Business students differ from Medicine students on: ability,

difficulty of studies, level of fees. Treated separately from each other in

estimation.

Information on the student’s academic ’performance’: entrance mark, grades

(per module, academic year, course), number of times registered in a

module.

Information on economic and educational levels of the family and the

student: mother’s and father’s education, mother’s and father’s labour

situation, student’s working situation.

Other: age, gender.


Identification Strategy

Identification of causal effect of a ’policy intervention’: what the individual

would have done without intervention?: the ’counterfactual’.

Problem: the counterfactual is not observed.

Diff-in-diff approach (DID): how the difference between those treated

(individuals subject to the treatment) and a ’control’ group (those not

subject to the treatement) differs before and after the treatment.

DID approach: robust to idiosincratic permanent differences between the

treated and the control group.

In our setting:I Treated with the rise in tuition fees? All students with ’ordinary’

registration mode.I Control group: students exempt of paying tuition fees: in University of

Valencia → students of ’special numerous families’.



Standard DID regression:

Yimt = α + αDDi + γPostt + γDPosttDi + γxit + cm + ai + uit

where subscripts i, m and t denote the student, module and year,

respectively.

Postt is a set of dummy step variable for all periods (years) after treatment.

Di is a dummy variable for ’treated’ students.

xit stands for a vector of control variables (educational level of mother and

father, economic situation of mother and father, type of module, age,

gender and working situation of the student).

cm stands for module-effects (we control for by including the average of the

dependent variable for each module).

ai stands for student-fixed effects (we estimate both by RE and FE).

uit: iid error



Standard DID regression:

Yimt = α + αDDi + γPostt + γDPosttDi + γxit + cm + ai + uit

Based on 2 asssumptions:I 1. ’Parallel path assumption’: treated and control group do not

differ in their trends before the treatment. A crucial assumption.I 2. Treatment effects (if any) are equal in all periods after treatment

(static effects)



Fully flexible DID regression (Mora and Reggio, 2013): (i) it allows to

check for non-paralell pre-treatment trends; (ii) it allows for dynamic effects

after treatment.

Yimt = α + αDDi +T

∑τ=t0+1

βτIτ +T

∑τ=t0+1

βDτ IτDi + γxit + cm + ai + uit

I where Iτ is a set of dummy variables identifying years 2011, 2012,2013, 2014 (with 2010 absorbed in the constant)

With treatment ocurring at t∗ (sometime between 2011 and 2012):

If βDτ = 0 ∀τ < t∗ → parallel paths (pre-treatment) (1)

then βDτ ∀τ > t∗ → treatment effects (2)

I If pre-treatment trends are not parallel, take differences of thedependent variable and apply the DID regression: Diff-in-double-diff(DI2D)



Yit = α + αDDi +T

∑τ=t0+1

βτIτ +T

∑τ=t0+1

βDτ IτDi + γxit + cm + ai + uit

We estimate the DID model for 3 alternative ’outcome’ variables Yit:I (1) Number of times the student has ’paid’ tuition fees to pass the

module (N. of registrations until pass);I (2) Probability of passing the module in the first registration;I (3) Grades.

We distinguish in estimation between:I ’Top’ Students: those with entrance grade above the upper 80

percentile.I ’Average’ Students: those with entrance grade below the 80 percentile.


Table D1. Descriptives

Economics & Business Medicine All Averg.

Stud. Top

Stud. All Averg.

Stud. Top. Stud.

Number Observations 143.976 119.726 24.250 39.579 8743 30.836

Control group (N. Obs) 1.739 1.328 411 1.002 824 178

N registrations until pass 1.64 1.71 1.40 1.20 1.23 1.10

Before fees rise (2010-2011) 1.57 1.65 1.31 1.16 1.19 1.08

After fees rise (2012-2014) 1.72 1.77 1.51 1.26 1.29 1.17

Prob. of pass in 1st registration 0.45 0.42 0.59 0.73 0.71 0.78

Before fees rise (2010-2011) 0.42 0.40 0.57 0.71 0.69 0.77

After fees rise (2012-2014) 0.48 0.46 0.59 0.74 0.73 0.80

Grades (if presented to the exam) 5.21 5.06 6.08 6.65 6.49 7.30

Before fees rise (2010-2011) 5.06 5.39 6.01 6.59 6.42 7.21

After fees rise (2012-2014) 5.39 5.02 6.20 6.76 6.61 7.33


Table R1. ECONOMICS+ BUSINESS Students Number of registrations to pass Flexible Diff-in-Diff estimation

RE

RE

RE

FE

FE

All Students Averg. Stud. Top Stud. Averg. Stud. Top Stud. Treated 0.153 0.258 0.032 - - (0.146) (0.185) (0.218) Year 2011 0.408*** 0.426*** 0.314** 0.463*** 0.286*** (0.091) (0.100) (0.124) (0.097) (0.109) Year 2012 0.837*** 0.887*** 0.746*** 0.938*** 0.720*** (0.106) (0.117) (0.163) (0.100) (0.131) Year 2013 1.201*** 1.423*** 0.761*** 1.504*** 0.760*** (0.090) (0.114) (0.115) (0.094) (0.085) Year 2014 1.630*** 1.782*** 1.164*** 1.868*** 1.150*** (0.087) (0.094) (0.161) (0.082) (0.107) Treated in Year 2011 -0.022 -0.015 -0.032 -0.027 0.009 (0.092) (0.101) (0.126) (0.098) (0.110) Treated in Year 2012 -0.071 -0.080 -0.153 -0.092 -0.109 (0.106) (0.117) (0.163) (0.101) (0.129) Treated in Year 2013 -0.138 -0.311*** 0.080 -0.338*** 0.104 (0.090) (0.114) (0.113) (0.094) (0.078) Treated in Year 2014 -0.225*** -0.320*** 0.011 -0.344*** 0.051 (0.087) (0.095) (0.152) (0.083) (0.089) Constant -1.924*** -2.196*** -0.204 0.014 0.239 (0.276) (0.350) (0.442) (0.206) (0.347) Observations 51,912 40,699 11,213 40,699 11,213 R-squared 0.274 0.301 0.213 0.416 0.278 Number of Students 3,502 2,806 826 2,806 826 Hausman fixed effecs 913.71 259.94 [p-value] 0.000 0.000

RE: random effects estimation; FE: fixed effects estimation. Robust errors in parenthesis (* signif. at 10%; **signif at 5%; ***signif at 1%)


Table R2. MEDICINE Students Number of registrations to pass Flexible Diff-in-Diff estimation

RE

RE

RE

FE

FE

All Students Averg. Stud. Top Stud. Averg. Stud. Top Stud. Treated 0.323*** 0.362*** -0.058 - - (0.095) (0.095) (0.051) Year 2011 0.177*** 0.204*** 0.121*** 0.192*** 0.135*** (0.034) (0.043) (0.027) (0.043) (0.028) Year 2012 0.393*** 0.428*** 0.273*** 0.464*** 0.310*** (0.039) (0.053) (0.047) (0.070) (0.056) Year 2013 0.628*** 0.677*** 0.448*** 0.784*** 0.507*** (0.058) (0.076) (0.073) (0.090) (0.086) Year 2014 1.018*** 1.204*** 0.555*** 1.422*** 0.614*** (0.126) (0.187) (0.087) (0.138) (0.100) Treated in Year 2011 0.025 0.027 -0.001 0.075 0.012 (0.035) (0.044) (0.024) (0.047) (0.023) Treated in Year 2012 0.037 0.041 0.017 0.062 0.021 (0.036) (0.052) (0.025) (0.069) (0.031) Treated in Year 2013 0.035 0.040 0.035 0.021 0.023 (0.052) (0.072) (0.033) (0.084) (0.034) Treated in Year 2014 -0.211* -0.339* 0.058 -0.461*** 0.047 (0.123) (0.185) (0.050) (0.134) (0.052) Constant -1.708*** -2.132*** -1.053** -0.217 -0.090 (0.367) (0.448) (0.470) (0.230) (0.174) Observations 24,267 18,547 5,720 18,547 5,720 R-squared 0.242 0.257 0.244 0.224 0.128 Number of Students 1,326 1,018 343 1,018 343 Hausman fixed effecs 1151.39 343.02 [p-value] 0.000 0.000



Table R3. ECONOMICS+ BUSINESS Students Dependent variable: Probability of pass in 1st registration Linear Probability Model. Flexible Diff-in-Diff estimation

RE RE FE FE Averg. Stud. Top Stud. Averg. Stud. Top Stud. Treated -0.134*** -0.087 - - (0.048) (0.061) Year 2011 -0.063 -0.085 -0.040 -0.043 (0.046) (0.071) (0.045) (0.072) Year 2012 -0.058 -0.107 -0.020 -0.053 (0.050) (0.082) (0.051) (0.081) Year 2013 0.021 -0.053 0.042 -0.010 (0.063) (0.078) (0.066) (0.077) Year 2014 -0.092 -0.026 -0.068 0.029 (0.080) (0.148) (0.081) (0.146) Treated in Year 2011 0.061 0.033 0.045 -0.013 (0.046) (0.072) (0.045) (0.073) Treated in Year 2012 0.083* 0.068 0.066 0.017 (0.050) (0.083) (0.051) (0.082) Treated in Year 2013 0.052 0.046 0.059 0.005 (0.063) (0.078) (0.066) (0.077) Treated in Year 2014 0.212*** 0.015 0.224*** -0.035 (0.080) (0.149) (0.081) (0.146) Constant 0.834*** 1.135*** 0.732*** 1.070*** (0.065) (0.108) (0.096) (0.123) Observations 62,317 15,200 62,317 15,200 R-squared 0.426 0.438 0.049 0.035 Number of Students 2,848 827 2,848 827 Hausman test fixed effecs 336.96 73.46 [p-value] 0.000 0.000



Table R4. MEDICINE Students Dependent variable: Probability of passing in 1st registration

Linear Probability Model. Flexible Diff-in-Diff estimation RE RE FE FE Averg.

Stud. Top Stud. Averg.

Stud. Top. Stud.

Treated -0.050 0.081 - - (0.045) (0.082) Year 2011 -0.039 -0.000 -0.076* 0.006 (0.038) (0.062) (0.044) (0.063) Year 2012 -0.145*** -0.058 -0.143*** -0.037 (0.047) (0.074) (0.050) (0.076) Year 2013 -0.137** 0.119 -0.181** 0.121 (0.059) (0.116) (0.076) (0.118) Year 2014 -0.264** 0.001 -0.204 0.089 (0.106) (0.114) (0.237) (0.115) Treated in Year 2011 -0.010 -0.021 0.036 -0.028 (0.038) (0.063) (0.045) (0.064) Treated in Year 2012 0.093** 0.013 0.135*** 0.003 (0.047) (0.075) (0.051) (0.076) Treated in Year 2013 0.119** -0.139 0.217*** -0.120 (0.059) (0.116) (0.075) (0.118) Treated in Year 2014 0.340*** 0.028 0.408* 0.023 (0.107) (0.114) (0.237) (0.115) Constant 1.322*** 0.662*** 1.199*** 0.889*** (0.112) (0.210) (0.285) (0.058) Observations 22,643 6,750 22,643 6,750 R-squared 0.493 0.629 0.204 0.099 Number of Students 1,029 345 1,029 345 Hausman test fixed effecs 127.49 55.23 [p-value] 0.000 0.000



Table R5. ECONOMICS & BUSINESS Students Dependent variable: Grades Flexible Diff-in-Diff estimation

RE RE FE FE Averg.


Stud. Top. Stud.

Treated -0.652** -0.775** - - (0.282) (0.391) Year 2011 -0.092 0.371 -0.040 0.721 (0.222) (0.791) (0.217) (0.811) Year 2012 0.250 0.124 0.335 0.579 (0.297) (1.166) (0.293) (1.239) Year 2013 0.173 0.081 0.246 0.526 (0.432) (0.433) (0.432) (0.401) Year 2014 -0.341 1.231 -0.176 1.848 (0.502) (1.156) (0.514) (1.296) Treated in Year 2011 0.294 -0.331 0.278 -0.656 (0.224) (0.797) (0.218) (0.816) Treated in Year 2012 0.192 0.087 0.173 -0.287 (0.299) (1.168) (0.295) (1.237) Treated in Year 2013 0.698 0.461 0.717* 0.105 (0.434) (0.443) (0.435) (0.402) Treated in Year 2014 1.436*** -0.740 1.392*** -1.230 (0.507) (1.162) (0.519) (1.295) Constant 5.666*** 7.590*** 4.745*** 6.995*** (0.418) (0.738) (0.580) (0.528) Observations 119,726 24,250 119,726 24,250 R-squared 0.100 0.077 0.039 0.031 Number of Students 3,170 935 3,170 935 Hausman test fixed effecs 1245.23 194.08 [p-value] 0.000 0.000



Table R6. MEDICINE Students Dependent variable: Grades Flexible Diff-in-Diff estimation

RE RE FE FE Averg.


Stud. Top. Stud.

Treated -0.204 1.146 - - (0.498) (1.111) Year 2011 -0.429 0.318 -0.477 0.179 (0.350) (0.338) (0.481) (0.435) Year 2012 -0.518 -0.484 -0.474 -0.507 (0.326) (0.717) (0.432) (0.755) Year 2013 -0.435 0.228 -0.360 0.249 (0.551) (0.413) (0.627) (0.451) Year 2014 -0.945 0.951** -0.773 1.157** (1.218) (0.404) (1.225) (0.472) Treated in Year 2011 0.251 -0.498 0.381 -0.213 (0.354) (0.350) (0.488) (0.445) Treated in Year 2012 0.561* 0.177 0.686 0.415 (0.331) (0.723) (0.440) (0.758) Treated in Year 2013 0.758 -0.143 0.936 0.119 (0.557) (0.431) (0.637) (0.462) Treated in Year 2014 2.356* -0.269 2.551** -0.111 (1.226) (0.442) (1.236) (0.502) Constant 7.787*** 3.444* 5.808*** 5.703*** (0.914) (2.087) (1.098) (0.409) Observations 30,836 8,743 30,836 8,743 R-squared 0.100 0.077 0.061 0.033 Number of Students 1,081 364 1,081 364 Hausman test fixed effecs 564.30 151.12 [p-value] 0.000 0.000



Final comments


Final comments

The effects of modifiying tuition fees is diverse.

Negative effects include possible reduction in enrollment rates and increase

in drop-outs, probably affecting poorer individuals more sharply . (In our

research agenda).

Tuition fees’, however, also act as an incentive mechanism that may enhance

students’ academic effort and performance.

We find positive effects on the ’efficiency’ in the use of education subsidised

resources. Also evidence on better students’ achievements (grades).

We also find that responses are heterogenous: in particular, we find that

average students respond more to tuition fees rise than top students.

The design of the higher education policy needs to be ’integral’: tuition fees

rise + loans (or grants).


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