financing higher education: comparing alternative policiestridip/research/comparing... · education...

IntroductionPrivate Education SystemPublic Education System

Traditional Tax-Subsidy SystemA Pure Loan Scheme

Income Contingent Loans

Financing Higher Education: ComparingAlternative Policies

Mausumi Das Tridip Ray

Delhi School of Economics ISI, Delhi

National Conference on Economic Reform, Growth and PublicExpenditure

CSSS Kolkata; 8-9 October 2013

Tridip Ray (ISI, Delhi) Financing Higher Education: Comparing Alternative Policies




MotivationOur WorkModel Structure

Education as an Effective Anti-poverty Measure

Poverty is often self-perpetuating - especially in developingcountries.

Pervasive inequality along with imperfect credit marketsdistort the incentives to invest for the poor.

Poorer households not only earn less, but also investproportionately less - thereby hindering the earningcapabilities of the future generations.

Effective anti-poverty measure must take into account thesedynamic incentive effects (Ghatak et al, 2001; Mookherjee,2006; Mookherjee and Ray, 2008).

Education policy may work better than direct redistributivetransfers - precisely because it creates the right incentives.






This Paper

Compare alternative policies to finance higher education fromthe perspective of generating dynamic incentive effects.

— Private Education System;— Public Education System;— Traditional Tax-Subsidy System;— A Pure Loan Scheme;— Income Contingent Loans.

Develop a framework to compare alternative policies in adynamic set up.

Advocate a government-sponsored Income Contingent Loanscheme in generating the right incentives from a long runperspective.






Model Structure

Based on Galor-Zeira (1993)

— Two periods overlapping generations with no populationgrowth.

— Two sectors: Technical and Non-Technical

◦ Working in the technical sector requires specialized skills;◦ working in the non-technical sector does not.

— Skill formation requires indivisible investment in highereducation.

— Credit market is imperfect.

Extends Galor-Zeira in a specific direction:

— Adds uncertainty in the technical skill formation process.

◦ Accentuates the unskilled labour trap result of Galor-Zeira.






Risk and Returns

Constant Factor Returns:

— Imperfect credit market: borrowing interest rate (i) is higherthan the lending interest rate (r).

— Wage rate in the non-technical/unskilled sector is wn .— Wage rate in the technical/skilled sector is ws .

Indivisibility and Uncertainty in Skill Formation:

— Skill formation requires an indivisible investment in highereducation, E > 0.

— Investment is risky: may fail in acquiring technical skill evenafter making the lump-sum investment.

◦ Success with probability p; earns skilled wage rate ws .◦ Failure with probability 1− p; earns unskilled wage rate wn .






Households

Overlapping generations of dynastic households.Each agent born with same potential abilities and preferences.— They differ only in terms of the wealth they inherit from theirparents, x .

Each agent lives for 2 periods; has one parent and one child.Each agent can— either work as unskilled in both periods of life,— or invest in higher education when young and be a skilledworker with probability p in the second period of life.

Agents consume only in the second period of life.Utility function of an agent: u = α log c + (1− α) log b.— c : consumption; b: bequest.⇒ Agents are risk-averse.






Household Choices

An agent has to decide whether or not to invest in technicalskill formation.

We formulate this as two separate optimization problems:

(a) No investment in higher education;(b) Invest in higher education.

Then we compare the expected indirect utilities to determinethe optimal behaviour of the agent.





No Investment in Higher EducationInvestment in Higher EducationWhether to Opt for Higher EducationDynamics of Wealth Distribution

Private Education SystemNo Investment in Higher Education

Agent’s Problem:

max{c ,b}

u (·) = α log c + (1− α) log b

subject toc + b = (x + wn)(1+ r) + wn.

Optimal consumption and bequest choices:

cn = α [x(1+ r) + wn (2+ r)] ,

bn = (1− α) [x(1+ r) + wn (2+ r)] .

Indirect utility: VN = ε+ log [x(1+ r) + wn (2+ r)] ,

— ε ≡ α log α+ (1− α) log (1− α) .






Investment in Higher Education by Borrowing

Agent’s inheritance falls short of the investment requirement:x < E .

Agent’s Problem:

max{cs ,cf ,bs ,bf }

E [U(·)] = p [α log cs + (1− α) log bs ]

+(1− p) [α log cf + (1− α) log bf ]

subject tocs + bs = ws + (x − E ) (1+ i),cf + bf = wn + (x − E ) (1+ i).

— Here ‘s’and ‘f ’represent ‘success’and ‘failure’respectively.






Investment by Borrowing: Solution to Agent’s Problem

Optimal consumption and bequest choices under ‘success’:

— cs = α [ws + (x − E ) (1+ i)] ,

— bs = (1− α) [ws + (x − E ) (1+ i)] .

Optimal consumption and bequest choices under ‘failure’:

— cf = α [wn + (x − E ) (1+ i)] ,

— bf = (1− α) [wn + (x − E ) (1+ i)] .

Indirect utility:

V BE = ε+ p log [ws + (x − E ) (1+ i)]+(1− p) log [wn + (x − E ) (1+ i)] .






Investment in Higher Education from Own Inheritance

Agent’s inheritance is enough to fund the investmentrequirement: x ≥ E .Agent’s Problem:

max{cs ,cf ,bs ,bf }

E [U(·)] = p [α log cs + (1− α) log bs ]

+(1− p) [α log cf + (1− α) log bf ]

subject tocs + bs = ws + (x − E ) (1+ r),cf + bf = wn + (x − E ) (1+ r).






Investment from Own Inheritance: Solution to Agent’sProblem


— cs = α [ws + (x − E ) (1+ r)] ,

— bs = (1− α) [ws + (x − E ) (1+ r)] .Optimal consumption and bequest choices under ‘failure’:

— cf = α [wn + (x − E ) (1+ r)] ,

— bf = (1− α) [wn + (x − E ) (1+ r)] .Indirect utility:V LE = ε+ p log [ws + (x − E ) (1+ r)]

+(1− p) log [wn + (x − E ) (1+ r)] .






Whether to Opt for Higher Education

Compare indirect utility under no higher education

VN (x) = ε+ log [x(1+ r) + wn (2+ r)] ,

with indirect utility under higher education

VE (x) =

ε+ p log [ws + (x − E ) (1+ i)] for x < E ,+(1− p) log [wn + (x − E ) (1+ i)] ,

ε+ p log [ws + (x − E ) (1+ r)] for x ≥ E .+(1− p) log [wn + (x − E ) (1+ r)] ,






Wealth Threshold






Dynamics of Wealth Distribution

When xt < W Prv,

xt+1 = (1− α) [xt (1+ r) + wn (2+ r)] .

When W Prv ≤ xt < E ,

xt+1 =

{(1− α) [ws + (xt − E ) (1+ i)] , prob p,

(1− α) [wn + (xt − E ) (1+ i)] , prob 1− p.

When E ≤ xt ,

xt+1 =

{(1− α) [ws + (xt − E ) (1+ r)] , prob p,

(1− α) [wn + (xt − E ) (1+ r)] , prob 1− p.






Wealth Dynamics and the Long Run





How It Works?Intergenerational Dynamics and the Long Run

Working of the Public Education System

Works through the following inter-generation tax-and-transferpolicy (Glomm & Ravikumar, 1992).Government taxes the second-period income of old agents atthe rate τt and transfer the tax revenue to young agents inequal amounts (Rt):

Rt = τt ·[∫ytdFt (yt )

],

— Ft (y) is the distribution function of the second-period income.

τt is endogenously determined in each period throughmajority voting.An young agent treats this transfer Rt in exactly the sameway as she treats her bequest in the private education regime.






Majority Voting

An individual’s decision-making is a two-step procedure.

I. Chooses ct that maximizes her utility for a given post taxincome,(1− τt ) yt , treating the transfer received by her childas given.

⇒ Utility of period-t old agent with second-period income yt is

u (τt ; yt ) = α log [(1− τt ) yt ]+ (1− α) log[τt ·

(∫ztdFt (zt )

)].

II. Votes for the tax rate τt that maximizes the above utility.

⇒ Votes for τ∗t = 1− α.

Since every old agent votes for the tax rate τ∗t = 1− α, thisbecomes the tax rate under majority voting.






Intergenerational Dynamics and the Long Run





How It Works?Whether to Opt for Higher EducationDynamics of Wealth Distribution

Working of the Tax-Subsidy System

A lump-sum tax, T , is levied on all agents in the first periodof their lives; a subsidy sE is received by only those who optfor higher education.

Subsidy rate, s, is fixed; government decides the lump-sumtax so as to maintain a balanced budget:

Tt = sEft ,

— ft is the proportion of population opting for higher education.

Note that in any period t, Tt and ft are determinedendogenously.






Reverse Redistribution

Those who do not study pay a tax but receive no subsidy;those who study pay the same tax and receive a subsidy.

This implies a net transfer to those who study:

sE − Tt = sE (1− ft ) ≥ 0 since 0 ≤ ft ≤ 1.

Reverse redistribution is regularly found in empirical studies:

— US: Peltzman (1973), Radner & Miller (1970), Bishop (1977);— Ireland: Tussing (1978);— Australia: Hope & Miller (1988);— Germany: Gruske (1994), Holtzmann (1994).






Reverse Redistribution in India






Reverse Redistribution in India ...








V Nt (x) = ε+ log [(x − Tt ) (1+ r) + wn (2+ r)] ,


V Et (x) =ε+ p log [ws + (x − ((1− s)E + Tt )) (1+ i)] for x < (1− s)E + Tt ,+(1− p) log [wn + (x − ((1− s)E + Tt )) (1+ i)] ,

ε+ p log [ws + (x − ((1− s)E + Tt )) (1+ r)] for x ≥ (1− s)E + Tt .+(1− p) log [wn + (x − ((1− s)E + Tt )) (1+ r)] ,






Wealth Threshold under Tax-Subsidy System







When xt < W TSt ,

xt+1 = (1− α) [(xt − Tt ) (1+ r) + wn (2+ r)] .

When W TSt ≤ xt < (1− s)E + Tt ,

xt+1 =

{(1− α) [ws + (xt − ((1− s)E + Tt )) (1+ i)] , prob p,

(1− α) [wn + (xt − ((1− s)E + Tt )) (1+ i)] , prob 1− p.

When (1− s)E + Tt ≤ xt ,

xt+1 =

{(1− α) [ws + (xt − ((1− s)E + Tt )) (1+ r)] , prob p,

(1− α) [wn + (xt − ((1− s)E + Tt )) (1+ r)] , prob 1− p.






Working of the Pure Loan Scheme

A pure loan scheme is a policy designed to neutralise theeffects of capital market imperfections.

The government, a credible agency, can borrow from theinternational capital market at the lenders’interest rate r .

— It then passes the education loan amount, E , to the agent atthe same interest rate r .

But the agent has to repay the amount E (1+ r) irrespectiveof whether she succeeds or fails in higher education.








VN (x) = ε+ log [x(1+ r) + wn (2+ r)] ,


VE (x) = ε+ p log [ws + (x − E ) (1+ r)]+(1− p) log [wn + (x − E ) (1+ r)] .

— Note that VE (x) takes the same form irrespective of whetherx ≥ E , or x < E .






Wealth Threshold under Pure Loan Scheme

V (·) exhibits decreasing absolute risk aversion —differences ininherited wealth levels imply different attitudes towards risk.







When xt < W PLS,

xt+1 = (1− α) [xt (1+ r) + wn (2+ r)] .

When W PLS ≤ xt ,

xt+1 =

{(1− α) [ws + (xt − E ) (1+ r)] , prob p,

(1− α) [wn + (xt − E ) (1+ r)] , prob 1− p,





How It Works?Investment in Higher EducationWhether to Opt for Higher EducationDynamics of Wealth DistributionModified Income Contingent Loans

Working of Income Contingent Loans

Available only for higher education (NOT a consumptionloan).No collateral is required. Money is transferred directly to theeducational institution.Repayment is in the form of taxation.Repayment is made (in the second period) only if the agent issuccessful.— Exempted from repayment in case of failure.

Government balances budget intertemporarily.— Suppose L0 agents take the loan. Then

τwspL0 = L0E (1+ r) ,

⇒ pτws = E (1+ r) .






Investment in Higher Education by Borrowing through ICL

If an agent opts for the ICL, she has to borrow the entireeducation loan amount E ; she has no other choice.

— But she is free to lend her inheritance x in the credit market.

In case of success, she has to make the repayment

τws =E (1+ r)

p. But, in case of a failure, she does not have

to make any repayment.

Hence her budget constraints become

cs + bs = ws − τws + x(1+ r) = ws −E (1+ r)

p+ x(1+ r),

cf + bf = wn + x(1+ r).






Investment through ICL: Solution to Agent’s Problem


— cs = α

[ws −

E (1+ r)p

+ x(1+ r)],

— bs = (1− α)α

[ws −

E (1+ r)p

+ x(1+ r)].

Optimal consumption and bequest choices under ‘failure’:— cf = α [wn + x(1+ r)] ,— bf = (1− α) [wn + x(1+ r)] .

Indirect utility:

VE (x) = ε+ p log[ws −

E (1+ r)p

+ x(1+ r)]

+(1− p) log [wn + x(1+ r)] .








VN (x) = ε+ log [x(1+ r) + wn (2+ r)] ,


VE (x) = ε+ p log[ws −

E (1+ r)p

+ x(1+ r)]

+(1− p) log [wn + x(1+ r)] .






Income Contingent Loans Vs. Pure Loans Scheme

Let y denote life-time income of an agent with inheritance x .

Under success, y ICLs < yPLSs :

y ICLs = ws + x(1+ r)−E (1+ r)

p< ws + x(1+ r)−E (1+ r) = yPLSs .

Under failure, y ICLf > yPLSf :

y ICLf = wn + x(1+ r) > wn + x(1+ r)− E (1+ r) = yPLSf .

But their expected values are the same:

p · y ICLs + (1− p) · y ICLf = pws + (1− p)wn + x(1+ r)− E (1+ r)= p · yPLSs + (1− p) · yPLSf .






Income Contingent Loans Vs. Pure Loans Scheme ...

Since VE (·) is strictly concave, it follows that

V ICLE (x) > V PLSE (x) , for all x .

Hence the wealth threshold under ICL, is strictly lower thanthe wealth threshold under PLS:

W ICL < W PLS.

Intuition: ICL provides an insurance against failure.







When xt < W ICL,

xt+1 = (1− α) [xt (1+ r) + wn (2+ r)] .

When W ICL ≤ xt ,

xt+1 =

(1− α)

[ws −

E (1+ r)p

+ x(1+ r)], prob p,

(1− α) [wn + x(1+ r)] , prob 1− p.






Wealth Dynamics: Unskilled Labour Trap Removed






Wealth Dynamics: Unskilled Labour Trap Remains






Modified ICL: Strengthen Insurance Against Failure

Under failure, not only exempted from repayment, but alsoreceives a subsidy (lump-sum), S .

Subsidy is funded through additional tax to the successful sothat government budget is balanced.

— Suppose L0 agents take the loan. Then

τwspL0 = L0 [E (1+ r) + (1− p) S ] ,

⇒ pτws = E (1+ r) + (1− p) S .






Modified ICL ...

Under success, y ICL′

s < y ICLs :

y ICL′

s = ws + x(1+ r)− E (1+r )p − (1−p)S

p < ws + x(1+ r)− E (1+r )p = y ICLs .

Under failure, y ICL′

f > y ICLf :

y ICL′

f = wn + x(1+ r) + S > wn + x(1+ r) = y ICLf .

But their expected values are the same:

p · y ICL′s + (1− p) · y ICL′f = pws + (1− p)wn + x(1+ r)− E (1+ r)= p · y ICLs + (1− p) · y ICLf .






Modified ICL: Unskilled Labour Trap Removed


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