The Design of a University System Gianni De Fraja University of Leicester, Università di Roma Tor Vergata and CEPR Paola Valbonesi Università di Padova Public Economics UK 27 May 2011 Abstract This paper studies a general equilibrium model suitable to compare the organisation of the university sector under private provision with the structure which would be chosen by a welfare maximising government. To attend university, and earn higher incomes in the labour market, students pay a tuition fee, and each university chooses its tuition fee to maximise the amount of resources that can be devoted to research. Research bestows an externality on society; government intervention increases needs to balance labour market efficiency consideration -- which would tend to equalise the number of students attending each university --, with efficiency considerations, which suggest that the most productive universities should teach more students and carry out more research.
A penny for your thoughts on what are universities for? teaching and research? research only? university technology are teaching and research complements or substitutes? how would you organise the university sector? concentrate them relative to market? have many geographically spread? separate teaching from research? teaching only universities? research only universities?
wide variety of system designs: UK vs. Italy 1 0.75 0.5 0.25 0 0 0.25 0.5 0.75 1 Cumulative proportion of research funding as a function of the cumulative proportion of total funding to state sector universities in UK (2009; blue line) and in Italy (2005; incentive proportion only, pink line) Source: HEFCE (UK), and MIUR (Italy).
wide variety of system designs: private vs. public State Sector Private Sector Average Size of University in the State Percentage of PhD degrees over the Total number of Degrees awarded (excluding 2-year and professional degrees) Source: IES, National Centre for Education Statistics, 2008.
the paper I the model assumptions student behaviour II the private market monopolistic competition III government intervention information disadvantage vis-à-vis universities optimal control technique instruments constraints objective function interpretation of the solution implementation in practice IV comparisons private market outcome perfect information first best outcome V possible extensions
the model general equilibrium model universities have different efficiency capacity constraints/student mobility limit competition static model intertemporal funding issues are ignored
the model universities a potential university in each local education market continuum of local education markets separated students must attend local university (if any) university is characterised by a productivity parameter ( ] 0, > 1 f ( ) = F ( ) F( ) = 1 d ( 1 ) d ( ) ( ) f F < 0
the model universities a potential university in each local education market universities do teaching and research budget t 0 r 0 t n = + r no economies of scale or scope pt + g = yn objective function r research only revenues = salary costs type university employing n professors can do n units of research or teaching
the model students a continuum of students in each local education market cost of going to university tuition fee effort a p( ) with [ ] a min, a max ( a) = Φ ( a) a d Φ( a) φ da ( ) > 0 φ ( a)
the model students all students acquire education and join the s (degree necessary) and unskilled benefit of going to university students with university education: skilled labour market y students with basic education only: unskilled labour market y Δ
the model students education choices y Δ 0 amin Δ p( ) a max a y p( ) a hard working students: with low cost of effort lazy students: high cost of effort
analysis I private provision University of type maximises: Proposition University of type enrols y Z 1 Δ students 1 Proof f.o.c.: Z () t 1 = Δ y Z 1 ( t) Δ y lower 0 t
analysis I private provision Proposition University of type enrols y Z 1 Δ students 1 dt d dp < 0 d dr > 0 d dn > 0 d Corollary We have: > 0 economies of scale and of scope endogenously determined unobserved productivity parameter
analysis II public provision government does not know the type of each university government does not observe research at each university government does observe each university s total cost government maximises total utility + social value of research ωr increase in GDP universities utility prestige
analysis II public provision use revelation principle ask each university to reveal its productivity commit to a policy as a function of the report it is not possible to increase payoff relative to the best policy which ensures truth-telling
analysis II instruments t( ) p( ) r( ) g( ) number of students at university of type tuition fee at university of type amount of research at university of type grant to university of type R h total amount of research per capita (and total) tax h < y Δ lowest type university allowed to be active
analysis II constraints Incentive compatibility constraint Proposition r ( ) = p ( t( )) t( ) + g( ) y t ( ) 0 students demand constraint t( ) = Φ( Δ p( ) )
analysis II constraints university budget constraint ( ) + t( ) r y = p + ( ) t( ) g( ) positive number of students t( ) [ 0,1]
analysis II government objective function payoff from university y Δ h + 1 ( t( )) ( Δ p( )) t( ) aφ( a) sum for all universities and add social value of research ( t( )) ( Δ p( )) t( ) aφ( a) Φ 1 a min da Φ a min da ( 1+ λ) g( ) f ( ) d + y ΔF( ) + ωr
analysis II problem t max ( ), r( ), p( ) g ( ), R, subject to:, 1 ( t( )) ( Δ p( )) t( ) aφ( a) r ( ) = p Φ a min ( t( )) t( ) + g( ) y da ( 1+ λ) g( ) f ( ) d + y + ΔF( ) r ( ) = 0 r( ) free t ( ) Φ( Δ p( ) ) ( ) + t( ) r y = p + ( ) f ( ) R = r d ( ) t( ) g( ) t ( ) [ 0,1] t ( ) 0
analysis II solution Let
analysis II solution Proposition Let If a solution to the government s problem exists then it is t, r, p given by ( ) ( ) ( )
analysis II implementation total funding depends on student number (fee) y( R) T ( t) T () t = t ( ) F F T F t Corollary: T F ( t) Menu of contracts. is concave. t
analysis II solution with perfect information:
analysis II solution government s subsidy:
analysis II solution graphical analysis research as a function of productivity r max r( ) symmetric information asymmetric information government intervention private market 0 ( 1+λ ) y ω with symmetric information separate teaching and research
analysis II solution if total research is the same Efficiency at the top: asymmetry of information does not reduce number of students for the best university; with private provision each active university has fewer students than with a perfectly informed government; the government information disadvantage reduces the number of students at each university except the most productive. the universities active with private provision are the same that a perfectly informed government would allow to operate; the government information disadvantage reduces the number of active universities;
analysis II if total research is the same compared with private provision, government intervention concentrates students in the most productive institutions: the higher (lower) productivity institutions have more (fewer) students than they would in a private system. t( ) symmetric information asymmetric information government intervention private market 0
analysis II
analysis III extensions Quality dependant earnings. what if earnings depend on? linear utility? exogenous shadow cost of public funds? concave utility function implies a strictly positive shadow cost of public funds Demand variability what if students can move?
analysis III extensions one result we get is that better universities charge less peer group earnings depend on ability and peer group complementarities: y( R, a, a ) y aa ( ) > 0 more productive university can, ceteris paribus, charge more more able students will be more willing to pay more higher universities charge more, attract higher ability students and do more research
analysis IV endogenous Time is divided in periods universities are long lived workers live two periods - period 1: receive education - period 2: they are hired by employers - cannot change job until they retire. so: universities - train people in their first period of life - employ (some) people in their second period of life.
analysis IV endogenous A Let F describe the distribution of workers a at a university Let be a function Θ A Θ : F, [ 0 + ) associating distribution to quality e.g.: average quality of staff Θ A ( F ) = ( a) ( a) A adf = A df F adf A A( a) ( a max )
analysis IV endogenous stylised hiring process workers arrive randomly (sequentially) and a university must hire all that arrive until it stops at any point the university may decide to close down and dismiss all its workers.
analysis IV endogenous n( ) easy to have history dependence A [ 0, + ) F [ 0 + ) Θ :,
Conclusion designing a system from scratch more spread in size than private market would give no teaching only universities no research only universities (even if you would like) the second best system is a compromise between the first best and private provision.