Public Funding of Higher Education. By Jean-Marie Viaene and Itzhak Zilcha

Transcription

1 Public Funding of Higher Educaion By Jean-Marie Viaene and Izhak Zilcha

2 Main Issues In a hierarchical educaion sysem financed by axes should he governmen subsidize higher educaion? Under free inernaional capial mobiliy how does he exogeneously given ineres rae affec: (a) he allocaion of workers o skilled and unskilled (b) public funds in educaion in wo cases: Governmen decision vs. decision by majoriy voing.

3 The Model We use an OLG model wih heerogeneous households Human capial formaion: via hierarchical educaion sysem ha generaes skilled and unskilled workers Inergeneraional ransfers exis beween parens and heir children Higher educaion is financed privaely and possibly subsidized by public funds Public educaion funds are allocaed eiher by governmen or by majoriy voing

4 Relaed Lieraure Garra and Marshall (994): Public finance of privae goods: The case of college educaion. Driskill and Horowiz (2002): Invesmen in hierarchical human capial. Su, X. (2004): The allocaion of public funds in hierarchical educaion sysem. Blankenau e.al. (2005): Allocaing governmen educaion expendiures across K-2 and college educaion. Blankenau e.al. (2007): Public educaion expendiures, axaion and growh:linking daa o heory.

5 Main Resuls () Higher wage renal raio expands he se of skilled labor. (2) In some cases increasing public funding of higher educaion a dae will reduce oupu in equilibrium a dae bu increase i a all subsequen daes. (3) We may obain cases where he equilibrium wih no-public- funding for higher educaion dominaes he full-public funding equilibrium.

6 Preferences and Hierarchical Educaion Consider an overlapping generaion economy wih a coninuum of consumers in each generaion, each living for hree periods. During he early sage each child is engaged in educaion/raining, bu akes no economic decisions. Individuals are economically acive during he working period which is followed by he reiremen period. A he beginning of he working period, each paren gives birh o one offspring, hence we assume no populaion growh. Each household is characerized by a family name ω [ 0,] where Ω= [ 0,] denoes he se of all families in each generaion. We also denoe by µ he Lebesgue measure on Ω.

7 Innae abiliy of an individual ω, denoed by θ ( ) + ω, is assumed o be random and drawn (a birh) from a ime-independen disribuion. The human capial of individual ω in G, acquired by aending compulsory educaion, depends on parenal inpus as well as school inpus, and i is assumed o be given by he following process: h ( ω) = θ ( ω) h ( ω) X () ν ξ + + where h ( ω ) sands for parens human capial and in early-life and compulsory schooling X represens public invesmen

8 Enrollmen in higher educaion is cosly and, in mos counries, requires he paymen of a uiion fee a each dae, denoed by z and assumed o saisfy: z >. We assume ha he governmen may paricipae in he cos of higher educaion, and hese subsidies are financed by axing wage incomes of he working individuals. Denoe by g he governmen (or public) allocaion o each suden wishing o aain addiional skills via he higher educaion sysems. Thus, z( ω ) = z = z g is he ne paymen ha each individual pays a dae o access higher educaion

9 We assume ha acquiring higher educaion augmens each individual s basic skills by some facor B >. Thus if individual ω invess money z and ime o sudy in he eriary educaion sysem, hen his/her human capial accumulaion process increases o he level: h ( ω) = Bh = B θ ( ω) h ( ω) X ν ξ (2) He/she is hen called a skilled worker. To simplify our analysis (wihou resricing he generaliy) we assume ha B is ime-independen. In conras, if an agen ω does no enroll in higher educaion, his/her human capial is deermined solely by compulsory schooling educaion, hence: h ( ω) = h ( ω) = θ ( ω) h ( ω) X ν ξ (3) We call his agen a low-skilled worker. Insead of aending some higher educaion insiue, following he basic educaion aained, a low-skilled agen works during par of his youh period using basic skills given in (3). We assume ha all low-skilled individuals do work during a porion m ( 0 m <) of heir youh period. Since hey work fully a period + as well, he lifeime afer-ax

10 wage income earned by a low-skilled worker ω is: [ ] ( τ) h ( ω) mw ( + r ) + w where ( + r + ) is he reurn o capial a dae +; w and w + are he wage raes per uni of effecive labor a dae and + respecively. In conras, a skilled worker s afer-ax lifeime wage earnings are: ( τ) Bh ( ω) w + +

11 α α α (A) ( y ) ( o U ( ω) = c ( ω) c ( ω) ) ( y ( ω) ) (4) α+ α2 + α y o Consumpion when young and old is denoed by c ( ω) and c ( ω ) respecively; y ( ) + ω is he offspring s lifeime income. Inergeneraional ransfers ha arise from he alruisic moives represened by (A) ake hree forms.

12 Denoe by b ( ω) he ransfer of physical capial by household ω G o his/her offspring. Given he reurn o capial and wages { r w},, lifeime non-wage income of an offspring, wheher skilled and low-skilled, is ( + r+ ) b( ω). Thus, lifeime income of a low-skilled worker (denoed by l) is: y ( ω) = ( τ) h ( ω) mw ( + r ) + w + ( + r ) b ( ω) l (5) [ ] If he/she is a skilled worker (denoed by s) hen: s (6) y+ = h+ w+ + + r+ b ( ω) ( τ) ( ω) ( ) ( ω)

13 A denoe he subse of individuals in G who are skilled and le A be he complemen of A, namely he se of low-skilled individuals. Hence: (7) H = h ( ω ) dµω ( ) + m h + ( ω ) dµω ( ) ~ A Therefore, governmen ax revenues are simply τ wh where H is defined in (7). On he oher side of is balance shee he governmen faces oal educaion expendiure (in boh sages). Denoe by µ ( A ) he measure of skilled individuals who receive some public funding for higher educaion. Then he governmen budge consrain a dae is: (8) τw[ h( ω ) dµω ( ) + m h + ( ω ) dµω ( )] = X + gµ ( A) ~ A

14 We say ha an educaion policy {( X, g )} is feasible if a each dae : (a) given X and g, he se of skilled A is deermined by each individual's opimal choice and (b) condiion (8) holds in all periods.

15 Compeiive Equilibrium Given K0, H 0, educaion policy {( X, g)} 0 labor { } =, he inernaional prices of capial and r, w, and he ax rae τ, each agen ω a ime wih inergeneraional ransfers b ( ) ω chooses he level of savings s ( ω ) and beques b ( ω ) ogeher wih he financial invesmen in higher educaion z ( ω ), so as o maximize: y o (9) Max U ( ω) = ( c ( ω) ) ( c ( ω) ) ( y ( ω) ) subjec o consrains α α α (0) z ( ω ) = 0 or z ( ω ) = z g () c y ( ω) = y ( ω) s ( ω) b( ω) z ( ω) 0 o (2) c ( ω) = ( + r+ ) s ( ω) 0

16 where y ( ω ) and y ( ) + ω are he corresponding incomes given eiher by (5) or (6), while h ( ) + ω is defined eiher by (2) if z ( ω ) = 0, or by (3) if z ( ω ) = z g. Given K 0, H 0,{( y o c ( ω), c ( ω), s ( ω), b( ω), z ( ω)); w, r} 0 equilibrium if: = is a compeiive (i) For each dae, given facor prices r, w ) and public educaion policy ( {( X, g )} = 0, he opimum under condiions (9)-(2) for household ω wih beques y o b ( ) is ( c ( ω), c ( ω), s ( ω), b( ω), z ( ω)) 0. ω (ii) Given he aggregae producion funcion, he wage rae of effecive labor w is deermined by he marginal produc of (effecive) human capial. (iii) The educaion policy {( X, g )} 0 = is feasible, hence he governmen budge consrain in (8) holds a each dae.

17 y c ( ω) α 3) = y ( ω) α ( + r ) y c ( ω) α (4) = o c ( ω) α 2 ( + r+ ) From (2), (3) and (4): α3 (5) y+ ( ω) = ( + r+ ) s( ω) α 2 (6) [ mw r w ] α ( τ ) ( + ) + b s h ( ω) = ( ω) + ( ω) 0 α2 ( + r + ) α3 ( τ) w + (7) b( ω) = s( ω) h+ ( ω) 0 α ( + r ) 2 +

18 (8) α α ( ) ( ) ( ) + α U y 2 + α 3 ω = Φ r ω Table : Cross-Counry Variaion of he Skilled Work Force a,b OECD Counries Ialy Korea Mexico Neherlands Porugal Turkey Age Group wih a leas Upper Secondary Educaion Parner Counries Brazil Chile Esonia Israel Russian Fed Slovenia Age Group wih a leas Upper Secondary Educaion Noes: (a) The skilled workforce is approximaed by he percenage of he populaion of age group wih a leas upper secondary educaion; (b) In percenage, in Source: OECD (2009, Table A.2A, column )

19 ν Define Z ( ω) = θ ( ω) h( ω) and call i he iniial endowmen of ω. + + Proposiion : Le A denoes he se of individuals who choose o inves in higher educaion a dae. Then: (a) A is nonempy if and only if he following condiion holds: w + m (9) w + r B + (b) Assume ha condiion (9) holds. Define z g Λ = [ ]( ). Then: ξ τ w + X ( B ) mw + r (20) A = { ω Z+ ( ω) Λ } +

20 (A2) Given he exogenous wages and ineres raes, he economy's parameers m and B, condiion (9) holds a all daes, =0,, 2,.. Some monooniciy resuls ha can be verified from condiion (20) are repored in Table 2 and should be inerpreed as follows. Suppose ha a dae an increase occurs in one of he model parameers of he firs row, hen he sign of he comparaive saics of his change on eiher Λ or A is given in each relevan cell. Table 2: Monooniciy Resuls for w + / ( + r+ ) w X z Λ and A g τ B m ξ Λ A

21 Corollary : Under he above assumpions, we obain in equilibrium ha: a higher wage-renal raio w+ / ( + r+ ) a dae + expands he se of skilled agens a ha dae, while a lower wage-renal raio enlarges he se of low-skilled labor. Table 3: Esimaes of Parameer m a,b OECD Counries Ialy Korea Mexico Neherlands Porugal Turkey Ending Age of Compulsory Schooling m Parner Counries Brazil Chile Esonia Israel Russian Fed Slovenia Ending Age of Compulsory Schooling m Noes: (a) Parameer m is compued as he difference beween 24 (he average graduaion age) and he ending age of compulsory schooling divided by 24 (he number of years in he firs generaion); (b) In 2006, wih no change in Source: Auhors own compuaions and OECD (2009, Table C.).

22 Human Capial Formaion (A3) B > +m holds. Proposiion 2: Under he condiion assumed in (A3), oupu declines a he curren dae bu expands in all subsequen periods + k, k, in each of he following wo cases aking place a dae : (a) An unexpeced increase in he wage-renal raio; (b) A echnological progress in he educaion secor (higher B or higher ξ ). Lemma : Under he condiion assumed in (A3), expanding he se A a dae resuls in a lower H bu a higher H + kfor all k.

23 The Value of Public Funding of Higher Educaion ( g z ) represens he share of privae invesmen Table 4: Privae Funding of Teriary Educaion a,b,c OECD Counries Ialy Korea Mexico Neherlands Porugal Turkey Privae Funding g z Parner Counries Brazil Chile Esonia Israel Russian Fed Slovenia Privae Funding g z Noes: (a) Privae funding of eriary educaion as a percenage of oal eriary expendiure; (b) In 2006; (c) - indicaes no available. Source: OECD (2009, Table B3.2b)

24 Denoe by γ,0 γ, he fracion of governmen revenues a dae allocaed o compulsory schooling. Then: (2) X = γτwh (22) g µ ( A ) = ( γ ) τwh Wihγ =, public funding of higher educaion is zero ( g = 0 ) and eriary educaion is fully privaely financed. Wih Using he above equaions: g = z, higher educaion is fully publicly financed. (23) ( z ) z ( ) wh / ( A) g γ τ µ = X ξ ( τγ wh ) ξ

25 (24a) ξ (( z g ) / X ) ξ = X ( ) z g + ξ ξ γ γ ( ) ( A ) τwh ξµ >0 X µ ( A)( z g )> ξ Namely, he parial derivaive is posiive as long as X µ ( A)( z g )> ξ. This condiion holds generally since (i) per-suden public expendiure on compulsory schooling X is higher han per-suden privae expendiure on higher educaion, and (ii) µ ( ) < (less han 0.5 in many economies) and ξ <. Using hese ( z g) A observaions, we obain a posiive effec of increasing he funding of compulsory schooling on he hreshold parameer Λ when he governmen budge is balanced: (24b) δ ( Λ ) > 0 δγ

26 Proposiion 3: Assume ha X µ ( A) z > ξ holds a some period. Increasing he public funding of higher educaion g leads in equilibrium o: (i) a larger se of skilled agens a dae +; (ii) a lower oal expendiure on educaion a dae ; (iii)a lower sock of human capial H used in producion a dae. Corollary 2: In equilibrium wih balanced budge he opporuniy cos of increasing resources in favour of higher educaion is larger han uniy. The reason is ha some unskilled workers who previously conribued o ax revenues now become users of higher educaion subsidies o become skilled.

27 Dynamic Analysis Now le us consider he effec of increasing public funding of higher educaion o enhance he formaion of skilled labor (along a feasible educaion program). Consider he case where he governmen proposes wo policies: eiher no public funding, i.e. g = g = 0, or he long-run policy { } 0, which guaranees a each dae he persuden funding a a posiive level g. A dae, le he se of families who op for a skilled child under he no funding policy be defined by: (25) A z { ( ) { } } 0 0 = ω Z+ ω =Λ ξ ( τ)( B ) w + m [ w ] [ τwh ] + r + B

28 Le us denoe he se of families a period who op for a skilled child under he 'per-suden public funding g ' policy by: (26) A z g { ( ) { } } = ω Z+ ω =Λ ξ ( τ )( B ) w [ + m w ] X + r + ( B ) Le us rewrie he aggregae human capial of generaion +: H h ( ω ) dµω ( ) X [ B Z ( ω ) dµω ( ) Z ( ω ) dµω ( )] ξ (27) + = + = A ~ A

29 Proposiion 4: Assume ha iniially here is no governmen inervenion in financing higher educaion. Inroducing public funding of higher educaion a he levels { } 0 g = varies he corresponding hreshold levels from Λ o { Λ }. Define: 0 { } (28) Λ =Λ 0 ( d ), for =,2,. If d g z holds for all, hen he inroducion of such public funding policy increases he sock of human capial a all daes; namely, H 0 < H holds for all. The Possibiliy of Inefficiency of Public Funding Proposiion 4 has implicaions for economic growh. The human capial accumulaion resuling from he public funding of higher educaion is expeced o increase domesic marginal reurns o physical capial and, hence, generae a foreign inflow of physical capial. The increase in boh primary inpus will increase oupu. Bu does his oucome jusify he diversion of public funds o finance higher educaion?

30 To subsaniae he asserion ha sociey as a whole is no always beer off when some public funds are used o finance higher educaion, consider he compeiive equilibrium from some iniial condiions of his economy and a given feasible educaion policy {( X, g )}. The ne value of labor a dae, denoed by W ( X, g ), is defined as: W ( X, g ) = [ mw + w ] θ ( ω) h ( ω) X + Bw θ ( ω) h ( ω ) X g µ ( A) ν ξ ν ξ ~ A A

31 Given some iniial condiions a =0, we say ha a feasible educaion policy X g dominaes anoher feasible educaion policy {( X, g )} if a any dae, {(, )} swiching from ( X, g ) o (, ) X g is desirable in he following sense: (a) (, ) > (, ). W X g W X g (b) A each dae k, k>, if he governmen has o choose beween hese wo educaion policies, hen ( k, k) X g will have a higher ne value of labor, i.e., W X g > W X g. k( k, k) k( k, k)

32 Proposiion 5: Assume ha he following wo condiions hold: 0 (29) X z > ξ for all daes, and (30) ξ 0 [ τ ], for all daes. B z wh Then, he no-public funding policy dominaes he full-public funding policy.

33 Poliical Equilibrium In economies wih heerogeneous agens, he choice of an opimal γ can be deermined via he oucome of some poliical process a each dae. I is possible o esablish a mapping beween he se of heerogeneous agens, given heir preferences regarding educaion, and an opimal educaion policy deermined by majoriy voing. Economies a differen sages of developmen, wih a differen composiion of he labor force beween skilled and low-skilled workers, are hen expeced o reach differen poliical equilibria regarding his educaional budge allocaion. Table 5: Public Expendiure on Teriary Educaion a,b OECD Counries ( γ ) Parner Counries ( γ ) Ialy Korea Mexico Neherlands Porugal Turkey Brazil Chile Esonia Israel Russian Fed Slovenia Noes: (a) As a percenage of oal public expendiure on educaion; (b) In Source: Auhors own calculaions based on OECD (2009, Table B4.)

34 l α3 ( τ)( w + + mw ( + r ) + ξ ξ ξ ξ y+ ( ω) = ( + r+ ) Z+ ( ωγ ) τ wh + y( ω) α α2 α ( + r + ) s α3 ( τ) w ( ) ( ) ( ) + ξ ξ ξ ξ γ y r BZ ( ) w H y( ) z + ω = ωγ τ + ω + τwh α+ α2 + α 3 ( + r+ ) µ ( A) Assume now ha each individual voes eiher for no public funding, i.e., g = 0, or for public funding a level g = g. The choice will be deermined by comparing he income of his/her offspring under hese wo policies; namely, given Z+ ( ω ) we l compare y + ( ω ) s under g = 0 o y + ( ω ) under g = g. Denoe by γ he fracion of he educaion budge assigned o compulsory schooling when higher educaion is publicly funded wih g = g. The condiion ha deermines voing in suppor of g = g is given by: ( τ ) + r + r τ w + BZ ( )[ w H ξ + ω τ γ)] z g y ( ω) ω τ + + ξ [ ] [ w+ mw( r+ ] Z+ ( )[ wh ] y( ) ω

35 Rearranging erms implies: where Z + ( ω ) v, (3) v = ξ τ ξ w + B γ ( τ ) + r + ( z g)[ wh ] [( ( ) ) mw ] Like Λ in Proposiion, v in (3) is anoher hreshold ha pariions he disribuion of endowmens, namely beween hose who favour public funding for higher educaion a level g= g versus hose in favour of he alernaive policy 0 g =. Namely, all voers whose endowmen is such ha Z+ ( ω ) v will voe in favour of public funding, all ohers will voe agains.

36 The hreshold v is anoher channel hrough which inernaional marke condiions affec he educaion sysem. () a higher wage/renal raio a he nex period (resuling from globalizaion and liberalizaion of capial markes) implies a larger group of individuals who suppor g = g (2) In a sociey endowed wih a larger sock of human capial H more people suppor larger public resources be allocaed o higher educaion; (3) As public educaion expendiures ( τ wh ) increase more individuals suppor an increase in resources for higher educaion; (4) A lower value of m or larger value of ξ imply more suppor for he policy g = g. Again, i is noable ha v does no depend on he inensiy of alruism.

37 Corollary 3: Some of he agens who voed agains insiuing public funding for higher educaion will inves in higher educaion when public funding is provided. Corollary 4: Some of he households who did no inves in higher educaion under he no-public funding regime will inves in higher educaion when public funding is provided. Majoriy Voing In order o reach a poliical equilibrium, wha maers is o know he relaive posiion of he median voer in he disribuion of iniial endowmens. Le 'M' denoe he median voer and le Z ( M) = θ ( M) h( M) ν be his/her iniial endowmen. Hence: + + Proposiion 6: When he allocaion of resources invesed in public educaion is deermined by a poliical equilibrium, applying he Median Voer heorem implies ha public funding is approved, i.e., g = g, if and only if Z ( M ) v +. Thus he shape of he disribuion of endowmens in generaion maers for he deerminaion of he equilibrium.