Ruhr Economic Papers. Wolfram F. Richter. The Double Dividend of Taxing Nonqualified Labour More Heavily Than Qualified Labour #12

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1 Wofram F. Ricter Te Doube Dividend of Taxing Nonquaified Labour More Heaviy Tan Quaified Labour #12 Rur Economic Papers

2 Rur Economic Papers Pubised by Rur-Universität Bocum (RUB), Department of Economics Universitätsstraße 150, Bocum, Germany Universität Dortmund, Department of Economic and Socia Sciences Vogepotsweg 87, Dortmund, Germany Universität Duisburg-Essen, Department of Economics Universitätsstraße 12, Essen, Germany Reinisc-Westfäisces Institut für Wirtscaftsforscung (RWI Essen) Hoenzoernstrasse 1/3, Essen, Germany Editors: Prof. Dr. Justus Haucap RUB, Department of Economics Competition Poicy and Industria Economics Pone: +49 (0) 234/ , e-mai: Prof. Dr. Wofgang Leininger University of Dortmund, Department of Economic and Socia Sciences Economics Microeconomics Pone: +49 (0) 231 / , emai: Prof. Dr. Voker Causen University of Duisburg-Essen, Department of Economics Internationa Economics Pone: +49 (0) 201/ , e-mai: Prof. Dr. Cristop M. Scmidt RWI Essen Pone: +49 (0) 201/ , e-mai: Editoria Office: Joacim Scmidt RWI Essen, Pone: +49 (0) 201/ , e-mai: Rur Economic Papers #12 Responsibe Editor: Wofgang Leininger A rigts reserved. Bocum, Dortmund, Duisburg, Essen, Germany, 2007 ISSN (onine) ISBN Te working papers pubised in te Series constitute work in progress circuated to stimuate discussion and critica comments. Views expressed represent excusivey te autors own opinions and do not necessariy refect tose of te editors.

3 Rur Economic Papers #12 Wofram F. Ricter

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5 Wofram F. Ricter* Taxing Human Capita Efficienty Te Doube Dividend of Taxing Nonquaified Labour More Heaviy Tan Quaified Labour Abstract Assuming isoeastic returns to education and an endogenous suppy of quaified and nonquaified abour, it is sown to be second-best efficient not to distort te coice of education. Furtermore, taxation soud set incentives so tat quaified abour is substituted for nonquaified abour. As a resut, it is efficient to tax abour income regressivey wit respect to quaification and to tax te monetary cost of education at a eve tat restores efficiency in education. A tax on capita income aeviates te distortion tat progressive taxation of abour income exerts on uman-capita investment. JEL Cassification: H21, I28, J24 Keywords: Endogenous coice of education and abour, efficient taxation of uman and nonuman capita, doube-dividend ypotesis May 2007 *Wofram F. Ricter, University of Dortmund, Department of Economics, Dortmund, Germany; pone: , fax: -5404, e-mai: Wofram.Ricter@uni-dortmund.de,

6 4 1. Introduction Human-capita accumuation is expected to be te driving engine of economic growt and deveopment in te new century. Hence uman-capita poicy soud be igy ranked on te agenda. Unfortunatey, te economic understanding of optima umancapita poicy is sti in its infancy. In particuar, an integrated approac is sti acking wic aows one to cope wit te various sources of tax distortions and market faiure. Economic anaysis is rater ecectic in tis fied. Te ist of issues researced is ong. It covers reasons of potentia market faiure suc as positive externa effects of education, incompete markets for educationa oans, and missing private opportunities to insure against educationa risks. It extends to issues raised by distortionary taxation and incudes key words suc as income uncertainty (Eaton and Rosen, 1980; Varian, 1980), informationa asymmetry (Mirrees, 1971), credibiity of government poicy (Boadway et a., 1996; Andersson and Konrad, 2003), and asymmetric income taxation of uman and pysica capita (Heckman, 1976; Nerove et a., 1993; Niesen and Sörensen, 1997), to mention just a few prominent ones. One of te areas were systematic anaysis as ony begun is tat of te imperfect taxation of rent income generated by te endogenous coice of education. Te anaysis as been triggered off by some numerica simuations carried troug by Troste (1993) on te basis of a representative-agent genera-equiibrium mode. Tis study finds a significant negative effect of proportiona income taxation on uman capita. By means of furter simuation experiments, Troste (1996) sows tat it is secondbest efficient to suppement an income tax wit a subsidy to iger education. In independent teoretica studies Wigger (2003 and 2004) and Bovenberg and Jacobs (2005) ook more cosey at te question of wen educationa subsidies are efficiencyenancing. Tese studies differ from Troste (1996) and te present one in te attempt to integrate two sources of imperfections in one singe mode: te imperfect taxation of rent income generated by education, and te imperfect taxation of rent income generated by informationa asymmetry in te Mirrees tradition. Atoug simiar in design, te studies suggest strikingy different concusions. Wereas Bovenberg and Jacobs (2005) find strong teoretica evidence for subsidizing uman-capita

7 5 investment, Wigger (2004) proves tat socia wefare can never be increased by suppementing a noninear income tax wit a subsidy to iger education. Te concusions raise te question ess of wo is rigt or wrong tan of wic modeing features are abe to expain suc contradictory resuts. Tis is were te present paper ties in. It offers a simpe framework of anaysis wic aows one to give structure to a strand of iterature wic treatens to become more and more confusing. It does so by going one step back in te iterature and returning to te isoated anaysis of te effects tat te imperfect taxation of abiity rents as on efficient uman-capita poicy. It is te autor s strong beief tat tese effects ave not been we understood ti now and tat tey are of key importance for te design of optima uman-capita poicy. Te paper is structured as foows. Section 2 sets up a simpe mode of a representative taxpayer, wit te ony endogenous coices concerning education and abour suppy. Returns to education are decreasing and are te source of rent income, wic cannot be fuy skimmed off by a proportiona tax on consumption. As a resut, te production efficiency teorem of Diamond and Mirrees (1971) is not appicabe. Section 3 introduces poicy instruments and te panner s objective function. In Section 4 it is sown to be efficient not to distort educationa decisions. Ony distortions in te suppy of abour soud be toerated. Te resut is iustrated by means of an exampe in Section 5. Section 6 derives te resut tat it is second-best efficient to tax abour income regressivey wit respect to quaification and to restore efficiency in education by taxing its monetary cost. If regressive abour taxation is poiticay not feasibe, tis eads us to study tird-best poicies. Options are discussed in Section 7. Section 8 deas wit te question to wat extent education subsidies are needed to enance efficiency. Section 9 igigts te confict between distributive equity and efficiency in education. Section 10 summarizes. Major proofs are reegated to a tecnica Appendix. 2. A representative ouseod mode Consider a representative ouseod wic as to coose between suppying nonquaified and quaified abour, L and L, respectivey. Te ouseod derives

8 6 utiity U C, L, L ) from consumption C and te two differentiated forms of abour. ( Nonquaified abour as to be divided between time spent in te market, L E, and time spent on education, E. It earns a constant wage rate if suppied to te market. Te productivity of quaified abour depends on te amount of education. Te coice of E is part of te ouseod s optimization probem. Quaified abour is paid H (E), were is constant wie te earnings function H(E) dispays positive but diminising returns, H >0>H. It is we known tat te aggregate empirica earnings function tends to be og-inear wit increasing returns in E. Te focus of te present anaysis is owever on te individua coice of education, and tus diminising returns are more pausibe. Te representative ouseod is assumed to maximize utiity in C, L, L te budget constraint, E subject to qc ( L E) H ( E) L E L H ( E) L ( E. ) Education as a cost in forgone earnings, wic is captured by E. Monetary costs of education ike coege fees come on top of tese and are modeed by E. Te effective (unit) cost of education is given by. Finay, q is te consumer price of consumption. A prices are after tax and subsidy, and te question is wic combination of taxes and subsidies is second-best efficient. It must be stressed tat te mode assumes two separate time constraints, one for nonquaified abour and one for quaified abour. A more structured mode woud ave to differentiate between two expicit ifetime periods, wit te ouseod providing nonquaified abour wen young and quaified abour wen od (Bovenberg and Jacobs, 2001). Not to differentiate consumption C impicity requires utiity of consumption to be omotetic and weaky separabe from eisure. Te anaysis reies on te dua approac to optima taxation. Tis means tat te focus is sifted from te ouseod s (indirect) utiity function to its (net) expenditure function. Te task of minimizing (net) expenditures subject to an exogenous utiity constraint is best soved in a two-step approac. At te first step rent income derived from education is maximized wie keeping te eve of quaified abour suppy, L,

9 7 fixed. Let rent income be denoted by Y (,, L ) max[ H ( E) L E], and te optima amount of education by E,, L ). Note tat te primary source of rent ( income is education and its diminising return. Te quaified-abour suppy increases rent income ony indirecty via increased incentives for education. Let te socia cost of quaified abour be denoted by, and te effective socia cost of education by p. w Ceary, E(,, L ) E( w, p, L ) ods if / p / w. In wat foows / p / is interpreted as te condition guaranteeing an efficient coice of w education reative to te given vaue of efficiency in education wenever / p / ods. L E. For te sake of brevity, we refer simpy to w Te expenditure function is defined as e( q,,, ; u) min[ qc L Y (,, L )] in C, L, L suc tat U ( C, L, L ) u. Hoteing s emma yieds e q C, were C C( q,,, ; u) soves te optimization and were te subscript q denotes a partia derivative. One ikewise derives te e identities e =E and e ( L E). Just ike C, te functions L and L are Hicksian ones to be evauated at q,,, and u. As a resut, te fuy specified, education function reads E E(,, L ( q,,, ; u)). 3. Poicy instruments Te anaysis studies te efficient mix of tree poicy instruments. Te caracteristic of te bencmark regime is tat consumption is taxed. As it turns out, it is convenient to define te tax rate t in incusive form. Treating consumption as a numéraire good wit a producer price of one, tis means tat t satisfies te condition q(1t) = 1. In oter words, te base of te consumption tax incudes te tax payment. Te second instrument is a tax on nonquaified abour. It is convenient to define tis tax in

10 8 excusive form. Tis requires w ( 1 ), were stands for te wage rate before tax. In te bencmark regime, quaified abour is assumed to remain untaxed: w. Given tat consumption is taxabe, noting is gained by introducing a tax on quaified abour. It woud ony provide a redundant instrument wic coud be dupicated by an appropriate coice of te tree oter poicy instruments. If quaifiedabour income remains untaxed, a negative (positive) can be interpreted as impying progressive (regressive) taxation of abour income. Te tird and fina instrument is a subsidy to education, s. Tis is again defined in excusive form, requiring f ( 1 s), were f is te monetary socia cost of education. A socia costs, w, w, and f, are treated as exogenous parameters of te panner s optimization. Tere is a need to raise tax revenue in order to finance exogenous government expenditures. Government s net tax revenue amounts to w t s T C w ( L E) 1 t 1 1 s fe. By invoking Hoteing s emma, tis can be written as T = ( q 1) e ( w ) e ( f e. (1) q ) Te socia panner is assumed to maximize tax revenue T subject to te condition tat private net expenditure remains constant at zero eve, e=0. A set of instruments t,, and s is said to be second-best efficient if it soves te panner s maximization probem. As it turns out, te effective subsidy to te cost of education wi pay a key roe in caracterizing efficient poicy. Te effective subsidy is denoted by and defined by ( 1 ) / p / w ( w f ) / w. As w f 1 1 s ods by definition, efficiency in education ods in te bencmark regime wit w if, and ony if, =0 s f 1 s w. (2) 1

11 9 Efficiency in education ence requires subsidizing (taxing) te monetary cost of education if abour income is taxed progressivey (regressivey) wit respect to quaification. 4. Efficient education poicy Maximizing government s net tax revenue T in t,, and s, subject to a baancedbudget constraint on te taxpayer (e=0), yieds a probem tat can easiy be soved by appying standard Lagrangian tecnique. Maximizing in t,, and s is obviousy equivaent to maximizing in q,, and. After taking partia derivatives wit respect to q, and after eiminating te Lagrange mutipier, one ends up wit a system of, two first-order conditions: e q eq ( q 1) = e e e qq eq ( q 1) = eq e e e ( w ) + e e e eq ( w ) + e eq e e ( f ), (3) e e e e q ( f ). (4) e eq Tis system is best restated in a form tat admits interpretation in te spirit of Ramsey. For tis purpose define te derivation operator to be appied to functions X X ( q,, ; u) as foows: X ( q 1) X q ( w ) X ( f ) X. (5) Making use of te -notation, it is sown in te Appendix tat te system of equations (3) and (4) can be transformed and restated in equivaent form: L L E, (6) E C E. (7) C E

12 10 Tis sows tat efficiency is acieved if te poicy induces equiproportionate reductions in consumption C, education E, and nonquaified abour beavioura functions are interpreted in te Hicksian sense. L wen a tese Proposition 1: Efficient poicy requires equiproportionate reductions in consumption, education, and nonquaified abour. It is informative to restate (6) and (7) in sti anoter form by making use of easticities denoted by X / x = x X X : x t ) = ) + s ), (6) ( L / q E / q ( L / E / ( L / E / t ) = ) + s ). (7) ( C / q E / q ( C / E / ( C / E / Tis form draws attention to te question of wic vaues te poicy instruments t,, and s soud take on in te optimum. A remarkaby strong resut is obtained if te individua earnings function is assumed to be isoeastic in education: H ( E) E, 1. Proposition 2: If te individua earnings function is isoeastic, it is efficient not to distort te coice of education: =0. Te proof is given in te Appendix. Te generaity of Proposition 2 is striking. Beyond te standard reguarity assumptions of ouseod optimization, tere are no additiona ones needed to constrain te coice of utiity functions. However, isoeasticity of te individua earnings function is indispensabe. It is needed to prove te foowing remark, of wic te proof of Proposition 2 makes eavy use. Te proof is again reegated to te Appendix.

13 11 Remark 1: Assuming H ( E) E, 1, one obtains Y / q = E / q and Y / x = E / x + x for x,. (8) According to te remark, isoeasticity of H aows one to transate reative canges in education into reative canges in te rent income of education according to te stated simpe formuae. Proposition 2 is strongy suggestive of a resut derived by Bovenberg and Jacobs (2005) and by Jacobs and Bovenberg (2006). Tese autors equay identify circumstances under wic te coice of education soud remain undistorted. Tere are notabe differences, owever. Bovenberg and Jacobs focus on te optima trade-off between equity and efficiency wen ski formation is endogenous, and tey enarge te set of poicy instruments by assuming tat a po tax is avaiabe. In substituting te equity objective for te objective of generating tax revenue, teir anaysis goes beyond te present one. On te oter and, tese autors are ony abe to derive efficiency of education for a scenario in wic te costs of education are purey monetary ones. Costs of forgone earnings are rued out. It is as if nonquaified abour were exogenousy fixed. As a resut, education E degenerates to an intermediate good and in contrast to te autors own suggestions in Jacobs et a. (2006) te production efficiency teorem of Diamond and Mirrees (1971) appies. Tis is different ere. Proposition 2 ods for costs of forgone earnings and ence for a scenario for wic Bovenberg and Jacobs fai to derive any efficiency resut. Te anaysis of Bovenberg and Jacobs seems to suggest tat Proposition 2 is muc ess robust tan te production efficiency teorem. Te proposition ods ere were te government is assumed to meet fisca needs, wie it apparenty does not extend to te setting integrating an equity objective. Tis kind of concusion gains support from Bovenberg and Jacobs (2001). Tat paper is an earier version of Bovenberg and Jacobs (2005), and it comes coser to te present anaysis by additionay modeing forgone earnings. Te paper sows tat it is not optima to eave education undistorted if individuas differ wit respect to te productivity of quaified abour, w, and if L

14 12 efficiency as to be traded off against equity. In Section 9 it is owever argued tat tis may not be te end of te story. Tere is evidence tat redistributive poicy just needs we-designed instruments, and if tese are avaiabe, Proposition 2 is conjectured to survive. Proposition 2 requires setting =0. According to (2) tis can be ensured by eiter subsidizing te monetary cost of education and taxing abour income progressivey wit respect to quaification or by doing just te reverse, i.e., by taxing te monetary cost of education and taxing abour income regressivey. Te former strategy is ceary te more conventiona one, found trougout te word. It wi be sown next tat te competing strategy is more efficient. Tis wi first be sown by means of an exampe. 5. An Exampe Assume quasi-inear utiity, U C V L ) V ( L ), equay eastic disutiity of abour, ( 1 V ( L) L, 1, and isoeastic returns from education, H ( E) E, <1. It turns out tat te probem is we beaved ony in te sense tat conditions of second order are fufied if < 1. Te specific appea of tis exampe comes from vanising income effects. Maximizing te ouseod s utiity yieds te foowing conditions of first order: '( L ) q V, H ( E) V '( L ), and H '( E) L. Soving tese q equations for L, L E yieds, 1 1 q E [ a ], q 1 L a, and q 1 E L a wit q 1 a ( ) 1. Tis impies te foowing easticities: L / q ( 1), / 1 L, 1 1 E / q, E / x x 1 1 for x,. Pugging tese vaues into (6) and setting =0 yieds t. 1

15 13 Hence it is efficient to tax nonquaified abour, >0, if consumption is taxed as we, t>0. Furtermore, increases in t and in te easticities of te individua earnings function and te disutiity of abour. Te foowing section is an attempt to generaize te efficiency resut concerning positivity of. Before proceeding, note tat is a function of te consumption tax rate and independent of te wage rates w i (i=,). Tis wi be interpreted beow as evidence tat Proposition 2 may we extend to a setting were te government targets an equity objective. More precisey, te panner wi not trade off equity against efficiency in education if te necessary poicy instruments are avaiabe. 6. Te doube dividend of taxing abour income regressivey According to Proposition 2, efficient poicy soud refrain from distorting umancapita investment. In more tecnica terms, wen setting t,, and s, te panner soud respect =0 w f p as a constraint. On substituting p, te expenditure function takes te form e( q,, ; u) min[ qc L Y (, p, L )] in C, L, L suc tat U ( C, L, L ) u. In tis case, Hoteing s emma yieds e q C and e L, so tat te government s tax revenue can be written as t s T = C w ( L E) 1 t 1 1 s fe = ( q 1) C ( w )( L E) ( f E ) = ( q 1) C ( w ) L ( p E = ( q 1) eq ( w ) e q ). Consider a margina cange in wen starting from w 0. Te cange is compensated in q subject to te baanced-budget constraint e=0. Te atter impies dq e. Te effect tat suc a margina reform as on government revenue is d e captured by

16 14 dt d w T T dq [ ] q d w T e T [ ] e q q w e ( [ eq ( q 1) eqq] e = q 1) e q e q = eq e ( q 1)e e e qq q q 1 q = L [ C q - q ]. L Te bracketed expression on te RHS is negative if, and ony if, te direct effect tat a cange in q as on consumption is stronger tan te indirect effect tat q as on te suppy of nonquaified abour: < q. (A1) C q L Te assumption (A1) ods if te demand for consumption and nonquaified eisure is not too substitutiona. (A1) fais to od if nonquaified abour reacts strongy and negativey to an increase in q, i.e., if nonquaified eisure reacts strongy and positivey to an increase in q. For constant utiity te atter is conceivabe ony if bot consumption and nonquaified eisure decrease in q. If, instead, te demand for consumption is compementary to nonquaified eisure, ten te RHS is positive wie te LHS is negative, and (A1) ods triviay. Proposition 3: Assume (A1), and consider a margina tax on nonquaified abour wic is compensated by a decrease in te consumption tax and by a margina tax on te monetary cost of education wic restores efficiency in education. Suc a reform enances efficiency. Consider a scenario in wic consumption remains untaxed and in wic quaified abour is taxed instead at te rate. One way of subsidizing education is by granting tax deductibiity to monetary costs. Te question ten arises at wat rate and to wat

17 15 extent deductibiity soud be granted. Coroary 1 provides an answer. Te coice of education remains undistorted if p w p /(1 ) w /(1 ). s Under suc circumstances = impies s. Coroary 1: Assume (A1) and a tax on nonquaified-abour income wic marginay exceeds te tax on quaified abour. Efficiency is enanced if te effective cost of education is subsidized at te eve of. Tis requires setting s<. In oter words, it is efficient not to grant fu tax deductibiity to te monetary cost of education. Of te two options (i) subsidizing te monetary cost of education and taxing abour income progressivey and (ii) taxing te monetary cost of education and taxing abour income regressivey, te atter tends to be te more efficient poicy. Te intuition is straigtforward, and tere is a strong parae wit te doube-dividend ypotesis (in weak form) known from environmenta taxation (Gouder, 1995; Bovenberg and de Mooij, 1994). According to tis ypotesis, it is more efficient to encourage sociay desirabe beaviour by taxing non-compiance tan by subsidizing compiance. By taxing non-compiance, wic means suppying nonquaified abour to te market in te present framework, tax revenue is increased, wic aows one to decrease te overa eve of distorting taxes. Te competing poicy woud mean subsidizing compiance in te form of education, wic owever requires increasing revenue via distorting taxes. By taxing nonquaified abour income more eaviy, te ouseod is induced to reduce L E and to increase E. Note owever tat tis sift in te use of time is not induced by subsidizing te monetary cost of education, but by giving incentives to

18 16 substitute quaified abour for nonquaified abour. By setting incentives to increase L at te cost of L, incentives to increase E are given indirecty. 7. Tird-best poicies Poicy makers wi find it itte appeaing to tax abour income regressivey wit respect to quaification. Te confict wit equity is obvious. Hence a natura question is to ask wic poicy is efficient in a tird-best sense if abour income cannot be taxed regressivey for exogenous poitica reasons. Te answer requires a more toroug anaysis tan can be given ere. Tis section is meant to give tentative answers ony and to indicate connections to te iterature. 7.1 Taxing abour income proportionay Te most straigtforward way of excuding regressive taxation of abour income is to assume proportiona taxation. In te bencmark case tis can be modeed by excuding from te set of avaiabe poicy instruments. Hence, assume w, and focus on te efficient coice of t and s or of q and. Government s net tax revenue ten amounts to t s T C 1 t 1 s fe. By Hoteing s emma, tis can be written as T = ( q 1) eq ( f ) e. Consider a margina cange in wen starting from compensated in q subject to te budget constraint e=0. Te atter impies dq e d e q 0, f s=0. Te cange is i.e., an increase in s must be compensated by an increase in t. Te tota variation of tax revenue is captured by

19 17 dt d f T T dq [ ] q d f T e T [ ] e q q f e ( ] = q 1) eq e [ eq ( q 1) eqq eq = eq ( q 1) e e e e qq q q 1 = E [ E q - C q ]. q Te bracketed expression on te RHS is negative if te easticity of education is arger in absoute terms tan te easticity of consumption wit respect to te price of consumption, E q < C q. (A2) Proposition 4: Introducing a margina subsidy to te monetary cost of education and compensating tis by a margina increase in te consumption tax enances efficiency if, and ony if, (A2) ods. Te assumption (A2) ooks different from (A1). Coser inspection, owever, reveas tat te two assumptions are equivaent if te individua earnings function is isoeastic. Remark 2: If H ( E) E, te assumptions (A1) and (A2) are equivaent. Te equivaence is easiy proved as foows. By differentiating te expenditure function e qc L Y wit respect to q and by making use of e q C, one obtains q qc L Y L. (9) q L q

20 18 Reying on e=0, some simpe agebraic manipuation yieds equivaence of (A1) and te inequaity C q > Y q. By Remark 1, equaity of Y q and E q ods if te individua earnings function is isoeastic. Tis proves Remark 2. Coroary 2: Assume (A1) and an isoeastic earnings function. Introducing a margina subsidy for te monetary cost of education and compensating tis by a margina increase in te consumption tax enances efficiency. Te intuition for tis resut is as foows. Te consumption tax reduces te demand for consumption. Utiity remains constant ony if te abour suppies L and/or L are reduced as we. If quaified abour reacts negativey, incentives to invest in education are weakened. Tis case ten cas for subsidizing te monetary cost of education. However, te taxpayer coud aso react by reducing nonquaified abour. If tis effect is strong, ten (A1) ods wit reversed inequaity sign and it is efficient to tax te monetary cost of education. However, tis is te ess ikey case. From an a priori point of view, te case for subsidizing education is not tat obvious. See aso te discussion in Section 8. Education is a factor generating quasi-rent income wic cannot be fuy taxed away. Tere are resuts in te iterature suggesting tat poicy soud not encourage profit-generating beaviour if te profit accrues to te private sector. More precisey, it may we be efficient to tax factors wen tey generate pure profit and pure profit cannot be taxed away. See e.g. Huizinga and Niesen (1997). In te present context, tis migt ave given support to te expectation tat tax efficiency cas for taxing te cost of education (Ricter, 2006). Tis is so because education generates non-taxabe rent income and tis effect conficts wit tax efficiency in a framework wit distortionary taxation. Proposition 4 invaidates tis kind of reasoning. In te present framework a consumption tax is perfecty equivaent to a proportiona tax on abour income,. Given suc proportionaity of abour taxation, subsidizing te monetary cost of education transates into coosing a rate s wic marginay exceeds rate. If subsidization is provided by means of granting tax

21 19 deduction to te monetary cost of education, te rate of deduction soud exceed one undred percent. 7.2 Taxing capita income By investing in one s own uman capita, future consumption is increased at te cost of current consumption. Te same effect is reaced by saving out of nonquaified abour income. If te return to saving is taxed, tis way of providing for te future becomes ess attractive. Hence taxing capita income sets incentives to reduce te market suppy of nonquaified abour and to substitute quaified abour for nonquaified abour. As is we known, tere are many furter effects of taxing capita income (Troste, 1993). Sti, te effect of discriminating against saving is a major one and one wic is easiy integrated in te present anaysis. Just assume tat ifetime fas into two expicit periods. In te first one, te ouseod as to divide non-eisure time between education, E, and abour suppied to te market, E. For te sake of simpicity assume tat a consumption is sifted to te second period. As a resut, a income earned in te first period must be spent eiter on education or on savings: S ( L E) E L ( E. ) Second-period consumption is constrained by income earned: qc S H ( E). L As before, q is te price of consumption, wie is te gross rate of return to saving. For some exogenous poitica reasons et te panner be constrained to tax abour income progressivey, w, w. Assume, furtermore, tat te ony poicy instruments avaiabe are a tax on consumption, q>1; a tax/subsidy to te monetary costs of education, f; and a tax on capita income, <r. By appying te same tecnique as before and by assuming an isoeastic earnings function, one can sow tat it is efficient not to distort te coice of education, r. (10) w f w L

22 20 Tis condition is ceary fufied if capita and te monetary costs of education are w r taxed so tat r r and f f resuts. Starting from tis situation and assuming (A1), te foowing reform enances efficiency: is decreased marginay, and tis decrease is compensated by variations in and q so tat (10) continues to od and te utiity of te taxpayer remains constant. Te resut suggests tat a positive tax on capita income as te potentia to aeviate te negative incentives tat progressive taxation of abour income as on uman-capita investment. Tis confirms earier concusions of Jacobs and Bovenberg (2005). Te concusions are not, owever, fuy compatibe wit Niesen and Sörensen (1997). In fact, tey are just te ogica reverse of wat Niesen and Sörensen try to convey. Tose autors argue in favour of a poicy wic aims at discouraging uman-capita investment. Tey derive teir recommendation by keeping te capita income tax exogenous, by ignoring monetary costs of education, and by ten proving optimaity of progressivity in abour income taxation. Tis resut is compatibe wit (10) ony if f=0 as ten r impies / w / w. Te resut does not owever od if f>0. In tis case it is ceary more efficient to sustain efficiency in education by taxing te monetary costs of education tan by subsidizing non-quaified abour income. 8. To wat extent are education subsidies efficiency-enancing? Te roe of subsidies paid to education and te effect suc subsidies ave on te equity efficiency trade-off in te taxation of abour income is a big topic in te iterature. Te concusions derived are irritatingy opposing. According to Bovenberg and Jacobs (2005) redistribution and education subsidies are Siamese twins. Subsidies on education are sown to aeviate te tax distortions on earning induced by redistributive poicies. Te more eager te distributive objectives are, te more strongy poicy must rey on educationa subsidies. Quite to te contrary, Wigger (2003, 2004) proves tat socia wefare can never be increased by suppementing a noninear income tax wit a subsidy to te cost of education. Atoug te present

23 21 paper focuses on efficiency ony, it eps to understand tese seemingy conficting views of education subsidies. From te iterature on te optima abour taxation in te Mirrees tradition it is we known tat igy productive abour income soud not be taxed at te margin if te tax panner wants to redistribute income between two productivity types of individuas and if ow and ig types cannot be identified on an individua basis. In present notation tis requires setting 0. Reying on tis famous resut and on quasi-inear utiity functions, Wigger proves tat a subsidy to te monetary cost of education effectivey owers socia wefare. Hence it is optima to set s< 0. Tis comes cose to Coroary 1 above. In fact, Coroary 1 is stronger tan Wigger s resut in tat it reies on weaker assumptions. Utiity functions need not be quasi-inear. Tey ave to satisfy (A1) ony. Furtermore, te present anaysis makes cear tat s< foows from pure efficiency considerations, wie 0 foows from te government s need to respect an informationa participation constraint wen redistributing income from ig to ow productivity types of individuas. Bovenberg and Jacob s (2005) resuts are ess easy to summarize. Te reason is tat tese autors study education subsidies in varying frameworks. Te most genera one aows for costs of forgone eisure. Wit respect to te feasibe coice of utiity functions it is even more genera tan Wigger s anaysis. Te price Bovenberg and Jacobs pay is a oss in te simpicity and carity of resuts. Tey are ony abe to prove tat non-pecuniary educationa costs may ave an increasing effect on optima education subsidies, especiay if tey are compementary to work effort. In te ess ambitious part of teir paper, Bovenberg and Jacobs ignore non-pecuniary educationa costs. Tey demonstrate tat optima subsidies on education ensure efficiency in uman-capita accumuation even if te government vaues equity and pursues a redistributive poicy. If tax rates on abour increase, optima subsidies on education soud do so as we in order to aeviate te tax distortions on earning. Suc a concusion comes cose to Propositions 3 and 4 above. Proposition 3 suggests tat it is efficient to combine regressive taxation of abour income wit a tax on te monetary cost of education. If, owever, equity concerns rue out te use of regressive

24 22 taxation, ten efficiency requires subsidizing education, as stated by Proposition 4. As as aready been argued, te present anaysis soud owever not be considered a repication of Bovenberg and Jacobs (2005). Bovenberg and Jacobs ony derive an efficiency resut wen ignoring non-pecuniary educationa costs. In tis case, education degenerates to an intermediate good, and te production efficiency teorem of Diamond and Mirrees (1971) is appicabe. In contrast, Proposition 2 ods even in te case wen education is a eisure-time consuming activity generating rent income tat cannot be fuy taxed away. In Bovenberg and Jacobs (2005) te argument runs as foows. Because of distributive concerns it is efficient to rey on a distortiona tax on abour income. As a po tax aows skimming off pure abiity rents, te production efficiency teorem is appicabe, and tis requires eaving educationa investment undistorted. In te present anaysis distortions arise from taxing consumption. A po tax is not avaiabe, but abour income can be taxed according to quaification, wic is not te case in Bovenberg et a. (2005). Abiity rents accrue to te taxpayer, and yet it is efficient to eave te educationa coice undistorted. One may we debate weter tax rates soud be aowed to depend on educationa caracteristics or not. From a positive point of view it is difficut to justify any dependence. No country is known to condition tax rates on educationa caracteristics expicity. Tis common reuctance is owever more and more questioned from a normative perspective. Most prominent is te idea of introducing graduate taxes; see e.g. Garcia-Penaos and Wäde (2000) or Poutvaara (2004). Suc taxes are attractive in tat scoo quaification and university degrees are certainy not difficut to verify by tax autorities. Even more, faiure to use tis information is conceptuay not reay pausibe, given te framework of Bovenberg and Jacobs (2005). Tese autors assume tat te government can subsidize individua monetary costs of education. Hence te government soud be abe to differentiate tax rates according to subsidies received. If not, te framework is not too far from te one discussed in Section 7.1. It reies on te assumption tat abour income tax rates cannot be differentiated according to quaification for some unspecified exogenous reason:. Te anaysis in Section 7.1 sows tat, given non-differentiation, te monetary cost of

25 23 education soud be subsidized at a rate s tat exceeds. Tis resut confirms simuation resuts of Troste (1996). It owever contradicts Bovenberg and Jacobs (2005), wo prove s= in te ess ambitious part of teir paper. Tis is furter evidence to te caim tat te resuts of Bovenberg and Jacobs (2005) and te ones presented ere are ony simiar in spirit but different in substance. As as aready been stressed, Proposition 3 is best interpreted wit reference to te doube-dividend ypotesis known from te iterature on environmenta taxation. If it is sociay desirabe to encourage education at te margin, one soud do so by taxing noncompiant beaviour and not by subsidizing compiant beaviour. Tis is te socaed weak form of te doube-dividend ypotesis. See Gouder (1995). Te first dividend is te positive effect on education, and te second dividend comes from te generated revenue, wic can be used to cut back distorting taxes. Tere ave been oter, ess convincing attempts in te iterature to reate doube dividends to optima education poicy. Jacobs (2005) suggests speaking of a doube dividend if education subsidies produce more equaity in before-tax incomes and aso generate efficiency gains in taxation. He refers to Dur and Teuings (2004). Tese autors argue in favour of educationa subsidies. By promoting education and reying on genera-equiibrium effects, te distortionary cost of progressive taxation may be reduced. According to Jacobs (2005), a doube dividend of education subsidies generating more equaity in before-tax wages troug genera-equiibrium effects and ower distorting tax rates is owever not ikey to occur. Coroary 1 of te present paper is anoter bow against te tesis of Dur et a. Te monetary cost of education soud not even be granted fu tax deductibiity if abour income can be taxed according to quaification. In oter words, for pure reasons of efficiency, education soud be taxed and not subsidized on a net basis. Te conjecture is tat tis resut perfecty extends to a genera-equiibrium framework.

26 24 9. Efficiency in education and distributive poicy According to Bovenberg and Jacobs (2001), efficiency in education fais to be optima wen education causes costs of forgone earnings and wen tere are distributiona concerns. If noting more coud be said, tis resut woud provide a critica argument against te practica reevance of Proposition 2. However, more can be said wen taking a coser ook at te exampe discussed in Section 5. According to tis exampe it is efficient not to distort uman-capita investment and to tax nonquaified abour income at a rate wic is a function of te consumption tax rate but ese independent of te wage profie w i (i=,). Bovenberg and Jacobs (2001) mode taxpayers eterogeneity by assuming a non-degenerate distribution of te productivity of quaified abour as measured by. Taxpayers are assumed to differ neiter by w and nor by te easticity of te individua earnings function,. In te exampe of Section 5, differences in w woud not sow up in te efficient ratio of w to t but in teir absoute vaues ony. Tis observation suggests conjecturing tat an optimizing panner woud coose to address equity concerns by reying on a persona tax on ifetime consumption. Tis is not beyond wat economists consider a reasonabe idea. Te ony probem is tat woud ave to increase in t. Te more productive te taxpayer is, te more regressivey is or er abour income as to be taxed wit respect to quaification. Tis recommendation is ceary difficut to transate into practica poicy. Wen te taxpayer is young and not quaified, te necessary information concerning w is typicay missing. Te idea of differentiating according to w wi fai in practice. If owever a non-differentiating tax is appied, te panner runs into a confict. Equity cas for ig tax rates on abour income wen w is ig, wie efficiency cas for just te reverse monotonicity. In practice, te panner as no coice but to compromise on efficiency in education wen enancing equity. Atoug tis concusion is not reay surprising, it makes one point cear: Te practica imits to te appicabiity of Proposition 2 are not set by equity concerns as suc, but by te ack of information about future productivity differentias before individuas start to reap te returns to teir uman-capita investments.

27 25 Tis discussion deserves to be quaified in one notabe respect. Te strongest predictor of educationa success is known to be te famiy background. Hence parents income soud be an empiricay informative signa of. Insofar as tis is te case, it gives reason to tax nonquaified abour income at a rate wic increases wit parents income. Atoug tis is a daring idea, it is teoreticay not witout appea. It is an idea tat may ave practica potentia in reaxing te confict between equity and efficiency in education. A more conventiona poicy is to subsidize te education of igy productive individuas at a iger rate tan te education of ess productive individuas. Te German practice of financing university education by taxes and eaving it to te private sector to finance apprenticesips may we be interpreted aong tese ines. Suc a poicy, owever, fais to be second-best efficient. w 10. Summary Te poicy concusions derived from tis paper s anaysis are as unambiguous as tey are unpopuar. Tey are unambiguous in te sense tat it coud be sown under fairy broad assumptions to be efficient not to distort educationa coice wen education generates abiity rents. Distortions soud be toerated ony in te suppy of abour. Given tat te necessary poicy instruments are avaiabe, it is second-best efficient to tax abour income regressivey wit respect to quaification and to tax te monetary cost of education at a eve tat aows one to sustain efficiency in education. Suc a poicy aims at eaving education undistorted wie setting incentives for substituting quaified abour for nonquaified abour. Te intuition reminds one of te doubedividend ypotesis we known from environmenta taxation. According to tis ypotesis it is more efficient to tax noncompiant beaviour tan to subsidize compiant beaviour. In te present context noncompiant beaviour takes te form of suppying nonquaified abour to te market, wie compiant beaviour refers to noneisure time spent on education. Te resuts derived in tis paper aow one to give a consoidated interpretation of various oter resuts tat ave been produced in te iterature and tat tend to be contradictory and confusing.

28 26 Te poicy impications derived from tis paper s anaysis are certainy not very popuar. Not many peope woud be wiing to tax nonquaified abour more eaviy tan quaified abour. Te impications are, owever, not so unreasonabe if interpreted wit care. Tere are two options of carefu and reasonabe interpretation: a defensive one and an offensive one. According to te offensive interpretation, te anaysis suggests pursuing te equity objective by redistributing ifetime consumption and providing incentives to restore efficiency in educationa coice. A teoreticay appeaing way to acieve tis goa is to tax nonquaified abour at a rate tat increases in a reiabe predicator of te returns to education. Parents income may be a good candidate. Atoug it is a daring idea to tax nonquaified abour income according to parents income, it certainy deserves to be discussed in more detai tan coud be done ere. According to te defensive interpretation, no particuar poicy recommendation is derived. Te primary vaue of te anaysis is seen in stressing te socia efficiency cost of progressive taxation. Progressive taxation wit respect to quaification is just te opposite of wat is needed to encourage uman-capita investment. Tis negative incentive effect magnifies te negative disincentives for abour coice igigted by Mirrees (1971) and oters. A fina remark concerns te simpicity of te mode used in te present paper. One must admit tat major resuts do not od if te individua earnings function fais to be isoeastic. Even if tis assumption is accepted, it is not cear weter te resuts derived od in more reaistic settings. Te time structure as ony been impicit and rudimentary, and te accumuation of pysica capita as not been modeed at a. Furtermore, abour as been assumed to be immobie, and te mode is te one of a cosed economy. Atoug suc modeing sortcomings cannot be denied, tere is ope tat some of tem can be overcome by future researc. For exampe, tere is evidence (Scuppert, 2007) tat efficiency in education is someting to wic jurisdictions soud stick even if migration incentives are distorted. Hence, more researc is needed to find out ow robust te poicy impications of tis paper are.

29 Appendix Te proof of Proposition 1 makes use of e q C, e ( L E), and =E. Equation e (7) is easiy seen to be perfecty equivaent to (4). Equation (6) foows just from verifying te equaity E E e e e (3) e ( L E) L E. L E L E L ( Remark 1 is ony proved for te case in wic te equaity of easticities is caimed to od wit respect to variations in q. Te cases concerning variations in and are proved aong te same ines. Te definition Y,, L ) HL E and te firstorder condition H ' impy Yq HLq and E q H ' L H" L q. Making use of 1 EH '/ H, one obtains Y H E ( 1) E. Hence Y / q = E / q H ' HLq Yq Eq H ' Lq 1 ( 1) E Y E H" LE ods if H is isoeastic. 1 H H ', wic ceary 1 1 ( 1) EH ' H" E Te proof of Proposition 2 requires some preparatory considerations. Note first tat (9) ods in more genera terms: qc L Y L for x q,,. (11) x x L x Making use of (5) and (11), one easiy derives qc L Y L. (12) L Assuming (6) and isoeasticity of H, (7) is sown to od if, and ony if, p : C C 1 [ ] L YL L ( 12) qc

30 28 E L ( 6) qc E 1 qc + Y L L E L ( 8) qc E + 1 qc Y E E Y qc ( w ) ( f ) = L Y qc E E + Y qc p = E E if, and ony if, p. References: Andersson, F. and K.A. Konrad, 2003, Human capita investment and gobaization in extortionary states, Journa of Pubic Economics 87, Boadway, R., N. Marceau, and M. Marcand, 1996, Investment in education and te time inconsistency of redistributive tax poicy. Economica 63, Bovenberg, A.L. and B. Jacobs, 2001, Redistribution and education subsidies are Siamese twins, CEPR Disc. Paper No Bovenberg, A.L. and B. Jacobs, 2005, Redistribution and education subsidies are Siamese twins, Journa of Pubic Economics 89, Bovenberg, A.L. and R.A. de Mooij, 1994, Environmenta evies and distortionary taxation, American Economic Review 94, Diamond, P. and J.A. Mirrees, 1971, Optima taxation and pubic production, I Production efficiency, II Tax rues, American Economic Review 61, 8 27, Dur, R. and C.N. Teuings, 2004, Are education subsidies an efficient redistributive device? in: Labor Market Institutions and Pubic Reguation, J. Age, M. Keen, and A.J. Weicenrieder, eds., Cambridge, MA, Eaton, J. and H.S. Rosen, 1980, Labour suppy, uncertainty, and efficient taxation, Journa of Pubic Economics 14,

31 29 Garcia-Penaosa, C. and K. Wäde, 2000, Efficiency and equity effects of subsidies to iger education, Oxford Economic Papers 52, Gouder, L.H., 1995, Environmenta taxation and te doube dividend: A reader s guide, Internationa Tax and Pubic Finance 2, Heckman, J.J., 1976, A ife-cyce mode of earnings, earning, and consumption, Journa of Poitica Economy 84, S11 S44. Jacobs, B., 2005, Te doube dividend of education subsidies for redistribution, Discussion Paper. Jacobs, B. and A.L. Bovenberg, 2005, Human capita and optima positive taxation of capita income, Tinbergen Institute, Disc. Paper TI /3. Jacobs, B. and A.L. Bovenberg, 2006, Redistribution and education subsidies are Siamese twins (II) A Correction and Furter Generaizations, mimeo. Huizinga, H.P. and S.B. Niesen, 1997, Capita income and profit taxation wit foreign ownersip of firms, Journa of Internationa Economics 42, Mirrees, J.A., 1971, An exporation in te teory of optimum income taxation, Review of Economic Studies 38, Nerove, M., A. Razin, E. Sadka, and R.K. von Weizsäcker, 1993, Compreensive income taxation, investment in uman and pysica capita, and productivity, Journa of Pubic Economics 50, Niesen, S.B. and P.B. Sörensen, 1997, On te optimaity of te Nordic system of dua income taxation, Journa of Pubic Economics 63, Poutvaara, P., 2004, Educating Europe: Soud pubic education be financed wit graduate taxes or income-contingent oans? CESifo Economic Studies 50, Ricter, W.F., 2006, Efficiency effects of tax deductions for work-reated expenses, Internationa Tax and Pubic Finance 13, Scuppert, C., 2007, Does mobiity of educated workers undermine decentraized education poicies? Disc. Paper, University of Dortmund.

32 30 Troste, P.A., 1993, Te effect of taxation on uman capita, Journa of Poitica Economy 101, Troste, P.A., 1996, Soud education be subsidized? Pubic Finance Quartery 24, Varian, H.R., 1980, Redistributive taxation as socia insurance, Journa of Pubic Economics 14, Wigger, B.U., 2003, Finanzierung der Hocscubidung und Einkommensbesteuerung, in: Hocscuökonomie Anaysen interner Steuerungsprobeme und gesamtwirtscafticer Effekte, U. Backes-Gener and C. Scmidtke, eds., Berin, Wigger, B.U., 2004, Are iger education subsidies second best?, Scandinavian Journa of Economics 106,