Can more education be bad? Some simple analytics on financing better education for development

Transcription

1 55 an more education be bad? ome simple analytics on financing better education for development Rossana atrón University of Uruguay Investigaciones de Economía de la Educación

2 1092 Investigaciones de Economía de la Eduación 5

3 an more education be bad? ome simple analytics on financing better education for development Rossana atrón University of Uruguay Wile te model in tis paper remains close to te Heckscer-Olin tradition, it is sown tat, contrary to te standard results, it is te net effect of prices, taxation, and accumulation of endowments tat determines te Rybcynski-type growt effects, wic may elp explain te lack of consensus in te empirical literature on education and growt. A central feature of te model is tat te accumulation of endowments depends on te output of education, wile te canges in labour supply, wic determine te effective production possibilities frontier, also depend on individuals decisions on allocation of time, affected by relative prices and fiscal policy. On te one and, in te model te composition of te output of education depends on education quality, so te composition of te inflow of entrants to te labour market can be upgraded by suitable policies. On te oter and, te risks of a skill supply-reducing government intervention are discussed. Te analysis as implications for policymakers in developing countries were bot te economy s production possibilities and te education sector need to be enanced, as it reveals te possibility of a bad reform were te expected benefits of government s interventions in education can be contradicted by te general equilibrium effects of te policy. A sufficient condition to avoid tis situation is identified in te paper. 1 Introduction Almost all governments, bot in developed and developing countries, allocate significant amounts to finance public education. For instance, in 2005, te United tates allocated 5.3% of its GD to public education; te United Kingdom, 5.6%; France, 5.7%; and Italy, 4.5%. In atin America, te fraction of GD allocated to public education in general is not tat ig but is still significant. For instance, in 2004, for Brail it was 4%; Argentina, 3.8%; ile, 3.7%; Mexico, 5.4%; araguay, 4%; and Uruguay, 2.6% (UNEO, 2008). Moreover, in all cases, te vast majority of education provision is public (UNEO, 2007). Tese facts seem to sow tat relevance of education activities are not overlooked by any government. However, even wen te importance of education for growt as been igligted by te endogenous growt literature (for instance, Romer, 1986; ucas, 1988), te evidence of effects on Investigaciones de Economía de la Educación

4 Rossana atrón growt is mixed: te empirical literature on te contribution of education to growt is surveyed for instance by Temple (2000). o, wat s te matter? ould education be good, neutral, or bad, depending on te case? It could be any of tem; in particular, it could be bad for two reasons: inefficient educational expenditure (see, for instance, lements, 1999; Hanusek, 2002) and a distorting tax system to finance education (see, for instance, Glomm and Ravikumar, 1998; Blankenau and impson, 2004; Blankenau et al., 2007). Tis paper focuses on te latter aspect, identifying te general equilibrium effects of taxation in a simple model, making it possible to deal wit some analytics. Moreover, a sufficient condition for a growt-enancing government intervention is identified. A central feature of te modelling of te education sector in tis paper is te presence of systemic inefficiencies in terms of expected results (i.e., successful students and production of labour), wic is te typical situation in developing countries. As education is publicly provided, systemic inefficiencies can be targeted by policymakers, and tus te process of accumulation of endowments can be enanced by education policy. However, te way in wic an increase in te education budget is financed affects te net effects on te economy of enanced education, and suc cannels ave been identified in tis paper. Te effects of indirect and income taxes are made explicit by means of some simple analytics; it is sown tat taxation affects te consumptionleisure coice by canging te relative prices, tus modifying te labour supply. Tis, in turn, determines te actual production possibilities. Te paper is organised as follows. ection II describes te model. ection III describes te properties of te model as well as some policy implications. ection IV presents te conclusions. Te Annex presents additional details for te ouseold modelling. 2 Model description Te model presented ere remains close to te standard Heckscer-Olin tradition, wic is extended to include te public education activities tat produce endowments (skilled and unskilled labour). Te pattern of endowment growt (skilled and unskilled labour) is te result of te output of education, leaving aside demograpic considerations and retirement rates. In addition, people make a consumption-leisure coice, so tat te supply of labour is endogenous. Te government raises revenue from taxes to provide education. 2.1 Te education sector Education is publicly provided, wit a budget exogenously determined. Te government raises revenue from taxes to finance te provision of education. Te government runs a balanced budget, financed via income and indirect taxes. Following te tradition in te education production function literature (for a review, see evačić and Vignoles, 2002), te output of education activities 1094 Investigaciones de Economía de la Eduación 5

5 an more education be bad? ome simple analytics on financing better education for development is given by Q = F( G, E), Q is te output of te activity given te resources G, and E is te enrolment. Te function F is subject to constant returns to scale, so te output per student can be written as q Q E = F( g) q =, were g measures te resource intensity per student, and g > 0. For eac student, q is te amount of knowledge embodied in im/er on te successful completion of scooling, wic builds is/er uman capital. Following Hanusek (1979), students acquired knowledge defines scool quality, terefore, te output per student ( q ) measures scool quality. Education produces bot unskilled workers and skilled workers, according to time of exit. cool quality (output per student) is modelled as a major determinant of students pat, as Barnes (1999) wo points out tat students drop out of scool if tey fail to learn, ten, students acievement is taken as a determinant of early exit rates, θ ( q) 2 2 θ q > 0 θ =, were θ q < 0 and Te accumulation of endowments in te economy depends on time of exit. Tus, te composition of te inflow of labour to te market are given by d Z, i.e., d U d = θ E = ( 1 θ )E were θ is te early exit rate, and d U and d are te inflow of unskilled and skilled labour, respectively, wic determine endowment growt. Tus, te rate of endowment growt in te economy is given by ˆ = d ˆ = d U U U were and U are te stocks of skilled and unskilled labour, respectively, and a ut (^) placed over te variables denotes rate of growt. Ten, te production of skills may be indered by inefficient education systems, wic is te typical situation in developing countries were education quality is in general low. Tus, a government intervention consisting in an increase in te educational budget could enance te process of production of skill formation, by allowing a iger resource intensity per student and tus a iger education quality, improving te productivity of te activity (in terms of graduates), and also causing a sift in te composition of educational output toward skilled labour. Investigaciones de Economía de la Educación

6 Rossana atrón 2.2 Houseolds Tere are two representative ouseolds: one tat owns only unskilled labour and te oter tat owns only skilled labour. Teir decisions are taken in a two-stage process. In te first stage, ouseolds make a consumption-leisure coice, so tat te total supply of labour is endogenous. In te second stage, ouseolds allocate all teir income (post-tax for formal activities) to all te consumption goods (see Annex for details). It is assumed tat eac ouseold s utility function is an increasing function of consumption goods and leisure time. In te description tat follows, te same subscript associates ouseolds and factors: labour of type. R =, U for skilled and unskilled, respectively. et be te stocks of units of = H ), and H represents te units tat te ouseold cooses to work (so, leisure time is is a composite of consumption goods. Te E utility function for 1 µ µ ( ) µ ouseold is U α + ( 1 α) ( H ) substitution is σ = ( 1 ) =, were α > 0, and te elasticity of 1, µ < 1. At te top level, consumers coose and µ maximise utility subject to teir budget constraint one unit of H and = wh, were H to w is te wage rate for is te price index of te composite consumption good for ouseold computed at consumer s prices (see Annex for details). Te optimal values for consumption and labour supply are w = σ 1 σ σ 1 σ α + α R w α σ 1 σ (1) H = σ 1 σ σ 1 σ α α σ + α 1 σ R w (2) From (1) and (2) te elasticities may be derived. Te elasticity of time worked wit respect η = (σ 1) H, wic is positive provided σ >1. Te elasticity to te wage rate is H w ( ) of demand for is negative. Z wit respect to prices is given by η = ( σ ( H ) H ) +, wic 2.3 roducers Tere are two tradable sectors and tat use skilled and unskilled labour, te exporting activities are unskilled-intensive, wereas te import-competing activities are skilled-intensive. Tere are competitive markets for goods and factors. All production functions are subject to constant returns to scale; in te long run, equilibrium profits are ero, so prices are equal to unit costs Investigaciones de Economía de la Eduación 5

7 an more education be bad? ome simple analytics on financing better education for development 3 roperties and policy implications Te economy s supply of skills is affected by canges in real wages and in te output of education. It is easy to sow tat te increase in te supply of skills, totally differentiating (2), is given by H w ( w ) ˆ Hˆ = η + (3) Expression (3) sows tat canges in total labour supply are determined by canges in te output of education ( ˆ ) and canges in real wages (wic are affected by international prices and tax policy), depending on te elasticity of labour supply to te wage rate. o, fiscal policy as general equilibrium effects on individuals decisions on labour supply and consumption. According to (3) increases in income and indirect taxes ave a negative effect on labour supply, by reducing te real wage. roperty 1: Te net effects of taxation and education output on factor supply (for constant international prices) determine te Rybcynski effect on productive sectors, causing a biased sift in te production possibilities frontier. Te model merits te reinterpretation of te standard growt effects from canges in stocks of endowments (see Rybcynski, 1955) using expression (3). Tis is, canges in stocks of endowments (second term in te rigt-and side of expression (3)), jointly considered wit te effects from taxation (first term in te rigt-and side of expression (3)), determine te effective supply of factors, and tus, te actual possibilities of expansion of productive sectors. olicy implication 1: Given prices and taxes, a better performance in education activities leads to increased growt rates in te labour supply and tus, in te economy production possibilities. Also from expression (3) it can be sown tat, for constant prices and taxes, an increase in te output of education not mainly based on expanded funds (for instance, improving efficiency and/or effectiveness of scools) determines te canges in te supply of factors, equal to te canges in endowments. Tus, only in tis case, education alone determines te standard Rybcynski-type growt effects. olicy implication 2: ommon sense rule : onsidering te economy as a wole, te government would engage in a tax reform intended to finance an increase in te economy s availability of skills by enancing education activities only if te expected expansion of endowments more tan compensates te effects of taxation on factor supplies. It can be sown tat factor supplies rise, recalling (3), wen ( w ) ˆ > η H w (5) Investigaciones de Economía de la Educación

8 Rossana atrón A tax reform designed to finance an increase in te education budget may undermine te benefits intended to be reaped from iger production of skills, by causing a fall in te supply. A condition to avoid tis situation is given in expression (5), tus tis is a sufficient condition for a skill supply-enancing government intervention. 4 onclusiones A central feature of te model is tat te accumulation of endowments depends on te output of education, wile te canges in labour supply, wic determine te effective production possibilities frontier, also depend on individuals decisions on allocation of time. It is sown tat, in contrast to te standard approac, it is te net effect of prices, taxation, and accumulation of endowments tat determines te Rybcynski-type growt effects, wic may elp explain te lack of consensus in te empirical literature on education and growt. A main contribution of te model is tat it allows te discussion of te general equilibrium effects of an expansion of education by means of some simple analytics. It is sown tat te overall effects of te expansion of educational activities depend on ow te government finances suc an expansion. Te analysis as policy implications for developing countries were skill formation is deficient due to inefficiencies in te education sector, wic may justify a government intervention to enance te sector. In particular, te risks of a skill supply-reducing government intervention are igligted, as te way in wic te government finances te budget may undermine te benefits from enanced education. Tat is, a tax reform designed to finance an increase in te education budget may undermine te benefits from iger production of skills by causing a fall in te supply. o, it would be convenient to follow a common sense rule : considering te economy as a wole, te government sould engage in a tax reform to raise te revenue needed to expand te availability of skills by enancing education, only if te expected expansion of skills produced more tan compensates for te effects of taxation on te supply. But, interesteringly, te analysis also sows tat any improvement in te efficiency/effectiveness of providing education not mainly based on expansion of resources (as tose coming from better organiation of scools or teacing processes) will unambiguously expand production possibilities. 5 References Barnes, D. 1999, auses of Dropping Out from te erspective of Education Teory, in Randall,. and J. Anderson (eds.) cooling for uccess. reventing Repetition and Dropout in atin American rimary cools, M. E. arpe, New York. Blankenau, W., impson, N., and Tomljanovic, M. 2007, ublic education expenditures, taxation and growt: linking data to teory, American Economic Review apers and roceedings, vol. 97, no. 2, pp, Investigaciones de Economía de la Eduación 5

9 an more education be bad? ome simple analytics on financing better education for development Blankenau, W. and impson, N. 2004, ublic education expenditures and growt, Journal of Development Economics, vol. 73, no. 2, pp lements, B. 1999, Te efficiency of education expenditure in ortugal, IMF Working aper no Glomm, G. and Ravikumar, B. 1998, Flat-rate taxes, government spending on education, and growt, Review of Economic Dynamics, vol. 1, pp Hanusek, E. 2004, ome simple analytics of scool quality, NBER Working aper no Hanusek, E. 2002, ublicly provided education, NBER Working aper no Hanusek, E. 1979, onceptual and empirical issues in te estimation of educational production functions, Journal of Human Resources, vol. 14, no 3, Heckman, J. and Masterov, D. 2004, kill policies for cotland, Te Allander eries. evačić, R and Vignoles, A. 2002, Researcing te links between scool resources and student outcomes in te UK: a review of issues and evidence, Education Economics, vol. 10, no. 3, pp ucas, R. 1988, On te mecanics of economic development, Journal of Monetary Economics, vol. 22, pp Romer,. 1986, Increasing returns and long run growt, Journal of olitical Economy, vol. 94, pp Rybcynski, T. M. 1955, Factor endowments and relative commodity prices, Economica, 22, pp Temple, J. 2000, Growt effects of education and social capital in te OED countries, OED, ountries Economics Department Working aper no UNEO, 2008, Finance indicators by IED level, UNEO Reports, webpage ttp://stats.uis.unesco.org/unesco/tableviewer/tableview.aspx?reportid=172 accessed 04/10/08. UNEO, 2007, Wat do societies invest in education? ublic versus private spending, UNEO Institute for tatistics, eriodical no. 4, October. Webpage ttp:// accessed 28/03/09. 6 Annex: Te composite consumption good Te composite consumption good is produced by tradable goods, its price being equal to te cost of its inputs. Te composite good expressed as a E function is D φ 1 φ = δ > 0 δ, δ = 1 Investigaciones de Economía de la Educación

10 Rossana atrón were D is te demand for by ouseold. Te elasticity of substitution is ϕ 1 ( 1 φ ) =, φ <1. Te ouseold spends its (post-tax) income on consumption goods. Y is te (post-tax) income of ouseold, Y = D, were o, te problem to solve is D Min s t D = are consumer prices... A δ D φ 1 φ were is te composite consumption good and A is a scaling term used to ensure tat te price of te composite equals te cost of producing it. From te first-order conditions, te optimal demands are D = A. δ δ ϕ ϕ ϕ 1 ϕ ϕ ϕ 1 Using tis expression, te price of,, may be derived manipulating te equivalence D =, resulting 1 = δ A ϕ 1 ϕ 1 1 ϕ 1100 Investigaciones de Economía de la Eduación 5