Fiscal Policy and Growth: a Survey

Marzo, Massimiliano Working Paper Fiscal Policy and Growth: a Survey Quaderni - Working Paper DSE, No. 314 Provided in Cooperation with: University of Bologna, Department of Economics Suggested Citation: Marzo, Massimiliano (1998) : Fiscal Policy and Growth: a Survey, Quaderni - Working Paper DSE, No. 314, Alma Mater Studiorum - Università di Bologna, Dipartimento di Scienze Economiche (DSE), Bologna, https://doi.org/10.6092/unibo/amsacta/4994 This Version is available at: https://hdl.handle.net/10419/159156 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc/3.0/ FISCAL POLICY AND GROWTH: A SURVEY MASSIMILANO MARZO MARZO 1998 Introduction The lack of convergence of growth rates among the world economies is probably one of the most debated topics in the last few years in theoretical and empirical research.In this period we have observed astrong resurgence of the debate about long-run growth, starting from the initial contributions by Paul Romer (1986)and Robert Lucas (1988)who opened the so called “Endogenous Growth Theory”or “New Growth Theory”.The reason of this resurgence of interest lies in two important aspects left unsolved by the theoretical attempts of the 60sand 70s: first,the need to explain long-run growth determinants and secondly,to provide acareful explanation to the lack of convergence of growth rates among world economies footnote . The biggest achievement of the Endogenous Growth Theory is represented by the reconciliation of the diminishing returns hypothesis with the typical finding of empirical analyses,i.e.agrowth rate continuously increasing. There are many explanations of the lack of convergence of growth rates.Among the empirical studies on convergence we consider Barro and Sala-i-Martin (1992)who analyzed the different definition of convergence expressed as absolute and relative,according to the emphasis given to the initial endowments and the saving rate footnote . However,probably,one of the most important explanations for the divergence of growth rates lies in the heterogeneity of fiscal policies adopted by different countries.The present paper tries to explain the lack of convergence by invoking differences in fiscal policies,as explained by the more recent literature. Differently from the growth theory of 60sand 70s,the endogenous growth theory shows many interesting features to the link between fiscal policies and growth.When growth is endogenous,policy actions affecting the saving rate (fiscal policy can be though as atypical example of such apolicy),have growth effects and not only level effects.This means that fiscal policy affects the steady state growth rate on aBalanced Growth Path (BGP,thereafter)and not only during the transition from one steady state to the other. Fiscal policy in growth models can be analyzed within awide range of contexts:(i) representative agents models with infinite horizon;(ii)overlapping generations models;(iii) redistributive models with electoral competition about the level of fiscal pressure.Given the enormous degree of development reached in each of the above fields,the present survey will concentrate mostly on representative agent models with infinite horizon,with aspecial emphasis on two-sector models with human capital footnote . The reason of this choice has to do with the goal of analyzing the growth effect of flat rate taxes and how various assumptions on the production function for physical and human capital,will interact to assess the magnitude of fiscal policy.The models under point (ii)-(iii)focus more on the redistributional effects of fiscal policy,and they take as given the effect of fiscal policy on growth. Avery important point concerns the endogeneity of public expenditure in endogenous growth models:unfortunately,not much work has been done in the infinite horizon framework apart the initial contribution by Barro (1990),Barro and Sala-i-Martin (1992)and the literature on redistributional issues.In this survey Iwill present both the aforementioned contributions and some extensions to the two-sector framework by Corsetti and Roubini (1996). In what follows the focus will be only on deterministic models,without exploring the implications of the stochastic growth models with fiscal policy.The goal of stochastic growth models is different:they take as given the existence of aBGP to explain the origins and causes of economic fluctuations originating around it.To do so,they try to replicate the observed behavior of time series of income,consumption,investment and other relevant macroeconomic variables, by adding to the model shocks -technological or fiscal -which could generate such fluctuations. The model is evalued according to its ability to replicate the observed behavior of time series. Those models are in the tradition of Real Business Cycles (RBC)literature.The difference with the RBC typical assumption is that afiscal policy shock -together with apure technological shock -is assumed to be the origin of economic fluctuations footnote around aBGP exogenously given.In the case of pure deterministic growth models,instead,we keep fluctuations as exogenous to the model and the goal is to explain the existence of an unceasing growth. Iwill not touch empirical aspects of the relationship between fiscal policy and growth.For a survey of the empirical results on fiscal policy and growth Iaddress the reader to other surveys, like,fore example,Easterly et al.(1992),Engen and Skinner (1992),Levine and Renelt (1992). The remainder of this paper is organized as follows.Section 2introduces the reader to the analytical context employed in the subsequent sections,by surveying the basic mechanisms underlying endogenous growth mechanisms.Section 3analyzes endogenous growth models driven by human capital accumulation,while the role of the innovative activity as engine of growth is discussed in section 4. Income taxation is discussed in section 5under the usual two formulation of an income tax and atax on private inputs.In section 6there is an extensive discussion on endogenous fiscal policy.In this context,. models without and with human capital are analyzed in order to evaluate different distorsive effects of taxation.Section 7studies a growth model with monopolistic competition and differentiated goods.The effect of endogenous labor supply under various specifications is discussed in section 8. The effect of consumption and investment taxation is discussed respectively in section 9and 10. Section 11 provides abrief discussion on optimal taxation issues. Concluding Remarks close the paper. Endogenous growth:an introduction The fundamental question to which endogenous growth theory deals with is:why can long-run growth be kept constant and unceasing over time ? From the exogenous growth models we know that if the production function respects the Inada conditions,the law of diminishing returns makes the long run growth rate equal to zero.In fact,the traditional literature on growth stopped in the early 70sbecause of its inability to explain the continuously increasing growth rate empirically observed for all developed economies.During past years,this problem has been brilliantly solved by Paul Romer and Robert Lucas who offered two alternative explanations to the long-run growth.On the one hand,the proposed solution hinges on the role played by externalities in the production function of final goods.The presence of externalities has acountervailing effect on the law of diminishing returns,as stressed by Romer (1986).On the other hand,there is the two-sector growth model by Lucas (1988)which is built on the previous work by Uzawa (1964),where the growth engine is represented by human capital accumulation. As discussed by Barro and Sala-i-Martin (1995),quite all the models of endogenous growth can be represented along the lines discussed by these models.To introduce the analytical framework employed throughout the paper,in what follows Iwill sketch the two classes of models just mentioned. Let us start by considering aCobb-Douglas production function such as: Yt=AtKt JZt 1?J # where 0<J²1. In ( ref: uno )Ktindicates physical capital and Ztis awhatsoever input having acountervailing effect on the decreasing returns to scale associated with Ktfor which an appropriate qualification will be offered later on. Atis ascale parameter.In aone good model like this,the aggregate final product can be either invested or consumed.The capital accumulation is governed by the following equation: . Kt=Yt?Ct?NKKt # where NKis the depreciation rate on physical capital. With competitive markets for the productive inputs,the real interest rate must equate the marginal product of capital: rt=JAt J?1 # From ( ref: tre ) we observe that Ztshould operate in such away that real interest rate never declines over time when Ktincreases.The countervailing effect will be complete if J=1. The preference structure in this context is subsumed by the following utility function of CRRA-type (Constant Relative Risk Aversion)with constant relative risk aversion coefficient a: Ut=X0 Ke?_tCt 1?a?1 1?adt # where _>0is the discount rate.The representative agent chooses the optimal quantity of consumption Ctand investment by maximizing ( ref: quat )subjected to ( ref: due ).After rearranging the first order conditions,we obtain the following expression for the growth rate of consumption: L= 6 Ct Ct =rt?_?NK a # Moreover,L³0if and only if rt³_+NK.It is also easy to verify that when J=1the growth rate Lwill be strictly positive if and only if A>_+NK. The above mechanism is aschematic description of the basic features of the endogenous growth models:the growth rate is always positive because of the presence of some mechanism able to contrast the effects of the law of diminishing returns. Growth driven by Human Capital The simplest way to represent the role of human capital is to imagine an aggregate production function like y=Ak where kcan be interpreted as aggregate capital in abroad sense. The definition of kencompasses both physical and human capital.In this context,it is just the assumption that human and physical capital are included in one term that gives the production function having the property of constant returns to scale.In this case,the marginal product of aggregate physical capital is constant as well, making the growth rate constant and positive. An explicit treatment of human capital requires the analysis of atwo-sector growth model with separate accumulation and production processes for physical and human capital. Therefore,let us assume in ( ref: uno )that Z=H,where His the level of human capital. The accumulation constraint for human capital: 6 Ht=IH?NHHt # where IHis the amount of new human capital produced net of depreciation NHHt,with NHbeing the human capital depreciation rate.In order to get tractable closed-form solutions,assume that the production function of new human capital IHis: IH=BtÝv2tKtÞKÝz2tHtÞ1?K # with 0<K²1and with Bt=B-ton aBGP.Also,( ref: uno )can be rewritten as footnote : Yt=AtÝv1tKtÞJÝz1tHtÞ1?J # with 0<J²1and with At=A-ton aBGP. In ( ref: sette )and ( ref: otto )v1t(v2t)indicates the fraction of physical capital employed in the production of final goods (human capital),while z1t(z2t)represents the fraction of human capital employed in the production of final goods (human capital).This model is generalization of Lucas (1988)model and Rebelo (1991).In particular,Lucas (1988)assumes that the production function of human capital is linearly homogeneous in Ht:this means that with K=0 the only argument of the human capital production function is human capital itself, because IH=Btz2tHt.To obtain aclosed-form solution,Iassume that the depreciation rate for both physical and human capital are the same,i.e.NK=NH=N.Given the utility function ( ref: quat ) we obtain an expression for the growth rate still given by ( ref: cinque )but with the following expression for the interest rate r: r=ÝJAÞKÝÝ1?KÞBÞ1?JJ 1?J1?K K K1 1?J+K # From ( ref: nove ) we observe that interest rate ris afunction of all the technological parameters of the model which are assumed to be constant on aBGP.Therefore,the growth rate of this economy will be constant as well and positive if r>_+N.The expression for the interest rate in the Lucas (1988)model can be obtained as particular case of the model considered here,after imposing K=0in ( ref: nove )to get r=B. The two-sector model has atransitional dynamics which has been carefully studied by Mulligan and Sala-i-Martin (1992)using the time elimination method.Without entering into the details of the model,it is possible to say that if there are not adjustment costs for physical and human capital,all the inputs are totally free to move from one sector to another and there does not exist any transitional dynamics at all.Therefore,without adjustment costs, the two-sector model has the same qualitative behavior of the ‘Ak model’,as discussed by Barro and Sala-i-Martin (1995) footnote . Growth driven by innovative activity In this class of models the engine of growth is represented by the activity of technological innovation conducted at level of each single firm,having the goal of obtaining amonopoly profit from selling new goods on the market,as originally pointed out by Schumpeter and Kaldor. Aggregate knowledge derived from investment in R&Dis considered as an externality and has the characteristics of public good nonrival and partially excludable.After that new goods entered into the market,the innovative component of those goods becomes afraction of aggregate knowledge available to all other firms that can imitate these goods and erode the initial monopoly power of the firm who started first.Those issues can be treated in two class of models. The first assumes the presence of externality connected to the accumulation of aparticular good, like knowledge,which are external to the firm but internal to the industrial sector or amarket. This allows to keep together the structure of aperfectly competitive market,and the profit motivation for accumulating knowledge is implicit in the model.The second class of models, instead,explicitly considers the profit motivation leading to the innovative activity in amodel with monopolistic competition in the final goods sector. In the first class of models,according to Romer (1986),Ztin ( ref: uno )represents the aggregate level of knowledge available to agiven economy.Ztis apublic good non-rival and non-excludable:knowledge is freely available to every agent of the society at no. The diffusion of knowledge is realized in two ways:through specialized journals,reviews and newspapers and, most importantly, through the sales of final goods produced by using investment in R&Drealized at the level of each single firm.Given nthe number of producer-consumers of an economy footnote , Zcan be defined as Z=nk.The interest rate is by r=JAwhich,evidently, is independent from k,and is therefore constant.The consequence of this will be agrowth rate continuously increasing over time.On the other hand,if J<1the BGP just obtained is suboptimal because of the presence of the externality deriving from Z,which is not taken into account by asingle-profit maximizing firm.Asocial planner will choose the optimal accumulation path by taking into account the externality effects:in this case interest rate would be r=A. The second class of models can be analyzed along the lines of Romer (1990)where the production function for final goods is Yt=AÝHt?HRÞJX0 NtzÝiÞdi 1?Jwhere Ais ascale parameter (constant),and the Ztfactor is given by Zt=X0 NtzÝiÞdi.Ztcan now be interpreted as the sum of all the i-th capital goods zÝiÞproduced by using the i-th project.HRis the amount of human capital employed in the production of new designs,while Ntindicates the total amount of designs of the economy.In this model the growth engine is entirely represented by the production of new projects which is assumed to be alinear function of Nt: 6 Nt=DHRNt # where Dis ascale parameter.. Equation ( ref: dod )describes the growth rate of new designs:the amount of new projects Ntdepends linearly on the existing level of projects footnote . The level of scientific knowledge represents the basis for further development of new projects.It is precisely in this sense that the existing amount of projects represents apositive externality.The growth rate of the economy is then given by ( ref: dod ),and it is constant because HRis assumed to be constant on aBGP.The mechanism just described and the relationship expressed by ( ref: dod )offsets the decreasing returns to scale,keeping bounded away from zero the growth rate of this economy footnote . Income Taxation In this section,Istart with the analysis of the role of fiscal policy in endogenous growth models.This section considers the effects of fiscal policy created by income taxation under two qualifications:apure income tax and aset of differentiated taxes on the returns on productive inputs.The income tax Consider now the introduction of aflat tax rate bon the aggregate income Ytproduced by using aCobb-Douglas production function ( ref: uno ).The income net-of-taxes is: Yt=Ý1?bÞAtKt JZt 1?J # Clearly,from ( ref: tred )the rate of return on the invested capital will be: rt=Ý1?bÞJAtKt Zt J?1 # After aquick inspection of ( ref: tred )-( ref: quatdici ) we note that the income tax reduces the real return on invested capital and inhibits the incentives to capital accumulation.As an example, consider now the Ak model.Given the utility function ( ref: quat ),the growth rate for the Ak model with atax rate on income is: L=Ý1?bÞA?N?_ a # In the model with knowledge spillover, as in Romer (1986,1989),the growth rate is: L=Ý1?bÞJA?N?_ a # In the two-sector model with human capital accumulation àla Rebelo (1991),the growth rate after tax will be: L=1 aßÝ1?bÞKQà1 1?J+K?N?_ # where Q=ÝJAÞKÝÝ1?KÞBÞ1?JJ 1?J 1?K K K. In the model with capital accumulation àla Lucas (1988)with IH=Btz2tHtinserted in ( ref: sei ),the growth rate will be: L=B?N?_ a # Finally,in the technological innovation model,we have: L=JD?_ a+J # From ( ref: quind )-( ref: dicia9 ) we can conclude that only for three cases out of five the growth effect of income tax rates is negative.In fact,this happens only for ( ref: quind )-( ref: dicias7 ):in all the other cases,fiscal policy does not have any effect at all on growth rate.There is asimple explanation of this result:in the models by Lucas (1988)and Romer (1990),the growth rate is entirely determined by the growth rate of human capital and that of accumulated projects.Therefore,since those activities are produced in non-taxed sector, the growth rate will not be affected by the fiscal structure introduced on the final goods sector. Thus, in atwo-sector model where human capital production is not taxed at all,growth rate is not affected by tax rates applied on the production of final goods. Moreover,it is easy to verify from ( ref: quind )-( ref: sed )that it does not exist any level of bsuch that the growth rate turns out to be maximized footnote . To highlight the mechanism behind this result we need to distinguish between direct and indirect effects of tax rates.Consider first direct effects:the introduction of atax rate lowers the rate of return on capital and,through the investment channel,produces anegative impact on the long-run growth rate.For the indirect effects,it is clear that in the Ak model they do not exist at all (see ( ref: quind )).However,the assumptions on the technology producing human capital are crucial in the determination of the effects of fiscal policy on the growth rate.In fact,from the growth rate given by ( ref: dicias7 ),if the production of human capital is not taxed,when income tax rate raises there will be the incentive to shift resources from the taxed sector to the untaxed one,by lowering the steady state ratio physical/human capital (thereafter K/H). Moreover,if the production of human capital is realized without physical capital -as in Lucas (1988)-the decline of the ratio K/Hincreases the real interest rate and this completely offsets the negative (direct)effect created by taxation. Instead,if human capital sector employes physical capital,as in ( ref: sette ),then the offsetting mechanism is only partial and the net effect on growth rate is negative. This discrepancy between Lucas (1988)and Rebelo (1991)model,is aconsequence of the fact that the production of human capital is indirectly taxed when physical capital is anecessary input,because the production of physical capital (final goods)is taxed.In fact,the taxation effects go from the sector producing final goods (physical capital)to the sector producing human capital, making impossible aperfect offsetting of fiscal distortions through movements in K/H. In Romer (1986),the global effects of taxation are somehow ambiguous.It was stressed before that this model produces asuboptimal equilibrium,since if J<1the growth rate of this model is lower than what it could be obtained by aSocial Planner.This non-optimality represents the main reason for the public intervention in this model.To restore Pareto optimality, it would useful to subsidize production through the revenue from alump sum tax or from a proportional tax on income. The taxation on private inputs The analytical context previously developed can be extended to the two-sector growth models of endogenous growth àla Lucas (1988)and Rebelo (1991),where income taxation is considered as taxation on the real returns of private inputs.If human capital is anon-market good,only the real returns on factors employed in the production of final goods will be taxed. The accumulation constraint for human capital sector is still given by ( ref: sei ).Also,the production functions for the final goods sector and human capital are given,respectively,by ( ref: otto )and ( ref: sette ).The real returns on Kand H,are given,respectively by rt kand rt h: rt k=JAv1tKt z1tHt J?1 # rt h=Ý1?JÞAv1tKt z1tHt J # Moreover,Iconsider the same the same depreciation rate for both physical and human capital, i.e.NK=NH=N.The accumulation constraint for the final goods sector is becomes footnote : 6 Kt=rt kv1Kt+rt hz1Ht?Ct?NKt?Gt # where Gtis public expenditure.The government budget constraint for this economy is: 6 Bt=rtBt+Gt?Tt # where Btrepresents the total amount of public debt issued at time t.The fiscal revenue Ttis defined as Tt¯bt krt kv1Kt+bt hrt hz1Ht.Therefore, considering ( ref: venti2 ),( ref: venti3 )and the definition of fiscal revenue Ttthe accumulation constraint for the final goods sector can be rewritten as:6 Bt+6 Kt=rtBt+Ý1?bt kÞrt kv1Kt+Ý1?bt hÞrt hz1Ht?Ct?NKt # To simplify matters,Iconsider the existence of no public debt,i.e.6 Bt=0. In this case,the government budget is continuously balanced at each instant t,i.e.Gt=Tt.Although in amodel with distortionary taxation public debt is not neutral,the growth rate effects of taxation do not change when government issues public debt. As discussed previously,the impact effect of taxation on growth depends upon the characteristics of human capital production function. In fact,if we consider the same analytical specification assumed by Lucas (1988),the growth rate is still given by ( ref: dici8 ),which establishes that any form of fiscal restraint imposed on the production of final goods does not have growth effects.As it was said before,this is due to the countervailing effect between resources employed in the two sectors:physical and human will tend to shift to the untaxed sector and the reduction of the ratio K/Hwill be compensated by an analogous offsetting of the real returns of both Kand H. If human capital is produced with physical capital as essential input,according to equation ( ref: sette )the growth rate will be affected by both tax rates bk,bh: L=1 aQÝ1?bkÞJKÝ1?bhÞKÝ1?JÞ1 1?J+K?N?_ # with Q=ÝJAÞKÝÝ1?KÞBÞ1?J1?J JK 1?K KÝ1?JÞ. From ( ref: venti5 )it is immediate to verify that both tax rates on physical and human capital have anegative impact on growth rate in amultiplicative manner.The magnitude of these effects depends upon technological parameters J,K,A,B,and the index of relative risk aversion a. Moreover,if the technology employed in the production of physical capital and human capital is the same,i.e.if J=Kand A=B,the steady state growth rate will be: L=1 aAßJÝ1?bkÞJàJßÝ1?JÞÝ1?bhÞJà1?J?N?_ # From ( ref: venti6 )it is still true that taxation produces distorsive effects,whose magnitude is directly related to the magnitude of J.Furthermore,if the level of fiscal pressure on both sectors is equal and production functions are the same,after setting bk=bh=b,equation ( ref: venti6 ) will be modified as follows: L=1 aJJÝ1?JÞ1?JAÝ1?bÞJ?N?_ # On the other hand,when technologies are different but bk=bh=b,the growth rate expression given by ( ref: dicias7 )is still valid here. Comparing equations ( ref: venti5 )-( ref: venti7 ) we can recognize the crucial role played by the parameters in the determination of the impact effect of taxes on growth rate.However,the cross substitution effects among factors induced by taxation will imply that an economy characterized by growth rate ( ref: venti5 )will grow at aslower growth rate than an economy characterized by ( ref: venti6 )or ( ref: venti7 ). It is worth to stressing that one crucial assumption of the above model is that human capital is not amarket good.By relaxing this assumption,it will be possible to extend to the production of human capital the same kind of tax structure on inputs above considered only for the sector producing physical capital,as in Stockey and Rebelo (1995)and Pecorino (1993).It is not difficult to justify the production of human capital as amarket activity.In fact,in many advanced economies it is possible to observe that human capital formation and educational activities can be activities market oriented,not dissimilarly from the production of physical capital.In this case,those activities become subjected to taxation as well.Since human capital enters directly into the production of final goods,as in ( ref: otto ),we may interpret human capital as an intermediate good produced by aseparate sector not integrated with the production of final goods. Thus, when the real returns of inputs employed in the production of final goods and human capital are taxed,we will end up with an expression of the growth rate depending upon all fiscal parameters of the model,showing up the problem of the double taxation of productive factors. In terms of the convergence issue two economies will exhibit the same growth rate and the same convergence rate not only if they are similar with respect to their technological parameters, but also if their fiscal structure will be equal.Those issues are crucial especially if we consider how many parameters enter into the definition of the growth rate. ytÝjÞ=X0 1ct jÝiÞdi.Let Ytbe the aggregate demand over all goods and agents expressed as: Yt=X0 1ytÝjÞdj.According to these considerations,we can rewrite ( ref: quaranta8 )as: ytÝiÞ Yt ?1 S=ptÝiÞ Pt # Consider now the problem for the representative firm.The production function for the i-th firm producing the i-th differentiated good is: ytÝiÞ=AitXit JLit 1?J # where Xit is the amount of differentiated good employed in the production of the i-th good. Define the capital aggregate Xjt as: Xjt =XtÝjÞ¯X0 1Kt jÝiÞS?1 S S S?1 # where Kt jÝiÞindicates the capital stock of good jemployed in the production of good i.In ( ref: 52 )Iassume the same elasticity of demand for final goods,S>1. Therefore,each firm i producing good iowned by agent jmaximizes its profit ^t jÝiÞdefined as: ^t jÝiÞ=ptÝiÞytÝiÞ?Rt jÝiÞKt jÝiÞ?WtÝiÞLtÝiÞ # In each instant firm ichooses the optimal amount of Kt jÝiÞand Lt jÝiÞin order to maximize its profit given by ( ref: 53 )subjected to ( ref: cinquanta )-( ref: 52 ).From the profit maximization condition we obtain the following expressions for the Rate of return on the productive factors Kt jÝiÞand Lt jÝiÞ: Rt jÝiÞ=1?1 SJAitXit J?1Lit j1?JKt jÝiÞ XtÝiÞ ?1 SytÝiÞ Yt ?1 S # Wt jÝiÞ=1?1 SÝ1?JÞAitXit JLit j?JytÝiÞ Yt ?1 S # From ( ref: 54 )-( ref: 55 ) we observe that the assumption of monopolistic competitive market makes factor remuneration different from what should be in aperfectly competitive market.In fact,if S=1then ( ref: 54 )-( ref: 55 )will be the same as in aperfect competitive market for final goods.In this formulation the mark-up over marginal cost is defined as W¯1?1 S S(the demand elasticity of final goods),higher will be the market power of the representative firm and higher will be the margin over costs. On the other hand,since Sis always strictly bigger than one (by assumption),then from ( ref: 54 )-( ref: 55 ) we have that factor remuneration are lower than in perfectly competitive markets. To get the equilibrium representation of the economy above described,Inormalize ( ref: quaranta5 )with respect to the aggregate price index which for simplicity is set equal to one,i.e.Pt=1. Moreover,Iassume the existence of asymmetric equilibrium across goods and agents,by supposing that all agents and firms are the same and that everybody makes the same choices among the differentiated goods to be consumed and invested. In order to aggregate over all agent,let Vt jÝiÞbe the total demand of good iexpressed by agent j,then the total demand for good iexpressed by all agents is VtÝiÞ=X0 1Vt jÝiÞdj.Therefore,under symmetry,we have: KtÝiÞ=Kt,XtÝiÞ=Xit =Xt,RtÝiÞ=Rt,WtÝiÞ=Wt,LtÝiÞ=Lit =Ltfor all i5ß0,1à. Moreover,we have that X0 1ptÝiÞctÝiÞdi =Ctwhich is the total consumption expressed by each agent i.The aggregate accumulation constraint ( ref: quaranta5 )will be: 6 Kt=Ý1?bÞRtKt?NKt+^t+WtLt?Ct # To make easier all the comparisons with the previous models,define with rtthe rate or return on capital in aperfectly competitive market (with S=0in the above model),i.e.rt=JAKt J?1Lt 1?J. Therefore,the rate of return in an economy with monopolistic competition is given by: Rt=1?1 Srt. L= 6 Ct Ct =1 aÝ1?bÞ1?1 Srt?N?_ # From ( ref: 57 ) we note that the presence of monopolistic competition adds an additional distortion to the growth rate which has amultiplicative effect with respect to the distorsive taxation.In other words:the distorsive effect of taxation is magnified by the presence of imperfectly competitive markets.The background just discussed represents agood starting point for the optimal taxation analysis as in Judd (1997),where it is shown that in presence of monopolistic competition,the optimal taxation on capital must be negative in order to compensate for the distortion coming from an imperfect good market. The model just presented is highly stylized.The same kind of framework can be easily generalized to all the models previously discussed, without changing the main result. Endogenous Labor Supply One of the typical assumptions of the neoclassical growth model is that agents adjust instantaneously their labor supply in response to whatsoever shock either on the production side or on the demand side.Recently,however,we have several models trying to analyze the growth effects of flat-rate taxes when an endogenous choice between labor and leisure is introduced in the model.Among the more representative papers in this area we have Jones,Manuelli and Rossi (1993),Roubini and Milesi-Ferretti (1994a,b),Milesi-Ferretti and Roubini (1995),Devereux and Love (1994, 1995).It does not exist neither aunique way to define “leisure”nor aunique, standard way to endogenize the choice between labor and leisure,as witnessed by the literature on Real Business Cycles (RBC).Among RBC studies,it is worth mentioning here Benhabib, Rogerson and Wright (1991),and Greenwood and Hercowitz (1991),who follow the definition of leisure as homework production,as in Becker (1965).With endogenous labor supply,the utility function ( ref: quat )can be generalized as follows: uÝCt,§tÞ=Ct SbݧtÞ1?S1?a 1?a # where §trepresents leisure in raw form and bis afunction such that b:ß0,1ษ+,with bv>0, bvv <0. Finally,Srepresents the fraction of utility allocated to each argument,interpreted also as the elasticity of intra-temporal substitution between consumption and leisure.The leisure in raw form §is defined as the total amount of time remaining to the single agent,after the fraction of time devolved to human capital accumulation and to the final goods production.One particular function for bis asimple linear case as bݧtÞ=§t.The model can be completed by considering together with ( ref: 58 )atwo-sector model as described by equation ( ref: sei )-( ref: otto ):in this case,§tis defined as §t=1?z1t?z2t(when we normalize to 1the endowment of time disposable to the single agent). The extension considered by ( ref: 58 )will add to the model another state variable §and one more first order condition that will make the set of first order conditions no more block-recursive.As aconsequence,in the expression of the growth rate we would have aterm depending upon z1and z2.To be more explicit,in atwo-sector economy let ®be aconstant term formed by all the parameters of the model,and let æ bݧÞbe afunction of z1and z2representing the fraction of human capital employed in the production of final goods (or physical capital)and human capital,whose sum can vary as response to fiscal policy shocks.The growth rate of this economy can be expressed as: L=1 a®æ bݧÞ?N?_ # Devereux and Love (1994, 1995)showed that fiscal policy has always adistorsive effect on growth rate when leisure is considered in araw form, independently upon the assumptions on the production function of final goods and human capital. Under alternative definitions of leisure we obtain different results.One possibility is to replace in ( ref: 58 )bݧtÞwith bݧtÞHt.In this case,leisure in raw form is adjusted by the level of human capital Ht:this extension defines the Quality time model of endogenous labor supply.In this case leisure is represented by aproduction function whose unique input is human capital and the output is interpretable as the result of aworking activity which uses afraction of labor different from what is supplied in the market or in the accumulation of human capital. In abroader sense,it is possible to extend the Quality time model to amore complex production function whose inputs are now physical and human capital.Let YNbe the final output obtained by using YN=fßÝ1?v1?v2ÞK,Ý1?z1?z2ÞHà.The utility function ( ref: 58 )can be extended to be: uÝCt,§tÞ=ßCt SYNt 1?Sà1?a§t ^Ý1?aÞ 1?a # Basically,the introduction of the production YNis like to insert athird sector into amodel producing anon-market good.In this context,fiscal policy will affect the choice between consumption and non-market activities (homework production function)and the intersectoral factor allocation.In fact,afiscal shock in the market oriented sectors will inhibit the supply of inputs to be employed in market sector by distracting resources in favor of the homework activities.In this sense,the production YNcan be interpreted as acomplex set of activities out of control of fiscal authorities:under this interpretation it represents apotential source of tax evasion.In fact,if non-market activities are produced with the same technology as market goods, then afiscal policy shock will shift the production from the “legal”sector to the “illegal”one, whose income is unobservable and therefore non taxable.Moreover,an high level of fiscal pressure on the “legal”sector will shift resources in favor of the “illegal”one, making even worse the problem of fiscal revenue collection,given the reduction of the tax base following from areallocation of productive resources. Finally,in atwo-sector model the functional specification of the non-market activities does not affect at all the analytical expressions of the growth rate,which is still given by ( ref: venti5 )-( ref: venti7 ),according to the various assumptions on the model. The Consumption Tax In the public finance literature consumption taxation has always played an important role. John Stuart Mill and more recently Fischer (1937)and Kaldor (1955)have offered arguments in favor of consumption taxes rather than income taxes.The traditional debate focused on both efficiency and equity arguments footnote . In particular,the Mill’sconcern is mainly related with an efficiency argument and is about the principle of double taxation of savings as aconsequence of an income tax,but not of aconsumption tax.In fact, taxing income distorts the consumption-saving decision,while aconsumption tax uniform over time imposes the same burden on current and future consumption.On the other hand,the relative optimality of consumption versus income taxation can be expressed as aquestion on the optimality of tax rates over current and future consumption.In fact,consumption tax introduces adistortion into the work-leisure choice.Therefore,the final judgement has to do with the relative substitutability of consumption and leisure at different point in time.According to standard optimal taxation principles,given that leisure is untaxed,we should tax more heavily goods that are more complementary and/or substitutable with consumption.Moreover,in aworld where labor supply is exogenous,auniform consumption tax is equivalent to awage tax when there is no leisure. Thus, in this last case,we are back to the traditional debate on relative optimality.between a wage (or consumption)tax rate and acapital tax rate.By following the same kind of argument about efficiency,it is also possible to reach different conclusions according to the particular specification adopted in the model.Ageneral presumption,however,implies that auniform consumption tax will be superior to income taxation if the utility function is separable between consumption and leisure and preferences are homothetic over consumption at different dates. Equity arguments are manly based on the view that it is fairer to tax people on what they consume rather than on what they produce,as stressed by Kaldor (1955). In the endogenous growth context,Devereux and Love (1994, 1995)showed in atwo-sector model that consumption tax affects negatively growth rate only if leisure is modelled in araw form.In fact,for amodel similar to that described by ( ref: 58 )and ( ref: 59 )with bݧtÞ=§t,we have that growth rate depends on the total amount of time spent in the market sector and in the human capital accumulation activity through the function bݧtÞ=§t.Therefore,aconsumption tax affects the choice on labor supply in both productive sectors through the usual mechanisms of income and substitution effects footnote . If leisure is modelled according to the homework production or Quality Time approach,then the consumption tax does not produce any effect at all on the growth rate.In fact,the mechanism at work here is exactly the same as we have seen in the discussion on taxation of the non-reproducible factors.There are no links between the homework activities and the aggregate consumption,given the fact that in the expression for the growth rate there is any variable describing the leisure allocation. The Investment Tax Following Rebelo (1991),assume that the production of new investment goods uses a proportion 1?ft, 0 <ft²1, of the entire amount of capital in amodel where the production function is of the Ak type.The accumulation constraint is:6 Kt=It=AÝ1?ftÞKtwhere It indicates the gross investment,and the other variable have the usual meaning.Suppose also that the production of consumption good Ctrequires aproportion ftof the aggregate capital stock with aCobb-Douglas production function: Ct=BÝftKtÞJTt 1?J # with 0<J²1. In ( ref: 60 )Ttis afixed non-reproducible factor and Bis aconstant productivity parameter.Let ptbe the relative price of investment goods in term of consumption goods and Ytbe the aggregate income.The resource constraint for this economy is Yt=Ct+ptIt. Suppose now that between the interest rate for loans denominated in consumption-goods term rcand the real return to capital rkholds the following arbitrage relation: rct =rkt + 6 pt pt # where 6 pt/ptindicates the rate of variation of the investment goods price expressed in terms of consumption good.It is just the non-constancy of ptwhich makes rct and rkt different.From the profit maximization condition for each single firm we obtain the usual condition of equality of the marginal product in both sectors (consumption and investment): ptÝ1?ftÞA=JBÝftKtÞJ?1 # Therefore,if ftis constant over time,we will have that 6 pt/pt=ÝJ?1ÞLkwhere Lkis the growth rate of physical capital.In other words:the price of capital good decreases with arate which is proportional to the growth rate of physical capital itself. The equilibrium on the aggregate capital markets requires that for agiven tax rate on physical capital bkthe rate of return rkwill be: rk=Ý1?fÞÝ1?bkÞA?N # Finally,from the arbitrage condition ( ref: 61 ) we have: rc=Ý1?fÞÝ1?bkÞA?N+ÝJ?1ÞLk # Therefore,with an isoelastic utility function having aconstant degree of relative risk aversion like ( ref: quat ),the consumption growth rate Lccan be expressed as:Lc=Ýrc?_Þ/a.By inserting ( ref: 64 )into the expression for Lcand using from ( ref: 60 )the fact that Lc=JLkwe get: Lk=Ý1?fÞÝ1?bkÞA?N?_ 1?Ý1?JÞa # Lc=JÝ1?fÞÝ1?bkÞA?N?_ 1?Ý1?JÞa # From ( ref: 65 )-( ref: 66 ) we have that taxation on investment is somehow similar to capital taxation and has negative consequences on the growth rate,as it appears from the fact that /Lc//bk<0. Moreover,the tax rate on physical capital which maximizes the consumption growth rate is equal to zero and corresponds to the optimal long-run tax rate on capital. The model just described is extremely stylized and does not consider aset of complex interactions deriving,for example,from the degree of substitution between factors in the production function of the two goods.However,even in amore complex model the results will be similar to what has been showed here:the investment tax is interpretable as atax on new capital and it affects growth and accumulation exactly in the same fashion as we have described in the previous sections. Optimal taxation The problem of optimal taxation has been implicitly treated in many cases considered in the previous sections.One of these examples is certainly represented by the Barro (1990)model where the growth maximizing tax rate is the same of the tax rate which maximizes the welfare of the representative agent,with aCRRA utility function. Probably,the more interesting case is the two-sector model where income taxation assumes the form of taxation of real returns of the productive inputs. The optimal taxation analysis can be thought as apart of the well known “Ramsey Problem” where the choices of the social planner on the optimal tax are constrained by the conditions describing the optimizing behavior of the representative agent.We can generally distinguish between two approaches:the first is adopted by Chamley (1985, 1986)and Judd (1987)in a growth model with exogenous technical progress.This approach finds the optimal tax structure as the result of the maximization of the indirect utility function of the representative agent subjected to the first order conditions derived as result of the optimal choice of the consumption plan.The second approach,mainly followed by Lucas (1990),Chari,Christiano and Kehoe (1991),Bull (1993a),Jones,Manuelli and Rossi (1993),Roubini and Milesi-Ferretti (1994a,b), Milesi-Ferretti and Roubini (1995),Corsetti and Roubini (1996),leaves directly to the social planner the task of finding the optimal quantities of consumption,production and investment plans subjected to the intertemporal budget constraint and the resource constraint.This method will deliver functional forms linking the optimal quantities to the tax rates.The comparison between the first order condition of the choice problem of the social planner and the first order of the representative agent will show the optimal tax structure. The optimal taxation analysis in exogenous growth models reveals that the optimal tax on capital should be zero,while the tax on labor should be positive. However,in endogenous growth models we obtain amultiplicity of results depending upon the particular assumptions considered in the model.In particular,if public expenditure is endogenous as,for example,in Barro (1990),Barro and Sala-i-Martin (1992),Jones,Manuelli and Rossi (1993),Judd (1990), Zhu (1992),then the optimal long-run tax on capital must be equal to zero.On the other hand,if public expenditure is endogenous and generates externalities in atwo-sector model along the same lines of Corsetti and Roubini (1996),then the optimal tax on physical and human capital strictly depends upon which factor appropriates the rents generated by public expenditure.For example,if physical capital is the factor appropriating rents from public expenditure,then the optimal tax on it will be positive and zero the tax on human capital (the reverse is true when human capital is the factor appropriating rents). On the other hand,if the externalities in the production function are generated by other factors and not by public expenditure,as in Romer (1987, 1990)and Lucas (1988),the optimal taxation plan considers subsidies for the activities with generating positive externalities footnote . When we consider some upper limits to tax rates on certain inputs,like for example human capital,the long run optimal tax rate on capital is positive again,as showed by Jones,Manuelli and Rossi (1993b). Adiscussion on the optimal structure of indirect taxation is conducted by Bull (1993a,b)and by Jones,Manuelli and Rossi (1993a).Moreover,the issue of an optimal consumption tax rate is discussed by Milesi-Ferretti and Roubini (1995). In an open economy context,the same type of analysis is conducted by Rebelo (1992),and Razin and Yuen (1992a,b). In the literature above cited it is generally showed that the results on the zero-tax rate on capital can be maintained even in the endogenous growth context, unless some particular assumptions are inserted in the model.Moreover,for awhatsoever functional form assumed for the homework activities in amodel with human capital accumulation,if there are not limits to human capital taxation,the optimal long-run tax rates on both human and physical capital should be zero.In particular,if labor supply is exogenously given and human capital formation does not require physical capital as necessary input,the optimal long run tax rate on physical capital is zero,while on human capital is positive. However,this is the unique case the two-sector model of endogenous growth without endogenous public expenditure where we have an asymmetry between long run optimal taxes on physical and human capital.In general,we have symmetric optimal tax rates on physical and human capital:both they are either positive or zero.Moreover, the positive optimal tax rate is obtained when there are rents to be appropriated or when there are some upper limits on taxation of some inputs footnote (in these cases we could also get asymmetry,as previously discussed).In exogenous growth models,instead,the asymmetry between the two tax rates is the usual result. Probably,one of the more striking result coming from the endogenous growth literature is the symmetric results on the fiscal tax rates on productive inputs,and its ability in discerning several particular cases where the asymmetric result cannot be obtained.It is worthwhile to stress that the symmetric result is almost anatural consequence,given the fact that with an asymmetric long run optimal tax structure the representative agent will have the incentive in misreporting the source of its income,in order to avoid fiscal pressure. Concluding Remarks This paper surveys some of the more important and recent results on the literature on fiscal policy and growth,in the endogenous growth context.Given the enormous amount of literature, this survey concentrated on infinite-horizon representative agent models with one and two productive sector, considering also the case of imperfectly competitive markets.It has been shown that the heterogeneity of results and point of views present in the literature strictly depends upon the particular assumption of the underlying model.This is also reflected on the optimal taxation analysis. 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