Economic Growth and the Role of Taxation-Theory

Transcription

1 Please cie his paper as: Myles, G. (2009), Economic Growh and he Role of Taxaion-Theory, OECD Economics Deparmen Working Papers, No. 713, OECD Publishing, Paris. hp://dx.doi.org/ / OECD Economics Deparmen Working Papers No. 713 Economic Growh and he Role of Taxaion-Theory Gareh D. Myles JEL Classificaion: H2, H3, O4

2 Unclassified ECO/WKP(2009)54 Organisaion de Coopéraion e de Développemen Économiques Organisaion for Economic Co-operaion and Developmen 15-Jul-2009 English - Or. English ECONOMICS DEPARTMENT ECO/WKP(2009)54 Unclassified ECONOMIC GROWTH AND THE ROLE OF TAXATION - THEORY ECONOMICS DEPARTMENT WORKING PAPERS NO.713 By Gareh D. Myles Universiy of Exeer and Insiue for Fiscal Sudies English - Or. English All Economics Deparmen Working Papers are available hrough OECD's inerne web sie a JT Documen comple disponible sur OLIS dans son forma d'origine Complee documen available on OLIS in is original forma

3 ABSTRACT/RESUMÉ Economic growh and he role of axaion Theory Economic growh is he basis of increased prosperiy. This makes he aainmen of growh a key objecive for governmens across he world. The rae of growh can be affeced by policy choices hrough he effec ha axaion has upon economic decisions and hrough producive public expendiures. This paper provides a self-conained inroducion o he economic modelling of growh and reviews he heoreical evidence on he exen of he link beween axaion and growh. JEL Classificaion: O4; H2, H3 Keywords: Economic growh; axaion; public policy La croissance économique e le rôle de la fiscalié - Théorie La croissance économique es au fondemen du progrès de la prospérié. Ceci fai de la croissance un objecif majeur pour les gouvernemens du monde enier. Le aux de croissance peu êre influencé par des choix de poliique économique relaifs à la fiscalié, laquelle a un effe sur les décisions économiques des agens e es liée aux dépenses publiques producives. Cee éude fourni une inroducion auonome à la modélisaion économique de la croissance e résume les résulas empiriques raian du lien enre la fiscalié e la croissance. Classificaion JEL : O4 ; H2 ; H3. Mos-clef : Croissance économique ; fiscalié ; poliique publique. Copyrigh OECD 2009 Applicaion for permission o reproduce or ranslae all, or par of, his maerial should be made o: Head of Publicaions Services, OECD, 2 rue André-Pascal, Paris CEDEX 16. 2

4 TABLE OF CONTENTS ABSTRACT/RESUMÉ... 2 ECONOMIC GROWTH AND THE ROLE OF TAXATION THEORY Inroducion Taxaion and Growh Exogenous Growh Solow Growh Model The Golden Rule Convergence Tax Policy Observaions Endogenous Growh The AK Model Human Capial Governmen Expendiure Innovaion Learning-By-Doing Technology Transfer Taxaion and Growh Concluding Commens Theoreical Predicions Level and Growh Effecs Tax Reforms Componens of Growh Educaion Research and Developmen Governmen spending Addiional issues Summary Conclusions APPENDIX 1. CALCULATING GROWTH RATES APPENDIX 2. OPTIMAL TAXATION REFERENCES Tables 1. Welfare Cos of Taxaion Growh Effecs of Tax Reform Effec on Seady-Sae Growh Rae Income Tax Elasiciies Effec of ax reform on capial and oupu

5 6. Educaion indicaors Esimaed rae of reurn o R&D Fla-ax reforms Figures 1. Dynamics of he Capial Sock The Seady Sae The Golden rule Consumpion and he saving rae Tax Rfae and Consumpion Growh Level and Growh Effecs Conribuion of R&D o produciviy growh

6 ECONOMIC GROWTH AND THE ROLE OF TAXATION THEORY 1 By Gareh D. Myles Universiy of Exeer and Insiue for Fiscal Sudies This discussion paper is he firs in a series of hree ha review he economic lieraure on he links beween axaion and economic growh. These papers are exraced from he repor Economic Growh and he Role of Taxaion prepared for he OECD under conrac CTPA/CFA/WP2(2006)31. The second and hird papers discuss he analysis of aggregae empirical daa and disaggregae daa respecively. 1. Inroducion 1. Economic growh is he basis of increased prosperiy. Growh is aained by he accumulaion of capial (boh human and physical) and from innovaions which lead o echnical progress. Accumulaion and innovaion raise he produciviy of inpus ino producion and increase he poenial level of oupu. 2. The rae of growh can be affeced by policy choices hrough he effec ha axaion has upon economic decisions. An increase in axaion reduces he reurns o invesmen (in boh physical and human capial) and Research and Developmen (R&D). Lower reurns mean less accumulaion and innovaion, and hence a lower rae of growh. This is he negaive aspec of axaion. Taxaion also has a posiive aspec. Some public expendiure can enhance produciviy, such as he provision of infrasrucure, public educaion, and healh care. Taxaion provides he means o finance hese expendiures and, indirecly, can conribue o an increase in he growh rae. 3. In mos developed counries he level of axes rose seadily over he course of he wenieh cenury: an increase from abou 5 10% of gross domesic produc (GDP) a he urn of he cenury o 30 40% a he end is ypical. Such a significan increase raises serious quesions abou he effec axaion has upon economic growh. This does no imply ha i is sraighforward o infer he effecs of axaion from aggregae economic daa. The posiive and negaive effecs of axaion will be muually offseing and only he ne effec (which may be very small) will be observed. 1 Thanks are due o Chrisopher Heady for iniiaing and supporing he projec, Nigar Hashimzade, Joel Slemrod, Sephen Bond, and paricipans a OECD presenaions as well as Irene Sinha for excellen ediorial suppor. Correspondance: Deparmen of Economics, Universiy of Exeer, Exeer, EX4 4PU, UK, gdmyles@ex.ac.uk 5

7 4. Unil recenly, economic models ha could offer insigh ino how o proceed beyond aggregae daa were lacking. Much of he lieraure on economic growh focused on he long-run equilibrium where oupu per head was consan or modelled growh hrough exogenous echnical progress. By definiion, when echnical progress is exogenous i canno be affeced by policy. The developmen of endogenous growh heory has overcome hese limiaions by explicily modelling he process hrough which growh is generaed. This allows he effecs of axaion o be raced hrough he economy and predicions made abou is effecs on growh. 5. The cenral quesion around which he paper focuses is how ax policy affecs growh. To answer his i is firs necessary o undersand wha deermines he rae of growh. The consrucion of economic models of he growh process has lead o many imporan insighs. This paper describes hese models of economic growh and heir employmen in simulaion analysis. Consequenly, he focus is almos enirely upon heoreical research. To complemen his analysis he following papers in he series review he empirical evidence on axaion and growh. 6. The paper is divided ino four main secions. Following his inroducion Secion 2 describes a simple concepual framework for reflecing on he link beween ax insrumens and economic growh. Exogenous growh models are reviewed in Secion 3 and endogenous growh models in Secion 4. Paricular emphasis is given o he channels hrough which endogenous growh can arise. Idenifying hese is essenial o racing he numerous roues hrough which he ax sysem can inerac wih he growh process. Secion 5 reviews simulaions of he basic endogenous growh model wih human capial accumulaion and hen proceeds o simulaion resuls in a wider range of models. This analysis is inended o clarify he effec ha axaion may have and o provide a poin of reference for he empirical research. Appendix 1 provides an inroducion o he compuaion and manipulaion of growh raes. Appendix 2 demonsraes he influenial resul ha in he long-run i is opimal o have a zero ax on capial. 2. Taxaion and Growh 7. Taxaion is linked o growh hrough he decisions of individual economic agens. A change in a ax modifies opimal choices and, via he equilibrium of he economy, ulimaely affecs he rae of growh. Many models have been employed o represen his process wih widely varying deails. Puing hese deails o one side i is always he case ha he effec of a ax change upon he growh rae of oupu is deermined by wo separae componens. These componens are now idenified in a very general framework. 8. Le he growh rae of oupu, g Y, be defined by g ( a (, ), a ( )) Y = gy , 2, (1) where a 1 and a 2 are wo acions (e.g., R&D expendiure and educaion) chosen by economic agens and i, i =1, 2 are he levels of wo axes (or of some oher policy insrumens). The funcions a i ( 1, 2 ), i = 1, 2, are reduced forms ha capure he dependence of acion choice upon policy. The funcion g Y ( ) represens he equilibrium growh rae as a funcion of acions. 9. Using (1) he effec of he variaion in ax i on growh can be calculaed as dg d Y i gy dai =. (2) a d i i 6

8 The oal effec is comprised of he effec of he ax upon acion, and he effec of acion upon he growh rae. Now even if he ax has a significan effec on he acion, so ha da i / di is large, i need no have a significan effec on growh if gy / ai is small. Conversely, even if he effec on he acion is small, he growh effec can sill be large if g / a is large. Y i 10. The consequence of his observaion is ha counries need no be alike in he response o axaion. Even if he economic agens behave in he same way (i.e. all reduce heir human capial invesmen in he same way when income ax is raised) he effec on growh may no be he same. If counries are srucurally differen - perhaps some obain growh from human capial accumulaion whereas ohers rely on R&D expendiure - hen he same ax policy may have very differen growh consequences. 11. Hence, undersanding he effec of axaion requires an undersanding boh of he componens ha comprise he oal change in growh. Looking a he response of acions o axes is no sufficien since he ax elasiciy of acions is only one par of he sory. This is he reason why i is imporan o undersand he channels hrough which growh originaes and why i is no enough o jus sudy componens individually. 12. A fair summary of he empirical evidence on growh is ha fairly firm esimaes of he ax effecs da i / d i are available in he lieraure and, in cases for which hey do no exis, here is an esablished and successful mehodology for obaining hem. Wha does no seem o exis is comprehensive knowledge of he growh effecs gy / ai. There are numerous heoreical predicions bu he empirical lieraure has been unsuccessful in obaining convincing esimaes. 3. Exogenous Growh 13. The exogenous growh heory ha developed in he 1950s and 1960s focussed upon he accumulaion of capial as he source of growh. If he level of saving exceeded he sum of depreciaion and populaion growh he capial-labour raio would rise over ime and generae growh in oupu per capia. Growh could also arise if he produciviy of a given sock of capial increased because of echnical progress. The emphasis upon capial accumulaion lef invesigaion of he source of echnical progress ouside he heory. I was assumed insead o arise as he oucome of an exogenous process. 14. The canonical form of hese growh models was based upon a producion funcion ha had capial and labour (wih labour measured in man-hours) as he inpus ino producion. Consan reurns o scale were assumed, as was diminishing marginal produciviy of boh inpus. Given ha he emphasis was upon he level and growh of economic variables, raher han heir disribuion, he consumpion side was modelled by eiher a represenaive consumer or a seadily growing populaion of idenical consumers. 15. The simples represenaion of consumers assumes ha boh he rae of saving and he supply of labour are consan. This model is a special case of he general Solow (1956) growh model. Alhough he assumpion of a consan saving rae eliminaes issues of consumer choice, he model sill reveals imporan lessons abou he limis o growh and he poenial for efficiency of he long-run equilibrium. The key finding is ha if growh occurs only hrough he accumulaion of capial, here has o be a limi o he growh process if here is no echnical progress. 16. The fac ha here are limis o growh in an economy when here is no echnical progress can be mos easily demonsraed in a seing in which consumer opimisaion plays no role. Insead, i is assumed ha a consan fracion of oupu is invesed in new capial goods. This assumpion may seem resricive bu i allows a precise derivaion of he growh pah of he economy. The basic model has also been used o 7

9 moivae much empirical work. In addiion he main conclusions relaing o limis on growh are lile modified even when an opimising consumer is inroduced. 3.1 Solow Growh Model 17. Consider an economy wih a populaion ha is growing a a consan rae. Each person works a fixed number of hours and capial depreciaes parially when used. There is a single good in he economy which can be consumed or saved. The only source of saving is invesmen in capial. Under hese assumpions, he oupu ha is produced a ime, Y, mus be divided beween consumpion, C, and invesmen, I. In equilibrium, he level of invesmen mus be equal o he level of saving. 18. Wih inpus of capial K and labour L employed in producion, he level of oupu is ( K L ) Y = F,. (3) I is assumed ha here are consan reurns o scale in producion. Oupu can be eiher consumed or saved. The fundamenal assumpion of he model is ha he level of saving is a fixed proporion s, 0 < s < 1, of oupu. As saving mus equal invesmen in equilibrium, a ime invesmen in new capial is given by ( K L ) I = sf,. (4) The use of capial in producion resuls in is parial depreciaion. Assume ha his depreciaion is a consan fracion δ, so he capial available in period + 1 is given by new invesmen plus he undepreciaed capial, or K +1 = I + δk ( K L ) + ( δ ) K = sf, 1. (5) Equaion (5) is he basic capial accumulaion relaionship ha deermines how he capial sock evolves hrough ime. 19. The fac ha he populaion is growing makes i preferable o express variables in per capia erms. This can be done by exploiing he assumpion of consan reurns o scale in he producion funcion o wrie Y = L F( K / L,1) = L f ( k ) where k K / L. Dividing (5) hrough by L, he capial accumulaion relaion (5) becomes K L + 1 = sf ( k ) + 1 ( δ ) L K. (6) 20. Denoing he consan populaion growh rae by n, labour supply grows according o L + 1 = ( 1+ n) L. Using his growh relaionship, he capial accumulaion relaion shows ha he dynamics of he capial/labour raio are governed by ( + n) k + = sf ( k ) + ( 1 δ ) k 1 1. (7) 8

10 The relaion in (7) races he developmen of he capial sock over ime from an iniial sock a ime 0, k 0 = K0 / L0. To see wha is implied by (7) consider an example where he producion funcion has he α form f ( k ) = k. The capial/labour raio mus hen saisfy k + 1 sk = α ( 1 δ ) + 1+ n k. (8) For he parameers k 0 = 1, n = 0. 05, δ = 0. 05, s = 0. 2 and α = 0. 5, Figure 1 plos he firs 50 values of he capial sock. I can be seen ha saring from he iniial value of k 0 = 1 he capial sock doubles in 13 years. Afer his he rae of growh slows noiceably and even by he 50h year i has no ye doubled again. The figure also shows ha he capial sock is ending o a long-run equilibrium level which is called he seady sae. For he parameers chosen, he seady sae level is k = 4 which is virually achieved a = 328, hough he economy does reach a capial sock of 3.9 a = 77. I is he final par of he adjusmen ha akes a significan period of ime. k Figure 1: Dynamics of he Capial Sock The seady sae is defined by a consan capial-labour raio, so k +1 = k. Denoing he seady sae value of he capial-labour raio by k, he capial accumulaion condiion (7) shows ha k mus saisfy or ( + n) k = sf ( k ) + ( 1 δ )k 1, (9) ( k) ( n + ) k = 0 sf δ. (10) The soluion o equaion (10) is called he seady sae capial-labour raio and can be inerpreed as he economy's long-run equilibrium value of k. 22. The naure of he soluion o equaion (10) is illusraed in Figure 2. The seady sae occurs sf k and ( n + δ )k inersec. If his poin is achieved by he economy, he capial-labour where he curves ( ) 9

11 raio will remain consan. Since k is consan, i follows from he producion funcion ha Y / L will remain consan as will C / L, where C is aggregae consumpion a ime. (However, i should be noed ha as L is growing a rae n, hen he values of Y, K and C will also grow a rae n in he seady sae.) I is he consancy of hese variables ha shows here is a limi o he growh achievable by his economy. Once C / L is consan, he level of consumpion per capia will remain consan over ime. In his sense, a limi is placed upon he growh in living sandards ha can be achieved. The explanaion for his limi is ha capial suffers from decreasing reurns when added o he exogenous supply of labour. If excessive capial is employed he reurn will fall so low ha he capial sock is unable o reproduce iself. Figure 2: The Seady Sae Oupu Consumpion f ( n + δ )k sf () k ( k ) k Capial 23. Alhough no policy variables have ye been included, his analysis of he seady sae can be used o reflec on he poenial for economic policy o affec he equilibrium. Sudying Figure 2 reveals ha he equilibrium level of k can be raised by any policy ha engineers an increase in he saving rae, s, or an upward shif in he producion funcion, f ( k). However, any policy ha leads only o a one-off change in s or f ( k) canno affec he long-run growh rae of consumpion or oupu. By definiion, once he new seady sae is achieved afer he policy change, he growh raes of he per capia variables will reurn o zero. Furhermore, any policy ha only increases s canno susain growh since s has an upper limi of 1 which mus evenually be reached. If policy inervenion is o resul in susained growh i has o produce a coninuous upward movemen in he producion funcion. In he model as so far formulaed here is no mechanism hrough which his can be achieved. 24. A means for growh o be susained wihou policy inervenion is o assume ha oupu increases over ime for any given levels of he inpus. This can be achieved hrough labour or capial (or boh) becoming more producive over ime for exogenous reasons summarised as echnical progress. A way o incorporae his in he model is o wrie he producion funcion as f ( k, ), where he dependence upon capures he echnical progress which allows increased oupu. Technical progress resuls in he curve f ( k, ) in Figure 2 coninuously shifing upward over ime, hus raising he seady sae levels of capial and oupu. The drawback of his approach is ha he mechanism for growh, he growh engine, is 10

12 exogenous so prevening he model from explaining he mos fundamenal facor of wha deermines he rae of growh. This deficiency is addressed by he endogenous growh models described in he nex secion ha explore he mechanisms ha can drive echnical progress. 3.2 The Golden Rule 25. Reurning o he basic model wihou echnical progress, condiion (10) shows he seady sae capial/labour raio is dependen upon he saving rae, s. The observaion of his dependence raises he quesion of wheher some saving raes are beer han ohers. 26. To address his quesion, i is noed firs ha for each value of s here is a corresponding seady-sae capial/labour raio a he inersecion of sf ( k) and ( n + δ )k. I is clear from Figure 2 ha for sf will inersec he curve ( n + δ )k a low values of k. As s is increased, low values of s, he curve ( k) sf ( k) shifs upwards and he seady sae level of k will rise. The relaionship beween he capial-labour raio and he saving rae implied by his consrucion is denoed by k = k() s. The consrucion shows ha k = k s is an increasing funcion of s up unil he maximum value of s = 1. () 27. Taking accoun of he link beween s and k, he level of consumpion per capia can be wrien c () s ( s) f ( k() s ) = f ( k( s) ) ( n + δ ) k( s) = 1, (11) where he second equaliy follows from definiion (10) of a seady sae. Wha is of ineres are he properies of he saving rae ha maximises consumpion. The firs-order condiion for defining his saving rae can be found by differeniaing c () s wih respec o s. Doing so gives () s dc ds Since k' () s is posiive, he saving rae, [ f '( k() s ) ( n + )] k' () = 0 = δ s. (12) * f ( k( s ) = ( n +δ ) * * * s deermines a level of capial k( s ) * s, ha maximises consumpion is defined by '. (13) The saving rae k = which is called he Golden Rule capial-labour raio. If he economy achieves his capial-labour raio a is seady sae i is maximising consumpion per capia. 28. The naure of he Golden Rule is illusraed in Figure 3. For any level of he capial-labour raio, he seady sae level of consumpion per capia is given by he verical disance beween he curve ( n + δ )k and he curve f ( k). This disance is maximised when he gradien of he producion funcion is equal o ( n +δ ) which gives he Golden Rule condiion. The figure also shows ha consumpion will fall if he capial/labour raio is eiher raised or lowered from he Golden Rule level. An economy wih a * seady-sae capial sock below he Golden Rule level, k, is dynamically efficien - i requires a sacrifice of consumpion now in order o raise k so a Pareo-improvemen canno be found. An economy wih a * capial sock in excess of k is dynamically inefficien since immediae consumpion of he excess would raise curren welfare and place he economy on a pah wih higher consumpion. 11

13 Figure 3: The Golden rule Oupu f ( k ) Consumpion ( n + δ ) k * k Capial 29. As an example of hese calculaions, le he producion funcion be given by For a given saving rae s he seady sae is defined by he soluion o α y = k, wih α < 1. sk α = ( n + δ )k. (14) Solving his equaion deermines he seady sae capial/labour raio as soluion, he per capia level of consumpion follows as k * s = n + δ 1/ ( 1 α ). Using his * ) ( * α k ) ( n + δ ) * c( s = k s = n + δ α / ( 1 α ) ( n + δ ) s n + δ 1/ ( 1 α ). (15) 30. Adoping he parameer values n = , δ = and α = 0. 75, he level of consumpion is ploed in Figure 4 as a funcion of s. The figure shows ha consumpion rises wih s unil he saving rae is reached a which he equilibrium capial sock is equal o he Golden Rule level and hen falls again for higher values. 12

14 Figure 4: Consumpion and he saving rae c s 31. Formally, he fac ha he saving rae is assumed fixed leaves lile scope for he analysis of policy. However, sudying he effec of changes in he saving rae reveals he facors ha would be a work in a more general model in which he level of saving is a choice variable ha can be affeced by policy. The degree o which a change in saving can affec welfare is limied by he fac ha he per capia levels of all economic variables are consan once he seady sae has been achieved. Consequenly, for any given saving rae, he sandard of living in he economy reaches a limi and hen canno grow any furher unless he producion funcion is coninually raised. Changes in he saving rae affec he long-run level of consumpion bu no is growh rae. 3.3 Convergence 32. The Solow model has a furher implicaion ha is imporan for undersanding he oucome of he growh regressions discussed in Myles (2007a). This is he propery of convergence beween counries. 33. The seady-sae level of per capia income depends only upon he saving rae. As a consequence, wo counries ha have access o he same producion echnology and have he same saving rae mus evenually converge o he same seady-sae level of per capia income. Since here are decreasing reurns o he accumulaion of capial an addiional uni of capial added o he sock of a low-capial counry will lead o a greaer increase in oupu han an addiional uni added o he sock of a high-capial counry. Along he ransiion pah o he seady sae counries wih low capial-labour raios mus herefore grow faser han counries wih high capial-labour raios. This is he only way in which hey can ulimaely arrive a he same seady sae. Hence, cross-counry daa on growh and oupu levels can be expeced o show ha he rae of growh is inversely relaed o he capial-labour raio. If here is rade beween economies he rae of convergence should be faser han wihou. A counry wih a low capial-labour raio will offer a higher reurn o capial so should arac invesmen. This will cause quicker growh in he capial sock and hence faser convergence. 34. A formal demonsraion of convergence can be given as follows. The change in he capial sock wih respec o ime in he Solow growh model is 13

15 so he growh rae of he capial sock is Therefore g k ( k) ( n + δ )k k & = sf, (16) ( k ) k& sf = = n k k ( + δ ) ( k). (17) g k s f = f '( k) < 0. (18) k k k The inequaliy in (18) shows ha he higher is he level of capial he slower is he rae of growh. 35. Now consider wo counries ha differ in heir capial socks bu are oherwise idenical. From (18) he counry wih he lower capial sock and consequenly lower oupu - will grow faser. This is ermed absolue convergence (or absolue β convergence). The daa sugges ha absolue convergence does no apply when a large number of heerogeneous counries are considered bu is a characerisic for more homogeneous ses of counries or regions (see Barro and Sala-i-Marin, 1995). 36. A weaker concep of convergence is condiional convergence (or condiional β convergence). If counries differ in underlying parameers hen heir seady saes will also be differen. Condiional convergence is he proposiion ha counries furher from heir own seady sae grow faser. 3.4 Tax Policy 37. The Solow model wih a consan saving rae leaves lile role for ax policy o affec he rae of growh. The saving rae could be made variable bu here would sill be a limied number of economic choices ha can be axed in he Solow framework. Consequenly he appendix o his chaper analyses opimal axaion in he more general Ramsey model of growh. This model assumes a single consumer bu endogenises he choice of consumpion, labour supply, saving, and invesmen. This permis axaion o disor decisions over hese four variables. 38. The cenral resul of he ax analysis is he Chamley (1986) and Judd (1985) finding ha in he long-run he opimal ax on capial income should be zero. Several commens can be offered on his resul. Firsly, noe ha he resul does no say ha he ax should be zero along he growh pah o he seady sae - i is derived assuming he economy is in he seady sae so applies only o ha siuaion. This does no preven he ax being posiive (or negaive) along he growh pah. Secondly, he zero ax on capial income implies ha all axaion mus fall upon labour income. If labour were a fixed facor his conclusion would no be a surprise, bu here labour is a variable facor. Finally, he reason for avoiding he axaion of capial is ha he reurn on capial is fundamenal o he ineremporal allocaion of resources by he consumer and because of he ineremporal srucure he consequences of he disorion accumulae over ime. The resul shows ha i is opimal o leave his allocaion undisored o focus disorions upon he choice beween consumpion and labour wihin periods. 39. Since he opimal ax rae is zero, any oher value of he ax on capial mus lead o a reducion in welfare compared o he maximum ha is achievable. An insigh ino he exen of he welfare cos of deviaing from he opimal soluion is given in Table 1. These resuls are derived from a model wih a Cobb-Douglas producion funcion and a uiliy funcion wih a consan elasiciy of ineremporal subsiuion (see (31) below). The policy experimen calculaes wha would happen if a ax on capial was 14

16 replaced by a lump-sum ax. The increase in consumpion and he welfare cos are measured by comparing he seady sae wih he ax o he seady sae wihou. When a ax rae of 30% on capial income is replaced by a lump-sum ax, consumpion increases by 3.3% and he welfare cos of he disorionary ax is measured a 11% of ax revenue. The increase in consumpion and he welfare cos are boh higher for an iniial 50% ax rae. In boh cases he increase in consumpion and he welfare cos are significan. Table 1: Welfare Cos of Taxaion Iniial Tax Rae (%) Increase in Consumpion (%) Welfare Cos (% of Tax Revenue) Source: Chamley (1981) 40. In summary, he opimal ax policy is o se he long-run ax on capial o zero. This oucome is explained by he need o avoid ineremporal disorions. As a consequence, all revenue mus be raised by he axaion of labour income. This will cause a disorion of choice wihin periods bu does no affec he ineremporal allocaion. The conclusion is very general and does no depend upon any resricive assumpions. Simulaions of he welfare cos of non-opimal policies show ha hese can be a significan percenage of he revenue raised. 3.5 Observaions 41. The Solow model inroduces he concep of a seady sae and demonsraes ha capial accumulaion is no sufficien o ensure coninuing growh if no mached by echnological progress or equal increases in oher inpus. The appeal o echnological progress as he source of growh illusraes he need for an undersanding of he source of echnical progress - he assumpion of progress deriving from some exogenous process is jus no good enough. The model also predics convergence if counries have he same echnology. This is a helpful observaion for undersanding he resuls of cross-counry comparisons of growh. Finally, he Solow model provides he basis for underaking growh accouning exercises (see Myles, 2007a) ha provide key insighs ino he sources of growh. 4. Endogenous Growh 42. The growh of oupu per capia is limied in he exogenous growh model because of decreasing reurns o capial. The marginal produc of each addiional uni of capial falls bu he rae of depreciaion is consan. As he capial sock is increased a poin is reached a which he marginal produc of capial maches he rae of depreciaion, so he ne marginal oupu is zero. The removal of he limi o growh requires he decreasing marginal produc of capial o be removed from he model. Ideally, his removal should also reflec choices of economic agens. Models ha allow boh susained growh and explain is source are said o generae endogenous growh. 43. There have emerged in he lieraure numerous ways hrough which endogenous growh can be achieved. All of hese approaches achieve he same end - ha of susained growh - bu by differen roues. These approaches are now described and hen aenion is focused on he role of ax policy in growh from he perspecive of hese models. 15

17 4.1 The AK Model 44. The firs, and simples, approach o modelling endogenous growh is he AK model (Romer, 1986). This model assumes ha capial is he only inpu ino producion and ha here are consan reurns o scale. This may seem a firs sigh o simply remove he problem of decreasing reurns by assumpion, bu Secion 4.2 will show ha he AK model can be given a broader inerpreaion involving he combinaion of human and physical capial. 45. The producion funcion for he AK model is given by Y = AK, (19) whose form explains he model's name. The assumpion of consan reurns o scale ensures ha oupu grows a he same rae as he capial sock. 46. To show ha his model can generae coninuous growh, i is simples o reurn o he assumpion of a consan saving rae. Wih a saving rae s he level of invesmen in ime period is I = sak. Since here is no labour, he capial accumulaion condiion is jus K + 1 = sak + 1 ( δ ) K ( + sa δ ) K = 1. (20) Provided ha sa > δ, so invesmen is in excess of depreciaion, he level of capial will grow linearly over ime a rae sa δ. Oupu will grow a he same rae, as will consumpion. The model is herefore able o generae coninuous growh. 47. The only variable ha is he oucome of an economic choice in he AK model is he saving rae, s. This limis poenial policy effecs bu does draw aenion o he effec ha axaion can have upon saving. The empirical evidence on he effec of axaion upon saving is discussed in Myles (2007b). 4.2 Human Capial 48. The second approach o ensure susained growh is o mach an increase in capial wih equal growh in oher inpus. One way o do his is o replace labour ime as an argumen in he producion funcion wih a more general concep of human capial. Assuming ha he level of human capial is a sock variable hen permis is accumulaion over ime. 49. A model including human capial involves wo invesmen processes: one for invesmen in physical capial and anoher for invesmen in human capial. There can eiher be one secor, wih human capial produced by he same echnology as physical capial, or wo secors wih a separae producion process for human capial. These differences become significan when policy simulaions are discussed in Secion The human capial variable can be enered ino he producion funcion in wo differen ways. The firs reamen is o view he level of human capial as he produc of he qualiy of labour, h, and he quaniy of labour ime, L. Human capial is hen given by H = h L. In his approach labour ime is made more producive by invesmen in educaion and raining which raise he qualiy of labour. Technical progress is hen embodied in he qualiy of labour. The sandard form of producion funcion for such a model would be 16

18 ( K H ) Y = F,, (21) where H is he level of human capial. If he producion funcion has consan reurns o scale in human capial and physical capial joinly, hen invesmen in boh can raise oupu wihou limi even if he quaniy of labour ime is fixed. 51. The one-secor model wih human capial reduces o he AK model - his is he broader inerpreaion of he AK model referred o above. To see his, noe ha under he one-secor assumpion oupu can be used for consumpion or invesed in physical capial or invesed in human capial. The wo capial goods are perfec subsiues for he consumer in he sense ha a uni of oupu can become one uni of eiher. The perfec subsiuabiliy implies ha in equilibrium he wo facors mus have he same rae of reurn. Combining his wih he assumpion of consan reurns o scale in he producion funcion implies he wo facors are always employed in he same proporions. Therefore he raio H / K is consan for all. Denoing his consan value by H/K, he producion funcion becomes H Y = KF = AK, (23) K where A F( H / K). This reduces he producion funcion o he AK form. 52. The second reamen is o consider human capial as a disinc variable o labour ime. This gives a producion funcion of he form ( K, H L ) Y = F,. (22) This formulaion is less common bu is encounered in he imporan work of Mankiw e al. (1992) ha is discussed in Myles (2007a). 53. In a wo-secor model i is possible o have differen producion funcions for he creaion of he wo ypes of capial good. This eliminaes he resricion ha hey are perfec subsiues and disinguishes he model from he AK seing. A wo-secor model also allows differen human and physical capial inensiies o be incorporaed in he producion of he wo ypes of capial. This can make i consisen wih he observaion ha human capial producion ends o be more inensive in human capial inpu hrough he requiremen for skilled eaching saff ec. 54. When human capial is incorporaed ino he model he role for policy is exended. The accumulaion of human capial can be viewed as he oucome of an educaional process. This focuses aenion on how he ax sysem affecs he decision o underake invesmens in educaion. The ineracion wih labour supply also raises he issue of axaion and labour supply. The empirical evidence on hese issues is considered in Myles (2007b). However, labour supply is naurally bounded. This makes i impossible o susain growh hrough increases in labour alone. 4.3 Governmen Expendiure 55. Endogenous growh can arise when capial and labour are augmened by addiional inpus in he producion funcion. One case of paricular ineres for undersanding he link beween governmen policy and growh arises when he addiional inpu is a public good financed by axaion (Barro, 1990). The exisence of a public inpu provides a posiive role for public expendiure and a direc mechanism hrough which policy can affec growh. This opens a pah o an analysis of wheher here is a sense in which an opimal level of public expendiure can be derived in a growh model. The analyical deails of his model 17

19 are described below because i is an imporan ool for hinking abou he channels hrough which public expendiure can impac upon growh. 56. A public inpu can be inroduced by assuming ha he producion funcion for he represenaive firm a ime akes he form 1 α α 1 α Y = AL K G, (24) where A is a posiive consan and G is he quaniy of he public inpu. The srucure of his producion funcion ensures ha here are consan reurns o scale in L and K for he firm given a fixed level of he public inpu. Alhough reurns are decreasing o privae capial as he level of capial is increased for fixed levels of labour and public inpu, here are consan reurns o scale in public inpu and privae capial ogeher. For a fixed level of L, his propery of consan reurns o scale in he oher wo inpus permis endogenous growh o occur. 57. I is assumed ha he public inpu is financed by a ax upon oupu. Assuming ha capial does no depreciae in order o simplify he derivaion, he profi level of he firm a ime is 1 α α 1 α ( τ ) AL K G r K w L π = 1, (25) where r is he ineres rae, w he wage rae, and τ he ax rae. From his specificaion of profi, he choice of capial and labour by he firm saisfy and 1 α α 1 1 α ( τ ) αal K G = r 1, (26) α α 1 α ( τ )( 1 α ) AL K G = w 1. (27) The governmen budge consrain requires ha ax revenue equals he cos of he public good provided, so G = τ. (28) Y 58. Now assume ha labour supply is consan a L = L for all. Wihou he public inpu, i would no be possible given his assumpion o susain growh because he marginal produc of capial would decrease as he capial sock increased. Wih he public inpu growh can be driven by a join increase in privae and public capial even hough labour supply is fixed. Using (24) and (28), he level of public inpu can be wrien as G 1/ α ( A) L ( 1 α τ ) / α K =. (29) This resul can be subsiued ino (26) o obain an expression for he ineres rae as a funcion of he ax rae 1/ ( ) α ( ) ( 1 τ α τ α ) / 1 A α r = L. (30) 18

20 59. The economy's represenaive consumer is assumed o have preferences described by he uiliy funcion U β = = 1 1 σ C 1. (31) 1 σ This specific form of uiliy is adoped o permi an explici soluion for he seady sae. The consumer chooses he pah { C } over ime o maximise uiliy. The sandard condiion for ineremporal choice mus hold for he opimisaion, so he raio of he marginal uiliies of consuming a and a + 1 mus equal he gross ineres rae. Hence U / C U / C + 1 C βc σ σ + 1 = 1+ r + 1. (32) Solving for C + 1 / C and hen subracing C / C from boh sides of he resuling equaion allows his opimaliy condiion o be wrien in erms of he growh rae of consumpion C C 1/ ( β ( 1+ r )) σ = + 1 C. (33) Finally, using equaion (30) o subsiue for he ineres rae, he growh rae of consumpion is relaed o he ax rae by C C 1/ α ( ( ) ( ) ( 1 α 1 1 ) / α 1/ σ + τ αa Lτ ) / σ = β C. (34) 60. The resul in (34) demonsraes he wo channels hrough which he ax rae affecs consumpion growh. Firsly, axaion reduces he growh rae of consumpion hrough he erm ( 1 τ ) which represens he effec on he marginal reurn of capial reducing he amoun of capial used. Secondly, he ax rae increases growh hrough he erm ( 1 α )/ α τ which represens he gains hrough he provision of he public inpu. 61. Furher insigh ino hese effecs can be obained by ploing he relaionship beween he ax rae and consumpion growh. This is shown in Figure 5 for he parameer values A = 1, L = 1, α = 0. 5, β = 0.95 and σ = The figure displays several noable feaures. Firs, for low levels of he public inpu growh is negaive, so a posiive ax rae is required for here o be consumpion growh. Secondly, he relaionship beween growh and he ax rae is non-monoonic: growh iniially increases wih he ax rae, reaches a maximum, and hen decreases. Finally, here is a ax rae which maximises he growh rae of consumpion. Differeniaing (34) wih respec o τ, he ax rae ha maximises consumpion growh is τ =1 α. (35) For he values in he figure, his opimal ax rae is τ = To see wha his ax rae implies, observe ha 19

21 Y G = Y α, (36) G ( 1 ) = 1 using G = τy and τ =1 α. Hence he ax rae ha maximises consumpion growh ensures ha he marginal produc of he public inpu is equal o 1 which is also is marginal cos. Figure 5: Tax Rfae and Consumpion Growh c s 62. This model reveals a posiive role for governmen in enhancing growh hrough he provision of a public inpu. I illusraes ha here can be an opimal level of governmen. Also, if he size of governmen becomes excessive i reduces he rae of growh because of he disorions imposed by he ax used o finance expendiure. Alhough simple, his model does make i a legiimae quesion o consider wha he effec of increased governmen spending may be on economic growh. 63. The oucome of his analysis should be borne in mind when empirical evidence on he link beween axaion and growh is analysed. In paricular, even his basic model is able o demonsrae ha axaion used o finance producive governmen expendiure can have a beneficial effec on he growh rae. Furhermore, if counries opimise in he choice of ax rae (or, equivalenly, in he level of governmen expendiure) hen variaions in he ax rae will have lile effec upon he growh rae around he opimum. This poin is discussed furher in Myles (2007a). 4.4 Innovaion 64. The innovaion approach o endogenous growh develops he ideas of Schumpeer (1934) abou creaive desrucion - he idea ha new producs and processes appear ha are superior o exising ones and evenually replace hem. The firs aemp o formally model his process is aribued o Segersrom e al. (1990) bu mos focus has been placed on he work of Aghion and Howi (1988, 1992). This line of research is surveyed in Aghion and Howi (1998). 65. The firs aspec of he creaive process ha has been modelled is he inroducion of new inermediae goods. Assume ha oupu depends upon he quaniy of labour used and a range of oher inpus. Technological progress can hen ake he form of he inroducion of new inpus ino he producion 20

22 funcion wihou any of he old inpus being dropped. This allows producion o increase since he expansion of he inpu range prevens he level of use of any one of he inpus becoming oo large relaive o he labour inpu. 66. The second aspec is he replacemen of exising producs by beer producs. In his represenaion echnological progress akes he form of an increase in he qualiy of inpus. Expendiure on research and developmen resuls in beer qualiy inpus which are more producive. Over ime, old inpus are replaced by new inpus and oal produciviy increases. Firms are driven o innovae in order o exploi he posiion of monopoly ha goes wih ownership of he laes innovaion. This is he process of creaive desrucion which was seen by Schumpeer as a fundamenal componen of echnological progress. 67. The mechanics of a basic model of research and developmen can be described as follows. Assume ha here is a coninuum of ypes of final good available. Final good i is produced using a unique inermediae good according o he producion funcion a ime α Y i = Ai xi. (37) In his expression x i is he quaniy of inermediae good used and A i is he level of echnology. Each inermediae good is supplied by he firm ha made he mos recen innovaion for ha inermediae good. Being he sole innovaor gives he inermediae supplier a monopoly posiion. 68. The research secor for inermediae good i employs n i unis of labour and innovaions arrive a he Poisson arrival rae λ ni. When an innovaion arrives for good i i raises he echnology parameer max max from A i o A, where A is he highes aainable echnology a ime. The firm making he new innovaion hen has a monopoly posiion unil he nex innovaion. The maximum aainable echnology rises over ime a a rae proporional o he oal flow of innovaions, and hence proporional o he labour employed in research. In a symmeric equilibrium each secor employs n unis of labour in research and & max max A A = bλn, (38) where b is a facor of proporionaliy. 69. The level of research in equilibrium equaes he cos of labour in research o he expeced benefi of making he nex innovaion. The level of expeced benefi is dependen on he reurn ha is earned by an innovaor during he ime operaing as a monopolis unil he nex innovaion is made. An increase in he value of λ encourages research by making innovaions arrive more quickly bu discourages research by reducing he expeced enure as a monopolis. The same effecs are presen for a change in he value of he innovaion parameer, b. 70. The focus for policy analysis suggesed by hese models of creaive desrucion is he effec of axaion on he incenive o innovae. The ax reamen of profi operaes on he ne reurn o innovaion. A subsidy o R&D reduces he cos of innovaion. These observaions are he basis of he empirical lieraure discussed in Myles (2007b). 21

23 4.5 Learning-By-Doing 71. The fourh major approach o endogenous growh is o assume ha here are exernaliies beween firms ha operae hrough learning-by-doing. This idea has been esablished in he economics lieraure a leas since Arrow (1962). The presence of an exernaliy resuls in a divergence beween privae and social reurns o capial accumulaion. 72. The basis of learning-by-doing is ha invesmen by a firm leads o parallel improvemens in he produciviy of labour as new knowledge and echniques are acquired. Moreover, his increased knowledge is a public good so he learning spills over ino oher firms. This makes he level of knowledge, and hence labour produciviy, dependen upon he aggregae capial sock of he economy. The imporan consequence is ha decreasing reurns o capial for a single firm (for a given level of labour use) hen ranslae ino consan reurns for he economy. 73. The policy focus suggesed by learning-by-doing is he ax reamen of invesmen and how policy can encourage invesmen by firms. The empirical lieraure on invesmen and axaion is discussed in Myles (2007b). 4.6 Technology Transfer 74. In addiion o hese models of endogenous growh i is worh menioning he role of foreign direc invesmen (FDI) in he growh process. 75. FDI ha akes he form of physical invesmen (raher han he form of acquisiions) provides a source of echnological improvemen for he hos counry. This will be he case if he invesing firm uilises a level of echnology above ha currenly in use in he hos counry. Much FDI in pracice has aken precisely his form wih firms from developed counries locaing heir mos recen echnologies in developing hos counries. This raises he produciviy of labour in he hos counry and conribues o growh. 76. For many developing counries FDI is an imporan source of economic growh and i receives much policy aenion. From a world perspecive here may be zero-sum elemens abou hese policies bu here are privae gains. The empirical assessmen of he sensiiviy of FDI o policy incenives is reviewed in Myles (2007b). 4.7 Taxaion and Growh 77. The discussion of models of endogenous growh has idenified a range of channels hrough which axaion can affec growh. I is helpful o invesigae hese furher wihin he conex of a model. A simple bu informaive model for illusraing how a range of ax insrumens can affec economic growh is provided in Zagler and Durnecker (2003). This model capures several of he imporan elemens of endogenous growh heory. 22

24 Oupu a ime is deermined by he aggregae producion funcion α β 1 α Y = X G L, (39) where X denoes he aggregae quaniy of a composie inermediae inpu. This aggregae is composed of a se of n specialised inermediae inpus via he defining relaion where i of producion α n i= 1, α X = x i, (40) x, is he quaniy of inermediae inpu i. The inpu levels { } L, are chosen o minimise he cos x i C = ( 1+ ) w L + ( 1 τ ) n τ + p x, (41) L i= 1 xi i, i, where τ L is he ax on labour, τ xi he ax on inermediae good i. Defining an aggregae price index, P, and a corresponding aggregae ax, τ X, he cos of producion can also be wrien C ( + τ L ) w L + ( + τ X ) P X = 1 1, (42) The necessary condiions for cos minimisaion can be solved o show ha and ( α 1) / α α / [ ] ( α 1) P xi pi,, (43) i1 ( 1 τ ) = ( 1 + τ ) n + X x i, = ( 1+ τ xi ) ( 1+ τ ) X p i, P 1/ ( α 1) X. (44) Each inermediae good is produced by a differen monopolisic firm. The firm ha produces good i maximises profi subjec o he demand funcion (44). This leads o he opimal price 1 p i, =. (45) α As a consequence he aggregae price index when all inermediae axes are equal is 1 1+ τ x ( α 1) / α P = n. (46) α 1+ τ X A concep of physical capial can hen be defined by aggregaing he individual inermediae goods o give 23

25 K n i i=1, 1 ( α x n )/α = X. (47) This aggregaion allows oupu o be expressed as a funcion of capial, public inpu, and labour The equilibrium capial sock can be shown o be 1 ( nl ) α Y = K α G β. (48) K 2 1 τy = α Y. (49) 1 + τ x This implies ha he growh rae is given by Yˆ β = Gˆ + nˆ + Lˆ. (50) 1 α 78. Assume ha a consan fracion, s, of disposable income is saved and used o finance he aciviies of R&D firms. Denoing he ax on saving by τ s and ha on R&D by τ RD, he expendiure on labour for R&D saisfies Innovaions arrive a he rae D ( τ s ) sy = ( 1+ τ RD ) w E 1. (51) nˆ = φh E, (52) where h is publicly provided human capial. 79. Using here resuls he per capia growh rae can be found o be Yˆ Nˆ β = Gˆ 1 α s + αs + φ 1+ τ + τ RD ( 1+ τ L )( 1 τπ τ x ) h + αs( 1+ τ L )( 1 τ τ x ) n s π N, (53) where τ π is he profi ax on he producers of inermediae goods. The firs erm capures he posiive effec ha axaion has on growh hrough he financing of he public inpu. The second erm capures ax effecs ha operae hrough changes in he level of innovaion. Boh he ax on R&D and he ax on saving reduce he growh rae. The ax on R&D reduces innovaion and he ax on saving reduces capial accumulaion. The oher axes have an ambiguous effec on growh, wih he oucome depending on he value of he savings rae, s, relaive o he value of 1 +τ + τ. 80. This model could be furher developed by closing he sysem o relae governmen expendiure on he producive inpu and on human capial accumulaion o ax revenue. Furhermore, as se ou above he model has no opimisaion by he household. This could also be added. Bu even wihou hese addiions he model sill illusraes he effec ha axaion can have upon growh. RD s 24