www.sciedu.ca/rwe Research in World Economy Vol., No. ; March 0 Opimal Growh axaion Marcus Davidsson Nygaan 7 55 6 Jonkoping, Sweden E-mail: davidsson_marcus@homail.com Received: December, 0 Acceped: January 4, 0 Published: March 5, 0 doi:0.540/rwe.vnp5 URL: hp://dx.doi.org/0.540/rwe.vnp5 Absrac Governmen usually ends o have wo opions. hey can eiher pursue a ax revenue maximizing sraegy or a growh maximizing sraegy. he wo approached do no necessarily go hand in hand. his paper derives and empirically esimaes a simple laissez faire opimal axaion model from he perspecive of economic growh. he finding is ha governmens end o sysemaically over ax he economy which leads o subopimal allocaions. Poliicians end o prefer high axaion over a cu in public spending i.e. a reducion in public secor jobs. Keywords: Economic Growh, Fiscal Policy, Public Economics. Inroducion Economic growh is a resul of many differen facors such as capial, consumpion, innovaion, employmen, expors, populaion growh, increased wage levels ec. Previous sudies such as for example Solow 956 Ramsey 98 and Rebelo 99 have all discussed differen ypes of heoreical growh models. In he Solow model he savings rae is assumed o be exogenously given and consan. he Solow model derives a basic differenial equaion for capial in he economy. he Ramsey model combines he equaion of moion for capial derived in he Solow model and a new equaion of moion of consumpion in an expanded growh framework. Noe ha in he Ramsey model he savings rae is no longer consan bu raher dependen on he equaion of moion of consumpion. radley e al. 995 explain ha he neoclassical growh models such as he Solow and Ramsey model assume diminishing reurn o capial. his implies ha rich counries wih an abundance of capial will have lower reurn o capial and poor counries wih a scarciy of capial will have higher reurn o capial. Assuming free and global capial markes i means ha capial will flow from rich o poor counries and over ime income raios beween counries will converge o uniy. Razin and uen 996 furher explain ha he imporance of endogenous populaion growh and free capial markes are ofen overlooked by he neoclassical growh heory. In heir paper hey found ha capial income axes have a much larger effec on he long-erm growh for an economy under endogenous populaion growh and free capial mobiliy. DeLong and Summers 99 on he oher hand provide evidence in suppor of he neoclassical model and is focus on capial invesmen. he same wih Lawrance 99 who found ha low-income households have a much higher consumpion rae lower savings rae compared o high-income households. High income households are also likely o ge richer over ime which would lead o lower risk preference. Endogenous growh or new growh heory was developed in he 980s as a direc response o he limied neoclassical growh hinking. he mos basic version of he endogenous growh is he AK-model Rebelo, 99. In he AK-model he reurn o capial is no longer diminishing as in he Solow and Ramsey model due o he broad definiion of capial i.e. human and physical capial. he main advanage of he AK-model is ha i can explain long run growh wihou relying on echnological progress and populaion growh. Economic growh in he AK-model is deermined by he accumulaion of physical and human capial. Human capial represens he knowledge and skills ha people accumulae over ime hrough educaion, on-he-job raining, learning-by-doing or specializaion ang & orland, 99. Now economic growh is essenial in order o creae new jobs, economic developmen and increase a naion s living sandard. In his paper we will invesigae he relaionship beween axaion and economic growh. More specifically we will answer he quesion is i growh opimal for a counry o have a high or low ax rae? here are wo basic schools of hough when Published by Sciedu Press 5
www.sciedu.ca/rwe Research in World Economy Vol., No. ; March 0 i comes o he purpose of he governmen from a fiscal policy perspecive. In a Laffer model he main goal of he governmen is o maximize governmen ax revenues. In a Scully 99 model he main goal of he governmen is o maximize economic growh. Dominaing governmens such as Sweden, Germany, and France se he ax rae o maximize economic revenue, which is in line wih he Laffer model. Ohers more liberalized governmens such as Ireland se i o maximize economic growh, which is in line wih he Scully model.. heoreical Modeling Framework Scully 99, 995, 996, 999 found ha on he average, counries reaches heir maximum economic growh raes when hey collec no more han 9. percen of GDP in axes. In general he growh opimal ax rae is much lower han he revenue maximizing ax rae. Some counries end o prefer o pursue a growh maximizing policy over a revenue maximizaion policy. Scully furher calculaed ha such revenue maximizing ax rae would be around 0 percen of GDP. Scully s parsimonious model axaion model is also direcly relaed o he opimal size of he governmen given ha all spending are financed hough ax revenues. he producion funcion in he Scully model is given by: Where, and are basic parameers, is he oupu in he economy a ime, G is he governmen produced goods a ime -, is he ax rae and is he oupu in he economy a ime -. he expression can furher be inerpreed as he privae produced goods a ime -. I is also ineresing o noe ha given a 5% annual increase in governmen spending i.e. G.05G oupu in he Scully model will grow exponenially faser wih a low ax rae han wih a large ax rae. his is illusraed in Figure-. We can also see ha if he ax rae is higher han % hen he economy will no grow a during hose en years. We can now analyze some dynamics in coninuous ime. If we subrac from boh sides of our previous equaion and noice ha [ ] [ ] lim 0[ [ ] [ ] diff [ ], hen we will ge he firs equaion seen below. he second equaion represens he equaion of moion for governmen spending. We can see ha governmen spending has a posiive growh over ime. he expression G / ^ represen he supply side sluggishness in he economy i.e. he non responsiveness governmen spending and ax cus. diff, G G diff G, We can now plo he phase diagram as seen in Figure-. Poin A represens a siuaion wih small sluggishness and large axes. Poin represens a siuaion wih small sluggishness and small axes. We can see ha a ax cu increases GDP and hence he governmen can afford o increase spending. Now Poin D represens a siuaion wih large sluggishness and large axes. Poin C represens a siuaion wih large sluggishness and small axes. We can see ha a ax cu did no increase GDP. he increase in governmen spending o force economic growh will in his case increase deb. We can now look a some oher resuls derived from of he Scully model. As previously we assume ha he producion funcion is given by: G G 4 he governmen produces goods ha can now eiher be finance hrough axes, deb D or seniorage S ie prining money which means ha he governmen produced goods a ime - can be wrien as: G D S which gives us: D S 5 We now need o acknowledge he exra cos relaed o deb and money prining D S D S D S where represens he marginal cos of deb and money prining which is given by he ineres rae i plus he inflaion rae ii. If we plug in hose expressions ino our previous equaion we ge he following expression: D S i ii D S 6 We now ake he firs difference of he above equaion which gives us: 7 D S i ii D S We can now analyze he dynamics. Figure- illusraes wo difference scenarios. One scenario where he governmen prins a lo of money as a fracion of deb S=D*0.7 and one scenario where he governmen prins a smaller amoun of 6 ISSN 9-98 E-ISSN 9-99X
www.sciedu.ca/rwe Research in World Economy Vol., No. ; March 0 Published by Sciedu Press 7 money as a fracion of deb S=D*0.. I urns ou ha boh equilibriums are sable equilibriums. A sable equilibrium is characerized by he fac ha he rae of change becomes zero i.e.. he only difference beween he equilibriums is he equilibrium value. he economy in he firs scenario will converge o a much higher GDP equilibrium han in he second scenario. I also unes ou ha for he firs scenario o happen he money-prining-o-deb raio has o be equal o or larger han 44%. his means ha borrowing wihou any seniorage is no a valid sraegy for a governmen ha wans o maximize GDP over ime. he firs sraegy is also called an inflaion axaion sraegy because significan amoun of wealh is ransferred beween he privae and public secor due o inflaion. We can now assume ha he oal cos of deb and money prining is larger han he revenue of deb and money prining S D S D ii i. his effecively means ha he governmen will no pursue "non-opimal" sources of financing such as deb and money prining which leads o ha he governmen will finance all is governmen produced goods hough axes G. his means ha our previous equaion: S D ii i S D 8 is reduced o: 9 We simplify he above expression and divide boh sides by - so we ge: 0 We now assume ha he producion funcion has consan reurn o scale which means ha 0 Since 0 we can wrie our previous equaion as: which can be wrien as: We now define he growh rae of oupu G which means ha we can wrie he previous equaion as: 4 We again noe ha we have consan reurn o scale which means ha we can wrie he previous equaion as: 5 We can now solve for he opimal ax rae growh maximizing by seing 0, diff 0 6 We solve for which means ha he opimal ax rae is given by. In Figure-4 we can see he differen opimal ax raes given a fixed amoun of economic growh. We again noe ha he economic growh in he economy is given by 7 We will now manipulae such an equaion inorder o esimae he parameers empirically. 8 which can be wrien as: 9 or as 0 We now ake he logarihm on boh sides which gives us: ln ln ln
www.sciedu.ca/rwe Research in World Economy Vol., No. ; March 0 We can again inerpre a he opimal ax rae i.e. how much of GDP per capia should a counry ax in order o maximize economic growh.. Empirical Esimaion We can now esimae he above equaion by running a simple regression. he daa is colleced from he World ank Developmen Indicaor, 004. he daa consised of wo differen series: GDP per capia growh and percen of GDP colleced in ax revenues. he analysis was done on welve differen counries all wih differen growh and ax raes. he counries ha were included are New Zealand, Chile, razil, Ausralia, Mexico, Argenina, Pakisan, Paraguay, Souh Africa and Unied Saes, Germany and Kuwai. he analysis consised of daa from he years 98 unil 00. We can in Figure-5 see he growh rae in GDP per Capia for he welve counries. In Figure-6 we can see he percenage of GDP colleced in ax revenue for he differen counries. We can in Figure-7 see he regression line and he empirical observaions. On he x-axis we have he ransformed expression for he ax rae and on he y-axis we have he ransformed expression for he growh rae. We can see ha he fi is comparaively good. We should also noe ha Rsquare is very high 0.66. he inerpreaion is ha ha our model explains 66 percen of he variaion in economic growh per capia which mus be considered very good. Since he absolue value of sa is larger han i means ha our opimal ax rae variable is significan so we can inerpre he resul. Now is equal o 0. which means ha he opimal ax rae is reached when a counry collecs % of GDP in ax revenues. his means ha anyhing above % would be considered a dead weigh loss which he governmen could reclaim by lowering he axes o a growh opimal level of % of GDP. 0.95 sa 9. 74 0. sa 0. 959 R 0.6667440 4. Conclusion Significan rue Significan rue he governmen can eiher run an expansive fiscal policy, which means a reducion of axes or increased spending, or hey can run a conracive fiscal policy, which means an increase in axes or a reducion in spending, or hey can simply keep a neural posiion. In general, an expansive policy is said o be growh-enhancing will a conracive policy is said o be growh conracive. here are wo main reasons for why he governmen choice o implemen axes. he firs reason is o finance public goods such as for example naional defence, schooling or healh care. he second reason is o change he exising allocaion of resources i.e. wealh redisribuion. If he exising allocaion of resources is inefficien hen he governmen can implemen a Pigouvian ax ha correcs he negaive exernaliy and increase he efficiency. One example of a Pigouvian ax in for example environmenal economics can be a polluion ax. Noe ha if he exising allocaion of resources already is efficien hen he governmen will inroduce a dead weigh loss when hey inroduce a ax. he size of he dead weigh loss will depend on he size of he ax. A large ax will have a larger dead weigh loss han for example a small ax. his paper has discussed opimal axaion from a growh maximizaion perspecive. he conclusion derived from he empirical esimaion is ha a counry will maximize heir economic growh rae by collecing percen of GDP in axes. I is obvious ha no many counries are perusing such an aggressive growh policy. he quesion herefore becomes why? he only reason he auhor can hink of is ha poliicians usually ends o solve a budge defici wih an ax increase raher han a cu in spending which in many cases involves reducing he number of public secor jobs. he quesion ha one should ask oneself is if i is realisic for a governmen o ensure ha public secor jobs have a larger job securiy han privae secor jobs in a recession when he cos of such job securiy for a fracion of people is reduced economic growh for he whole economy. 8 ISSN 9-98 E-ISSN 9-99X
www.sciedu.ca/rwe Research in World Economy Vol., No. ; March 0 References radley, J., O Donnell, N., Sheridan, N. & Whelan, K. 995. Regional Aid and Convergence, Ashgae publishing Limied, Aldersho, UK DeLong,. & Summers, H. 99. Equipmen Invesmen and Economic Growh, Quarerly Journal of Economics 06:, pp. 445-50. hp://dx.doi.org/0.07/97944 Dornbusch, R. & Fischer, S. 99. Macroeconomics, McGraw-Hill, New ork Lawrance, E. 99. Povery and he Rae of ime Preference: Evidence from Panel Daa, Journal of Poliical Economy, vol. 99, no, pp 54-77. hp://dx.doi.org/0.086/6740 Ramsey, F. 98. A Mahemaical heory of Saving, Economic Journal, Vol. 8, No 5, pp.54-559. hp://dx.doi.org/0.07/4098 Razin, A. & uen, C. 996. Capial Income axaion and Long-run Growh: New Perspecive, Journal of Public Economics, vol 59, nr, pp 9-6. hp://dx.doi.org/0.06/0047-77950504- Rebelo, 99. Long-Run Policy Analysis and Long-Run Growh, he Journal of Poliical Economy, Vol 99, No, pp 500-5 Scully, G. 99. ax Raes, ax Revenues and Economic Growh, Policy Repor No. 98, Dallas, X: Naional Cener for Policy Analysis. Scully, G. 995. he growh ax in he Unied Saes, Kluwer Academic Publishers, Public Choice 85 7-80 Scully, G. 996. axaion and economic growh in New Zealand, Pacific Economic Review, 69-77. hp://dx.doi.org/0./j.468-006.996.b008.x Scully, G. 999. Unfinished reforms: axaion and economics growh in New Zealand, Journal of Privae Enerprise, 9-4 Solow, R. 956. A conribuion o he heory of economic growh, Quarerly Journal of Economics, Vol 70, pp 65--94. hp://dx.doi.org/0.07/8845 ang, X. & orland, J. 99. A Microeconomic Mechanism for Economic Growh, he Journal of Poliical Economy, Vol. 99, No., pp. 460-48. hp://dx.doi.org/0.086/676 Figure. GDP Growh and ax Rae Published by Sciedu Press 9
www.sciedu.ca/rwe Research in World Economy Vol., No. ; March 0 Figure. Opimal axaion and Economic Growh Figure. Seniorage over ime 40 ISSN 9-98 E-ISSN 9-99X
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www.sciedu.ca/rwe Research in World Economy Vol., No. ; March 0 Figure 6. Percen of GDP colleced in ax revenues Published by Sciedu Press 4
www.sciedu.ca/rwe Research in World Economy Vol., No. ; March 0 Figure7. Regression and Parameer Esimaion axaion Model 44 ISSN 9-98 E-ISSN 9-99X