International Journal of Economic Sciences and Applied Research 6 (3): Spending and Growth: A Modified Debt to GDP Dynamic Model.

Transcription

1 Inernaional Journal of Economic Sciences and Applied Research 6 (3): 2-33 Spending and Growh: A Modified Deb o GDP Dynamic Model Camilla Yanushevsky, Rafael Yanushevsky 2 Absrac The paper addresses a opical issue how expansionary fiscal policy affecs he deb o GDP raio. I examines wheher he projeced fuure economic growh (simulaed by governmen spending) is susained wih he resuling naional deb. I is discussedif governmen invesmen in infrasrucure is an effecive approach o boos he economy in imes of economic downurn. The auhors develop he deb o GDP raio dynamics model and perform a series of simulaions (based on US daa) o forecas he evoluion of he deb o GDP raio over a -year horizon. I is shown ha for he daa characerizing he curren sae of he U.S. economy he governmen invesmen in infrasrucure canno decrease he deb o GDP raio. Keywords: deb dynamics, deb o GDP raio dynamics, invesmen in infrasrucure, simulus JEL Classificaion: C2, C6, O4. Inroducion The 28 global financial crisis has resuled in large deficis and public deb burdens across many counries. According o IMF (29) esimaes, he level of public deb for advanced counries would reach over percen of GDP by 24, a level unseen since World War II. The Unied Saes has a huge naional deb (abou 6. rillion dollars in 22) and i has surpassed % of gross domesic produc. The European Union average deb was abou 85% of GDP in 22. Tha is why Germany and he majoriy of EU counries have underaken auseriy measures. Neverheless, even as consrains on spending and borrowing have grown, many governmens have been emphasizing he imporance of infrasrucure in assising economic growh. A number of counries have explicily recognized his as par of heir simulus packages. The $84 billion simulus package enaced by he U.S. Congress conained $5 billion for infrasrucure, which is significanly less han $2.5 rillion worh of simulus launched by he Chinese governmen, mos of which wen o special purpose Universiy of Maryland, Deparmen of Finance, Rober H. Smih School of Business, College Park, 2742, USA; cyanushe@gmail.com 2 Research & Technology Consuling, 56 Danbury Rd., Behesda, MD 284, USA; r.yanushevsky@randc.com,

2 Camilla Yanushevsk, Rafael Yanushevsky vehicles o build rail, bridges, airpors, condo buildings, ec. Many economiss consider he over-invesmen underaken in China as an aemp o aver an economic slowdown. The wo camps of economiss have differen views concerning how o improve he economy in imes of economic downurn. In conras o hose who consider governmen spending on infrasrucure as an efficien sraegy and suppor he approach based on addiional governmen borrowing wih a hope ha his will help decrease he deb in he fuure, anoher group of economiss, concerned wih high governmen deb which, as hey believe, can ineviably undermine economic growh, suppors auseriy measures. The deb o GDP raio is widely used o measure he impac of deb on he economy. I was inroduced similar o he bank deb raio oal deb as a percenage of income deermining he level a which businesses can afford o owe. There exiss jusifiable criicism of he deb o GDP raio as he insufficienly informaive and mos overused economic index. The menioned raio as if ignores such imporan parameers as he ineres raes associaed wih he deb and when he deb maures. Some economiss sae ha he deb o GDP is a very poor measure of he healh of a naion or is economy; he bes measures are real GDP per capia, real GDP growh raes, unemploymen rae, and inflaion rae. Neverheless, many economiss and leading economic organizaions use GDP and deb o GDP o evaluae he healh of he counry s economy, is abiliy o handle he increasing deb load and o predic he fuure economic environmen. The European Union requires ha member sae s public deb no exceed 6 percen of GDP. The lieraure on he relaionship beween governmen deb and economic growh is scarce. According o Reinhar and Rogoff (29), deb o GDP raios below a hreshold of 9 percen of GDP raios have no significan impac on growh; above he hreshold of 9%, median growh raes fall by %, and average growh falls considerably more. Recenly, Herndon e al. (23) found an error in calculaion of he hreshold; hey indicae ha he average real GDP growh rae for counries carrying a deb o GDP raio of over 9 % is acually 2.2 percen, and he relaionship beween public deb and GDP growh varied significanly by ime period and counry. Despie he menioned error, he obained resuls of Reinhar and Rogoff (2) are qualiaively correc. However, he findings of boh Herndon e al. (23) and Reinhar and Rogoff (2) are suggesive, raher han conclusive, since hey operae wih pas daa. I is dangerous o build fuure financial policy by using blindly such findings since picures of he world economy are changing wih ime, and saisics of he pas may no apply o a curren or fuure economic siuaion in a counry. More reliable mahemaical models should be developed. Paul Krugman quesioned he validiy of he above finding relaed o he linkage beween governmen deb and economic growh (Krugman, 22). He criicized he conclusion ha sepping over he 9% border of he deb o GDP raio is harmful for growh and believes ha increasing governmen deb can increase growh, if he money is invesed well, which he links o infrasrucure spending (Krugman, 22). Alhough he impac of governmen spending programs in he pas ha were inended o increase economic growh by using infrasrucure-focused simulus packages was very modes and did no resore economic aciviy, Krugman (22) saes ha fiscal expansion will be 22

3 Spending and Growh: A Modified Deb o GDP Dynamic Model even beer for America s fuure if a large par of he expansion akes he form of public invesmen of building roads, repairing bridges and developing new echnologies, all of which makes he naion richer in he long run. For him big governmen spending is a soluion of problems of high unemploymen and low GDP growh: Bu he essenial poin is ha wha we really need o ge ou of his curren depression is anoher burs of governmen spending. Krugman believes ha i is he deb o GDP raio ha maers and no he deb iself. In Krugman (29) he wroe: How, hen, did America pay down is deb? Acually, i didn... Bu he economy grew, so he raio of deb o GDP fell, and everyhing worked ou fiscally... Which brings me o a quesion a number of people have raised: maybe we can pay he ineres, bu wha abou repaying he principal?...bu why would we have o do ha? Again, he lesson of he 95s - or, if you like, he lesson of Belgium and Ialy, which brough heir deb-gdp raios down from early 9s levels - is ha you need o sabilize deb, no pay i off; economic growh will do he res. Being a supporer of Keynesian economic docrine, he believes ha i is governmens role o creae jobs more eachers, consrucion workers for public works projecs, ec., when he privae secor canno, and ha such a sraegy resuls in economic growh, so he raio of deb o GDP should fall, and everyhing should work ou fiscally. Research resuls relaed o he deb o GDP raio were based mosly on analysis of he exising saisical economic daa. Differen conclusions and following dispues reflec differen inerpreaion by economiss of he available saisical maerial. Using regression models and/or he exising hisoric daa mos of he above menioned publicaions examined he impac of governmen spending o simulae he economy on GDP or analyzed he influence of he deb o GDP raio on economic growh. However, hey did no esablish he direc relaionship beween GDP, he relaed governmen spending and he deb o GDP raio. This paper considers a model describing he deb o GDP raio dynamics and examines he linkage beween he GDP growh rae, he relaed governmen spending (is effec is presened by relaed fiscal mulipliers) and he deb o GDP raio. Based on he developed model giving he lower esimae of he deb o GDP raio, he impac of expansionary fiscal policy inended o reduce unemploymen and increase economic growh by using infrasrucure-focused simulus packages is analyzed. The paper is organized as follows. Secion 2 discusses he developed deb o GDP raio dynamics model, is specifics he abiliy o obain he lower esimae of he deb o GDP raio. Secion 3 describes he simulaion resuls grounded upon he developed heoreical model. In Secion 4, some conclusions are drawn. 2. Deb o GDP raio dynamics The deb dynamics can be described by he following equaion D D rd G T () 23

4 Camilla Yanushevsk, Rafael Yanushevsky where D is general governmen deb; r is he ineres rae on deb; G and T are governmen purchases (expendiure excluding ineres paymens on he deb) and revenues, respecively; he lower index indicaes discree ime - years. Governmen revenues are presened in he form T Y (2) where τ is a ax rae and he Cobb-Douglas funcion Y represens GDP (in many models he Cobb-Douglas funcion is used as he esimaion and forecasing of GDP from he supply side) Y AK L (3) where A is a measure of echnology, α and β are he oupu elasiciies of capial K and lab or L, respecively. The Cobb-Douglas funcional form of producion funcions and is modificaions are widely used o represen he relaionship of an oupu o inpus in macro- and microeconomic models (see, e.g., Glomm and Ravikumar, 997; Yanushevsky, 992). Various economic models, saring from he Solow growh model (see, e.g., Romer, 26), used he Cobb-Douglas funcion o examine long-run growh analyically and deermine he economy s balanced-growh pah. If iniially capial was represened by one parameer, laer in some models privae and public capial were considered separaely (see, e.g., Aschauer s, 989; Cassou and Lansing, 998; Glomm and Ravikumar, 994; 997; Lynde and Richmond, 993; Munnell, 99). Economiss began o sudy he influence of governmen spending on consumpion-savings decisions in models which allow he possibiliy of persisen growh; long-run growh models wih producive governmen spending combine several goods and services, such as roads and highways, sewer sysems, harbors, public secor R&D, ogeher ino one caegory called public capial. Governmen spending is mainained by axes and governmen borrowing. To obain visible analyical resuls he menioned models conain unrealisic assumpions, such as ha he governmen s budge is balanced and ax revenues are used only o finance public invesmen in infrasrucure (see, Glomm and Ravikumar, 997). In conras o he above menioned long-run dynamic models operaing wih privae and public capial, he model developed below belongs o he so-called shor-run models. I analyzes he siuaion when a cerain governmen policy focuses o move he economy on a more producive sage. Usually, such a siuaion is characerized by he unbalanced governmen budge, significan deb and unemploymen. As indicaed earlier, his siuaion is currenly in he U.S. and some European counries. Since he opinion of economiss, mosly only suppored by chosen hisoric examples, diverges wheher governmen spending focused on infrasrucure can improve he economic siuaion, he developed deb o GDP raio dynamics model focuses o resolve his problem rigorously. The deb o GDP raio d dynamics can be presened as 24

5 Spending and Growh: A Modified Deb o GDP Dynamic Model D D D rd G T D r g G T d d d Y Y Yg Y g Y (4) where Y Y AK K K L L L AK L ( ) K = (α K L + β L + O(ε)) Y = gy (5) K K g L L (6) g is a GDP growh rae (we neglec O(ε) = KL /( KL ), which has higher order of smallness han oher erms of (5)). Pracical applicaion of (4) requires knowledge of G and Y. However, hese parameers are inerconneced. In realiy, we deal wih a sysem of equaions since Y depends on K and L (see (5) and (6)) and (4) should be supplemened wih equaions describing dynamics of capial K and labor L. Analysis of such a sysem presens subsanial difficulies, especially when i is necessary o predic fuure values of he deb o GDP raio. Below we use (4) o build he model ha allows us o obain he analyical soluion of he lower esimae of d. Le for, gg r, and G l T, l (l characerizes he raio beween governmen expendiure excluding ineres paymens on he deb and is revenues, so ha l assumes he revenues o be less han he expendiures). As indicaed above, one of he approaches o simulae GDP growh and employmen is he use of addiional governmen spending G o resusciae he economy by invesing in infrasrucure repair and build roads, bridges, ec. I is assumed ha wih he increasing number of working people he consumpion will rise and his will simulae economic growh. This approach was esed in a case of economic recessions significan decline in he economic aciviy and high unemploymen and is recommended by many economiss as he necessary cure for he economic slump. The muliple effec of infrasrucure spending will be presened by he muliplier l. A classic quesion in macroeconomics abou he size of he governmen spending muliplier was exensively discussed in economics lieraure (e.g., Auerbach and Gorodnichenko, 2; Blanchard and Peroi, 22; Chrisiano e al., 2; Leeper e al., 2; Ramey, 2). Numerical esimaes of he value of he fiscal muliplier vary significanly across model classes. Wihin each class of models, hey vary a lo wih he economic and policy environmen. Using radiional macroeconomic models Chrisiano e al. (2) under raher rigorous assumpions show ha he muliplier varies enormously 25

6 Camilla Yanushevsk, Rafael Yanushevsky depending on how moneary policy reacs o he economy. They found he long-run effec o be posiive and he muliplier can be as high as abou 4. However, in mos of he relaed publicaions he muliplier s peak value does no exceed 2.5. The resuls of some researchers differ significanly since he heoreical models used o examine he impac of governmen spending on GDP conain many inerconneced parameers which canno be deermined precisely. Some resuls based on economeric models (e.g., Auerbach and Gorodnichenko, 2; Blanchard and Peroi, 22; Ramey, 2) canno be reproduced in he Neo-Keynesian models. Auerbach and Gorodnichenko (2) found ha in recessions he long-run muliplier s effec is as high as 2.5 bu as low as in expansions. Alhough he menioned publicaions analyze he muliplier s dynamics, usually in pracice, in simulaion models, he muliplier is presened as a consan parameer. Since addiional governmen spending conribues o he naional deb, i is of imporance o deermine wheher he projeced fuure economic growh (in accordance wih a chosen muliplier) is susained wih he resuling naional deb. The model analyzed below corresponds o he case of declining economic aciviy, subsanial deb and high unemploymen. I is assumed ha a, L and for, when he governmen simulus package focuses infrasrucure, he GDP growh he rae g g can be achieved by increasing employmen, i.e., in (6) for, L. For simpliciy, we consider he iniial momen, so ha,, 2,. Assuming ha he axes remain unchanged, he addiional governmen spending G a o increase Y and make i growing wih he rae g g, i.e., should be Y ( g ) Y, (7) G l [(g ) (g ) ] Y (8) (he above equaion follows direcly from he definiion of he fiscal muliplier). The assumpion ha he rae change is implemened immediaely, i.e., he governmen spending akes effec wihou delay, which usually conradics realiy (ineviable delays may produce even opposie effec) will allow us o consider he obained deb o GDP raio esimae as opimisic. In addiion, we assume ha he basic governmen spending G lt l Y is no only frozen a (as a percen of GDP; see (2)) bu for i will decrease by G, due o he increase in employmen gg ( ), 2 ( ) G l e G (9) where l characerizes he percen of welfare relaed spending a 2 ; he exponenial erm reflecs he sep g-rae change in (6), and o simplify he model we ignore he influence of he capial componen in (6) and operae wih he increased rae of employmen ( g g ) (his simplificaion, as well as menioned earlier, gives an opimisic esimae of he deb o GDP raio; in (6) L and K are coninuous variables). 26

7 Spending and Growh: A Modified Deb o GDP Dynamic Model Based on (7)-(9), he model describing he deb o raio dynamics under he governmen sraegy o decrease unemploymen ( L ) and boos he economy (increase he growh rae from g o g ) by invesing in infrasrucure has he form d r g g d g g ( ) 2( ) [(g ) (g ) ] ( g ) Y G l e G l Y,,2, () or since (see (7) and (9)) G lt l Y l3y, where l 3 l, he above equaion can be ransformed o d g g ( ) r g l3 l2l3 e l d g ( g ) ( ) [(g ) (g ) ],, 2, () Since he employmen growh rae in he considered model is (g g ) (see (9)), i is valid only for a finie ime inerval. Taking ino accoun he populaion growh, he curren and admissible levels of unemploymen, as well as reasonable values of g and g i is easy o conclude ha he resuls obained from he analysis of () are valid for he ime inerval of approximaely -5 years. The equaion () is a recursion formula ha specifies a recursive procedure for deermining d based on d,,, 2, Alhough he soluion of () is given for a consan ax rae, in realiy depends on ime. Bu in he case of he unchanged governmen ax policy and absence of sharp economic urns he changes are small. For example, he U.S ax revenues have averaged abou 8.3 percen of GDP over In 29, i dropped o 5. percen and grew slowly o 5.8 percen in 22. Since we operae wih he lower esimae of he deb o GDP raio, in he below examples is chosen o saisfy his requiremen. 3. Simulaion Resuls The below examples are given for several fiscal mulipliers examined in he lieraure (e.g., Auerbach and Gorodnichenko, 2; Blanchard and Peroi, 22; Chrisiano e al., 2; Leeper e al., 2; Ramey, 2). 27

8 Camilla Yanushevsk, Rafael Yanushevsky Table presens he deb o GDP raio esimae for he years period based on he soluion of () for he following parameers: d ; r =.289;.4 ;.75 ; l.7 ; l 2. (hey are very close o he daa characerizing he curren sae he U.S. economy). The able is buil for g =.2, g =.3, and g =.2, g =.4,respecively. The chosen muliplier l.59 is recommended by Mark Zandi, chief economis of Moody s Analyics. As seen from Table, for he considered muliplier he deb o GDP raio increasesal mos wice in years for g =.3 and g =.4. Table : Simulaion resuls for he considered deb o GDP raio dynamics model for l =.59 year deb/gdp g =.3 deb/gdp g = Since his and similarmuliplier s values are no suppored by rigorous mahemaics and heir validiy is argued by many economiss, in Table 2 we presened he deb o GDP raio esimae for l 3.8, he value given in Chrisiano e al. (2). As seen from Table and Table 2, he lower values of d correspond o he muliplier wih he higher value. Table 2: Simulaion resuls for he considered deb o GDP raio dynamics model for l = 3.8 year deb/gdp g =.3 deb/gdp g = Of course, he GDP growh rae g depends no only on he level of governmen invesmen in infrasrucure. I depends on many facors including ax policies and he sae of he world economy. Some economiss - advocaes of simulus packages - prefer o ignore hese facors and aribue economic growh only o simulus measures. Taking ino accoun ha since he second quarer of 2 he U.S. GDP rae has never reached he 5 percen level, we consider also he rosy scenario and evaluae he deb o GDP raio for g =.5 and l =3.8. The resuls presened in Table 3 show ha even for his case in years he deb 28

9 Spending and Growh: A Modified Deb o GDP Dynamic Model o GDP raio would increase by more han 5 percen. The reason of inefficiency of he described simulus policy is a very high (% of GDP) iniial deb and a high level of he federal governmen spending (24% of GDP). Table 3: Simulaion resuls for he considered deb o GDP raio dynamics model for l = 3.8 year deb/gdp g =.5 The above considered model assumes ha he governmen financial policy (excluding invesmen in infrasrucure) remains unchanged, and as i follows from daa of Table and Table 2 he deb o GDP raio increases wih ime. To analyze he efficiency of he policy combining invesmen in infrasrucure wih decreasing oher governmen spending we assume ha governmen spending no relaed o infrasrucure decreases wih a rae h, i.e., insead of he erm G in () we have G ha is he soluion of he equaion G ( ) h G,,, 2, (2) so ha he modified equaions () and () should have insead of he erms G and l 3 he erms ( h) G and ( ) h l3, respecively. Table 4 and Table 5 conain he simulaion resuls for his case; h =.2 is chosen o ge abou a 2% decrease in he governmen spending in years. As expeced, he deb o GDP raio esimae is less han in Table and Table 2. However, he deb o GDP raio is sill above is iniial value. Finally, we consider he siuaion ha a he governmen fiscal policy resuls in a condiionally balanced budge (revenues equal expendiure, excluding paymens on infrasrucure spending). This corresponds o g l3 and r = in (). The simulaion resuls in Table 6 show ha he balanced budge is a proper approach o decrease he deb o GDP raio, andgovernmen spending on infrasrucure may lead o a declining deb o GDP raio when a balanced budge approach is followed a he same ime. The daa in Table 6 allows us o assume(since he considered model deals wih a lower esimae, raher han he real value, of he deb o GDP raio) ha exensive infrasrucure spending o increase significanly he GDP rae (in years for g =.4 he lower esimae of d equals.883) can be less effecive, wih respec o he deb o GDP raio, han in he case of a moderae GDP growh (for g =.3 his esimae equals.855). 29

10 Camilla Yanushevsk, Rafael Yanushevsky Table 4: Simulaion resuls for he considered deb o GDP raio dynamics model for l =.59 year deb/gdp g =.3 deb/gdp g = Table 5: Simulaion resuls for he considered deb o GDP raio dynamics model for l = 3.8 year deb/gdp g =.3 deb/gdp g = Table 6: Simulaion resuls for he considered deb o GDP raio dynamics model for l = 3.8 and he condiionally balanced budge assumpion year deb/gdp g =.3 deb/gdp g = The Cobb-Douglas funcion (3) is considered for a consan A, i.e., i is assumed ha a period of economic downurn is no accompanied wih echnological innovaion ha can ignie economic and job growh. For example, a he end of 2 h cenury he Inerne and informaion echnology became acceleraors of he economy in many counries. In he lae 99s, he U.S. governmen moved ino fiscal surplus and he deb o GDP raio fell from 66% in 995 o 56% in 2. However, i is oo risky o spend lavishly on infrasrucure wih a hope of Inerne-ype miracles in he fuure. The above analysis shows ha governmen invesmen in infrasrucure alone canno decrease he deb o GDP raio and boos he economy. I shows ha Krugman, as well as 3

11 Spending and Growh: A Modified Deb o GDP Dynamic Model some oher economiss, are wrong in heir belief ha he raio of deb o GDP will fall and everyhing worked ou fiscally. Bu Krugman is righ by saying increasing governmen deb can increase growh, if he money is invesed well. Public-privae parnerships, individual and corporae conribuions o infrasrucure financing are innovaive ways o seek new funding mechanism in order o preven deficis from rising. To boos he economy, invesmen should focus on areas which would bring a subsanial profi and growh of capial, i.e., K in (6). Governmen simulus programs relaed o hese areas can increase growh and decrease he deb o GDP raio. However, usually, he privae secor (less bureaucraic and more dynamic han he public one) is more sophisicaed and faser han he governmen in finding and invesing in such areas. As menioned earlier, he exising publicaions focus mosly on invesigaing how efficien invesmen in infrasrucure is and how dangerous high deb o GDP raios are for economic growh, more precisely, how hey influence he GDP growh rae (see also Beyzalar and Kusepeli, 2; Ichoku e al., 22). The above simulaion resuls show ha economic growh reached by governmen invesmen in infrasrucure can increase is deb o such a degree ha he deb o GDP raio becomes dangerously high. The crises in Greece and Ireland show he consequences of high deb o GDP raios for counries wih previously fas growing economies. 4. Conclusion The developed deb o GDP raio dynamics model belongs o he so-called shor-run models. I analyzes wheher governmen spending focused on infrasrucure can improve he economic siuaion and wheher his governmen fiscal policy is an effecive ool in boosing he economy in imes of economic downurn. The paper is a useful addiion o he debae: is i bes o le deb increase in he hope of simulaing economic growh o ge ou of he slump or is i beer o cu spending o ge public deb under conrol? The simulaion resuls based on he developed deb o GDP raio dynamics model for he daa characerizing he curren sae of he U.S. economy show ha governmen invesmen in infrasrucure alone canno decrease he deb o GDP raio. Programs like public-privae parnerships, individual and corporae conribuions o finance infrasrucure projecs are poenial mechanisms hrough which public spending on infrasrucure can be more efficien. Governmen spending on infrasrucure may lead o a declining deb o GDP raio when a balanced budge approach is followed a he same ime.only invesmen in he areas which would bring a subsanial profi and growh of capial can increase growh and decrease he deb o GDP raio. Reforms o encourage privae invesmen are he proper financial policies o resore economic healh. Acknowledgmens The auhor hanks wo anonymous referees for helpful commens o make he paper more readable. 3

12 Camilla Yanushevsk, Rafael Yanushevsky References Aschauer, D., 989, Is Public Expendiure Producive?, Journal of Moneary Economics, 23, 2, pp Auerbach, A., Gorodnichenko, Y., 2, Measuring he Oupu Responses o Fiscal Policy, Naional Bureau of Economic Research, Working Paper 63. Beyzalar, M., Kusepeli, Y., 2, Infrasrucure, Economic Growh and Populaion Densiy in Turkey, Inernaional Journal of Economic Sciences and Applied Research, 4, 3, pp Blanchard, O., Peroi, R., 22, An Empirical Characerizaion of he Dynamic Effecs of Changes in Governmen Spending and Taxes on Oupu, Quarerly Journal of Economics, 7, 4, pp Cassou, S., Lansing, K., 998, Opimal Fiscal Policy, Public Capial, and he Produciviy Slowdown, Journal of Economic Dynamics and Conrol, 3, 9-, pp Chrisiano, L., Eichenbaum, M., Rebelo, S., 2, When is he Governmen Spending Muliplier Large?, Journal of Poliical Economy, 9,, pp Glomm, G., Ravikumar, B., 994, Public Invesmen in Infrasrucure in a Simple Growh Model, Journal of Economic Dynamics and Conrol, 8, 8, pp Glomm, G., Ravikumar, B., 997, Producive Governmen Expendiures and Long-run Growh, Journal of Economic Dynamics and Conrol,,, pp Herndon, T., Ash, M., Pollin, R., 23, Does High Public Deb Consisenly Sifle EconomicGrowh? A Criique of Reinhar and Rogoff, Poliical Economy Research Insiue, Working Paper Series 322, Universiy of Massachuses, Amhers. Ichoku, H., Agu, C., Aaguba, J., 22, Wha Do We Know Abou Pro-poor Growh and Regional Povery in Nigeria?, Inernaional Journal of Economic Sciences and Applied Research, 5, 3, pp Inernaional Moneary Fund, 29, The Sae of Public Finances: Oulook and Medium- Term Policies Afer he 28 Crisis, Inernaional Moneary Fund, Washingon. Krugman, P., 22, End This Depression Now! New York: W.W. Noron & Company. Krugman, P., 29, The burden of deb. The New York Times, Augus 28. Leeper, E., Walker T., Yang S., 2, Governmen Invesmen and Fiscal Simulus, IMF Working Papers, l, pp. -3. Lynde, C., Richmond J., 993, Public capial and oal facor produciviy, Inernaional Economic Review, pp Munnell, A., 99, How does public infrasrucure affec regional performance?, New England Economic Review, Sep./Oc., pp. l-32. Ramey, V. A., 2, Idenifying Governmen Spending Shocks: I s All in he Timing, Quarerly Journal of Economics, 26,, pp. -5. Reinhar, C. M., Rogoff, K.S., 29, This Time Is Differen: Eigh Cenuries of Financial Folly, Universiy Press, Princeon. 32

13 Spending and Growh: A Modified Deb o GDP Dynamic Model Romer, D., 26, The Solow Growh Model, Advanced Macroeconomics, hird ed. McGraw Hill, New York. Yanushevsky, R., 992, Opimal Sraegic Planning Problems in Manufacuring Based on he Inpu-oupu Models, Applied Mahemaical Modelling, 6, 6, pp