TEXTO PARA DISCUSSÃO N o 1092

Transcription

1 TEXTO PARA DISCUSSÃO N o 1092 ESTIMATING POTENTIAL OUTPUT: A SURVEY OF THE ALTERNATIVE METHODS AND THEIR APPLICATIONS TO BRAZIL Nelson H. Barbosa Filho Brasília, maio de 2005

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3 TEXTO PARA DISCUSSÃO N o 1092 ESTIMATING POTENTIAL OUTPUT: A SURVEY OF THE ALTERNATIVE METHODS AND THEIR APPLICATIONS TO BRAZIL* Nelson H. Barbosa Filho** Brasília, maio de 2005 O presene exo, em língua inglesa, não foi objeo de revisão ediorial. * Paper prepared for he join research program of he Comisión Economica para América Laina y el Caribe (CEPAL) of he Unied Naions and he Insiuo de Pesquisa Econômica Aplicada (IPEA), of he Brazilian Governmen. The views expressed in his work are hose of he auhor and do no reflec hose of CEPAL, IPEA or is members. The auhor would like o hank Lance Taylor, Duncan Foley, Carlos Mussi, Renao Baumann, Ricardo Bielschowsky, Franklin Serrano, Fabio Freias, Paulo Levy and Esevão Kopschiz for commens and suggesions. The usual disclaimer applies. ** Insiue of Economics, Federal Universiy of Rio de Janeiro ( address: [email protected]).

4 Governo Federal Minisério do Planejameno, Orçameno e Gesão Minisro Paulo Bernardo Silva Secreário-Execuivo Nelson Machado TEXTO PARA DISCUSSÃO Publicação cujo objeivo é divulgar resulados de esudos direa ou indireamene desenvolvidos pelo Ipea, os quais, por sua relevância, levam informações para profissionais especializados e esabelecem um espaço para sugesões. As opiniões emiidas nesa publicação são de exclusiva e de ineira responsabilidade do(s) auor(es), não exprimindo, necessariamene, o pono de visa do Insiuo de Pesquisa Econômica Aplicada ou o do Minisério do Planejameno, Orçameno e Gesão. Fundação pública vinculada ao Minisério do Planejameno, Orçameno e Gesão, o Ipea fornece supore écnico e insiucional às ações governamenais possibiliando a formulação de inúmeras políicas públicas e programas de desenvolvimeno brasileiro e disponibiliza, para a sociedade, pesquisas e esudos realizados por seus écnicos. Presidene Glauco Arbix Direora de Esudos Sociais Anna Maria T. Medeiros Peliano Direor de Adminisração e Finanças Celso dos Sanos Fonseca É permiida a reprodução dese exo e dos dados nele conidos, desde que ciada a fone. Reproduções para fins comerciais são proibidas. A produção ediorial desa publicação conou com o apoio financeiro do Banco Ineramericano de Desenvolvimeno (BID), via Programa Rede de Pesquisa e Desenvolvimeno de Políicas Públicas Rede-Ipea, o qual é operacionalizado pelo Programa das Nações Unidas para o Desenvolvimeno (Pnud), por meio do Projeo BRA/97/013. Ese Trabalho foi realizado no âmbio do Convênio com a Comissão Econômica para a América Laina e o Caribe (CEPAL). Direor de Cooperação e Desenvolvimeno Luiz Henrique Proença Soares Direor de Esudos Regionais e Urbanos Marcelo Piancaselli de Siqueira Direor de Esudos Seoriais Mario Sergio Salerno Direor de Esudos Macroeconômicos Paulo Mansur Levy Chefe de Gabinee Persio Marco Anonio Davison Assessor-Chefe de Comunicação Murilo Lôbo URL: hp:// Ouvidoria: hp:// ISSN JEL O110, O470, O490, O540

5 SUMÁRIO ABSTRACT 1 INTRODUCTION 7 2 BASIC DEFINITIONS 7 3 FIXED COEFFICIENTS AND INPUT-OUTPUT SIMULATIONS 15 4 FLEXIBLE COEFFICIENTS AND GROWTH ACCOUNTING 26 5 TRENDS AND CYCLES 36 6 ESTIMATES OF POTENTIAL OUTPUT FOR BRAZIL 42 7 CONCLUSION 55 REFERENCES 58

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7 ABSTRACT This paper presens he main issues involved in esimaing poenial oupu. The objecive is o describe he alernaive mehods and analyze heir applicaion and implicaions for growh forecass and macroeconomic policy in Brazil. The ex emphasizes he deerminans of poenial oupu under fixed and flexible coefficiens of producion. Given he wide use of aggregae measures of Toal Facor Produciviy in growh accouning, and he sensiiviy of such a variable o economic assumpions and errors of measuremen, he ex also presens he main applied criiques and alernaives o aggregae growh-accouning exercises. The main conclusions are: i) he annual poenial growh rae of Brazil s Gross Domesic Produc (GDP) varies subsanially depending on he mehod and hypoheses adoped and, wha is mos imporan, poenial GDP is no separable from effecive GDP in he long-run; ii) growh-accouning and ime-series sudies of Brazil resul in low poenial-oupu growh raes because hey exrapolae he slow growh of o he fuure; iii) capial seems o be he main consrain on growh in Brazil and, herefore, a demand-led increase in invesmen can raise boh is effecive and poenial oupu levels; iv) however, because of he slow adjusmen of he capial sock, an invesmen boom can also hi a supply consrain before he sock of capial has ime o adjus o he growh rae of invesmen; and v) aggregae measures of poenial oupu do no carry much informaion abou he economy and, herefore, hey should be complemened by secoral esimaes of capaciy uilizaion o idenify he bolenecks in iner-indusry flows and he corresponding demand pressures on inflaion.

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9 1 INTRODUCTION Poenial oupu is he capaciy of producion a a high level of resource use. In macroeconomics his corresponds o he level of Gross Domesic Produc (GDP) consisen wih a sable rae of inflaion, so ha he difference beween poenial and effecive oupu measures he demand pressures on prices. In mainsream growh heory poenial oupu is usually esimaed from he supply side, ha is, from he long-run or equilibrium values of he capial and labor inpus and heir corresponding produciviy levels. In non-mainsream growh heories demand facors also ener in he calculaion hrough he impac of invesmen on capial accumulaion and produciviy. One of he main objecives of Brazil s curren macroeconomic policy is o increase income and employmen wihou raising inflaion. In order o analyze he impacs of moneary and fiscal policy on growh, i is herefore necessary o esimae he poenial growh rae of he economy. This paper presens he main issues involved in such a ask. The objecive is o describe he alernaive mehods of esimaing poenial oupu, as well as o analyze heir applicaion and implicaions for growh forecass and macroeconomic policy in Brazil. The ex is organized in seven secions including his inroducion. Secion wo presens he basic definiions used in growh accouning and he mehods used for measuring labor, capial and he oupu gap. Secion hree analyzes he deerminans of poenial oupu under he assumpion of fixed coefficiens of producion and describes he disaggregaed inpu-oupu esimaes of capaciy uilizaion and employmen raes derived from a Leonief producion funcion. Secion four analyzes he deerminans of poenial oupu under he assumpion of flexible coefficiens of producion and describes he basic seps involved in growh-accouning exercises based on a Cobb-Douglas (CD) producion funcion. Given he wide use of aggregae measures of mulifacor produciviy in growh accouning and he sensiiviy of such a variable o economic assumpions and errors of measuremen, secion four also presens he main applied criiques and alernaives o aggregae growh-accouning exercises. Secion five shifs he invesigaion o he main saisical filers used o esimae rends and cycles in univariae economic ime series and discusses how his a-heoreical approach can subsiue, or be combined wih, heoreical approaches based on producion funcions. Secion six merges heory and economerics in a comparaive analysis of recen esimaes of he poenial growh rae of Brazil. The main objecive is o show how and why he esimaes differ, as well as how sensiive each esimae is o small changes in is underlying assumpions and iniial condiions. Secion seven concludes wih a summary of he main poins of he analysis and some commens on how Brazil can achieve high and susainable growh raes. 2 BASIC DEFINITIONS A producion funcion maps a se of inpus o he oupu of one or more goods and i is he basis of economic esimaes of poenial oupu. The inuiive idea is o express he real oupu of a firm, a secor or an economy as a funcion of he quaniy ipea exo para discussão 1092 maio

10 of inpus necessary for is producion. More formally, producion is represened by a funcion F, such ha Y = F( x, ), (2.1) where Y is real oupu, x is a vecor of conaining all inpus necessary o produce Y, and represens ime. The inclusion of ime as an independen inpu aims o capure he increase in oupu due o produciviy growh, ha is, he increase in oupu when we hold all oher inpus consan. The parial derivaive of F in relaion o ime is an index of he Toal Facor Produciviy (TFP) and, when we apply (2.1) o aggregae variables, such an index depends no only on echnological facors, bu also on relaive prices and on he composiion of oupus and inpus. For he momen, le us ignore hese accouning complicaions and assume ha (2.1) is in fac a good proxy of he echnology of producion. From he oal derivaive of ln Y in relaion o ime we have y = a + J I j= 1 α j x j (2.2) where y and x j are he growh raes of Y and X j, respecively, a is he growh rae of TFP, α j is he elasiciy of Y in relaion o X j, and J I is he oal number of inpus. 1 In economic erms, (2.2) allows us o decompose growh from he supply side, ha is, a represens he amoun of growh generaed by TFP growh, whereas α j x j represens he amoun of growh generaed by inpu j. In he growh-accouning lieraure i is common pracice o impose consan reurns o scale, profi maximizaion (or cos minimizaion) and perfec compeiion on he uni of producion o faciliae he applicaion of (2.2) o real-world economies. To see why, noe ha, if he producion funcion exhibis consan reurns o scale, he corresponding elasiciy parameers add up o one and he value of oupu equals he value of all inpus. Nex, because profi maximizaion under perfec compeiion implies ha he real price of each inpu corresponds o is marginal produc, he share of each inpu in oal oupu is necessarily equal o is elasiciy parameer. Pu ogeher, hese hree assumpions mean ha we can use he funcional disribuion of income, or he cos decomposiion of gross produc, as a guide for he elasiciy parameers of he producion funcion. Perfec compeiion and consan reurns o scale are obviously very srong assumpions o impose on real-world economies. Given he applied focus of his paper, secion four will analyze only he applied implicaions of he heoreical debae. Harcour (1969) provides a survey of he lieraure and, in response o he fragile heoreical foundaions of growh accouning, he mos common defense follows he as-if principle of Friedman (1953) and saes ha, even hough he assumpions seem unrealisic, he model gives good resuls when applied o real-world economies. As we shall see in secion five, his is no a surprise because he Naional Income and Produc Accouning (NIPA) ideniies can also be used o derive (2.2). 1. Unless saed oherwise, all growh raes are exponenial growh raes. 8 exo para discussão 1092 maio 2005 Ipea

11 To use a producion funcion we have o define and measure is oupu and inpu variables. The wo issues are obviously relaed and here are wo alernaives in he growh-accouning lieraure: he ne-value approach and he gross-value approach. 2 The firs approach is based on he work of Solow (1956 and 1957) and i concenraes he analysis on he value added by capial and labor on he assumpion ha inermediae inpus end o be a fixed proporion of gross oupu. In oher words, he ne-value approach assumes ha here is limied or no subsiuion beween inermediae inpus on he one side, and capial and labor on he oher side. The second approach is based on he work of Jorgenson and Grilliches (1967) and i decomposes real gross oupu in erms of all inpus used in is producion, ha is, capial, labor and all inermediae inpus. The basic idea is ha changes in he use and qualiy of inermediae inpus may also have an imporan impac on he ne value of oupu. As we shall see in secion four, his second approach is usually implemened in a disaggregaed way and, herefore, i is much more complex in erms of daa collecion han he firs one. Because of is easy applicaion and inuiive inerpreaion, mos exercises in growh accouning follow he ne-value approach and impose an aggregae producion funcion on he daa. The oher common sep is o follow he as-if principle and assume ha boh he capial and he labor elasiciies of ne oupu correspond o he average share of hese facors in income. Pu ogeher, hese wo assumpions reduce he analysis o calculaing TFP growh from he observed growh raes of income, labor and capial. The growh rae of income is usually obained direcly from he NIPA daa. The measuremen of labor and capial is no so sraighforward and depends on a series of economic assumpions. 2.1 MEASURING LABOR The wo main mehodological issues in measuring labor are how o define i and how o conrol for heerogeneiy. From he perspecive of producion, he labor inpu should be measured by he number of hours worked in producion. However, because daa on work hours are no usually available for many secors and economies, he sandard pracice in macroeconomic sudies is o define labor as he number of people employed in producion. The implici assumpion is ha he average number of work hours per worker does no vary much and, when his is no he case, he variaions are capured by he TFP residual. In oher words, if we do no adjus he employmen index for variaions in he lengh of work shifs, we end up inroducing a srong cyclical behavior in TFP. The second issue is how o conrol for labor heerogeneiy. To use Jorgenson s (1990, p. 24) example, should one work hour of an elecrical engineer coun he same as one work hour of a ruck driver? There are wo direc answers and, no surprisingly, here are basically wo sraegies o deal wih he problem. Firs, we can consruc a weighed index of work hours where he wage rae funcions as a proxy of he qualiy of work. For insance, if he wage paid for one hour of work A is wo 2. Unless saed oherwise, boh growh-accouning sraegies refer o he value of oupu a facors cos, ha is, hey exclude ne axes and subsidies from he analysis. For a survey of he hisory of hough on growh accouning and TFP, see, for insance, Jorgenson (1990), Denison (1993), Griliches (1996) and Hulen (2000). Ipea exo para discussão 1092 maio

12 imes he wage paid for one hour of work B, hen one hour of work A should be equivalen o wo hours of work B. To consruc an index of labor inpu we have o choose a uni of accoun (usually he unskilled work or a composie index of all ypes of work), and hen weigh all ypes work according o he deviaion of heir corresponding wages from he reference wage. In his approach a change in he composiion of employmen oward high-paying jobs appears as an increase in he labor inpu. To illusrae he above poin, le N be he qualiy-adjused Fisher index of work hours. Assuming ha here are J N ypes of work in he economy, each of which receives a wage W per hour, he growh rae of he labor inpu is J = N N n β n j= 1 j j j, (2.3) N where n j is he growh rae of labor inpu j and β j is is average paricipaion in he oal wage bill of he curren and previous periods, ha is N 1 β j = ( ω j + ω j 1) (2.4) 2 and ω j = J N W j= 1 j W N j j N j (2.5) for j = 1,, J N. Equaions (2.4) and (2.5) produce a chained labor index, so ha labor measuremen does no depend on he prices of a reference year. Only he prices of he previous and curren year ener in he calculaion and, whenever we wan o change he reference dae, he levels of he series change, bu heir growh raes remain he same. The second and mos usual sraegy o deal wih heerogeneiy is o ignore i and le TFP capure any change in he qualiy of work hours. The basic idea is o sum all work hours in a given period and pu he resul ino he producion funcion. Any change in he qualiy of work is inerpreed as a produciviy gain or loss, in he sense ha when a worker moves up in he occupaional ladder, his or her produciviy is usually increased. In conras o he previous approach, any change in he composiion of employmen oward more qualified jobs appears as an increase in TFP. Formally, he second approach can be represened by he growh rae of anoher Fisher index of work hours, ha is J = N N n~ ~ β n. (2.6) j= 1 j j 10 exo para discussão 1092 maio 2005 Ipea

13 N where he weigh β ~ j depends only on he paricipaion of labor inpu j in he oal work hours of he curren and previous periods, ha is ~ N 1 β ( ~ ~ j = ω j + ω j 1), (2.7) 2 where ω ~ j = J N N j= 1 j N j. (2.8) Because he weighs in (2.3) and (2.6) may differ, he wo mehodologies may resul in differen esimaes of he labor inpu. In economic erms, he dividing line is wheher o aribue differences in labor produciviy o occupaions or o workers. If one hinks ha he same worker may have a differen produciviy depending on his or her occupaion, hen he mos appropriae approach is o measure labor as he qualiy-adjused index given in (2.3). The logic is ha he same uni of analysis (he worker) can produce skilled and unskilled work depending on where i is employed. In his case i would be erroneous o associae an increase in produciviy o changes in occupaions because he qualiy, or human capial, of he uni producing he work hour remains he same. On he oher hand, if one hinks he same worker has he same produciviy independenly of his or her occupaion, hen changes in occupaions reflec changes in produciviy and, herefore, hey should be included in TFP raher han in he labor inpu. The choice of mehodology has imporan effecs on he esimaed growh of TFP, and we can measure he conribuion of labor qualiy o growh from he difference beween (2.3) and (2.6). 2.2 MEASURING CAPITAL The definiion and esimaion of he capial sock is one of he mos conroversial issues in economic heory. Once again, given he applied orienaion of his paper, we will concenrae he analysis on he assumpions and definiions behind he esimaes raher han on heir heoreical implicaions. In he growh-accouning lieraure i is sandard procedure o consruc a real index for capial based on he perpeual invenory mehod (PIM). The logic is clear and inuiive: he curren capial sock is he cumulaed sum of pas invesmen flows adjused for depreciaion. The crucial issue is how o define he service life and he depreciaion rae of each ype of capial good. To faciliae he analysis, consider he sock of one ype of capial good (say, producer equipmen). Following he polynomial benchmark approach, he dynamics of capial accumulaion can be represened simply as K K I (2.9) = 1 ( 1 δ) + 1 Ipea exo para discussão 1092 maio

14 where K is he sock of he capial good a he beginning of period, I 1 he gross invesmen of period -1 and, for simpliciy, δ is he consan rae of capial depreciaion. 3 By recursive subsiuion we have S j 1 S + 1 K = I j ( 1 δ) + (1 δ) K ( S + 1) (2.10) j= 1 and, herefore, we can esimae he curren capial sock from he previous S invesmen flows and he capial sock a he iniial period -(S+1). How does one esimae he capial sock a iniial period? Here eners he hypohesis abou he service life: if we assume ha he asse under analysis has a lifeime of S periods, meaning ha any good wih an age of S+1 is auomaically reired from producion, we can ignore he second erm on he righ-hand side of (2.10) and esimae he curren capial sock jus from he pas S invesmen flows. 4 The service life and he depreciaion rae are usually esimaed hrough price surveys of used equipmen and srucures in resale markes. The basic assumpion is ha he reducion in he price of an asse is a good proxy of is rae of economic depreciaion, which in is urn can be used o esimae is average service life. The longer he lifeime, he longer he series of invesmen flows needed o esimae he curren capial sock. The service life varies subsanially across asses. For insance, according o he mehodology of he US Bureau of Economic Analysis (BEA), he service life ranges from 4 o 33 years for privae nonresidenial equipmen, 16 o 54 years for nonresidenial srucures, and 11 o 80 years for residenial srucures. 5 Given he lack of long and disaggregaed invesmen series for mos economies, a simpler rule is o aribue an average and shorer service life o jus hree capial caegories: residenial capial, nonresidenial srucures, and machinery and equipmen. For insance, Hoffman (1992 and 2003) aribued a service life of 50, 40 and 15 years o hese hree caegories, respecively, and obained capial-sock esimaes for Lain-American counries saring in he 1950s. Marquei (2000) and Reis and Morandi (2003) followed a similar approach o obain heir capial-sock esimaes for Brazil. 6 Because NIPA daa became available only in he poswar period for mos economies in he world, a 50-year service life means ha capial esimaes would be available only for he 21 s cenury. To overcome his problem, some sudies ake an ad hoc shorcu and assume ha capial and oupu grew a he same rae in he 3. The calculaion is slighly more complex wih a variable rae of depreciaion bu he logic is he same. A deailed survey of he alernaive mehods for esimaing depreciaion can be found in Hulen and Wykoff (1981). Also o simplify he analysis, (2.9) assumes ha new asses are placed in service a he end of he year, so ha no depreciaion rae should be applied o he previous invesmen. One possible alernaive is o assume ha placemen occurs a midyear (see USDC BEA 2003), so ha half of he depreciaion rae is applied o he previous invesmen. 4. Noe ha his approach implies an insananeous ( sudden deah ) reiremen a age S. An alernaive and more realisic approach would be o assume ha reiremen is a probabilisic funcion of age. 5. Fraumeni (1997) presens he deailed numbers and he corresponding depreciaion raes for each ype of asse. 6. Differenly from Hoffman, Reis and Morandi aribued a service life of 20 years for machinery and equipmen. Marquei aribued 50 years o residenial capial and nonresidenial srucures, and 14 years o machinery and equipmen. 12 exo para discussão 1092 maio 2005 Ipea

15 period preceding he firs observaion of invesmen (he balanced-growh assumpion). In formal erms his reduces (2.10) o K I + 1 =, (2.11) g + δ where g is he average discree-ime growh rae of GDP in he years before. 7 Afer esimaing he capial sock for period, he values for he subsequen periods can be consruced from he observed invesmen flows. Given he fragiliy of capial-sock esimaes in he absence of good daa on invesmen, i is imporan o bear in mind how sensiive hese esimaes are o errors of measuremen. From (2.10) we have K K S S = ( 1 δ) > 0 (2.12) and K δ = S j= 1 I ( j 0. (2.13) j 2 j 1)(1 δ) < In words, he higher he iniial esimae of he capial sock, he higher he curren esimae of he capial sock and, he higher he depreciaion rae, he lower he curren esimae of he capial sock. The errors of measuremen due o he iniial capial sock end o die ou wih ime, whereas he errors due o he depreciaion rae end o grow wih ime. To obain an alernaive measure of he laer, we can use a modified version of (2.11) o obain K δ I = ( g + δ) I 2, (2.14) where g I > 0 represens he average discree-ime growh rae of invesmen beween he iniial and he curren periods. Since invesmen usually grows hrough ime, he errors due o a miscalculaion of he depreciaion rae also grow hrough ime. By analogy wih labor, he oher crucial mehodological issue regarding capial is how o conrol for heerogeneiy. In principle he PIM should be applied o each ype of capial good, so ha he availabiliy of invesmen series deermines he level of aggregaion of he analysis. Afer obaining he disaggregaed esimaes, an aggregaed Fisher index can be calculaed by aribuing prices o each ype of asse. 8 Similar o labor measuremen, he sandard approach in he growh-accouning lieraure is o define he aggregaed esimae as qualiy-adjused average of he disaggregaed esimaes, where he weigh of each ype of asse corresponds o is 7. Usually he average is aken over 5 o 10 years. See, for insance, Bernanke and Gurkaynak (2001). 8. Here lies one on he major heoreical criiques o growh-accouning exercises: in neoclassical growh heory one canno deermine asse prices wihou knowing he ineres rae and one canno know he ineres raes wihou knowing asse prices. The mainsream soluion is o subsiue a general-equilibrium approach for aggregae growh accouning. Ipea exo para discussão 1092 maio

16 paricipaion in he oal value of he capial sock. 9 The inuiive idea is ha, in he same way ha wages are a good proxy of he qualiy of each ype of labor inpu, renal prices of fixed asses are a good proxy of he qualiy of each ype of capial good. Assuming ha here exis J K ypes of asses, he growh rae of he aggregae capial sock is J = K K k β k j= 1 j j, (2.15) where, by analogy wih he labor index, he capial weighs are defined o produce a Fisher quaniy index, ha is K 1 β j = ( κ j + κ j 1), (2.16) 2 where κ j = J K R j= 1 j R K j j K j (2.17) is he share asse j in he oal value of capial income of period, and is renal price. R j represens As menioned above, he renal price of each asse is usually esimaed from surveys of asse prices in resale markes. When his is no possible, he renal price has o be impued from he expeced capial income and he corresponding depreciaion and ineres raes. Similar o he labor inpu, we can consruc an alernaive measure of he capial sock from he simple sum of he disaggregaed indexes, so ha he difference beween he qualiy-adjused and he non-qualiy-adjused indexes can be used as a proxy of he change in he qualiy of capial. 2.3 THE OUTPUT GAP The previous analysis described how o esimae he inpu series necessary o consruc a ne-value producion funcion. The nex wo secions will describe how o use such a funcion o esimae poenial oupu, bu, before we do ha, i is worhy o analyze he implicaions of an oupu gap for growh. In some siuaions i is possible for income o grow much faser (or slower) han poenial oupu while sill converging o he laer. In macroeconomic erms poenial oupu is usually defined as susainable oupu, ha is, he level of real GDP ha is consisen wih a sable rae of inflaion (CBO 2003). Poenial oupu is no maximum oupu and, in any given period, effecive oupu may be above or below i. When his occurs, he long-run growh rae of poenial oupu is no a good indicaor of he shor-run growh poenial of he economy. For insance, ake he case where oupu is below is poenial level, because 9. See Jorgenson (1990) and CBO (2001). 14 exo para discussão 1092 maio 2005 Ipea

17 of his gap, i is possible for effecive oupu o grow faser han poenial oupu in he nex period wihou necessarily reaching he laer. How fas? I obviously depends on he oupu gap: he larger he gap he faser he possible growh rae. In order o measure he possible deviaions beween shor-run and long-run * poenial-oupu growh raes, le g be he growh rae necessary for oupu o reach is poenial level in period. In discree ime we have 1 * + g Po, g = 1 1 (2.18) h 1 where g Po, is he growh rae of poenial oupu in period and h 1 is gap beween poenial and effecive oupu, expressed in erms of he laer, in period -1. Table 1 presens some simulaions of (2.18) and shows ha, for insance, if he curren oupu gap is 2% and poenial oupu is expeced o grow a 5%, effecive oupu can grow a approximaely 7% wihou rising above is poenial level in he nex period. Even hough g * is a nonlinear funcion of h, a linear approximaion indicaes ha every percenage poin of he oupu gap adds approximaely one percenage poin o g *. The opposie holds for a negaive oupu gap (when effecive oupu is higher han poenial oupu). See able 1. 3 FIXED COEFFICIENTS AND INPUT-OUTPUT SIMULATIONS In he previous secion we specified he producion funcion in a general way o emphasize ha (2.2) is consisen wih alernaive funcional forms. To avoid cluering he analysis wih many examples of producion funcions, in his and he nex secions we will concenrae he invesigaion on he implicaions of fixed and flexible echnological coefficiens of producion for growh accouning. 10 Saring wih fixed coefficiens and following he ne-value approach oulined earlier, assume ha F akes a Leonief form, ha is K N Y = Min,, (3.1) V B where V and B represen he fixed capial-income and labor-income raios, respecively. In words, (3.1) means ha producion uses capial and labor in a fixed proporion, so ha oupu can be limied by a shorage of any of hese wo inpus. When K / V < N / B, capial is uilized fully and here are idle labor resources in he economy. When he opposie happens labor is uilized fully and here are idle capial resources in he economy. 10. The mos used forms in he lieraure are he Cobb-Douglas (CD) funcion, he Consan-Elasicy-of-Subsiuion (CES) funcion, he Transcendenal Logarihmic ( ranslog ) funcion, and he Leonief funcion. The CD, CES, and Leonief funcions are prey sandard and can be found in mos graduae microeconomic exbooks. The basic reference for he ranslog funcion is Chrisensen, Jorgenson and Lau (1973), and a summary of is applicaions can be found in Kim (1992). Ipea exo para discussão 1092 maio

18 The fixed-coefficien hypohesis can obviously be exended o any number of inpus. The basic idea is ha we have as many consrains on oupu as he number of inpus, bu only he lowes consrain can be binding in any given period. In erms of he growh-accouning decomposiion given in (2.2), his implies seing one of he elasiciy parameers equal o one and he remaining equal o zero. The TFP erm is reduced o he growh rae of he produciviy of he scarces facor. In (3.1) we defined producion in he simples possible way o have jus wo possible consrains on oupu: labor and capial. The reason is ha mos heerodox sudies on growh and disribuion use a ne-value Leonief funcion and assume ha eiher capial or labor is he scarces facor in capialis economies. 11 Le us see he implicaions of each of hese wo consrains separaely before moving o general case. 3.1 THE LABOR CONSTRAINT If labor is he binding consrain, he growh rae of poenial oupu depends on he N growh raes of labor produciviy and he labor force. Formally, le Y max be he labor-consrained oupu level, by definiion N Y = = N Z N max, (3.2) B where Z = 1/ B is he average labor produciviy o simplify he noaion. Poenial oupu is usually defined as a long-run variable, ha is, a variable adjused o exclude cyclical variaions. To obain an esimae of he labor-consrained growh rae we have herefore o eliminae he cyclical componens from he righhand-side of (3.2). The sandard procedure is o apply a saisical filer o he corresponding ime series, so ha produciviy can be divided in a rend and a cyclical componen and only he former eners in he definiion of poenial oupu. Secion five will presen he main univariae mehods used o separae rends from cycles in economic ime series, for he momen le us jus assume ha labor produciviy can be defined as = Z, (3.3) Z un, rend where naurally rend Z is he rend componen of labor produciviy and u, = Z / Z is cyclical componen. N rend In a long-run analysis we can ignore he cycle componen and use jus he rend growh rae of labor produciviy o esimae poenial oupu. In a shor-run analysis he cyclical componen should be aken ino consideraion because labor produciviy ends o vary subsanially wih income. The basic sources of his cyclical paern are labor hoarding, economies of scale and changes in he composiion of employmen. 11. For a comparaive survey of heerodox and orhodox growh heories see, for insance, Marglin (1984), Du (1990), and Foley and Michl (1999). 16 exo para discussão 1092 maio 2005 Ipea

19 Labor hoarding occurs because firms do no auomaically adjus employmen o variaions in oupu. In oher words, he oupu-elasiciy of employmen is smaller han one, meaning ha during an upswing oupu rises faser han employmen and vice versa. In mainsream economic heory he foundaions of labor hoarding are usually asymmeric informaion and adjusmen coss. Because firms canno monior work effor perfecly, hey may reduce he variaion of employmen in order o improve labor relaions and, hrough his, give an incenive for workers o perform a he desired effor level. 12 In he same vein, firms can also reduce he variaion of employmen because of he sunken coss in labor raining. These wo hypoheses imply ha labor produciviy is pro-cyclical, especially a he urning poins of he cycle. Economies of scale are anoher source of cyclical behavior because no all employees are direcly involved in producion and because of oher non-labor fixed coss. Whie-collar jobs are usually more sable han blue-collar jobs and, herefore, when oupu grows, he average cos of he former falls. By analogy, because any oher average fixed cos also ends o vary in he opposie direcion of oupu, during an expansion economies of scale make income grow faser han he labor inpu. The opposie holds during a recession. The hird source of cyclicaliy is he change in he composiion of employmen beween high-produciviy and low-produciviy secors. During an expansion he former ends o grow and absorb workers from he laer, which raises he average level of produciviy in he economy. The inuiion is ha he economy can be divided ino a modern and a radiional secor, wih he laer funcioning as he residual employer of hose who canno find jobs in he modern secor. In developing low-income economies, indusry is usually he modern secor and agriculure he radiional secor. The same logic can be applied o an indusrialized middleincome economy as Brazil where low-produciviy urban jobs ake he role of agriculure as he residual employer. 13 The boom line is ha, in a dual economy, labor produciviy is a posiive funcion of he size of he modern secor, which in is urn ends o be procyclical. In addiion o cyclical facors, labor-produciviy can also be a funcion of economic growh in he long run. The inuiion comes from he classical proposiion ha growh increases he division of labor, which in is urn acceleraes growh and so on. In he modern growh lieraure, he endogenous deerminaion of labor produciviy is usually associaed wih he Kaldor-Verdoorn laws, according o which growh leads o faser produciviy growh via increasing reurns and changes in he composiion of income and employmen. As summarized by Thirlwall (1983), he original proposiion of Kaldor (1966) consised of hree laws: i) fas GDP growh is associaed wih fas growh of manufacuring; ii) because of increasing reurns, here is a posiive relaion beween labor-produciviy growh and oupu growh in manufacuring; and iii) he faser he growh of manufacuring, he faser he ransference of labor from non-manufacuring secors o manufacuring. 12. The logic is basically he same of he efficien-wage hypohesis, bu he incenive comes in he form of sable jobs raher han higher real wages. 13. The basic reference is Lewis s (1954) dual-economy model. Basu (2003) presens a survey of he more recen lieraure on he opic. Ipea exo para discussão 1092 maio

20 Overall, he idea is basically he same as oulined earlier, plus a long-run posiive relaion beween growh and labor produciviy. Moving o he number of work hours available for producion, he long-run componen of he labor inpu is usually defined by he growh rae of he workingage populaion and some saisical or economic assumpions abou he rae of paricipaion, he rae of employmen (or unemploymen), and he average number of work hours per employee. More formally, he labor inpu can be defined as N N L L E A = LW L E L (3.4) A LW where L E, L A, and L W represen he number of people ha are respecively employed, economically acive (meaning in he labor force), and in he working-age populaion. By definiion: LE LA LW. From (3.4) i is sraighforward ha he growh rae of he labor inpu depends no only on he growh rae of he working-age populaion, bu also on changes in he raes of paricipaion ( L A / Lw ), employmen ( L E / LA ), and in he number of work hours per employee ( N / LE ). Because hese variables are highly pro-cyclical, he growh rae of he labor force also ends o be highly pro-cyclical. I should be noed ha he cyclical behavior of he labor inpu does no mean ha he labor consrain is compleely endogenous. By definiion he paricipaion and employmen raes have an upper bound a 100%, and he number of work hours per worker has a physical or insiuional maximum. Because of his, in he long run he growh rae of he labor inpu canno deviae permanenly from he growh rae of he working-age populaion, which is usually a sable parameer deermined by migraion and feriliy and moraliy raes. The inuiion is ha cyclical variaions end o balance ou during a sufficienly long inerval of ime, whereas he precise lengh of such an inerval is a opic o be defined empirically. Long swings in he employmen and paricipaion raes are a common feaure of economic developmen and should be aken ino consideraion in medium-run projecions. 14 In conras, for a shor-run or year-o-year analysis we have o ake in consideraion how far effecive oupu is from he labor consrain. As discussed in he previous secion, a gap beween he wo variables can aler he shor-run susainable growh rae of he economy. In he case of he labor consrain, mos sudies emphasize he role of he unemploymen rae and focus he analysis on is deviaions from he Non-Acceleraing-Inflaion Rae of Unemploymen (NAIRU). The basic assumpion is ha here exiss one and only one rae of unemploymen consisen wih a sable inflaion rae, which hen becomes he mos imporan deerminan of he labor consrain. The NAIRU is usually esimaed hrough a single-equaion or muliple-equaion economeric model where inflaion is a funcion of he unemploymen rae and oher variables. From he esimaed coefficiens and he assumpions abou he oher cos 14. As we shall see in secion six, in he case of Brazil he shor-run seems o be any inerval beween zero and wo years, he medium run beween wo and eigh years, and he long run more han eigh years. 18 exo para discussão 1092 maio 2005 Ipea

21 deerminans of inflaion, we can obain he rae of unemploymen consisen wih a sable or arge rae of inflaion. However, precisely because inflaion has many oher deerminans han he rae of unemploymen, NAIRU esimaes end o be very sensiive o small changes in economic condiions, especially in small open economies. For insance, if he exchange rae falls more han implici in he NAIRU esimae, he rae of unemploymen can fall wihou increasing inflaion. As long as he increase in wages is compensaed by he reducion in he exchange rae, inflaion remains sable. A similar reasoning can be applied o he oher main deerminans of inflaion as, for insance, he price of energy, he ineres rae, and labor produciviy. The conclusion is ha he NAIRU is possibly endogenous and highly unsable and, as such, i is no a good guide for inflaion argeing. 15 Finally, i should be noed ha because he labor consrain is highly cyclical in he shor run and possibly endogenous in he long run, many analyss choose o ignore i on he assumpion ha income deermines employmen raher han he oher way around. The logic is Keynesian bu is implicaions can be analyzed from he equaions above, provided ha we change he direcion of causaliy. Given he oupu level and some assumpion abou he behavior of labor produciviy, we can derive he labor requiremen from (3.2). Given he labor requiremen and he growh rae of he labor force, we can use (3.4) o derive he employmen rae for some given rae of paricipaion and work-employee raio. The final resul is ha aggregae demand deermines income and employmen on he assumpion ha he labor consrain is almos never binding in capialis economies. 16 The simples way o represen he Keynesian view is o use a varian of Okun s law o model employmen as a funcion of income. For insance, assume ha he long-run GDP-elasiciy of employmen is 0.5. By consrucion he growh rae of labor-produciviy is 50% he growh rae of GDP and, if he labor force is assumed o grow 1.5% per year, as i seems o be he case of Brazil, GDP has o grow a leas 3% o keep he rae of unemploymen consan THE CAPITAL CONSTRAINT When labor is no he binding consrain he nex suspec is he capial sock. K Y By analogy wih he previous analysis, le be he capial-consrained oupu level, ha is 15. The possibiliy of muliple equilibrium poins canno be discarded a priori. For a summary of he debae over he usefulness of he NAIRU for inflaion argeing, see Gordon (1997), Blanchard (1997), Galbraih (1997) and Sigliz (1997) in he special issue of he Journal of Economic Perspecives on he opic. 16. This does no mean ha he labor marke does no maer for inflaion, bu only ha labor does no usually poses a quaniaive consrain on oupu. The consrain is usually on wage inflaion and i ends o be solved by macroeconomic policy, ha is, he rae of unemploymen is usually kep on he level necessary o conrol workers claims on income. For an ouline and he implicaions of social conflic and effecive demand for growh models, see, for insance, Taylor (1991 and 2004). 17. The argumen is basically he same as proposed by he Kaldor-Verdoorn laws, wih he difference ha produciviy is modeled hrough he GDP elasiciy of employmen. For an analysis of he wo demand-led approaches, see McCombie (1983). Ipea exo para discussão 1092 maio

22 K K K = u, (3.5) V K Y = V Trend K Trend where u = V / V represens he rae of capial or capaciy uilizaion, ha is, he raio of he rend value o he effecive value of V. During an upswing he rae of capaciy uilizaion ends o rise because he capial-oupu raio ends o fall below is long-run rend. The opposie holds during a downswing and, for mos indusrialized economies, he capial-oupu raio seems o be eiher consan or rising. Similar o he labor consrain, he capial consrain has an imporan cyclical componen because of flucuaions in capaciy uilizaion, bu we can assume ha such flucuaions balance ou in a long-run analysis. The growh rae of poenial oupu hen becomes idenical o he growh rae of he capial sock minus he growh rae of he rend capial-oupu raio. Also by analogy wih he labor consrain, he rend capial-oupu raio is usually obained by applying a saisical filer o he original series or by esimaing a Non-Acceleraing-Inflaion Rae of Capaciy Uilizaion (NAICU). 18 As we saw in he previous secion, he curren capial sock can be expressed as a funcion of pas invesmens flows. The same logic can be applied forwards, in which case he growh rae of he capial sock becomes a funcion of he invesmenincome, he capial-income, and he depreciaion raios. More formally, I k = δ (3.6) K where I is he gross invesmen in period. 19 Afer some algebraic operaions we have K su k = δ (3.7) Trend ρ V where s is he invesmen-income raio obained from NIPA daa, and ρ is he relaive price of invesmen goods (he price of invesmen goods divided by he oupu deflaor). 20 Le us consider he economic inerpreaion of each variable in (3.7) separaely. Firs, an increase in he relaive price of capial reduces he growh rae of he capial sock because his means ha he same amoun of income buys a smaller amoun 18. See Corrado and Maey (1997). 19. Recall ha he capial sock of period is he capial sock a he beginning of period, so ha he growh rae of capial measures he change beween he beginning and he end of. One can alernaively measure capial a mid-year, bu since his would complicae he formulaion wihou adding much qualiaive informaion, we prefer o work wih he simpler version given in (3.6). 20. Equaion (3.7) is a modified version of he one presened by Bacha and Bonelli (2004). Mos growh-accouning sudies define s as he saving-income raio and measure i by he invesmen-income raio. Boh variables are obviously idenical ex-pos, bu we prefer o use he laer name because a reducion in consumpion does no necessarily increase invesmen in absolue erms. In fac, aemps increase s by reducing oal consumpion may backfire by reducing invesmen in a higher proporion han income. 20 exo para discussão 1092 maio 2005 Ipea

23 of capial goods. In high-income economies he relaive of price of capial ends o be a saionary variable and, herefore, i eners only in shor-run growh forecass. In middle and low-income economies he relaive price of capial usually shows wide flucuaions and i ends o follow he behavior of he real exchange rae because of he high share of impors in he oal supply of capial goods. Second, an increase in he rae of capaciy uilizaion increases he growh rae of he capial sock because i means ha he exising sock of asses is producing more goods han usual and, herefore, he economy can accumulae more capial if he oher variables in (3.7) remain consan. Similar o he labor consrain, he exisence of a capaciy variable in (3.7) inroduces a srong cyclical componen in he growh rae of he capial sock. Third, an increase in he rend componen of he capial-income raio reduces he growh rae of he capial sock because i means ha we need a higher amoun of capial o produce he same amoun of oupu. An alernaive way o say he same hing is o noe ha he income-capial raio is he average produciviy of capial. When he laer falls, he producive capaciy of he economy falls (boh for consumer and capial goods) and, herefore, he growh rae of he capial sock deceleraes. Finally, considering he invesmen-gdp raio, he inerpreaion is clear and sraighforward: he higher he share capial goods in oal producion, he higher he growh rae of he capial sock. Mos sudies of he capial consrain emphasize he cenral role of he invesmen-income raio in he capial consrain on he assumpion ha he oher erms in (3.7) are consan in he long run. From such a perspecive, i is possible for effecive demand o raise he supply consrains on oupu, provided ha growh is generaed or accompanied by an increase in invesmen. If invesmen grows faser han he oher componens of aggregae demand, he growh rae of he capial sock acceleraes. To illusrae his, le us rewrie (3.7) as 1+ i i k 1 k = + δ r k 1 (3.8) 1+ k 1 1+ k 1 where i is he growh rae of gross invesmen in he previous period. 21 From (3.8) we can see ha he growh rae of he capial sock is sable when k 1 = i and, wha is mos imporan, given a change in he growh rae of invesmen, he growh rae of he capial sock follows residually. The adjusmen is demand-led bu no auomaic. For insance, assume ha he annual depreciaion rae is 4% and ha invesmen and capial have been growing a 3% in he previous years. 22 Afer a permanen one percenage-poin increase in he growh rae of invesmen, he pace of capial accumulaion slowly acceleraes unil i reaches 4%. In numbers, 35% of he adjusmen is compleed afer five 5 years, 55% afer 10 years, 21. See Barbosa-Filho (2000) and Freias (2002), respecively, for he derivaion of he coninuous-ime and discree-ime versions of (3.8). 22. We se depreciaion a 4% based on he esimae of Reis and Morandi (2003) for Brazil. As usual, he faser he depreciaion, he faser he adjusmen of he capial sock o invesmen. Ipea exo para discussão 1092 maio

24 69% afer 15 years and so on. Overall i akes approximaely 67 years for he adjusmen o be compleed. Because of he slow dynamics of he capial sock, i is highly probable ha an invesmen boom would make he economy hi a supply consrain before raising is capial sock subsanially. The reason is ha he share of invesmen in income is usually much higher han is share in he curren capial sock. In oher words, given a change in he growh rae of invesmen, he adjusmen of income is much faser han he adjusmen of he capial sock. If he growh raes of oher expendiures (consumpion and ne expors) do no decelerae o accommodae he increase in invesmen, he capial consrain ends o bind very fas even during an invesmen boom. The slow adjusmen of capial o invesmen is he main real consrain on a demand-led growh sraegy. I should be noed ha expressing he growh rae of capial as a funcion of he growh rae of invesmen is an imporan mehodological deparure from he supplydriven growh models of mainsream heory. If one allows he possibiliy ha an independen invesmen funcion deermines he capial consrain on he economy, i is hen possible o explain he dynamics of poenial oupu as a consequence of effecive demand. The causaliy runs from expendiures o supply raher han he oher way around INPUT-OUTPUT SIMULATIONS AND POTENTIAL OUTPUT So far we assumed ha only labor and capial could impose a supply consrain on oupu. In realiy here are many oher sources of consrains like, for insance, energy or impors. 24 In a muli-secor model wih fixed coefficiens of producion, he insufficien supply of any basic inermediae good can originae a boleneck in inerindusry relaions and, hrough his, creae a supply consrain on oal oupu. In oher words, oupu can be below he labor and capial consrains and sill be consrained from he supply side. In real-world economies growh is an unbalanced process. The growh raes of each secor in he economy hardly coincide bu, as long as he differences are no large and flucuae around a common value, growh can proceed wihou necessarily hiing a supply consrain. For insance, given a discrepancy beween he demand and poenial oupu growh raes in a secor, he rae of capaciy uilizaion changes in he shor run, while invesmen increases poenial oupu o aend he increase in demand in he long run. The aggregae models presened so far are inadequae o deal wih iner-indusry bolenecks. The alernaive is o use a muli-secor model and he simples and mos inuiive choice is he Inpu-Oupu (IO) model. The basic idea is o model he oupu of all secors or goods of he economy as a funcion of heir inermediae and 23. See Panico (2003) for an analysis of he role of effecive demand in economic growh. Barbosa-Filho (2003 and 2004a) presens a dynamical-accouning model of demand-led growh. 24. The impor-consrain is he origin of gap models and he balance-of-paymen (BoP) consrain on growh. For an ouline of he wo approaches, see Taylor (1994) and McCombie and Thirlwall (1997). In addiion o real variables, he BoP consrain also involves financial variables and is beyond he scope of his paper. For, he link beween rade and finance in he BoP consrain, see, for insance, Barbosa-Filho (2001 and 2004b). 22 exo para discussão 1092 maio 2005 Ipea

25 final demands. To faciliae he exposiion, we will organize he analysis in erms of goods on he assumpion ha each secor produces jus one good. 25 Assuming ha here exis m goods in he economy, he supply-demand equilibrium in all markes can be represen as x + m = c + c + f + f (3.9) d m d m where all enries are m 1 vecors a facors prices. The lef-hand side of (3.9) represens he oal supply of all goods in he economy, ha is, x is he vecor of gross domesic oupu and m he vecor of oal impors. 26 The righ-hand side of (3.9) represens he oal demand, which is divided in four componens: he inermediae demand for domesic, c d, and impored, c m, goods; and he final demand for d m domesic, f, and impored, f, goods. In mos counries NIPA disaggregaed daa are organized in a able of sources and uses of resources similar o (3.9). The main difference is ha he NIPA daa usually come in marke prices, whereas (3.9) should be expressed in erms of he coss of producion, ha is, i should exclude indirec axes and allocae he commercial and ranspor coss of every iner-indusry flow o he commercial and ranspor secors, respecively. 27 In he case of Brazil we have an addiional difference because he NIPA annual ables do no separae inermediae demand in a domesic and an impored componen. d d Since by definiion x = c + f, when he daa come in he form of (3.9), we can separae impors from domesic oupu and concenrae he analysis on he laer. The nex sep is o assume ha he inermediae-demand vecor is a linear funcion of he gross-oupu vecor, ha is c = A x, (3.10) d d d where A is a m m marix of inpu-oupu coefficiens, ha is, he a hj elemen of d A represens he amoun of good h necessary o produce one uni of good j in period. Assuming ha A is nonsingular, we have x d 1 d d = (I A ) f (3.11) where I is he m m ideniy marix. In he lieraure on economic sysems (3.11) corresponds o a saic open IO model. The model is saic because i considers only he demand-creaing effecs of invesmen and open because i does no express he final demand and impors as a funcion of gross or ne oupu. In dynamic models invesmen is usually modeled as a funcion of he change in oupu (he acceleraor principle), whereas in closed models consumpion is usually modeled as a funcion of he oal value added in he economy (he Keynesian muliplier). These exensions resul in slighly more 25. In he general case we need a marke-share marix o move from goods o secors. 26. Again o simplify he analysis, (3.9) is based on he assumpion ha all impors are compeiive, ha is, here exiss domesic producion of all m goods. Taylor (1975 and 1979) presens he case wih non-compeiive impors. 27. For he basic definiions and hypoheses used o consruc an IO marix, see, for insance, Miller and Blair (1985). Ipea exo para discussão 1092 maio

26 complicaed calculaions bu hey do no aler he basic logic of (3.11), ha is: we can forecas he oupu of each good in he economy based on an esimae of he coefficien marix and of he final-demand vecor for domesic goods. Given he focus of his paper, we will concenrae he analysis on he implicaions of his resul for poenial oupu. The firs issue o consider is how o esimae or forecas he righ-hand side of (3.11). The coefficien marix is usually consruced from a marix of iner-indusry relaions and secoral surveys of iner-indusry flows, bu i does no end o be updaed frequenly in he case of Brazil. The sandard approach is o use he coefficiens of a given year as guide on he assumpion ha hey did no change subsanially beween he reference and he forecas periods. An alernaive approach is o esimae he coefficien marix hrough a compuable general equilibrium model where, heoreically, he demand of each inpu depends on he price and quaniy of all inpus and oupus. For insance, we can assume ha a Cobb-Douglas or CES funcion represens he echnology of producion of each good, and hen use some hypoheses abou firm behavior and relaive prices o updae he coefficien marix o he curren period. The nex issue is how o forecas he level and he composiion of final demand and impors. This is obviously a nonrivial ask and he mehodology varies according o he ype of expendiure under analysis. For privae consumpion, he mos common sraegy is o esimae he corresponding vecor hrough a funcion ha links he consumpion of each good wih he level and he disribuion of income, or o use a arge vecor as reference. The former approach ransforms (3.11) ino a closed model for consumpion. For governmen expendiures he mos usual approach is o use he public expendiures implici in budge arges and plans. Since hese numbers are hardly expressed in IO erms, he governmen budge has o be ranslaed in erms of he m goods of he final-demand vecor. In he same vein, aggregae expors and impors are usually obained from macroeconomic or secoral sudies and based on some forecass for he exchange rae and he domesic and foreign income levels. The resuling aggregae esimaes are hen ranslaed in erms of he m goods in he economy. Privae invesmen ends o be deermined eiher by surveys of business plans and expecaions or by he level necessary for supply o grow a he same rae as demand. I should be noed ha he deerminaion of he final demand for domesic goods is no a one-way process, ha is, ieraive simulaions are necessary o adjus macroeconomic forecass o microeconomic evidence. In fac, his is one of he main advanages of IO models over aggregae models, IO models provide an channel of discussion beween macroeconomiss and secor specialiss o produce and check he consisency of aggregae and muli-secor forecass of oupu levels and inpu requiremens. In order o esimae poenial oupu, we can use (3.11) o check wheher he macroeconomic oupu forecass are consisen wih he capaciy of producion of each secor. A similar reasoning can be applied o he labor and capial requiremens. For insance, given he oupu vecor and an esimae of he labor-oupu coefficien of each secor, we can calculae he oal increase in employmen necessary for he economy o reach he macroeconomic oupu forecas. By analogy, 24 exo para discussão 1092 maio 2005 Ipea

27 he capial sock necessary o produce he oupu vecor can be esimaed hrough he capial-oupu coefficiens of each secor. The difference beween he effecive and he required capial sock can hen be used o calculae he change in each secors capial-oupu raio, as well as he invesmen necessary o increase he capial sock in line wih demand. All of he above procedures are implemened by pre-muliplying he oupu vecor by a diagonal marix conaining he appropriae coefficiens. More formally, le D be he diagonal operaor, ha is, a funcion ha ransforms a m 1 vecor z ino a m m diagonal marix D(z), in which he j-h enry of z is placed an he j-h diagonal enry of D(z). The labor inpu necessary o produce he oupu vecor is given by n = D(b )(I A ) f (3.12) d 1 d where n and b are he column vecors conaining he labor inpu and labor-oupu coefficiens of all secors in he economy, respecively. By analogy, he vecors conaining he capial requiremens ( k ) and raes of capaciy uilizaion ( u ) can be esimaed as and k = D(v )(I A ) f (3.13) d 1 d u = D(x Po ) 1 (I A d ) f 1 d (3.14) Po respecively, where v is he vecor of secoral capial-oupu coefficiens, and x is a vecor whose j-h enry is he poenial oupu of he j-h secor obained from secoral sudies. Finally, he marix version of (2.9) can be used o esimae he invesmen vecor necessary o keep he capial-oupu raios of all secors consan, ha is i = D(v )(I A ) f [I D(δ )]k, (3.15) d 1 d where i and δ are he column vecors conaining each secors invesmen and depreciaion raes, respecively. From he above equaions we can see ha even hough IO models are simple and inuiive, hey are much more daa-demanding han aggregae models. In order o forecas oupu, we need o esimae all iner-indusry relaions and he level and composiion of final demand. To esimae he capial and labor requiremens, we also have o esimae he labor-oupu and capial-oupu raios of all secors in he economy, whereas o esimae capaciy uilizaion we have o esimae of heir poenial oupu levels. Because of a lack of good daa and he many resricive assumpions involved in IO simulaions, mos growh analysis end o be done hrough aggregae models in which we need o esimae only a few variables and use jus one echnological parameer o represen all inpu-oupu coefficiens of he economy. 1 Ipea exo para discussão 1092 maio

28 4 FLEXIBLE COEFFICIENTS AND GROWTH ACCOUNTING Mos growh-accouning sudies assume ha he coefficiens of producion are flexible and use some version of (2.2) o esimae he growh rae of poenial oupu from he normal or long-run growh raes of TFP and he inpus used in producion. The oher common pracice is o assume profi maximizaion (or cos minimizaion), perfec compeiion, and consan reurns o scale in order o obain he elasiciy parameers direcly from he share of each inpu in he oal value of oupu. Wih a ne-value producion funcion hese shares correspond o he paricipaion of capial and labor in he valued added. Wih a gross-value funcion hey correspond he paricipaion of each inpu in he oal cos of producion. The simples and mos common growh-accouning sudies use a Cobb-Douglas funcion o decompose he growh rae of he ne-value of producion in erms of jus hree componens: capial, labor and TFP. The basic reference is he Solow-Swan growh model, in which he growh rae of TFP is an exogenous parameer THE SOLOW-SWAN MODEL AND POTENTIAL OUTPUT Assume ha here is perfec compeiion, consan reurns o scale, and ha firms maximize profi or minimize cos. When he echnology of producion can be represened by a Cobb-Douglas funcion, we have Y = A K N (4.1) α 1 a where A is he level of TFP and α is he average share of capial income in oal income. From (4.1) he growh decomposiion given in (2.2) can be reduced o y = a + αk + ( 1 α) n, (4.2) and we can calculae he growh rae of TFP direcly from he funcional disribuion of income and he growh raes of capial and labor. There are wo possible errors of measuremen in calculaing TFP from (4.1). Firs, when he capial sock is no fully uilized in producion, changes in he rae of capaciy uilizaion are measured as changes in TFP. Second, as we already saw in secions wo and hree, when labor is measured by he number of employees (or people in he work force), he TFP also capures he cyclical changes in labor K markes. More formally, assume ha u K is he amoun of capial effecively used K in producion, where u is he rae of capaciy defined in secion hree. From (3.4) we can rewrie (4.1) as where Error Y = A A K L, (4.3) α 1 α W 1 [( N / L )( L / L )( L / L ) L ] α Error A = u (4.4) K ( ) α E E A A W W 28. See, for insance, Barro and Sala-I-Marin (1995) for he origins and basic characerisics of he Solow-Swan model. 26 exo para discussão 1092 maio 2005 Ipea

29 is he error of measuremen implici he esimaes of TFP derived from (4.1). These errors respond for mos of he variaion in TFP growh in he shor and medium run. In he long-run he cyclical facors end o balance ou and, herefore, he growh rae of TFP is esimaed from he long-run or equilibrium values of he capial and labor inpus. In he case of capial, he equilibrium value is obained by muliplying he exising capial sock by he equilibrium rae of capaciy uilizaion, which in is urn can be defined from he long-run componen of he capial-income raio, from surveys of uilizaion raes, or from he non-acceleraing-inflaion rae of capaciy uilizaion. A fourh and simpler alernaive is o assume ha he poenial and effecive values of he capial sock are he same, so ha only he deviaions of he unemploymen rae from he NAIRU have an impac on prices. 29 In he case of labor, he equilibrium value is based on he average raio of work hours o employees during business flucuaions and on he long-run or nonacceleraing-inflaion raes of paricipaion and unemploymen. Mos of he sudies emphasizes he laer concep and esimae he NAIRU hrough some version of he Phillips curve expanded o incorporae inflaion expecaions. In addiion o he cyclicaliy creaed by errors of measuremen, TFP can also have a cyclical behavior iself. As we will see a he end of his secion, TFP is acually an index of all oupu-inpu coefficiens in he economy and, as such, i changes according o he changes in relaive prices and in he oupu and inpu composiion during he cycle. For he momen, le us follow he approach of he previous secion and assume ha A can be represened as he produc of a cyclical and a rend componen, ha is A = A A, (4.5) Cycle Trend where A = A / A. Cycle Trend The rend componen of TFP can be obained by applying a saisical filer o he effecive series or by a regression of is naural logarihm on a se of rends. These rends are usually defined by muliplying a linear rend by a group of dummy variables, which in heir urn are deermined by a quaniaive or qualiaive analysis of he hisory of he economy in quesion. 30 Puing all equaions ogeher, he growh-accouning equaion becomes y = a + a + a + αk + ( 1 α) l, (4.6) Trend Cycle Error Trend Cycle Error where a, a, and a are respecively he growh raes of he rend, cycle and error-of-measuremen componens of TFP. The growh rae of poenial oupu can be obained from (4.6) by assuming ha he error and cycle componens are zero in he long run, which in is urn is auologically defined as he period of ime necessary for hese variables o be equal o zero. W 29. This is he approach of he US Congressional Budge Office (CBO 2001). 30. For insance, he CBO (2003) includes a broken-rend dummy a he peak of each he business cycle of he US economy. The idea is ha long-run TFP growh may vary across cycles. Ipea exo para discussão 1092 maio

30 Formally, he growh rae of poenial oupu is given by y = a + αk + ( 1 α) l, (4.7) Po Trend LR W LR where k is he long-run growh rae of he capial sock analyzed in secion hree. Finally, if we assume furher ha he economy reaches a seady sae in he long run, hen he growh rae of he capial sock converges o he growh rae of invesmen, income grows a he same rae of invesmen, and he growh rae of poenial oupu is Po 1 Trend y = a + l 1 α W, (4.8) ha is, he ulimae sources of growh are TFP and he labor force. 4.2 HUMAN CAPITAL AND THE AK MODEL In conras o he exogenous naure of produciviy in he Solow-Swan model, he New Growh Theory aims o invesigae he deerminans of TFP by expanding he producion funcion o include oher echnological and insiuional variables. The lis of candidaes is as long as he economiss imaginaion bu, for he purpose of esimaing poenial oupu, we will concenrae he analysis on he implicaions of human and physical capial for growh because hese are he mos widely used variables in growh-accouning sudies. 31 The simples way o include human capial in he analysis is o rewrie (4.1) as α 1 α Y = K ( E N ) (4.9) 1/(1 α ) where E is an index of labor efficiency. By definiion E = A, ha is, TFP growh augmens he labor inpu. The nex sep is o assume ha labor efficiency is a posiive funcion of he sock of human capial in he economy H, ha is ζ E = Φ ( H ) (4.10) where Φ represens he non-human-capial deerminans of labor efficiency, and ζ is a posiive parameer ha represens he human-capial elasiciy of labor efficiency. From (4.10) and (4.9) we have y = φ + ζh + αk + ( 1 α) n (4.11) where φ and h are he growh raes of Φ and H, respecively. In relaion o he growh decomposiion of he Solow-Swan model, (4.11) divides he growh rae of TFP in a human-capial and a non-human capial componen. In economic erms, par of he increase in he efficiency of he economy 31. See, for insance, Barro and Sala-I-Marin (1995) for a survey of he mains aspecs of he new growh heory. Sala-I- Marin s (1997) four million regressions es almos all hypoheses regarding he deerminans of TFP. 28 exo para discussão 1092 maio 2005 Ipea

31 can be explained by he increase in he qualiy of is labor inpu, which is usually measured by he average schooling of he is working-age populaion. As before, all variables in (4.9) are subjec o errors of measuremen and can be divided in a rend and a cycle componen. In he same vein, an esimae of poenial oupu can be obained from he rend or equilibrium values of each variable under he assumpion ha he errors of measuremen and cycle componens balance ou in he long run. The AK model is anoher popular alernaive o he Solow-Swan model because of is simpliciy and high predicive power. 32 The basic idea is ha oupu depends only on he capial sock and, herefore, he deerminans of poenial oupu are he same as in he capial consrain analyzed in secion hree. The AK model can also be represened as a special case of he labor-efficiency model given in (4.9), provided ha we assume ha labor efficiency is proporional o he amoun of capial per uni of labor. For insance, le us redefine E as K K E = A (4.12) N K where A he average he impac of he capial-labor raio on labor efficiency. Afer subsiuing (4.12) in (4.9) we have K 1 α ~ Y = ( A ) K = A K (4.13) where raes, A ~ represens he average produciviy of he capial sock. In erms of growh y = ( 1 α) a + k (4.14) K K K where a is he growh rae of A. I should be noed ha, since A = 1 α E, we can also obain he growh rae of TFP from he AK model, ha is a K = 1 α)( a + k n ). (4.15) ( The difference beween (4.9) and (4.15) is ha he AK growh-accouning equaion models TFP as a funcion of he capial-labor raio. According o he AK model, poenial oupu is proporional o he capial sock in he shor run and, in he long run, is growh rae can be esimaed from he longrun or equilibrium growh raes of capial produciviy and he capial sock. By analogy wih he Solow-Swan model, he variables in (4.13) are subjec o errors of measuremen and can be decomposed ino a rend and a cycle componen for longrun growh forecass. The main difference beween he Solow-Swan and he AK models lies on he long-run impac of he invesmen-income raio on growh. In he Solow-Swan model 32. See Bernanke and Gurkaynak (2001). Ipea exo para discussão 1092 maio

32 income and capial end o converge o he same growh rae and variaions of he invesmen-gdp raio do no have any permanen impac on growh. In conras, in he AK model, an increase in he invesmen-income raio has a permanen effec on growh because i acceleraes capial accumulaion and raises labor efficiency and TFP. The opposie holds for a decrease in he invesmen-gdp raio and, assuming ha he long-run growh rae of capial produciviy is exogenous and he relaive price of invesmen goods is sable, he only way for an economy o accelerae he growh rae of is poenial oupu is o increase is invesmen-income raio. When applied o real-world economies, he AK model generally obains a similar or beer saisical fi han he Solow-Swan or human-capial models, ha is: fas-growing economies end o have a high invesmen-gdp raio. From he perspecive of growh heory, his resul can indicae eiher ha he AK model is in fac a beer represenaion of realiy, or ha he speed of convergence of he Solow- Swan or human-capial model is very slow. Independenly of he inerpreaion, he sylized fac is ha invesmen seems o be he key variable o increase poenial oupu in he medium run, which in he case of Brazil seems o be wo and eigh years, as we shall see in secion six DISAGGREGATING TFP So far we analyzed only aggregae growh models based on he ne-value approach. The unifying poin of hese models is ha, in he long run, growh depends on he growh raes of capial, labor and TFP. The laer was furher decomposed in erms of a human-capial and a non-human componen, or a physical-capial and a nonphysical capial componen. In boh approaches we have an exogenous echnological parameer o represen he exogenous par of TFP and, in some applicaions of growh accouning, he TFP residual responds for mos of he growh rae of income. The imporance of TFP is much reduced when we follow he gross-value mulisecor approach. The reasons are basically wo. Firs, in real-world economies supply shocks are common and end o aler he value added by producion for he same level of inpu usage. For insance, he oil shocks of he 1970s increased he cos of energy and, hrough his, hey reduced he value added by boh capial and labor even when he usage of hese facors did no change much. If we follow he ne-value approach, changes in he relaive price of a key inpu end o appear as changes in TFP when he underlying mechanism may acually be marke power raher han echnology. One can obviously solve his problem by assuming ha adverse supply shocks are a form negaive produciviy shocks, bu his makes TFP oo vague and highly uncerain. In fac, i is always possible o explain growh flucuaions in erms of a ne-value growh-accouning equaion ex pos. However, when TFP includes any possible supply shock, i is very difficul o forecas i from pas rends. Gross Ne More formally, le Y, Y and C be he value of gross oupu, ne oupu and inermediae consumpion, respecively. By definiion 33. When we apply he band-pass filer for periods beween wo and eigh years, we obain business flucuaions ha closely reproduce he evoluion (exogenous shocks, sabilizaion plans, insiuional crises, ec) of he Brazilian economy in exo para discussão 1092 maio 2005 Ipea

33 Y = Y + C (4.16) Gross Ne and, herefore Gross = θ 1y + θ 1c 1 y, (4.17) Gross where θ 1 = Y 1 / Y 1 is he share of he ne value in he gross value of oupu in Gross he previous period, and y, y and c are he discree-ime growh raes of he corresponding variables in (4.16). Combining (4.17) wih (2.2) we can rewrie he growh rae of TFP as a = y Gross αk (1 α) n 1 θ 1 Gross + ( y c ), (4.18) θ 1 Gross which clearly shows ha an adverse supply shock ( y < c ) deceleraes he growh rae of TFP and vice versa. In conras, when gross oupu and inermediae consumpion grow a he same rae, (4.18) is reduced o ne-value growh accouning given by (2.2). In he case of Brazil, supply shocks come ofen in he form of currency crises because devaluaion ends o increase he relaive price of inermediae radable goods. The second reason o reduce he imporance of aggregae TFP is o conrol for heerogeneous inpus. The idea is basically he same for he ne-value and gross-value approaches and we will presen i for former o faciliae he exposiion. So far we have been working wih aggregae variables, which, in principle, represen he average of all secors of he economy under he assumpion ha he composiion of inpus and oupus remain he same hrough ime. In realiy, he growh and developmen of capialis economies is marked by srucural ransformaions. For example, consider he case where growh is characerized by a change in employmen from low-produciviy o high-produciviy secors, as analyzed in secion hree. The average labor produciviy changes and, if we measure labor jus by he number of work hours, his change will be misrepresened as an increase in TFP. Even hough aggregae produciviy does increase, is ulimae cause is a change in labor allocaion insead of a change in he echnology of producion a he secoral or firm level. As before, one can raionalize his effec by saying ha he aggregae echnology changed, bu once again his enlarges he definiion of produciviy o include many oher variables han echnology. In order o conrol for changes in he composiion and qualiy of he labor inpus, le us assume, as in secion wo, ha here are J N ypes of labor. In addiion o his, le us also assume ha here are J m secors in he economy. The growh rae of he labor index of secor m can be defined as n m J N = β j=1 jm n jm = n Quaniy m + n Qualiy m, (4.19) Ipea exo para discussão 1092 maio

34 where ~ J N Quaniy n m = βmj 1n jm j= 1 (4.20) and J Qualiy = N ~ n m ( β β ) n, (4.21) j= 1 mj mj jm ~ where he weighs β j and β j 1 have he same definiion as in secion wo, bu are applied a he secoral level, and n jm is he growh rae of labor inpu j used in secor m during period. In economic erms, he growh rae of he quaniy index n Quaniy m is jus he sum of he growh rae of each ype of labor weighed by is paricipaion in he oal number of work hours in secor m. The growh rae of he qualiy index Qualiy n m depends on he deviaion of he qualiy-adjused labor index from he quaniy index, where he former is he sum of he growh raes of each ype of labor weighed by is paricipaion in he oal wage bill of secor m. If we measure he secor labor index jus by he quaniy index, changes in he qualiy of labor will be couned as changes in TFP. In addiion o changes in labor qualiy wihin secors, we can also conrol for changes in employmen across secors. By analogy wih (4.19), he growh rae of he aggregae labor index can be defined as n J M = β j=1 j n j = n Level + n Composiion (4.22) where J M Level n = β j n j j= 1 1 (4.23) and J = M Composiion n ( β j β j 1) n jm, (4.24) j= 1 Level where he growh rae of he level index n is he sum of he secor growh raes using he weighs of he previous period, and he growh rae of he composiion Composiion index n measures he change in he composiion of employmen beween periods. Puing (4.19) and (4.21) ogeher, we can decompose he growh rae of he labor inpu in erms of a quaniy, a qualiy and a composiion index. The same mehodology can be applied o he capial and inermediae inpus and, hrough his, we can obain a beer esimae of he echnological and non-echnological deerminans of 32 exo para discussão 1092 maio 2005 Ipea

35 aggregae TFP. To see why his is imporan, consider he disaggregaed growhaccouning sudy of he US by Jorgenson (1990). Table 2 presens his resuls and can be inerpreed as follows: he average annual growh rae of income was 3.28%, of which 1.46% came from he capial inpu, 1.12 % from he labor inpu and only 0.70% from TFP. In relaive erms, he conribuion of capial and labor represened 45% and 34% of he growh in he period, respecively, wih TFP coming in hird wih 21%. The conribuion of capial can be furher decomposed in erms of he changes in he qualiy and quaniy of he capial sock, each of which responded for 0.58% and 0.88% of he growh of income, respecively. In he same vein, he conribuion of labor can be divided in 0.39% from changes in qualiy and 0.73% from changes in he quaniy indexes. The conribuion of TFP can also be divided in wo componens, 0.88% from changes in produciviy a he secoral level, and -0.17% from changes in he composiion of oupu and inpu usage across secors. In oher words, 27% of he growh rae can be aribued o produciviy gains a he secoral level. If we had ignored qualiy and composiion effecs, he oal conribuion of TFP would be 1.67%, making i by far he mos imporan source of growh for he US in See able 2. For he purpose of decomposing growh ex-pos, he muli-secor approach is much more accurae han he aggregae alernaive. However, for he purpose of esimaing poenial oupu ex-ane, he muli-secor approach is much more difficul because i involves forecasing and solving a general equilibrium model wih many parameers and hypoheses abou echnology, relaive prices, and he composiion of oupu and inpus. Because of his, mos growh-accouning sudies coninue o follow he aggregae approach TFP AND ACCOUNTING IDENTITIES Growh accouning is usually based on an aggregae producion funcion bu i does no need such an assumpion. The NIPA ideniies can also be used o obain (2.2) wihou imposing any aggregae producion funcion on he daa. Despie he common resul, he inerpreaion is subsanially differen. Insead of being a echnological variable, TFP becomes a composie index of he real price of each facor of producion. As analyzed by Fisher and Felipe (2003), his dual measuremen of TFP was a well-known fac in he early lieraure on growh accouning, bu somehow i disappeared in he new growh heory. In fac, mos recen works on growh accouning coninue o impose an aggregae producion funcion on he daa wihou even menioning ha hey are acually esimaing an accouning ideniy. The accouning definiion of TFP can be obained eiher from he ne-value or he gross-value approach. I can also be obained a he macro, secoral and firm level. To faciliae he exposiion, we will presen he ne-value macroeconomic case and indicae he necessary modificaions o apply i o he oher levels of analysis. The saring poin is he income decomposiion of he value added by producion, ha is 34. For a defense of aggregae, ne-value, growh accouning, see CBO (2003). Ipea exo para discussão 1092 maio

36 Y = W N + R K (4.25) where W and R represen he real wage and he real renal price of capial, respecively. In erms of he NIPA definiions, (4.25) saes ha he value added by producion is he sum of he oal wage bill ( W N ) and he gross operaing surplus ( R K ), wih all variables in real erms. The growh rae of income in discree ime is y = ξ ( r + k + r k ) + (1 ξ 1)( w + n + w n ) (4.26) 1 where ξ 1 = R 1K 1 / Y 1 is he share of capial income in oal income in he previous period, and w and r are he growh raes of he real wage and he real renal price of capial, respecively. For shor inervals of ime, say, a quarer or a year, we can ignore he high-order erm ξ r k + 1 ξ ) w n and work wih 1 ( 1 y = ξ ( r + k ) + (1 ξ 1)( w + n ) (4.27) 1 To obain he growh-accouning decomposiion, le ξ A be he average share of capial income in oal income, insead of he capial-elasiciy of income as in (2.2). By consrucion ξ = ξ + ε, (4.28) A where ε is he difference beween he effecive and average values of ξ. Subsiuing (4.28) in (4.27) we have = ξ 1r + ( 1 ξ 1) w + ε 1( k n ) + ξ Ak + (1 ξ A y ) n. (4.29) The las sep is o define a oal-facor-income (TFI) index = ξ 1r + ( 1 ξ 1) w + ε 1( k a n ) r, (4.30) such ha (4.29) can be rewrien as A A y = a + ξ k + ( 1 ξ ) n (4.31) In economic erms, wihou using any producion funcion we can obain a growhaccouning equaion idenical o (2.2). The TFI income index in (4.31) is a random variable and i corresponds o he TFP index in (2.2). 35 The inerpreaion is obviously differen, ha is, he TFI index is a disribuional raher han a echnological variable. Moreover, he coefficiens muliplying he growh raes of capial and labor in (4.31) add up o one because he facors share of income add up o one, no because here is profi maximizaion under perfec compeiion and consan reurns o scale. Wha growh-accouning sudies acually do is esimae an accouning ideniy. As long as he funcional disribuion of income does no vary much and he growh rae of TFI is modeled appropriaely, he resuls will show a good fi because hey are based on 35. For long periods of ime he high-order erms should be included in he TFI index. 34 exo para discussão 1092 maio 2005 Ipea

37 an accouning ideniy, no because firms behave as if hey followed he resuls of old or new neoclassical growh heory. I should also be noed ha (4.32) allows an alernaive inerpreaion of changes in TFP. For insance, a macroeconomic policy ha reduces real wages and does no increase he real renal price of capial ends o resul in a negaive growh rae of he TFP index. Because i is always rue, he NIPA approach is very flexible and can be used in eiher a demand-led or a supply-driven inerpreaion of economic growh, as we will see in secion six. Given he dual naure of he residual in growh-accouning sudies, a naural poin of invesigaion is wheher we can sill reain a echnological inerpreaion of i. The answer is yes, provided ha we define TFP as an aggregae index of he oupuinpu coefficiens a he secoral or firm level. In his way we do no need o impose an aggregae producion funcion on he daa, bu sill reain he echnological inerpreaion of he residual. To see why, noe ha a posiive growh of TFP can be inerpreed as an increase in he efficiency of he economy because i means ha he same amoun of capial and labor can receive a higher real income. From (4.31): a = ξ y k ) + (1 ξ )( y n ), (4.32) A( A ha is, he TFI index is a weighed average of he growh raes of labor and capial produciviy. In capialis economies he capial-income raio is usually sable or increasing in he long run, which means ha he firs erm in he righ-hand side of (4.32) is eiher zero or negaive for long inervals of ime. The growh rae of TFP depends herefore on wheher or no he growh rae of labor produciviy exceeds he rae of capial deepening of he economy. I should be noed ha, because we do no need a producion funcion o obain (4.32), he average income-labor and income-capial raios are aggregae variables ha include no only he echnology a he micro level, bu also he composiion and scale effecs a he macro level. For insance, in he shor run growh can be achieved by increasing he uilizaion of capial, which will appear as a posiive growh rae of capial produciviy in (4.32). From he demand-led perspecive, causaliy runs from he aggregae oupu-inpu indexes o he TFP index, ha is, demand-led growh can increase poenial oupu by increasing he average labor and capial produciviies in he shor run. Wheher he same is valid for he long run is a poin o be invesigaed empirically, bu, since growh ends o happen ogeher wih srucural changes during long inervals of ime, i is heoreically possible and empirically likely for demand o have permanen effecs on TFP. The NIPA approach o growh accouning can be applied a any level of aggregaion (secor, firm, lines of producion wihin firms, ec) and o any definiion of oupu. For insance, in he gross-value approach we can decompose growh from he income side because he oal value of oupu equals he ne-value plus inermediae consumpion. The difference is ha insead of having jus wo facors of producion as in (4.32), we will have as many facors as he oal number of inpus o producion. As before, he TFI index can be expressed as a weighed average of all Ipea exo para discussão 1092 maio

38 oupu-inpu coefficiens and, hrough his, i provides an imporan link beween macro and inpu-oupu models. 5 TRENDS AND CYCLES In he previous secions we assumed ha he inpu and TFP series could be divided ino a rend and a cycle componen by some saisical mehods. This secion will presen four mehods ha are commonly used o de-rend univariae economic ime series, namely: linear rends, sochasic rends, he Hodrick-Presco filer, and he band-pass filer. 36 All of hese mehods are focused on he saisical properies of he series under invesigaion wihou making any economic assumpion abou is economic deerminans. Because of his, hese mehods are a-heoreical and can be applied o any heory ha separaes he analysis ino a rend and a cycle componen. In supply-driven heories, he rend componen of income is a proxy of is poenial level because i represens he value o which he effecive series evenually converges. In conras, in demand-led heories, he rend componen of income is deermined by he effecive level of income, ha is, given a permanen acceleraion or deceleraion of growh, he rend componen changes accordingly. Boh inerpreaions are correc saisically. In he one hand, he rend componen of income does represen is long run or low-frequency componen. In he oher hand, he rend componen is also a funcion (usually a weighed moving average) of he effecive income series. The same logic can be applied o any of he oher series involved in growh accouning. 5.1 LINEAR AND STOCHASTIC TRENDS Le z represen he level of he economic series under analysis. In he case of oupu and inpu series, z is usually he naural logarihm of he original variable. In he case of raios (capial-income, employmen, capaciy uilizaion ec) z is usually he original variable. Because mos economic ime series exhibi auo-correlaion and periodic flucuaions, he naural saring poin is o model z as an auoregressive process wih disribued-lags (ADL), ha is z J A j= 1 j J M j + j= 0 = φ0 + τ + φ z θ ε. (5.1) j In words, z depends on is previous values, on a linear ime rend and on he previous values of he disurbance erm ε. The linear ime rend is usually included for oupu and inpu series because hese variables end o grow wih ime. For raio and growh variables he rend is usually omied because hese variables end o flucuae around a fixed value. When 36. Given he mix of heory and economerics of his paper, we choose o presen only univariae mehods o simplify he analysis. The inuiion is ha he mulivariae mehods apply he same logic of univariae mehods o vecors. The mos usual way o find long-run rends in mulivariae economic ime series is o es wheher or no here exiss a coinegraing vecor for he variables under analysis. If so, heir dynamics can be modeled hrough a Vecor-Error- Correcion (VEC) model, as shown by Hamilon (1994). 36 exo para discussão 1092 maio 2005 Ipea

39 he evidence indicaes i, he linear ime rend can be subsiued by a nonlinear funcion of he ime index. The usual candidaes are polynomials or periodic funcions of. The linear ime rend can also have srucural breaks, which means ha we should muliply i by a se of dummy variables. 37 The pas values of z are included o represen he auocorrelaion of he series. The number of lags is normally deermined by specificaion ess and by he number of observaions available. If he roos of J A j 1 φ j z = 0 (5.2) j= 1 lie ouside he uni circle, z is rend-saionary if τ 0 and saionary if τ = 0. In boh cases i can be represened as an infinie moving-average process. 38 If he roos of (5.2) fall on or inside he uni circle, z is nonsaionary and saisical inference based on (5.1) is no valid because he variance of z is a linear funcion of ime. When his happens we move o he firs difference of he series and es i for he exisence of a uni roo. If his hypohesis is rejeced, we say ha z is I(1), ha is, inegraed of order one. If he firs difference is also nonsaionary, we move o second difference and so on. The order of inegraion of he series is he number of imes we have o difference i o obain a saionary series. The moving-average componen of (5.1) aims o capure he periodic flucuaions of z and, by assumpion, he disurbance erm ε is a whie noise, ha is, an Idenically and Independenly Disribued (IID) random variable. Mos inpu and oupu ime series are inegraed of order one, so ha we have o work wih heir firs difference. To faciliae he exposiion, assume ha z is already he firs difference of he naural logarihm of he original series. Because z represens a growh rae in his case, we do no include a ime rend in (5.1) and he long-run growh rae of he underlying variable is given by he consan and auoregressive coefficiens, ha is z Long run φ0 = J A. (5.3) 1 φ j= 1 j Possible srucural breaks of he growh rae are represened by exogenous changes in he consan coefficien φ 0. An alernaive bu similar approach is o divide a nonsaionary series explicily ino a saionary cycle componen and a nonsaionary rend componen. 39 For insance, assume ha z is he naural logarihm of an annual variable. We can model i as 37. Srucural breaks are usually deermined by esing he sabiliy of he residuals and he mos common approach is he Chow breakpoin es. For he applicaion of his es, see, for insance, Greene (2002). 38. The mos common ess of he uni-roo hypohesis are he Augmened-Dickey-Fueller (ADF) and he Phillips-Perron ess. For he economerics of ime series, see, for insance, Hamilon (1994). 39. This approach is based on Wason (1986). Ipea exo para discussão 1092 maio

40 z = z + z, (5.4) Trend Cycle where z Trend Trend = + z 1 φ 0 + ε (5.5) Trend and Cycle z J = M j= 0 θ j ε Cycle (5.6) Trend where z and z Cycle are he rend and cycle componens of z, and ε Trend and ε are uncorrelaed whie-noise disurbance erms. Cycle The rend componen is sochasic because i includes a disurbance erm and, even hough his disurbance is no observable, we can esimae i by combining (5.4), (5.6) and (5.7), or by he sae-space represenaion of he daa-generaing process. Taking he firs approach, assume for simpliciy ha J M = 1 and θ 0 = 1. Afer subsiuing (5.4) ino (5.5), and hen (5.6) in he resuling expression, we have z = φ + ( ε θ ε + ε, (5.7) Cycle 0 ε 1 θ1) Cycle Cycle Trend so ha we can esimae he sochasic rend componen from he residuals of (5.7). In oher words, he assumpions implici in (5.4), (5.5) and (5.6) imply ha he growh rae of z can be represened as a moving average process, and he residuals of such a regression are he esimaes of he sochasic componen of z Trend. The complee sochasic rend can be consruced ex-pos and, o forecas growh, we use he esimaed value of φ THE HODRICK-PRESCOTT AND THE BAND-PASS FILTERS The Hodrick-Presco (HP) filer separaes rends from cycles based on a pre-specified smoohing parameer. As in he sochasic-rend approach, he saring poin is o model z as where z = z + z, (5.8) HPT HPT z and HPC HPC z are respecively he HP rend and cycle componens. The innovaion of he HP approach is o measure he smoohness of he rend componen from he square of is second difference on he assumpion ha he average value of he cycle componen is zero over long inervals of ime. More formally, he rend componen is defined by minimizing T = 1 T HPT 2 HPT HPT HPT HPT 2 ( z z ) + λ [( z z 1 ) ( z 1 z 2 )] (5.9) = 3 HPT T for he sequence { z } = 1, where λ is he smoohing parameer. The larger he value of λ, he smooher he value of he rend. From he parial derivaive of (5.9) in 38 exo para discussão 1092 maio 2005 Ipea

41 relaion o λ we can see ha, for a sufficienly large λ, he rend componen approaches a linear rend. In conras, he lower he value of λ, he closer he rend componen is o he original series. For λ = 0, he wo series are he same. The inuiive idea of he HP filer is o define he rend componen o minimize he sum of he square of he deviaions of he original series from is rend, subjec o he resricion ha he sum of he square of he second differences of he rend series equals zero. The smoohing parameer is he weigh aribued o reducing volailiy in he consrained minimizaion exercise. The value of λ varies according o he periodiciy of he series in quesion and he assumpion of wha is a moderae variaion. One possible rule, proposed by Hodrick and Presco (1997), is o define λ as he square of he raio of he moderae change in he cyclical componen o he moderae change in he rend componen. Assuming ha z is a quarerly series expressed in logarihm erms, he mos common rule is o define more ha 5% as an excessive variaion of he cycle componen, and more han 0.125% as an excessive variaion of he rend componen. The resuling smoohing parameer is λ = [5/(1/ 8)] 2 = A similar reasoning can be applied o annual series, for which λ is usually se a One of he main advanages of he HP filer is is easy applicaion. As shown by Pedersen (1999), from he firs-order condiions of minimizing (5.9) we have for = 1; for = 2; HPT HPT HPT = λ z 2z z ) (5.10) HPC z ( HPT HPT HPT HPT = λ 2z + 5z 4z z ) (5.11) HPC z ( HPT HPT HPT HPT HPT = λ z 4z + 6z 4z z ) (5.12) HPC z ( for = 3,4,,T-2; z HPC = ( for = T-1; and HPT HPT HPT HPT λ z 4z + 5z 2z ) (5.13) HPC HPT HPT HPT z λ z 2z + z ) (5.14) = ( 2 1 for = T. In marix noaion: z HPC HPT = λcz (5.11) HPC HPT where z and z are he vecors conaining he cycle and rend componens of he series, and C is a T T block-diagonal marix of fixed weighs obained from he 40. Noe ha his value implies ha he raio of he excessive variaions of he cycle o he rend componens is 10 o 1. Ipea exo para discussão 1092 maio

42 HPT HPC firs-order condiions above. Since by definiion z = z + z, we can obain he rend series by a linear operaion on original series z, ha is z HPT 1 = (I + λc) z (5.12) Despie is wide use in applied macroeconomics, he Hodrick-Presco filer is no considered a good guide for cyclical flucuaions because, in some cases, i may creae spurious cycles and disor unresriced esimaes of cyclical componen. The main criique is ha, for many economic ime series, i is unreasonable o assume he exisence of a smooh rend a priori. 41 A second objecion o he HP filer is ha if filers only he low-frequency componen of he daa, leaving seasonal and cyclical effecs ogeher in he cycle componen. One possible way o reduce his problem is o apply he HP filer o seasonally adjused series, so ha he HP cycle variable measures flucuaions wih a medium-run periodiciy, ha is, longer han seasonal facors bu smaller ha longrun facors. Because his implies some arbirary definiion of wha is seasonal and wha is srucural, a more direc approach is o subsiue a band-pass filer for he HP filer, in which case he analys can direcly specify wha are he lower and he upper bounds of he cycle. More formally, he band-pass filer consiss of applying wo high-pass or wo low-pass filers o a ime series, so ha he remaining componen capures only he flucuaions whose periodiciy falls wihin he pre-specified bounds. The high-pass filer excludes he low-frequency componen of he daa, leaving only shor-run flucuaions, as, for insance, less han a year. The low-pass filer excludes he highfrequency componen from he daa, leaving only he long-run flucuaions as, for insance, more han en years. The band-pass filer is he combinaion of wo highpass or wo low-pass filers o exclude boh he low and he high-frequency flucuaions from he daa. The upper and lower bounds of he band-pass filer depends on he hisory of he economy in quesion and he objecive of he analysis. For he US economy, he NBER approach defines cycles as flucuaions wih a periodiciy higher han six quarers and lower han eigh years. As we will see in he nex secion, in he case of Brazil he quarerly GDP daa indicae a periodiciy beween wo and eigh years. 42 The heoreical foundaions and derivaion of he band-pass filer involve ranslaing he series under analysis from he ime domain o he specral domain, bu is applicaion is simple and inuiive. The band-pass filer is simply an infinie weighed moving-average of he original series, where he weighs of each componen are defined by a rigonomeric funcion of he pre-specified lower and upper frequencies. 43 More formally, le f lower and f upper be he lower and he higher frequency limis of he cycle componen, ha is 41. In subsiuion o HP filer, Harvey and Jaeger (1993) propose fiing srucural ime series models o he daa. Because heir rend-cycle approach is similar o he one adoped by Wason (1986), we will no consider i here. For a deailed analysis of srucural ime-series models, see Harvey (1989). 42. The origin of he NBER approach is he seminal work of Burns and Michell (1946). An updaed and recen version can be found in Zarnowiz (1992). For an analysis of he US cycles, see Sock and Wason (1998 and 2002). 43. See Priesley (1981) for he foundaions of low-pass and high-pass filers. 40 exo para discussão 1092 maio 2005 Ipea

43 f lower π = 2 (5.13) p higher and f higher π = 2, (5.14) p lower where p higher and p lower are he higher and lower bounds of he periodiciy of he cycle componen in he ime domain. For example, if we are working wih quarerly series and he cycle is defined as he sum of all flucuaions wih periodiciy beween 8 and 32 quarers, f = 2π/ 32 and f = 2π/8. lower higher Given he upper and lower frequency limis, he band pass filer is defined as z BPC L = lim ϕ z, (5.15) L j= L j j where he weighs are ϕ j = f upper f π lower, (5.16) for j = 0, and ϕ j sin( f = upper j) sin( f jπ lower j), (5.17) for j 0. Since we canno apply (5.15) o real-world economies because we do no have infinie ime series, we have o use an approximaion by limiing he number of erms in i. For quarerly series he common procedure is o use welve observaions in boh direcions, so ha we loose he firs and he las hree years of daa. This choice is no wihou cos, ha is, as we reduce he number of erms in (5.15), he precision of he band-pass filer diminishes because frequencies ouside he pre-specified range are parially capured by he cycle componen. In addiion o he above, when apply he BP filer o nonsaionary series, he sum of he weighs of he low-pass or (high-pass) filers in (5.16) and (5.17) has o be one for he resuling cycle componen o be saionary. The sandard procedure, proposed by Baxer and King (1995), is o compue he difference beween one and he sum of he unresriced coefficiens, divide he resul by he number of weighs in he filer, and hen add he resuling average o each unresriced coefficien. The band-pass filer gives us he cycle componen of a ime series for some pre-specified definiion of he periodiciy of he cycle. The same reasoning can be applied o obain he rend componen of he series hrough a low-pass filer. By analogy, he shor-run componen can be obained from a high-pass filer, or simply from he difference beween he effecive series and is medium-run and long-run componens. Ipea exo para discussão 1092 maio

44 6 ESTIMATES OF POTENTIAL OUTPUT FOR BRAZIL Mos growh-accouning sudies of Brazil follow he aggregae ne-value approach and derive he poenial growh rae of he economy from eiher a Cobb-Douglas funcion or from he growh rae of he capial sock. The labor consrain is no usually emphasized because of Brazil s fas populaion growh in he las decades, as well as because of is curren high rae of unemploymen. In addiion o his, he high percenage of workers in informal low-produciviy jobs also indicaes ha he labor inpu can respond very quickly o variaions in labor demand. In he nex paragraphs we will analyze he mos recen growh-accouning sudies and, o faciliae he exposiion, we will sar wih he labor and capial consrains, and hen move o he esimaes of TFP. In each subsecion we will presen some growh simulaions for alernaive values of he parameers and, in he las subsecion, we will apply he saisical mehods of secion five o esimae he cycle and rend componens of GDP. These mehods can be applied o all of he ime series under analysis bu we will resric our invesigaion o GDP o simplify he exposiion. 6.1 THE LABOR CONSTRAINT Assume for he momen ha labor is he scarces facor in Brazil. In his case he growh rae of poenial oupu depends solely on he growh raes of he labor inpu and labor produciviy. As we saw in secion hree, he labor inpu grows a he same rae as he working-age populaion in he long run. In he case of Brazil his rae is beween 1% and 2% per year depending on he evoluion of he rae of paricipaion. More specifically, he Brazilian populaion is expeced o grow a 1.1% per year in , 44 bu he working-age populaion is expeced o grow faser han ha because of a change in is age composiion. In he shor run i is imporan o calculae he impac of flucuaions of he rae of unemploymen on he growh rae of he labor inpu. Assuming ha he labor force grows 1.5% per year, able 3 presens he annual growh rae of he labor inpu based on alernaive reducions of he rae of unemploymen. For insance, if he curren rae of unemploymen is 10% and i remains a such a level in he subsequen year, he labor inpu grows a he exogenous rae of 1.5%. If he curren rae of unemploymen is 12% and i is expeced o fall o 10% in he nex year, he growh rae of he labor inpu acceleraes o 3.8%. In general, each 1.0 reducion in he rae of unemploymen adds 1.1 o 1.2 o he growh rae of he labor inpu, all numbers expressed in percenage poins. If we assume ha he naural or long-run unemploymen rae of Brazil is 6%, he growh rae of he labor inpu can reach somehing beween 6.0 and 8.4% in he shor run wihou making he economy hi is labor consrain. 45 See able See Oliveira (1997). 45. The curren unemploymen rae in Brazil is beween 10 and 12%, depending on he survey adoped. Muinhos and Alves (2003) and Areosa (2004) esimae he Brazilian NAIRU o be beween 5 and 6%. 42 exo para discussão 1092 maio 2005 Ipea

45 Labor produciviy is he oher (and mos imporan) componen of he labor consrain. As we analyzed in secion hree, his variable is highly procyclical and, o illusrae his for Brazil, figure 1 shows he growh raes of income and labor produciviy in based on Heson e al. (2002). There is clearly an almos perfec synchroniciy beween he wo series and, based on he HP rend of labor produciviy, is long-run growh rae was approximaely 1% a he end of he sample period. See figure 1. The synchronized flucuaions in figure 1 also indicae ha labor-produciviy growh may acually be a consequence raher han a source of income growh, as analyzed in secion hree. To see wheher he same paern is valid for more disaggregaed daa, figure 2 presens he growh raes of labor produciviy for he agriculural, indusrial and service secors of Brazil, in Despie he limied number of observaions, he growh raes show he same cyclical flucuaion observed in he longer aggregae series of Heson (2002). Agriculure had he highes and mos volaile growh rae, whereas he service secor had he lowes and mos sable one. For indusry, labor-produciviy growh was high during he expansion of , and mosly negaive afer ha. Considering he whole period, he cumulaive growh was 18.4% for he whole economy, 77.8% for agriculure, 30.6% for indusry and 0.4% for services. The corresponding annual average raes were 1.4%, 4.9%, 2.3% and zero, respecively. The zero growh of labor produciviy in he service secor should no be inerpreed only in erms of he echnology of producion, bu also as a resul of he dual naure of he Brazilian economy, ha is, in Brazil, low-skill aciviies in he service secor funcion as an employmen of las resor for hose who canno find jobs in he modern secors of he economy. See figure 2. Table 4 presens he growh raes of labor produciviy for all secors of he Brazilian economy. The average numbers indicae ha he fases growh occurred in he producion of elecrical equipmen and in oil refinemen (8.2% per year), followed closely by communicaions (8%). In conras, he reducion of labor produciviy was more severe in he clohing secor (-2.2%), followed by privae nonmarke services and plasic processing and producs (boh secors wih -1.4%), and services o households (-1.2%). Since mos of he fas growh happened in he producion of radable indusrial goods, we can conclude he average laborproduciviy growh may accelerae if economic growh comes ogeher wih an increase in he size of he modern radable secor of he economy, as analyzed in secion hree. See able 4. Alogeher, he long-run growh raes of populaion and labor produciviy indicae ha he mos conservaive esimae of poenial-oupu growh is 3% according o he labor consrain. 46 However, given he increase in Brazil s unemploymen rae in recen 46. Assuming ha he labor force and labor produciviy grow 1.5% per year. Ipea exo para discussão 1092 maio

46 years and he large discrepancy beween he secoral produciviy growh raes shown in able 4, oupu may acually growh much faser han 3% for several years as he rae of unemploymen falls and labor-produciviy growh acceleraes along he Kaldor-Verdoorn laws. In shor, he labor consrain is no an imporan limi o growh in Brazil. 6.2 THE CAPITAL CONSTRAINT The nex and mos imporan consrain comes from capial. From our previous analysis, assume ha capaciy uilizaion and he capial-income raios are consan in K rend he long run ( u = 1 and V = V ). In his case he only way o speed up poenial oupu growh is o increase he invesmen-gdp raio and/or reduce he relaive price of invesmen goods. For example, assume ha he annual rae of depreciaion is 3.9% and he capial-income raio is 3.1, as i seems o be he curren case of Brazil. Table 5 shows he growh rae of he capial sock for alernaive values of he invesmen-gdp raio and small changes in he relaive price of invesmen goods. If he relaive price is 1.00 and he invesmen-gdp raio is 18%, he capial sock grows only 1.9% per year. If he invesmen-gdp raio rises o 20%, he growh rae of he capial sock acceleraes o 2.6%. In he same vein, if he invesmen-gdp raio remains a 18% and he relaive price of capial falls 5%, he growh rae of he capial sock also acceleraes o 2.2%. See able 5. Comparing he wo ways o accelerae capial accumulaion, we can see ha an increase of he growh rae of capial from 2.0% o 2.6% can be achieved by eiher a 10% reducion of he relaive price of capial or by raising he invesmen-gdp raio in 2 percenage poins. This rade-off is obviously valid only in he shor run because he relaive price of capial canno be reduced coninuously. I should also be noiced ha he argumen run boh ways, ha is, given an increase in he relaive price of capial because of, say, a devaluaion of he domesic currency, capial accumulaion ends o slow down. 47 In he long run he relaive price of capial is sable and he deerminans of he capial consrain are fundamenally he invesmen-gdp and he capial-income raios. In he case of Brazil, he capial-income raio increased from 1.8, in 1950, o 3.1 in 2002, as shown in figure 3. Mos of he increase occurred beween 1973 and 1983 and i corresponded o invesmens in residenial capial and nonresidenial srucures. As shown in figure 4, he paricipaion of nonresidenial srucures in he oal capial sock rose from 34%, in 1950, o 52%, in During he same period he share of residenial capial fell from 38%, in 1950, o 20%, in , and hen rose o 30% in The counerpar of hese movemens was a reducion in share of machinery and equipmen in he oal capial sock, especially during he 1980s. In numbers, machinery and equipmen responded for 28% of he capial sock in 1950, 33% in 1976, and only 18% in Bacha and Bonelli (2004) find an increase of he relaive price of capial o be he main cause of he capial-growh deceleraion since he early 1970s. Even hough he auhors don emphasize i, mos of he changes in he relaive price of capial coincide wih changes in Brazil s real exchange rae, ha is, one can blame he foreign financial fragiliy of he economy for is slow capial accumulaion. 44 exo para discussão 1092 maio 2005 Ipea

47 See figures 3 and 4. Figure 3 also shows ha ha Brazil s effecive capial-income raio has a srong ani-cyclical componen. For insance, i increased subsanially during he recession of he early 1980s, decreased during he recovery of he mid-1980s, and increased again during he recession of he early 1990s. In order o obain a measure of capial uilizaion, we calculaed he Hodrick-Presco rend of he raio of non-residenial capial o income, and hen obained he corresponding rae of capaciy uilizaion as described in secion hree. Figure 5 shows he resuls, which no surprisingly coincide wih he growh flucuaions observed in Brazil. For example, he rae of capial uilizaion fell o approximaely 91% in he deb-crisis of early 1980s, and rose o 105% in he subsequen expor-led recovery. In addiion o he capial-income esimae of capaciy uilizaion, we can also use an index obained hrough muli-secor surveys of business decisions and expecaions. In Brazil, he longes series is he one calculaed by he Fundação Geulio Vargas (FGV) for he indusrial secor since Figure 5 compares i wih he capial-income esimae and, during mos of he period, boh variables moved in he same direcion. Using he las en years as a guide, average rae of capaciy uilizaion seems o be approximaely 82% according o he FGV measure. Considering he whole sample, he highes value is 90%, in 1973, and he lowes value is 72%, in See figure 5. Figure 6 shows he effecive and HP rend values of he growh rae of Brazil s capial sock in For he hree ypes of capial, here is a clear wave paern saring in he mid-1960s and ending in he early 1990s, wih a peak in he mid-1970s. A he end of he sample, he long-run annual growh rae of he oal capial sock was approximaely 2.3%. The corresponding numbers for residenial capial, non-residenial srucures and machine and equipmen were 3.7%, 1.7%, and 1.3%, respecively. Assuming ha he capial-income raios will remain approximaely he same, and ha nonresidenial srucures and machinery and equipmen are he mos relevan capial inpus o producion, he low growh raes a he end of he sample means ha poenialincome growh is less han 2% a Brazil s curren pace of capial accumulaion. On he good side, as we saw in secion hree, by definiion he growh rae of he capial sock converges o he growh rae of invesmen in he long run. The low growh raes of recen years should be inerpreed as a resul of he low invesmen-gdp raio of he 1980s and 1990s raher han an ineviable consrain. If and when he economy resumes growing and he growh of invesmen acceleraes, he pace of capial accumulaion will also accelerae. 48 See figure I should also be noed ha, because machinery and equipmen and nonresidenial srucures have a shorer service life han residenial capial, he growh rae of he capial sock effecively used in producion responds more rapidly o changes in invesmen han he aggregae measure. Ipea exo para discussão 1092 maio

48 6.3 INPUT-OUTPUT SIMULATIONS There are many ways for an economy o grow a some given aggregae rae. For insance, Brazil can grow 5% hrough an invesmen or a consumpion boom. Wih inpu-oupu models we can simulae hese alernaive hypoheses o check how differen growh sraegies impac on each secor, and hen compare he resuls wih esimaes of he producive capaciy derived from secoral sudies. In he case of Brazil he mos recen IO marix available was esimaed for 1996, ha is, eigh years ago and during a period of an appreciaed currency. Despie he unrealiy of he assumpion ha IO coefficiens remained he same since hen, able 6 presens some simulaions o illusrae he mehod described in secion hree. The underlying assumpion is ha he composiion of final demand and impors remain he same as in 1996, as well as ha he oupu-elasiciy of employmen is one for every secor of he economy. The analysis can be easily updaed when a more recen IO marix becomes available for Brazil. See able 6. In economic erms he resuls indicae ha, given an isolaed 1% growh in invesmen, he oupu of he agriculural secor grows 0.09%, he oupu of he mining secor grows 0.22%, he oupu of manufacuring grows 0.21% and so on. Comparing each expendiure caegory, able 6 shows ha an increase in invesmen has a high impac on he oupu of he consrucion secor, followed by mining and manufacuring. The impac of invesmen on he service and agriculural secors in almos zero, whereas is impac on impors is almos wo imes is impac on income. In conras, an increase in governmen consumpion has a high impac on he service secor and a negligible impac on agriculure and indusry. Governmen consumpion and invesmen have almos he same impac on employmen, bu governmen consumpion has a much lower impac on impors han invesmen. An increase in expors ends o pull agriculure and indusry almos a he same rae, having a lile impac on he service secor. Is impac on employmen is also low, and i ends o increase GDP and impors in he same proporion. Because i is he larges expendiure, consumpion has a high impac on he oupu of almos all secors of he economy, as well as on oal employmen. Moreover, he impac on consumpion on GDP and oal impors is almos he same. Wha abou capaciy uilizaion? If we assume ha poenial oupu does no change much in one year, we can use he numbers in able 6 o obain a conservaive esimae of he change of capaciy uilizaion in he indusrial secor. According o he FGV index, capaciy uilizaion was 82% in he second quarer of Given an 1% increase in invesmen, indusrial oupu is expeced o increase 0.33%, and capaciy is expeced o increase o (1+0.33%) 82% = 82.3%. In oher words, i would ake an approximaely 3.6% growh of invesmen o increase capaciy uilizaion in one percenage poin. The corresponding numbers for expors, governmen consumpion, and privae consumpion are 9.2%, 31.2% and 2.5%, respecively. In shor, moderae growh raes of consumpion and invesmen have a high impac on indusrial capaciy uilizaion, only a high expor growh rae would have a similar impac, and governmen consumpion have a negligible impac. The same calculaions can be done 46 exo para discussão 1092 maio 2005 Ipea

49 for each indusrial secor, provided ha we obain heir iniial raes of capaciy uilizaion from secoral sudies. 6.4 GROWTH-ACCOUNTING STUDIES Mos growh accouning sudies of Brazil follow he ne-value aggregae approach and impose a Cobb-Douglas funcion on he daa. The disaggregaed approach is no possible because of he lack of daa for mos of he previous 50 years. Because he Cobb-Douglas funcion acually mimics an accouning ideniy, when income growh acceleraed, Brazil s TFP growh also acceleraed and mos growh-accouning sudies inerpre he laer as he cause of he former. A demand-led inerpreaion is also possible and much more plausible, as we will see below. The firs sudy o impose an aggregae Cobb-Douglas funcion on he Brazilian quarerly NIPA daa was Silva Filho (2001). His basic assumpion was ha oupu could be modeled as a ne-value Cobb-Douglas funcion of capial and labor wih consan reurn o scales, as analyzed in secion five. To obain he facors elasiciy parameers, Silva-Filho used he funcional disribuion of income as guide and se he capial share of income a 49%. To consruc he capial-sock series, he applied he PIM wih a depreciaion rae of 5% and assumed ha growh was balanced prior o Through hese assumpions Silva-Filho was he able o consruc an index of he capial sock saring in 1970, which he used o explain growh flucuaions in To conrol for cyclical changes, Silva-Filho muliplied his esimae of he capial sock by he rae of capaciy uilizaion in he indusrial secor and obained he capial inpu. In he same vein, Silva-Filho muliplied he labor force by he rae of unemploymen o esimae he labor inpu. The TFP index followed residually from he Cobb-Douglas ideniy and, no surprisingly, he flucuaions of Silva-Filho s TFP esimae coincide wih he flucuaions of Brazil s income during he period. Table 7 presens his resuls, which indicae he negaive growh rae of TFP as he main responsible for he los decade of he See able 7. A demand-led inerpreaion of Silva-Filho s resuls is ha he slow income growh of he 1980s was he main responsible for he negaive TFP growh. Brazil s 1982 deb crisis and he subsequen ransfer of a high percenage of is real resources o res of he world reduced he value-added by he Brazilian capial and labor inpus in he early and mid-1980s. Afer ha, he sagflaion of he lae 1980s reduced he average produciviy of labor, and he low invesmen-gdp raio kep he average produciviy of capial relaively sable. As also shown in able 7, Silva Filho s esimae of TFP growh can be decomposed as follows: in he reducion in capaciy uilizaion and he slow growh of he economy reduced he average produciviies of capial and labor and, hrough his, resuled in a negaive TFP growh rae. In he opposie happened and TFP growh became posiive. Following he same approach of Silva-Filho, Pinheiro e al (2001) also imposed an aggregae producion funcion on he annual Brazilian daa. Using daa from he IBGE, he IMF and Maddison (2001), he auhors managed o consruc annual indexes for he Ipea exo para discussão 1092 maio

50 physical and human capial socks of he Brazilian economy saring in Similar o Silva Filho, Pinheiro e al. also measured he labor inpu by he number of people employed and se he capial share of income a 50%. From hese assumpions he auhors derived he growh rae of MFP and, since hey did no find he conribuion of human capial o be saisically significan in explaining Brazil s growh rae, we will consider only heir wo-facor growh accouning. Table 8 presens heir resuls and, for he period afer 1980, hey replicae he signs bu no he levels found by Silva Filho. Overall, capial appears as he main source of growh in See able 8. Similar o Silva Filho s resuls, he esimaes of Pinheiro e al can also be inerpreed in a demand-led way. From he NIPA perspecive, able 8 shows ha he conribuion of capial produciviy o TFP growh was negaive during mos of he period under analysis. This reflecs he increase in he capial-income raio of Brazil presened earlier, ha is, when capial deepening was more han compensaed by labor-produciviy growh, he final resul was a posiive growh rae of TFP. When capial deepening proceeded bu labor-produciviy growh deceleraed, he growh rae of TFP became negaive. Because of his, TFP can also be inerpreed as an endogenous variable deermined by he flucuaions of he labor-produciviy and capaciy-uilizaion indexes. Gomes e al. (2003) did anoher growh-accouning analysis of Brazil based on a Cobb-Douglas funcion. Differenly from Silva Filho and Pinheiro e al, hey included human capial in heir invesigaion by assuming ha he labor-efficiency index presened earlier is a funcion of he average schooling of he labor force. Their model is basically he same as he one presened in secion four. 49 Their capial sock esimae was obained from Reis and Morandi (2002) and, similar o he previous wo sudies, Gomes e al. defined he labor index as he number of people employed because of he lack of daa on he oal number of hours worked. Differenly from he previous sudies, Gomes e al. se he capial share of income a 40%. Table 9 presens heir resuls for he growh rae of per capia income. See able 9. Similar o he resuls obained by Silva Filho and Pinheiro e al., able 9 indicaes a negaive growh rae of TFP in he 1980s and a posiive rae aferwards. Also similar o he previous wo sudies, he resuls of Gomes e al. can also be inerpreed in he reverse direcion ha is, he slowdown of growh led o a reducion in he average produciviy of labor and an increase in he capial-income raio because of idle capaciy in indusry. These wo effecs resuled in he reducion in he TFP index in he 1980s. The difference beween able 9 and he previous growh accouning is he inclusion of human capial as an independen inpu. In ables 7 and 8 he conribuion of human capial is implici in he growh rae of TFP. 49. The main difference is ha Gomes e al divided MFP in a fronier and a discouned componen. The fronier componen is he average growh of rae of labor produciviy in he US economy, adjused o exclude he conribuion of human capial. The discouned componen is he difference beween he effecive and he fronier componens of TFP growh. The basic idea is ha par of he echnical progress is global, so ha he discouned componen measures only he share of i generaed locally. 48 exo para discussão 1092 maio 2005 Ipea

51 Bacha and Bonelli (2004) also esimaed he growh rae of TFP for Brazil. However, differenly from he previous auhors, hey modified he Cobb-Douglas funcion by assuming ha labor efficiency is proporional o he capial-labor raio, and hen modeled growh hrough he AK model. The mechanics of heir model are basically he same as presened in secion four. Bacha and Bonelli used he capialsock esimaes of Reis and Morandi (2002) and esimaed he global rae of capaciy uilizaion as a weighed average, where 35% of he economy is assumed o operae a full capaciy, and he remaining 65% is assumed o operae a he capaciy level indicaed by he FGV index menioned earlier. In order o obain an esimae of he long-run capial-income raio, he auhors se 87% as full capaciy uilizaion. The depreciaion rae was se a approximaely 4% and he capial share of income a 50%. Table 10 presens he resuling growh decomposiion and he economic conclusions are basically he same of he previous sudies. See able 10. In wo recen sudies, Muinhos and Alves (2003) and Areosa (2004) used a Cobb-Douglas aggregae funcion o esimae he oupu gap in Brazil. Their main objecive was o esimae a shor-run index of he demand pressures on inflaion raher han a long-run esimae of poenial-oupu growh. Despie his difference, heir heoreical approach is basically he same as he ne-value aggregaed growh accouning oulined in secion four. Muinhos and Alves used a Cobb-Douglas funcion o esimae he growh rae of TFP from he capial and labor inpus. To exclude cyclical variaions, boh inpus were muliplied by heir corresponding uilizaion raes, and he labor and capial elasiciy parameers were obained by a smoohing mehod similar o he HP filer 50 In relaion o he previous sudies, heir innovaion was o esimae he NAIRU and NAICU by minimizing he square of he firs difference of poenial oupu. In oher words, hey esimaed poenial oupu from he observed TFP and capaciyuilizaion and unemploymen-raes series under he consrain ha poenial oupu is no oo volaile. Their resuls indicae a NAIRU and NAICU of 5.3% and 84.9%, respecively. Areosa used a Cobb-Douglas funcion o esimae poenial oupu wihou direc measures of he capial and labor inpus. Her sraegy can be summarized in hree seps. Firs, as done by Muinhos and Alves, she modeled he oupu gap as a funcion of he deviaions of he raes of unemploymen and capaciy uilizaion from he NAIRU and NAICU, respecively. Second, because he NAIRU and NAICU are no observable, she esimaed boh of hem hrough a mulivariae version of he HP filer consrained o produce rend values ha saisfy he Cobb-Douglas consrain on oupu. Third, given he esimaed NAIRU and NAICU, she esimaed poenial oupu from he observed income growh and unemploymen and capaciy-uilizaion raes. Unforunaely, Areosa did no presen her esimae of he long-run growh of he economy or he NAIRU and NAICU raes. From he graphs of her paper we can conclude ha, a he end of 2002, he NAIRU and he NAICU were approximaely 50. Given he lack of quarerly daa, Alves and Muinhos minimized he square of he second difference of he unobserved quarerly series subjec o he consrains ha each quarerly measure is posiive, and he average quarerly measure is equal o he corresponding annual number. Ipea exo para discussão 1092 maio

52 5% and 76%, respecively. The low NAICU is probably a resul of he calibraion done by Areosa and should no be aken as a long-run consrain. In fac, because he NAIRU and NAICU are very sensiive o he weighs used in calibraing he minimizaion exercises done by Muinhos and Alves and by Areosa, he resuling oupu gap is very sensiive o he auhors assumpions. Given he cenraliy of he funcional disribuion of income for radiional growh accouning, i is worhy o check wha he Brazilian daa ell us. Table 11 shows he Brazilian funcional disribuion of income in The average paricipaions of labor and capial income in oal income are 47% and 46%, respecively. The remaining 7% correspond o he income of self-employed persons, which conains boh wages and profis. If we assume ha self-employed income is disribued in he same way as non-self-employed income, he average labor and capial shares become 50%. See able 11. Finally, o esimae he growh poenial of Brazil and based on he labor consrain analyzed earlier, assume ha employmen can grow 1.5% per year in he nex en years. Assume also ha he capial share adjused o include par of selfemployed income is 50%. Alogeher, hese assumpions imply ha he long-run growh rae of poenial oupu can be modeled as TFP growh capial-sock growh. For insance, if TFP and he capial sock grow 0.5% and 2% per year, respecively, poenial oupu grows 2.3% per year. If he capial growh rae acceleraes o 3%, poenial-oupu growh acceleraes o 2.8% and so on. Table 12 presens oher esimaes based on alernaive values of he growh raes of TFP and capial. The corresponding growh raes of labor and capial produciviies can be obained from he difference beween poenial-oupu growh and he corresponding inpu raes. See able 12. The naural quesion is wha is he mos appropriae number for Brazil? From our analysis of he capial consrain we can conclude ha he economy can susain a capial growh rae of 3% wih an invesmen-gdp raio of approximaely 21%. From he growh accouning sudies analyzed above we can conclude ha he average TFP growh ranges from 1% o 2%. 51 Combining hese assumpions, he long-run poenial growh rae is beween 3.3% and 4.3%, whereas he shor-run rae is probably wo or more percenage poins higher because of he low capaciy uilizaion and high unemploymen of he previous years. In summary, Brazil can sar growing much faser han in las 20 years, provided ha growh is led or accompanied by an increase in invesmen. The inuiion is ha if invesmen grows faser, he economy will probably ener in a viruous cycle where produciviy gains increase profis and wages, which raises aggregae demand, which leads o anoher increase in income and invesmen. 51. Recalling he TFP growh numbers: Gomez e al. esimaed 0.4% for , Silva Filho 0.9% for , Bacha and Bonelli 1.2% for , and Pinheiro e al. 2.1% for Because of he endogenous naure of TFP growh analyzed earlier, we believe ha somehing beween 1% and 2% is more likely o occur because of scale economies and demand-led labor produciviy growh. 50 exo para discussão 1092 maio 2005 Ipea

53 6.5 STATISTICAL ESTIMATES OF POTENTIAL-OUTPUT GROWTH So far we saw how o esimae of poenial-oupu growh from alernaive heoreical definiions of he supply consrain. The remaining ask is o check wheher hese heoreical esimaes are consisen wih saisical esimaes. Considering he annual daa firs, he ADF es indicaes ha Brazil s GDP is an I(1) variable and, herefore, is growh rae is I(0). 52 The firs mehod is o model GDP growh as an ARMA process and, afer esing alernaive specificaions, he resuls indicae ha an ARMA(1,2) model is a good proxy of he underlying daa generaing process. The resuls also indicae a srucural break afer 1980, which marks he beginning of Brazil s curren low-growh phase. Table 13 presens he economeric resuls and, based on he esimaed coefficiens, he expeced long-run growh rae of Brazil was [0.119/( )]=7.2% in , and jus [( )/( ]=1.8% in See able 13. The second saisical mehod is similar o previous one, excep ha i consrains he GDP series o be an ARMA (1,2) process wih a uniary AR coefficien. Given ha he ADF ess do indicae he exisence of a uni roo, his assumpion is also a reasonable approximaion of he daa generaing process. In order o obain he sochasic componen of he rend we have o esimae he residuals of he resriced ARMA(1,2) specificaion of GDP, and hen add each residual o previous level of GDP. Table 14 presens he resuls of he ARMA(1,2) model under he consrain ha he AR coefficien equals one. 53 Similar o he resuls of he unconsrained ARMA model, he long-run growh rae was approximaely 7.2% unil 1980, and jus 2.0% since hen. Figure 7 shows he residuals obained from he resriced model. See able 14. See figure 7. Based on he rend-cycle decomposiion presened in secion five, we modeled he residuals shown in figure 8 as a MA(2) process. Table 15 presens he economeric resuls and figure 8 shows he corresponding effecive and sochasicrend componens of GDP. Because he wo series are basically he same, he sochasic rae of capaciy uilizaion says wihin 1% of is equilibrium value of 100 during he whole period, as shown in figure 9. Despie his limied volailiy, he flucuaions do replicae he hisorical growh flucuaions of Brazil s GDP, ha is, hey indicae eigh rough-o-rough cycles: , , , , , , , and See able 15. See figures 8 and Because of he limied number of observaions, he ADF es was applied o an AR(2) and an AR(1) specificaion of GDP for he sample. 53. No surprisingly, he Durbin-Wason saisic indicaes auocorrelaion of he residuals, which we expec o be a MA process. Ipea exo para discussão 1092 maio

54 The hird mehod is o apply he HP filer o he daa. Saring wih he annual series, figure 10 shows he rend and effecive levels of GDP when he smoohing parameer equals 100, and figure 11 shows he corresponding HP esimae of he global rae of capaciy uilizaion. Mos of he flucuaions say wihin 2% of he HP rend and indicae cycles ha are less frequen, bu more irregular, han he ones obained from he sochasic rend. In general, we can idenify seven rough-rough cycles in , ha is: , , , , , and Even hough he urning poins and he volailiy of he HP cycles do no coincide wih he cycles obained from he sochasic rend, he HP esimae of he rend growh rae is 2.1% a he end of he sample period, ha is, almos he same obained from he sochasic rend. See figures 10 and 11. Given he irregular and shor cycles in figure 11, figure 12 shows he effecive and HP-rend growh raes of Brazil s GDP in Based on he growh insead of he level of GDP, we can idenify one long-run growh wave in he Brazilian economy since 1947, ha is: during he 1950s he rend growh rae was approximaely 6.8% and, afer deceleraing o approximaely 6% in he early 1960s, i acceleraed and reached he peak value of 8.7% in Thereafer, he rend growh rae deceleraed coninuously unil i reached he rough value of 1.9% in Since hen, i has remained a approximaely 2.1%. See figure 12. The resuls are basically he same when we apply he HP filer o he quarerly seasonally-adjused daa, figures 13 and 14 show he corresponding level and capaciy-uilizaion variables. A he end of he sample period he HP-rend growh rae is 1.6% per year, bu his resul is highly influenced by he low growh raes since In oher words, because he HP income rend is a weighed moving average of effecive income, is growh rae follows he long-run flucuaions of he laer. To illusrae his, figure 15 shows he effecive and HP-rend growh raes of income for The quarerly daa clearly reveal wo medium-run growh waves since 1980, wih peaks in 1985 and 1994, and a rough in A he peaks, he value of he growh rae was 1.1% and 0.9% per quarer (4.5% and 3.6% in annual erms), respecively, whereas a he rough value i was only 0.14% per quarer (0.6% in annual erms). Since 2002 he HP-rend growh rae has remained a 0.4% per quarer, ha is, 1.6% per year. See figures 13, 14 and 15. Finally, o obain cycles hrough he band-pass filer, le us define he laer o capure any flucuaion wih a periodiciy beween wo and eigh years. We chose o se he lower bound a eigh quarers insead of six quarers, as done for he US, because his makes he urning poins of he cycles coincide wih major evens in he recen economic hisory of Brazil. 54 In he oher hand, we chose o se he upper bound a eigh years because his currenly represens wo presidenial erms in Brazil and, 54. In addiion o his, excep for he early 1990s, he cycle componen is basically he same wih he lower bound a six or eigh quarers. We did no se he lower bound a one year because his inroduces high-frequency flucuaions in he medium-run componen of GDP. 52 exo para discussão 1092 maio 2005 Ipea

55 herefore, i bes reflecs he poliical business cycle of he economy. Anyway, he resuls are basically he same when we increase he upper bound o nine, en years or even weny years. Figure 16 shows he corresponding decomposiion of Brazil s GDP in erms of a shor-run (seasonal), a medium-run (cycle) and a long-run (rend) componen. Because we have o use he firs and las 12 quarerly observaions o apply he BP filer o he daa, he filered series are presened for he period. See figure 16. The shor-run componen of GDP conains is high-frequency flucuaions and remains wihin ±2% of he esimaed rend during mos of he period under analysis. In addiion o his, here is a small increase in he volailiy of shor-run flucuaions during he sagnaion and inflaion acceleraion of In conras o he shor-run componen of GDP, he medium-run componen flucuaes wihin ±1% of he rend componen, as shown in figure 17. In addiion o his, figure 18 shows ha he capaciy uilizaion derived from he BP filer also moves in he same direcion as he esimae derived from he HP filer, bu wih smooher variaions. See figures 17 and 18. The BP quarerly filer reveals five well-defined cycles since Using he business rough as a reference, he firs cycle sared in he las quarer of 1983, peaked in he firs quarer of 1987, and ended in he hird quarer of The upswing represens he recovery of he Brazilian economy from is 1982 deb crisis and he expansionary effecs of he Cruzado sabilizaion plan (in 1986). The downswing corresponds o he failure of he laer and he growh deceleraion caused by he acceleraion of inflaion. The oal duraion of he cycle was 19 quarers, ha is, almos five years. The second cycle was very shor and i corresponded o he expansion of 1989 and he conracion of The peak occurred in he hird quarer of 1989, and he rough in he fourh quarer of The oal duraion of was jus 9 quarers (approximaely wo years) and he underlying mechanisms were he unsuccessful Summer and Collor sabilizaion plans of 1989 and 1990, respecively. The hird cycle was also shor because he recovery from he 1990 recession was quickly haled by he poliical crisis associaed wih he impeachmen of Presiden Collor in Is peak and rough occurred in he las quarer of 1991 and he second quarer of 1993, respecively. The oal duraion was jus 10 quarers (2.5 year). The fourh cycle sared a he end of 1993 and corresponded o he expansionary effecs of he real plan on he Brazilian economy. The peak value was reached in he firs quarer of 1995, and he rough value in he second quarer of The underlying deerminans were he consumpion boom ha followed he real plan and he resricive macro policy adoped in he beginning of 1995 o defend he Brazilian currency from he conagion of he Mexican crisis. Alogeher he cycle lased welve quarers (3 years). The fifh cycle sared in he second quarer of 1996 and corresponded o he loosening of he Brazilian macro policy afer inernaional financial markes absorbed Ipea exo para discussão 1092 maio

56 he Mexican crisis. The peak occurred in he hird quarer of 1997, which was marked by he Eas Asian crisis. To defend value of he real, he governmen once again resored o resricive macroeconomic measures bu devaluaion was unavoidable. The rough occurred in he second quarer of 1999, ha is, shorly afer Brazil s 1999 currency crisis. Similar o he fourh cycle, he fifh cycle also lased welve quarers (3 years). The sixh and las cycle sared in he second half of 1999 and i seems o have reached a peak in he las quarer of Afer ha growh deceleraed because of he negaive impac of he energy raioning and he Argenine crisis of Given he duraion of he previous cycles and he observed growh deceleraion of , i is probable ha he rough of he sixh cycle occurred in he second quarer of 2003, making i 16 quarers long (4 years). If so, a sevenh cycle may be under way and, if i follows he 3 o 4-year paern of he previous hree cycles, he Brazilian economy may reach a peak beween he end of 2004 and he middle of 2005, and a rough beween he middle of 2006 and However, i should be noed ha he peak urning poins of he hree previous cycles were associaed wih exogenous shocks (he Mexican crisis of 1995, he Eas Asian crises of 1997 and he energy raioning and Argenine crisis of 2001). In he absence of adverse exogenous shocks, we can expec he curren cycle o las longer han he previous hree. Figure 19 shows he long-run componen of GDP according o he BP and HP filers. Because he HP quarerly filer wih a smoohing parameer of 1600 is very similar o a low-pass filer for flucuaions of 32 quarers or more, he wo rend variables are basically he same. The growh rae of he BP rend variable shows he same wo long waves already derived from he HP cycle and, a he end of he sample, i indicaes a long-run growh rae of 0.4% per quarer, ha is, 1.6% per year. See figure 19. Overall he saisical mehods allow us o idenify he cycles and srucural breaks in he evoluion of Brazil s GDP. Their esimaes of he curren long-run growh rae of Brazil vary beween 1.6% and 2.1% per year, bu because mos of hese esimaes were derived from a moving-average of he effecive series, hey should no be inerpreed as consan. In fac, an increase in he effecive growh rae would evenually raise he long-run rend esimaes, provided ha i lass, say, more han four years. Conrary o he supply-driven approach of mos growh accouning sudies, causaliy runs from he effecive o he rend GDP series in he saisical approach. 7 CONCLUSION There are many ways o esimae poenial oupu. Economic heory does no give us a unique or righ answer, i ells us wha o look for. From he previous secions we can conclude ha we should look for he capial and labor consrains, as well as for he possible bolenecks in iner-indusry flows. We can also conclude ha PTF is an aggregae index of producive efficiency and income disribuion derived from an accouning ideniy, no necessarily from an aggregae producion funcion. In fac, aggregae PTF is a weighed average of all oupu-inpu coefficiens of he economy and, herefore, i can be inerpreed from a supply-driven or a demand-led 54 exo para discussão 1092 maio 2005 Ipea

57 perspecive. From he mainsream supply-driven perspecive, long-run TFP growh is usually an exogenous variable ha limis he effecive growh of he economy for some given growh raes of labor and capial. In conras, from he heerodox demand-led perspecive, TFP growh is an endogenous variable generaed by he effecive growh of he economy. The recen economic hisory of Brazil indicaes ha he laer is a much more plausible explanaion for he slow growh since Poenial oupu is highly procyclical in he shor run. For one or wo-year forecass we have o ake in consideraion he cyclical behavior of labor and capial produciviy, he changes in he composiion of oupu and employmen, he variaions in he raio of inermediae consumpion o income, and, wha is mos imporan, we have o measure he various sources of oupu gaps o esimae how fas an economy can grow wihou surpassing is shor-run poenial oupu level. In he long run poenial oupu is endogenous. I depends fundamenally on he labor and he capial consrains, ha is, on he growh of populaion, on capial accumulaion and on he increase in he long-run capial and labor produciviies. The growh rae of populaion is he exogenous and mos sable parameer. The growh rae of capial is endogenous in he sense ha i converges o he growh rae of invesmen over long inervals of ime. The growh rae of he capial sock is also conneced wih labor and capial produciviy because, during an invesmen boom, capial deepening ends o happen ogeher wih an increase in labor produciviy and, depending on wha is higher, TFP growh can accelerae of decelerae. In shor, and no surprisingly, invesmen is he key variable for long-run growh. In he case of Brazil labor does no seem o be an imporan consrain. Because of he high unemploymen raes of previous years and he large share of he labor force in informal low-produciviy aciviies, boh employmen and labor produciviy end o respond very fas o demand variaions wihou generaing significan wage-cos pressures on inflaion. In oher words, employmen and labor produciviy can be considered endogenous variables raher han a consrain on growh. The mos imporan shor-run consrain on Brazil seems o be he capial sock. Because of he low invesmen-gdp raios of he las wo decades, Brazil can only grow somehing beween 2% and 3% per year a he curren pace of capial accumulaion. The saisical esimaes indicae ha an annual rae of 2% is more likely, bu hey are heavily biased downward because of he low growh raes of he pas 20 years. Saisical esimaes end o exrapolae he pas average o he fuure and, herefore, are no a good guide o poenial-oupu growh if some srucural change is under way or expeced o happen. In he case of Brazil he srucural change needed is clear and sraighforward: he counry has o increase is invesmen-gdp raio. Wih a higher invesmen- GDP raio labor produciviy will increase because of echnological gains, scale economies and changes in he composiion of employmen. Wih a higher invesmen-gdp raio he capial sock will also grow faser if here are no major adverse changes in he relaive price of invesmen goods. TFP growh will follow residually from he changes in labor produciviy and he capial-income raio. Ipea exo para discussão 1092 maio

58 I should be noed ha, in he shor run, he naural limis o capaciy uilizaion and he possible bolenecks in iner-indusry flows may obsacle an acceleraion of income growh before he increase in invesmen has sufficien ime o raise poenial oupu. 55 If one or more key inpus become scarce, inflaion is likely o accelerae even when here are sill idle labor and capial resources in he economy. Because of his, i is no sufficien o increase invesmen, i is necessary o increase and plan invesmen o eliminae or alleviae he main bolenecks of he economy. From 1950 hrough 1980 he governmen was he main agen behind he invesmen drive and income expansion of Brazil. Afer he 1982 deb crisis he invesmen capaciy of he Brazilian governmen was much reduced and he privae secor has no ye aken is role in leading a long-run expansion. The challenge for he near fuure is o coordinae governmen and privae acions o promoe anoher susainable expansion of invesmen. Finally and mos imporanly, growh is never a balanced process. During an expansion he economy is bound o experience some bolenecks. Localized demand pressures are normal and necessary for susainable growh. Changes in relaive prices and in capaciy uilizaion are he main channels hrough which firms idenify profiable opporuniies for invesmen, which in is urn generaes anoher round of effecive and poenial oupu growh necessary o susain he expansion. Because i akes some ime for invesmen o increase poenial oupu, any susainable growh process is likely o experience high capaciy-uilizaion raes in is firs years. In fac, if we inerpre poenial-oupu growh as a long-run average, he economy mus be above i during some ime. When macroeconomic policy is managed o reduce growh a he firs sign of high capaciy uilizaion, as i seems o be he curren case of Brazil, he resul is a reducion of boh effecive and poenial oupu. Precisely when high capaciy uilizaion should lead o an increase in invesmen, macroeconomic policy eners he sage o slow down he economy. If he governmen does no allow poenial oupu o grow, he fear of inflaion becomes self-fulfilling and he economy ends o experiences a series of shor cycles. The obvious and raional alernaive is o give growh a chance. If anyhing, economic hisory shows us ha susainable growh experiences are based on a viruous cumulaive process where an increase in aggregae demand induces an increase in invesmen, which in is urn raises wages and profis and, hrough his, generaes anoher round of expansion. Our analysis shows ha Brazil is ready o sar such a process, provided ha he governmen suppors i. This does no mean ha he governmen should be careless wih inflaion, bu only ha macroeconomic policy should be guided by longer horizons han one year. I also means ha governmen auhoriies should complemen aggregae measures of he oupu gap wih a disaggregaed analysis of iner-indusry flows in order o avoid killing an expansion because of an unfounded fear of acceleraing inflaion. 55. Assuming obviously ha he economy keeps is curren accoun compaible wih he availabiliy of foreign finance, so ha he BoP consrain does no bind while growh acceleraes. When he BoP consrain becomes a problem, he capial and labor consrains become secondary, as indicaed by he recen hisory of Brazil. 56 exo para discussão 1092 maio 2005 Ipea

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63 TABLE 1 Annual growh rae necessary for oupu o reach is poenial level in he nex period given he curren gap beween effecive and poenial oupu and he growh rae of poenial oupu Oupu Gap* Poenial oupu growh 4.0% 5.0% 6.0% 7.0% -2% 2.0% 2.9% 3.9% 4.9% -1% 3.0% 4.0% 5.0% 5.9% 0% 4.0% 5.0% 6.0% 7.0% 1% 5.1% 6.1% 7.1% 8.1% 2% 6.1% 7.1% 8.2% 9.2% Noe: *Difference beween he poenial and effecive oupu levels as a percenage of he former. A posiive gap means ha effecive oupu is below poenial oupu and vice versa. TABLE 2 Aggregaed and disaggregaed growh accouning for he US economy, Variable Rae* % Average growh rae Disaggregaed accouning Conribuion of capial Conribuion of capial qualiy Conribuion of capial sock Conribuion of Labor Conribuion of labor qualiy Conribuion of hours worked Conribuion of produciviy Secoral produciviy growh Composiion effecs Reallocaion of value added Reallocaion of capial Reallocaion of labor Aggregaed accouning Average growh rae Conribuion of capial sock Conribuion of hours worked Conribuion of produciviy Noe: *Raes in percenage poins. Source: Jorgenson (1990, p. 4). TABLE 3 Annual growh rae of employmen for alernaive changes in he rae of unemploymen and a 1.5% growh rae of he labor force Final rae of Iniial rae of unemploymen unemploymen 10% 11% 12% 10% 1.5% 2.6% 3.8% 9% 2.6% 3.8% 5.0% 8% 3.8% 4.9% 6.1% 7% 4.9% 6.1% 7.3% 6% 6.0% 7.2% 8.4% Ipea exo para discussão 1092 maio

64 TABLE 4 Cumulaive and average labor-produciviy growh raes for Brazil, Cumulaive Average GDP growh 34.1% 2.5% Labor-produciviy growh 18.4% 1.4% Agriculure and cale 77.8% 4.9% Indusry 30.6% 2.3% Mining excluding fuels 63.3% 4.2% Oil, naural gas, coal and oher fuels 10.4% 0.8% Non-meallic mineral producs 45.8% 3.2% Siderurgy 136.9% 7.5% Meallurgy of non-iron producs 55.3% 3.7% Oher meallic producs 29.2% 2.2% Producion and mainenance of machines and racors 35.8% 2.6% Elecrical machines and equipmens 157.7% 8.2% Elecronic machines and equipmens 46.7% 3.2% Auomobile indusry 114.6% 6.6% Oher vehicles and vehicles pars 74.4% 4.7% Wood and furniure producs 6.9% 0.6% Paper and prining 50.5% 3.5% Rubber indusry 86.4% 5.3% Chemical indusry excluding perochemical producs 71.6% 4.6% Oil refinemen and perochemical producs 158.0% 8.2% Miscellaneous chemical producs 62.1% 4.1% Pharmaceuical indusry 27.3% 2.0% Plasic indusry -15.1% -1.4% Texile indusry 27.8% 2.1% Clohing indusry -23.5% -2.2% Shoe and leaher producs -0.7% -0.1% Coffee indusry 29.0% 2.1% Tobacco and oher processed vegeable producs 33.6% 2.4% Mea indusry 10.0% 0.8% Dairy indusry 19.2% 1.5% Sugar indusry 34.5% 2.5% Producion and refinemen of vegeable oil and fa for food producs 92.5% 5.6% Oher food and beverage producs 40.3% 2.9% Miscellaneous indusrial secors 19.5% 1.5% Public uiliy services 120.3% 6.8% Consrucion 8.4% 0.7% Services -0.4% 0.0% Commerce -9.8% -0.9% Transpor -0.8% -0.1% Communicaions 150.9% 8.0% Banking and finance 14.7% 1.1% Services o households -13.5% -1.2% Services o firms -1.2% -0.1% Rens 61.8% 4.1% Public adminisraion 10.5% 0.8% Non-marke privae services -15.8% -1.4% Source: IBGE, naional income and produc accouns, ( 62 exo para discussão 1092 maio 2005 Ipea

65 TABLE 5 Annual growh rae of he capial sock when he capial-oupu raio is 3.1, capaciy uilizaion is a is long-run value, and he rae of capial depreciaion is 3.9% Invesmen /GDP Relaive price of capial Raio* % 2.6% 2.2% 1.9% 1.6% 1.4% 20% 3.3% 2.9% 2.6% 2.2% 2.0% 22% 4.0% 3.6% 3.2% 2.9% 2.6% 24% 4.7% 4.2% 3.8% 3.5% 3.1% 26% 5.4% 4.9% 4.5% 4.1% 3.7% Noe: *Excluding changes in invenories. TABLE 6 Inpu-oupu simulaions of he impac of a 1% annual growh of Invesmen (INV), Expors (EXP), Governmen Consumpion (GOV), and Privae Consumpion (CON) in Brazil INV EXP GOV CON Agriculure 0.09% 0.11% 0.04% 0.76% Mining 0.22% 0.34% 0.04% 0.40% Manufacuring 0.21% 0.16% 0.04% 0.59% Public uiliies 0.09% 0.07% 0.12% 0.72% Consrucion 0.94% 0.00% 0.01% 0.04% Commerce 0.12% 0.05% 0.06% 0.77% Transpor 0.11% 0.16% 0.06% 0.68% Communicaions 0.09% 0.06% 0.11% 0.74% Finance 0.14% 0.07% 0.14% 0.66% Rens 0.01% 0.01% 0.01% 0.97% Governmen services 0.01% 0.01% 0.94% 0.04% Oher services 0.06% 0.04% 0.14% 0.77% Agriculure 0.09% 0.11% 0.04% 0.76% Indusry 0.33% 0.13% 0.04% 0.49% Services 0.06% 0.04% 0.30% 0.60% GDP 0.17% 0.07% 0.20% 0.56% Employmen 0.14% 0.07% 0.13% 0.66% Impors 0.30% 0.08% 0.06% 0.56% Source: 1996 inpu-oupu marix of Brazil, IBGE ( TABLE 7 Growh accouning for Brazil, Income growh 1.9% 3.2% Capial growh 2.4% 2.8% Labor growh 2.9% 2.0% Growh accouning from a Cobb-Douglas funcion MFP growh -0.7% 0.9% Capial conribuion 1.2% 1.4% Labor conribuion 1.5% 1.0% Sources of TFP growh from he NIPA ideniies Conribuion of capial produciviy -0.2% 0.2% Conribuion of labor produciviy -0.5% 0.6% Source: Silva Filho (2001), capial share of income = 49%. Ipea exo para discussão 1092 maio

66 TABLE 8 Growh accouning for Brazil, Income growh 5.1% 6.9% 7.8% 1.6% 3.1% Capial growh 5.3% 8.7% 9.0% 2.6% 2.3% Labor growh 1.8% 2.8% 3.3% 2.2% -0.4% Growh accouning from a Cobb-Douglas funcion MFP growh 1.6% 1.1% 1.7% -0.7% 2.1% Capial conribuion 2.7% 4.3% 4.5% 1.3% 1.2% Labor conribuion 0.9% 1.4% 1.6% 1.1% -0.2% Sources of TFP growh from he NIPA ideniies Capial produciviy -0.1% -0.9% -0.6% -0.5% 0.4% Labor produciviy 1.7% 2.0% 2.3% -0.3% 1.7% Source: Pinheiro e al. (2001), capial share of income = 50%. TABLE 9 Decomposiion of he growh rae of per capia income Per capia income growh 3.8% 3.4% 3.3% -1.4% 1.7% TFP growh 1.8% 1.8% 1.7% -2.6% 0.4% Conribuion of Physical capial 1.8% 1.1% 1.9% 0.4% 0.5% Conribuion of Human capial 0.2% 0.5% -0.2% 0.8% 0.8% Source: Gomes e al. (2003), capial share of income = 40%. TABLE 10 Growh accouning for Brazil according o he AK model, * Income growh 6.9% 6.4% 9.5% 3.9% 2.5% 2.7% Capial growh 2.3% 1.6% 0.4% 5.1% 1.6% -0.2% Labor growh 4.3% 4.9% 6.9% 6.0% 5.0% 3.2% Growh accouning from a Cobb-Douglas funcion TFP growh 3.6% 3.1% 5.8% -1.7% -0.8% 1.2% Capial conribuion 1.1% 0.8% 0.2% 2.5% 0.8% -0.1% Labor conribuion 2.2% 2.4% 3.5% 3.0% 2.5% 1.6% Sources of MFP growh from he NIPA ideniies Capial produciviy 2.3% 2.4% 4.5% -0.6% 0.5% 1.5% Labor produciviy 1.3% 0.8% 1.3% -1.1% -1.3% -0.3% Source: Bacha and Bonelli (2004). TABLE 11 Funcional disribuion of income in Brazil, Year Labor compensaion Self-employed Operaional surplus % 8% 38% % 8% 44% % 7% 43% % 7% 41% % 7% 46% % 7% 48% % 7% 48% % 7% 50% % 6% 48% % 7% 48% % 6% 48% % 6% 49% % 6% 51% Average 47% 7% 46% Source: IBGE ( 64 exo para discussão 1092 maio 2005 Ipea

67 TABLE 12 Annual poenial-oupu growh when he labor inpu grows 1.5%, he capial share of income is 50% Capial-sock TFP growh rae growh rae 0.5% 1.0% 1.5% 2.0% 2% 2.3% 2.8% 3.3% 3.8% 3% 2.8% 3.3% 3.8% 4.3% 4% 3.3% 3.8% 4.3% 4.8% 5% 3.8% 4.3% 4.8% 5.3% TABLE 13 ARMA(1,2) model of Brazil s annual growh rae, Variable Coefficien Sd. Error -Saisic Prob. Consan Dummy Growh in MA coefficien MA coefficien R-squared Mean dependen var Adjused R-squared S.D. dependen var Log likelihood F-saisic Durbin-Wason sa Prob(F-saisic) TABLE 14 Sochasic rend-cycle decomposiion of Brazil s annual growh rae, Coefficien Sd. Error -Saisic Prob. Consan Dummy R-squared Mean dependen var Adjused R-squared S.D. dependen var Durbin-Wason sa Sum squared resid TABLE 15 MA(2) model of he GDP residuals obained from he model of able 14 Variable Coefficien Sd. Error -Saisic Prob. C MA(1) MA(2) R-squared Mean dependen var Adjused R-squared S.D. dependen var Log likelihood F-saisic Durbin-Wason sa Prob(F-saisic) Ipea exo para discussão 1092 maio

68 0.15 FIGURE 1 Annual growh rae of Brazil s real GDP and real GDP per worker GDP GDP per worker Source: Heson e al. (2002) FIGURE 2 Annual growh rae of he average labor produciviy in Brazil s Agriculural (AGR), Indusrial (IND), and Service (SER) secors AGR IND SER Source: IBGE ( 66 exo para discussão 1092 maio 2005 Ipea

69 FIGURE 3 Brazil s capial income raio, : Residenial Capial (RES); Non-Residenial (NRS) Srucures; and Machinery and Equipmen (ME) TOTAL NRS RES ME Source: IPEADATA ( FIGURE 4 Brazil s capial sock composiion, : Residenial Capial (RES); Non-Residenial Srucures (NRS); and Machinery and Equipmen (ME) RES NRS ME Source: IPEADATA ( Ipea exo para discussão 1092 maio

70 115 FIGURE 5 Rae of capaciy uilizaion in Brazil, (according o he deviaions o he capial-income raio from is rend* and he FGV indusrial index) Capial-Income esimae FGV esimae Source: IPEADATA ( Auhor s calculaion. Noe: *Capial-income esimae on he lef scale. FIGURE 6 Growh rae of he capial sock of Brazil, : Residenial Capial (RES); Non-Residenial Srucures (NRS); and Machinery and Equipmen (ME) TOTAL HPT RES HPT NRS HPT ME HPT Source: IPEADATA ( Auhor s calculaion. 68 exo para discussão 1092 maio 2005 Ipea

71 FIGURE 7 Residual erms from a regression of he log of Brazil s GDP on a consan, is previous value, and a srucural break in Period: Source: IPEADATA ( Auhor s calculaion. FIGURE 8 Effecive and sochasic rend of Brazil s real GDP (in log erms), Sochasic rend Effecive series Source: IPEADATA ( Auhor s calculaion. Ipea exo para discussão 1092 maio

72 101.0 FIGURE 9 Rae of capaciy uilizaion measures as he raio of he effecive o he sochasic rend of Brazil s real GDP, in log erms, Source: IPEADATA ( Auhor s calculaion. FIGURE 10 Effecive and Hodrick-Presco-rend (HP) value of Brazil s annual GDP, in log erms, in The HP esimae corresponds o a smoohing parameer of HP rend Effecive series 70 exo para discussão 1092 maio 2005 Ipea

73 FIGURE 11 Rae of capaciy uilizaion according o Hodrick-Presco (HP) rend of Brazil s annual GDP, in log erms, in The HP esimae corresponds o a smoohing parameer of FIGURE 12 Annual growh rae of he Hodrick-Presco (HP) rend of Brazil s real GDP. The HP rend corresponds o a smoohing parameer of Effecive HP rend Ipea exo para discussão 1092 maio

74 FIGURE 13 Hodrick-Presco rend of Brazil s real quarerly GDP, seasonally adjused and in log erms. The HP rend corresponds o a smoohing parameer of GDP HP rend FIGURE 14 Brazil s global rae of capaciy uilizaion, in percenage poins, based on he Hodrick-Presco rend of he quarerly real GDP, in log erms, and wih a smoohing parameer of exo para discussão 1092 maio 2005 Ipea

75 FIGURE 15 Quarerly growh rae of he Hodrick-Presco rend of Brazil s quarerly real GDP, The HP measure corresponds o a smoohing parameer of FIGURE 16 Decomposiion of he log of Brazil s real GDP in a shor-run (less han 8 quarers), medium-run (beween 8 and 32 quarers), and long-run (more han 32 quarers) componen Toal Long-run componen Medium-run componen Shor-run componen Ipea exo para discussão 1092 maio

76 FIGURE 17 Medium and shor-run flucuaions of Brazil s real GDP, in log erms, normalized by is long-run rend. All variables are expressed in percenage poins of he rend and he medium-run componen measures all flucuaions wih periodiciy beween 8 and 32 quarers Medium run Shor run FIGURE 18 Hodrick-Presco (HP) and Band-Pass (BP) esimaes of business cycles in Brail s real GDP, The HP measure corresponds o a smoohing parameer of 1600, and he BP measure corresponds o flucuaions beween 8 and 32 quarers HP esimae BP esimae 74 exo para discussão 1092 maio 2005 Ipea

77 FIGURE 19 Hodrick-Presco (HP) and Low-Pass (LP) esimaes of he long-run rend of Brazil s real GDP, in log erms, for The HP measure corresponds o a smoohing parameer of 1600, and he LP measure corresponds o flucuaions of 32 quarers or more LP rend HP rend Ipea exo para discussão 1092 maio

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79 Insiuo de Pesquisa Econômica Aplicada ipea 2005 EDITORIAL COMITÊ EDITORIAL Coordenação Silvânia de Araujo Carvalho Supervisão Iranilde Rego Revisão Valdinea Pereira da Silva Elizabee Anunes de Souza (esagiária) Raquel do Espírio Sano (esagiária) Secreário-Execuivo Marco Aurélio Dias Pires SBS Quadra 1 Bloco J Ed. BNDES, 9 o andar, sala Brasília DF Fone: (61) Fax: (61) Correio elerônico: [email protected] Edioração Aeromilson Mesquia Elidiane Bezerra Borges Brasília SBS Quadra 1 Bloco J Ed. BNDES, 9 o andar Brasília DF Fone: (61) Fax: (61) Correio elerônico: [email protected] Rio de Janeiro Av. Presidene Anônio Carlos, 51, 14 o andar Rio de Janeiro RJ Fone: (21) Fax: (21) Correio elerônico: [email protected] Tiragem: 130 exemplares