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1 Universidade Federal do Rio de J a neiro Insiuo de Economia Esimaing poenial oupu: a survey of he alernaive mehods and heir applicaions o Brazil TD. 016/2004 Nelson H. Barbosa Filho Série Texos para Discussão

2 December 20, 2004 Esimaing poenial oupu: a survey of he alernaive mehods and heir applicaions o Brazil * Nelson H. Barbosa-Filho ** Absrac: 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 oal 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: (1) he annual poenial growh rae of Brazil s 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; (2) 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; (3) 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; (4) 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 (5) 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. JEL codes: O110, O470, O490, O540 Keywords: growh, poenial oupu, effecive demand, Brazil * 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 Economia 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: nhbarbosa@ie.ufrj.br). 2

3 1 INTRODUCTION Poenial oupu is he capaciy of producion a a high level of resource use. In macroeconomics his corresponds o he level of 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 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 3

4 or an economy as a funcion of he quaniy of inpus necessary for is producion. producion is represened by a funcion F, such ha More formally, 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 oal 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 lny in relaion o ime we have y = a + J I j= 1 α j x j (2.2) where y and x are he growh raes of Y and X, respecively, a is he growh rae of TFP, j j α j is he elasiciy of Y in relaion o X, and J is he oal number of inpus. 1 In economic erms, (2.2) allows j I 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 1 Unless saed oherwise, all growh raes are exponenial growh raes. 4

5 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). 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 nevalue 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 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. 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). 5

6 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 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 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 N, (2.3) N where is he growh rae of labor inpu j and is is average paricipaion in he oal wage bill of he n j curren and previous periods, ha is N 1 β j = ( ω j + ω j 1) (2.4) 2 and β j j 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 6

7 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 where he weigh N 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 capial 7

8 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 (2.9) = K 1 ( 1 δ) + I 1 where is he sock of he capial good a he beginning of period, he gross invesmen of period K I 1-1 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 righhand 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 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. 8

9 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 capialsock 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 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 and S S = ( 1 δ) > 0 (2.12) 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) 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. 7 Usually he average is aken over 5 o 10 years. See, for insance, Bernanke and Gurkaynak (2001). 9

10 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 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 R j represens is renal price. 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 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. 9 See Jorgenson (1990) and CBO (2001). 10

11 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 oupu 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 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 g Po, h 1 where is he growh rae of poenial oupu in period and 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 a negaive oupu gap (when effecive oupu is higher han poenial oupu). See able 1. * g. The opposie holds for 11

12 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. 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 consrain If labor is he binding consrain, he growh rae of poenial oupu depends on he growh raes of labor produciviy and he labor force. Formally, le N Y max be he labor-consrained oupu level, by definiion 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). 11 For a comparaive survey of heerodox and orhodox growh heories see, for insance, Marglin (1984), Du (1990), and Foley and Michl (1999). 12

13 N max N Z, (3.2) N Y = = 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 righ-hand-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 un, = Z, (3.3) rend rend rend where naurally is he rend componen of labor produciviy and u Z / Z is cyclical Z componen. 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. 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, N, = 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

14 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 highproduciviy 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 middle-income 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. 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 working-age 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 A L (3.4) W where L, L, and L represen he number of people ha are respecively employed, economically E A W acive (meaning in he labor force), and in he working-age populaion. By definiion: L E L L. A W 13 The basic reference is Lewis s (1954) dual-economy model. Basu (2003) presens a survey of he more recen lieraure on he opic. 14

15 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 / ), employmen ( L / ), and in he number of work hours per employee ( N / L ). Because hese variables E L A 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 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 E A L w 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. 15

16 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 capial consrain When labor is no he binding consrain he nex suspec is he capial sock. By analogy wih he previous analysis, le K Y be he capial-consrained oupu level, ha is K K K = u, (3.5) V K Y = V Trend where u = V / V K Trend 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. 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). 16

17 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 invesmen-income, 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 invesmen goods (he price of invesmen goods divided by he oupu deflaor). 20 ρ is he relaive price of 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 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 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 expos, 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. 17

18 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. 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, 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 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. 18

19 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 supply-driven 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 Inpu-oupu simulaions and poenial oupu 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 iner-indusry 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 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 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). 25 In he general case we need a marke-share marix o move from goods o secors. 19

20 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: d m he inermediae demand for domesic,, and impored,, goods; and he final demand for domesic, d f m, and impored,, goods. f c 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 c 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. Since by definiion x = c + f d d, 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 d where A is a m m marix of inpu-oupu coefficiens, ha is, he a elemen of represens he hj A amoun of good h necessary o produce one uni of good j in period. Assuming ha d A is nonsingular, we have x = (I A ) f (3.11) d 1 d 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 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. 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). 20

21 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, 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 21