The Role of Enrepreneurship in Produciviy Growh: Decenralized versus Cenrally Planned Economies Clausre Bajona Universiy of Miami and Luis Locay Universiy of Miami January 28, 2007 Absrac: Trends in GDP and TFP growh in he former socialis economies seem o indicae ha hese economies were converging o unusually low long-run growh raes in he lae 1980s. In his paper we develop an endogenous growh model of enrepreneurship ha is able o accoun for he difference in long-run performance beween cenrally planned economies and marke-oriened ones. Long-run growh raes of oupu and produciviy are deermined by he growh of he sock of enrepreneurial knowledge, which in urn depends on he share of he populaion involved in enrepreneurial aciviies and on he ime ha hey spend on hose aciviies. We analyze he effec of wo characerisics of cenrally planned economies on heir growh performance. Firs, in cenrally planned economies facors of producion are disribued by he cenral planner o he firms managers hrough a cones ha uses up some of he managers producive effor. Second, he leadership is egaliarian, in he sense ha i reas individuals wih differen abiliies equally. We show ha hese wo feaures reduce he fracion of people becoming enrepreneurs/managers, as well as heir enrepreneurial effor, which in urn reduces long-run oupu and TFP growh. We also find ha he cenrally planned economies have lower income inequaliy and slighly higher capial-oupu raios. Key words: endogenous growh, enrepreneurship, cenrally planned economies JEL codes: O4, P5 1
here are a variey of roles among which he enrepreneur s effors can be reallocaed, and some of hose roles do no follow he consrucive and innovaive scrip ha is convenienly aribued o ha person How he enrepreneur acs a a given ime and place depends heavily on he rules of he game he reward srucure in he economy ha happens o prevail. [Baumol (1990), p. 894] 1. Inroducion One of he inriguing aspecs of he 20 h cenury s experimens in cenral planning is he decline over ime in he economic performance of socialis economies relaive o heir more marke-oriened, and usually more developed, conemporaries. This economic decline was widespread and significan, and may have conribued o he collapse of he Sovie sysem [Easerly and Fisher (1995)]. As expeced, growh raes for Easern Europe and he former Sovie Union following World War II declined as he economies of he region recovered from he war. Less expeced was ha hese counries appeared o be converging, if a all, o unusually low long-run growh raes. The mos sudied of he cenrally planned economies was ha of he Sovie Union. Is pos-wargrowh experience is summarized in he firs row of Table 1, which shows real per capia growh raes based on Wesern esimaes of Sovie GNP. By he 1980s he Sovie Union s growh rae was less han half ha of he U.S. and falling. The same general paern of declining growh can be seen in he official figures of ne maerial produc (NMP), hough hese raes are generally believed o be exaggeraed [Easerly and Fisher (1995)]. 1 The growh experience of Easern European counries in Table 1 mimics ha of he Sovie Union, bu a even lower raes. Furhermore, since heir growh raes are in erms of NMP, hey may be biased upward as hey are for he Sovie Union. This apparen 1 NMP does no include consumer services. 2
convergence of growh o very low raes is also seen ouside of Easern Europe. Using official daa, Madrid-Aris (1997) esimaed Cuba s growh rae of gross maerial produc (GMP) per capia in he period 1980-88 a 2.7 percen despie Sovie subsidies ha had reached 30 percen of GMP by he 1980s. In he laer half of ha period, before he collapse of he Sovie Union and he end of is subsidies, growh had fallen o 0.3 percen. More imporanly for our work, he same paern of decline is also seen in oal facor produciviy (TFP) growh. Based on a Cobb-Douglas producion funcion wih labor s share equal o 0.62, Bergson (1989) calculaed ha TFP growh for he Sovie Union declined from 1.87 percen in he 1950s o 1.51 percen in he following decade, and 0.11 percen in he period 1970-75. Using Wesern Daa and he same procedure (wih labor s share se a 0.6), Easerly and Fisher (1995) obain similar resuls. For he hree decades saring in 1950 hey calculae TFP growh raes of 2.8 percen, 0.8 percen and 0.1 percen, wih TFP growh urning negaive a 0.2 percen for he period of 1980-87. A similar paern has been found for Cuba. Using an esimaed Cobb-Douglas producion funcion insead of assuming a value for labor s share, Madrid-Aris (1997) found ha TFP growh for Cuba wen from 1.0 percen during 1963-70, o 0.8 percen in 1971-80, and hen fell sharply o -1.7 percen during 1981-88. While i is easy o hink of reasons why cenrally planned economies should be less producive han marke-oriened ones, formal models of he growh process under cenral planning are no common. Robers and Rodriguez (1997) models Sovie-ype economies as consising of a self-ineresed cenral planner who owns all capial, is a monopsonis in he labor marke, has a discoun rae ha is lower han ha of households, and who is ineresed only in maximizing a discouned sream of unproducive sae consumpion. In 3
he ransiion from marke o cenral planning he planner s bias in favor of capial leads o higher invesmen and growh. As he economy approaches is new seady sae pah, he rae of growh declines oward exogenously deermined long-run TFP growh. More recenly Brixiová and Bulír (2003) provide a wo-period model where he focus is on he incenives for eliciing high effor from managers of enerprises. Exogenous TFP growh makes he low effor equilibrium more likely, which ogeher wih (exogenously) declining penalies for underperformance can resul in a growh slowdown. As wih he model of Robers and Rodriguez, he cenrally planned economy is less efficien han is marke-oriened counerpar, bu he growh slowdown is simply a emporary phenomenon of he ransiion o a new seady sae. Unlike previous work, his paper focuses on he effec of cenral planning on long-run seady sae growh pahs. Ours is a model of endogenous TFP growh in which cenral planning leads o a misallocaion of enrepreneurial alen ha boh lowers he level of oupu and lowers long-run growh raes. Our explanaion is very much in he spiri of Baumol (1990), where he allocaion of enrepreneurial resources depends on he incenive srucure facing invenive and producive individuals. We propose ha in cenralized economies enrepreneurs mus diver some effor o compee for resources for heir enerprises from a cenral auhoriy. This view is consisen wih ha of Robers (1990) who saes ha he main role of he planning apparaus in he Sovie Union was o ac as a replacemen for he marke as a supply mechanism for enerprises. Having o devoe effor o his form of nonproducive aciviy reduces he effor enrepreneurs can devoe o producive ones, so ha all else equal, oupu and produciviy are reduced. To derive implicaions for growh, we adap he model of enrepreneurship in Murphy, 4
Scheifler, and Vishny (1991), which in urn builds on ha of Lucas (1978). In heir model, as in ours, producive enrepreneurial aciviies conribue o a sociey s sock of enrepreneurial knowledge, which in urn direcly increases produciviy. The sock of enrepreneurial knowledge is a public good, and is growh leads o oupu and TFP growh. The aim of his paper is o provide a unified framework for sudying decenralized and cenrally planned economies ha we believe will prove useful for analyzing he differences in performance beween hese wo ypes of economies. Our framework highlighs wo main differences beween decenralized and cenrally planned economies: he mechanism used o disribue resources among enerprises, and he social weigh given o individuals of differen characerisics. We consider a model economy wih infinie lived individuals who differ in heir level of enrepreneurial abiliy. Individuals wih high abiliy become enrepreneurs and hose wih low abiliy become producion workers. Individuals are endowed wih one uni of ime ha hey can devoe o producion or o lobbying for resources. In he decenralized framework, he resources ha each enrepreneur ges are deermined by he marke and, hus, no lobbying is necessary. In he cenralized economy, where he governmen owns and disribues all resources, managers (he equivalen o enrepreneurs in a decenralized sociey) need o spend ime lobbying he cenral planner o obain inpus for heir enerprises, which reduces he amoun of ime devoed o producive aciviies and, hus, oupu. Even if he governmen disribues oupu in an efficien way (ha is, in a way ha disors individuals decisions he leas, compared o he decenralized economy), he reducion in producion effor ranslaes ino a reducion in he rae of accumulaion in he 5
sock of enrepreneurial knowledge. Therefore, our framework shows he lack of a marke mechanism o redisribue resources as one of he sources of inefficiencies in cenrally planned economies. The second source of inefficiency derives from he weigh given o each individual in deermining social welfare. If cenralized economies end o seek a more egaliarian disribuion of resources, i will furher disor he behavior of individuals by reducing he incenives o work as enrepreneurs and reduce he counry s producive aciviy. Our framework is able o capure his effec. The paper is organized as follows: secion 2 presens he decenralized framework and characerizes he balanced growh pah of our model economy. Secion 3 describes he cenrally planned economy, characerizes is balanced growh pah, and develops a framework for comparing he balanced growh pahs of decenralized and cenralized economies. In secion 4 we calibrae he parameers of he model o U.S. daa and compare he generaed balanced growh pahs for boh ypes of economies. Secion 5 concludes. 2. The Economy Under Decenralized Decision-Making This secion inroduces he basic srucure by modeling he economy under decenralized decision-making. The environmen is one of infinie horizon wih infinielylived consumers. There is a measure N of consumers in he economy. Individuals are born wih an innae level of enrepreneurial abiliy, a. The abiliy level is privae informaion o he individual, wih abiliy levels disribued among he populaion according o a disribuion funcion Ga ( ) wih coninuous densiy ga ( ) and suppor S R +. The disribuion funcion is exogenously given and does no change over ime. 6
Individuals of abiliy a are endowed wih k ( ) 0 a unis of capial in he iniial period. Individuals are also endowed wih one uni of ime every period ha hey can use eiher in he producion of he economy s single good or in lobbying aciviies (in siuaions where lobbying generaes some benefi). Individuals also have a level of educaion h which we assume is homogeneous across abiliy levels. Individuals derive uiliy from consumpion, wih CES period uiliy funcion uc () = ( c σ 1)/ σ. Every period hey choose an occupaion (worker or enrepreneur), ime devoed o producion aciviies, x, consumpion, and savings in order o maximize he presen discouned value of heir uiliy. In all specificaions of our model, workers canno gain anyhing from lobbying aciviies and, herefore, hey choose o devoe all of heir ime o he producion process. We assume ha markes are complee, implying ha people can borrow and lend from each oher in order o smooh consumpion. All savings in he economy are done by accumulaing capial. The problem faced by an individual wih abiliy a is: max cb, u( c( )) 1 0 a + = (1) s.. c ( a) b ( a) m ( a) (1 r ) b ( a) b + + 1 = + + where c is consumpion, b is savings, b r is he ineres rae, and m is labor income earned in period. The labor income of an individual of abiliy a is equal o wh if he individual chooses o work as a laborer or i is equal o π ( a) if he individual chooses o be an enrepreneur, where π ( a) represens he profis of an enrepreneur of abiliy a. From he firs order condiions of he consumer we obain: c ( a) c + 1 ( a) b ( 1 r + 1 ) = β + 1/( σ 1) (2) 7
Noice ha his raio is also independen of he abiliy of he consumer: he marginal rae of subsiuion beween consumpion a differen poins in ime is he same for all consumers. Enrepreneurs have access o a producive echnology ha uses capial, raw labor, and he enrepreneur s abiliy. The producion funcion faced by an enrepreneur who devoes a fracion x of his ime o he producion process is given by: y a xa k nh 1 θ α 1 α x( ) = λ( ) ( ) θ (3) where k is he amoun of capial rened by he enrepreneur, n is he number of workers he enrepreneur employs, λ is a echnology parameer (discussed below), and αθ, (0,1). Noice ha his producion funcion exhibis consan reurns o scale in enrepreneurial abiliy, capial and labor, bu decreasing reurns in capial and labor alone. 2 Le r be he renal rae of capial a period. An enrepreneur chooses how much capial and raw labor o hire in order o maximize profis. Formally, he enrepreneur solves he problem 3 : π { ( ) ( ( ) ) } 1 1 θ θ α α λ x( a) maxn, k xa k nh wnh rk =, (4) where π ( a) are he profis made in period by an enrepreneur of abiliy a who spends x a fracion of ime x working, k is he capial rened and n is he number of workers 2 The individual firm s producion funcion is similar o Lucas (1997). 3 In he decenralized version of he model here is no gain from lobbying and, herefore, all enrepreneurs choose x = 1. We keep he noaion, hough, since i is useful for he analysis of he cenralized version of he problem. 8
hired by he enrepreneur. In wha follows, we eliminae he subscrip x for simpliciy. We recover his explici noaion in proposiion 2. Le κ = k/ nh be he capial-labor raio. From he firs order condiions on he enrepreneur s problem we obain: κ α w =. (5) 1 α r Noice ha he capial labor raio employed by an enrepreneur depends only on he economy s wage-renal raio and no on his abiliy. Therefore, all enrepreneurs use he same capial-labor raio in any given period. From here, we obain he capial and labor hired by each enrepreneur: k ( a) = λ xaκ 1/(1 θ) 1 α 1/(1 θ) α λ xaκ n ( a) =, h (6) α where = θ( α/ ) ((1 α)/ ) 1 1 1 r w α θ is a funcion of prices and he capial-labor raio. The oupu produced by an enrepreneur of abiliy a, and his profis are given by: y a 1/(1 ) ( ) λ θ xa θ = (7) and π ( a) = (1 θ) y ( a). (8) An individual of abiliy a chooses o be a worker or an enrepreneur according o which aciviy yields he highes income. Le ã as he abiliy of an individual in period whose income is he same independenly on wheher he becomes an enrepreneur or a worker. Given ha enrepreneurs profis are an increasing funcion of heir abiliy, all individuals wih abiliy level below he hreshold ã become workers and all individuals 9
wih abiliy level above he hreshold become enrepreneurs. The hreshold ã can be expressed as a funcion of he period prices, he fracion of he enrepreneur s ime used in producion aciviies, and he echnology parameer in he following way: wh a =. (9) (1 ) x 1/(1 ) θλ θ θ Given he hreshold ã, he oal supply of laborers in period is equal o NG( ã ). By aggregaing producion and demand for inpus over all enrepreneurs we obain he aggregae oupu and capial and labor demands. Le us define S = { a A a a } and Ma ( ) adg( a) as he average enrepreneurial abiliy of pracicing enrepreneurs in = S he counry. By inegraing over all enrepreneurs, we obain ha he demand for capial and raw labor a period is given by: L N = λ h x M a K = Nλ x M a ( ) d 1/(1 θ) α ( ) d 1/(1 θ) 1 α κ κ (10) and Y = x M( a ) N. (11) 1/(1 ) λ θ θ The single good produced in he economy is used for boh consumpion and invesmen in new capial. Given ha all savings is done in he form of capial, he supply of capial in he economy is equal o oal savings: s K = N badg ( ) ( a). (12) S Non-arbirage opporuniies imply ha he reurns on savings have o be equal o he renal rae of capial, ne of depreciaion: 10
r = r δ. (13) b Feasibiliy implies ha in equilibrium boh he labor and he capial markes clear: L d = NG( a ) (14) and K d = K. (15) s Finally, he marke for he single good in he economy has o clear as well. Tha is, oal expendiure equals oal oupu: C + K+ 1 (1 δ) K = Y, (16) where C = N c ( adg ) ( a) is he economy s aggregae consumpion. S In order o close he model, we need o explain how he echnology parameer λ changes over ime. Following Murphy, Scheifler, and Vishny (1991), he change in he level of he sock of enrepreneurial knowledge depends on curren enrepreneurial pracice. 4 In paricular, we assume ha he parameer λ depends on he mean enrepreneurial effor of he enire populaion, wih workers receiving zero weigh because hey devoe no ime o enrepreneurial aciviies. 5 Formally, λ λ = γλ axdg ( a ) µλ + 1 S (17) where γ is a parameer and µ is he rae of depreciaion of enrepreneurial knowledge. Wih his formulaionλ will grow more rapidly he more effor is devoed o 4 In Murphy, Scheifler, and Vishny (1991) λ akes on he value of he previous period s bes pracice, which is simply he highes abiliy. 5 An alernaive formulaion would be ax( dg a Ga ) λ+ 1 λ = γλ ()1 ( ) µλ. Here he rae of growh of λ depends on he mean enrepreneurial effor of enrepreneurs only. S 11
enrepreneurship, x, as well as he greaer he fracion of he populaion ha are enrepreneurs (he smaller is ã ). Enrepreneurial effor provides a posiive exernaliy in his model, helping generae perpeual growh. Definiion 1. Given he fracion of human capial spen in producion aciviies, x, and a disribuion of iniial capial socks, { } k0 ( a ), a compeiive equilibrium for his economy is a se of sequences: savings and consumpion for each abiliy level for each period, { c ( a), b ( a) + 1 }, prices, { b,, } r r w, a hreshold separaing workers from enrepreneurs, { ã }, enrepreneurial choices, { y( a), k( a), n( a )}, and echnology levels, { λ } ha: (i) Given prices and echnology levels, { c ( a), b ( a) 1 } problem (1)., such + solve he consumer s (ii) Given prices and echnology levels, enrepreneurial choices { ( ), ( ), ( )} y a k a n a solve he profi maximizaion problem (4). (iii) (iv) (v) Given prices and echnology levels, ã solves (9). Feasibiliy condiions (14)-(16) are saisfied. The echnology level λ evolves according o he law of moion in (17). The equilibrium of his economy is characerized by a se of equaions ha is lised in he Appendix. Solving for he equilibrium of his economy may be complicaed, since i involves a coninuum of heerogeneous agens. The fac ha capial-labor raios and marginal raes 12
of subsiuion do no depend on he abiliy level, ogeher wih he homoheiciy assumpions, simplify he resoluion of he problem, since hey allow he use of aggregaion heory. In paricular, equilibrium prices and aggregae variables in his model are equivalen o he equilibrium prices and aggregae variables of a represenaive agen s problem wih a single ype of producer. The nex proposiion saes his resul formally. The proofs of all proposiions are in he Appendix. Proposiion 1. Assume ha here exiss an equilibrium of our model economy and le { ã } be he sequence of occupaional hresholds in his equilibrium. Then, he equilibrium prices and aggregae variables of he model economy are also an equilibrium soluion of an economy wih he same characerisics as our model economy bu wih a represenaive consumer and a single producer (who akes he evoluion of λ as exogenously given and behaves compeiively) ha uses he echnology θ 1 θ α ( ( ) ) ( ) 1 1 α Y = λ M a N x K hl. (18) θ From he firs order condiions of his problem we obain an expression of he renal raes of capial and labor in erms of he aggregae variables: r = αθ AK H αθ 1 (1 αθ ) w AK H αθ (1 αθ ) 1 = (1 αθ ), (19) where A = x N M a. This formulaion will be useful in comparing he soluion 1 θ 1 θ 1 θ λ ( ) of he decenralized economy o he cenrally planned economy ha we describe in secion 4. 13
Combining equaions (9), (10) and (14) we obain ha aga ( ) θ(1 α) = Ma ( ) 1 θ (20) which saes ha he value of he occupaional hreshold depends only of he disribuion of abiliies and he inpu shares in producion. I is easy o see ha he equaion above has only one soluion and, herefore, here is a unique equilibrium hreshold and i is consan over ime. Given ha he equilibrium occupaional hreshold is easy o compue, we can solve for he aggregae variables and prices of he model by solving a one-secor closed economy model wih he echnology described in equaion (18). Noice ha his echnology presens consan reurns o scale in capial, labor, and enrepreneurial effor. The nex proposiion shows how o derive individual variables from he aggregae ones. I complemens proposiion 1 in showing ha any soluion o he represenaive consumer economy can be disaggregaed ino a soluion of he decenralized economy. Proposiion 2. Assume ha an equilibrium exiss for he economy wih a represenaive consumer and a single firm. Then, for any iniial disribuion of capial { k0( a )} saisfying ˆ k 0( adg ) ( a ) = K 0, here exiss an equilibrium of he decenralized economy S wih he same prices and aggregae variables as he equilibrium of he represenaive consumer economy. Furhermore, le ν ˆ be any generic equilibrium variable of he represenaive agen problem. Then, he equilibrium consumpion of an individual wih abiliy a is given by: 14
where consumpion a period zero is obained as: b wih pˆ = 1/ ( (1 + rˆ ) s= 0 ) cˆ c ( a) = c0( a) (21) cˆ b pm ˆ 0 ( a) + (1 + rˆ ) k0( a) 0 ( ) = = ˆ b 0 pm ˆ ˆ (1 ˆ ) ˆ 0 + + r k = 0 c a c 0 (22), and m ( a ) is he income of an individual wih abiliy a a period when prices are he equilibrium prices of he represenaive consumer s economy. Proposiion 2 saes ha in his framework equilibrium prices and aggregae variables are independen of he iniial disribuion of capial across abiliy levels. The disribuion of capial only affecs individuals income levels and, herefore, heir consumpion levels. 2.1. Balanced growh in he decenralized economy In his secion we invesigae he behavior of balanced growh pahs in he decenralized economy. We define a balanced growh pah as an equilibrium where all variables are eiher consan or grow a he same rae over ime. From he condiions ha characerize equilibrium we observe ha under such condiions he wage and renal rae of capial, he capial-labor raio, and he abiliy hreshold ha separaes workers from enrepreneurs have o be consan over ime. Produciviy grows a a rae λ = γ xm( a ) µ, where λ (1 ) = + λ λ0 and ã is he abiliy hreshold. By manipulaing he equaions ha characerize equilibrium, we obain ha oupu, consumpion, capial and wage raes, a 15
boh he disaggregaed and aggregae level grow a he rae ( ) 1/(1 αθ η λ ) = 1+ 1. Given he naure of our producion funcions, he balanced growh pah can be solved analyically as a funcion of he equilibrium hreshold. In paricular, from he firs order condiions for he consumer, we obain ha he value of he ineres rae in he balanced growh pah is consan and equal o: b r 1 σ (1 + η) = 1 (23) β The wage rae is w (1 ) = + η w0, where w 0 1/(1 θ ) θ αθ αθ αθ θ xm a ( ) (1 )/(1 ) /(1 ) α = (1 α)(1 + η) hg( a ) r0 (24) b and r 0 = r + δ. The res of he equilibrium variables can be compued by using he equaions ha characerize equilibrium lised in he Appendix. 2.2. Sources of growh in he decenralized economy In wha follows we use growh accouning echniques o decompose he growh rae of oupu ino he porion due o facor accumulaion, and he porion due o oal facor produciviy growh. I is he laer ha we are ineresed in measuring. Taking logs in equaion (18) and comparing he value of he log of oupu beween wo consecuive periods, we obain he growh accouning equaion: ( ) ( ) y y = ( λ λ ) (1 θ) M( a ) M( a ) (1 αθ ) Ga ( ) Ga ( ) + 1 + + + 1 + 1 + 1 + (1 αθ)( N N ) + αθ ( K K ), + 1 + 1 (25) where ν = logν for any generic variable ν. 16
The righ hand side of he equaion shows he conribuion of changes in capial, labor, and oal facor produciviy o oupu growh. We observe ha each percenage increase in he labor force conribues 1 αθ percenage poins o oupu growh. The corresponding number for capial is αθ. Noice ha he weighs corresponding o he growh raes of capial and labor force add up o one, even hough he producion funcion does no exhibi consan reurns o scale in capial and labor. The erm in brackes on he righ hand side of (25) represens growh in oal facor produciviy. Along a balanced growh pah his erm becomes γ xm( a ) µ. From his expression we observe ha TFP growh depends on enrepreneurial effor and on he value of he abiliy hreshold ã : he higher he hreshold, he lower TFP growh, and he higher he ime spen in lobbying, 1 x, he lower he TFP growh. The model in his paper is, herefore, a model of endogenous growh, where economies have he poenial of converging o differen long-run growh raes of TFP and oupu. This growh rae depends on he average effor in enrepreneurial abiliy, xm( a ) xadg( a). Noice ha for all decenralized economies x = 1 and ã is = S deermined by parameer values. Therefore, he model predics he same long-run growh rae for all decenralized economies. 6 Furhermore, since a = a for all, he model is equivalen o an exogenous growh model where he rae of growh is deermined by he inpu shares in producion and he disribuion of abiliy across he populaion. In he nex secion we show ha a similar resul applies for cenrally planned economies. All 6 Assuming, of course, ha all decenralized economies have he same disribuion of abiliy and do no differ in x. 17
cenrally planned economies grow a he same rae in he long-run, bu will differ from he long-run growh rae of he decenralized economies. 7 Using more general producion funcions we could ge x and ã o differ across counries. In ha case, we could inerpre λ as a common parameer across counries ha inerac wih each oher hrough rade and echnology ransfers, and ha is deermined by he average enrepreneurship effor in he world. This inerpreaion would deliver he same long-run growh rae across counries, as long as hey inerac commercially wih each oher. Given ha he ineracions of cenrally planned economies and decenralized economies were limied, his more general framework would sill deliver differen long-run growh raes across boh organizaional sysems. In his paper we would inerpre he decenralized economy as being an aggregae of all decenralized economies, and he cenrally planned economy as being an aggregae of all cenrally planned economies. 3. The Cenrally Planned Economy In auocraic socieies where he op leadership has considerable conrol over he allocaion of resources, one would expec such a leadership o be quie ineresed in efficiency. Olson (1982) refers o such leaders as having an encompassing ineres, for hey can capure and allocae much of an economy s oupu. The abiliy o capure much or all of an economy s oal oupu, however, will no be enough o achieve efficiency. One difficuly is ha he op leadership will have o delegae much of he enrepreneurial and managerial funcions o ohers (even more so for he op leader). Under such a 7 Given he differen organizaion of boh ypes of economies, we believe ha his is a plausible 18
cenrally organized economy, individuals who would have been enrepreneurs in a decenralized economy now may become managers for he op leadership, wih he accompanying problems ha such a relaionship enails. Specifically, we assume ha enrepreneurial abiliy is privae informaion, unknown o he leadership. In order o allocae facors of producion o managers, each period he leadership holds a cones in which he more effor a manager exers, and he greaer his abiliy, he more resources he receives. We refer o he effor devoed o hese coness as lobbying. The producion srucure of he model remains he same as in he decenralized economy: people are born wih an exogenous level of enrepreneurial abiliy and hey decide wheher o use heir abiliy and become managers of he producion echnology or no o use i and work as laborers. The main feaure of he cenrally planned economy is he exisence of an eniy, which we call he leadership. The leadership owns he capial sock and receives all producion in he economy, which i disribues beween invesmen and consumpion goods o be delivered o he counry s consumers. As in Robers and Rodriguez (1997), we assume ha here is no sorage echnology and individuals canno borrow and lend from each oher. 8 Therefore, in each period individuals consume all he income disribued o hem by he leadership. The cenrally planned economy works as follows: a he beginning of each period he leadership announces a compensaion scheme o be delivered a he end of he period. We assume ha he compensaion scheme used by he leadership is such ha i pays a fixed amoun of goods, m, o all individuals who work as laborers in period and compensaes managers depending on heir producion level: a manager who produces inerpreaion of he daa. 19
oupu y in period will receive compensaion m = τy. 9 Furhermore, we assume he exisence of a perfec commimen mechanism, so ha he leadership canno change previously announced policies. 10 Once he compensaion scheme is announced individuals make heir occupaional choices. We describe he individuals and leadership decisions in deail in wha follows. 3.1. Individuals decisions As in he decenralized economy, workers devoe heir uni of ime working as laborers. The problem of he managers is more complicaed han in he decenralized economy. In he cenrally planned economy, managers canno rely on he marke o obain heir inpus, and have o ge hem direcly from he leadership, hrough lobbying. The leadership canno disinguish a manager s abiliy ex-ane and, hus, i holds a cones in which resources are disribued according o he manager s lobbying efficiency. The lobbying efficiency of a manager depends on his lobbying effor (he fracion of his ime spen in lobbying), as well as on his abiliy, and on he oal lobbying efficiency in he economy. In paricular, he fracion za ( ) of he available capial and raw labor in he period obained by a manager wih abiliy level a, who spends 1 x of his ime in lobbying aciviies, is given by he following cones success funcion: 8 Robers and Rodriguez (1997) sae ha savings were used o finance he purchase of expensive consumer durables and goods appearing unexpecedly on he marke. 9 This compensaion scheme, even hough no necessary here, would be opimal in a more generalized framework where he leadership could no infer he manager s abiliy. I ensures ha individuals are going o reveal heir rue abiliy level, ha managers are going o maximize heir producion, and ha only he mos able individuals become managers. 10 I is well known ha commimen is a problem in any framework wih governmen policy. We make he assumpion in order o avoid ime-inconsisency problems. A possible jusificaion is o assume ha failure o deliver pre -announced compensaions would cause revol, leading o a change in governmen. 20
(1 xa ) za ( ) = (26) v where v= N (1 xa ( )) adg( a) is he oal efficiency unis of lobbying. 11 Here we assume A ha xa ( ) = 1 for individuals of abiliy a who become workers. Noice ha under his disribuion scheme enrepreneurs receive he same amoun of resources as hey would in a decenralized economy ha had he same hreshold ã and iniial levels of endowmens. A manager of abiliy a chooses a producion effor level x so as o maximize his uiliy, aking he compensaion scheme as given. In our se up, his is equivalen o maximizing his producion level. Formally, he manager solves he maximizaion problem: 1 θ αθ { ( ) [ ] [ ] (1 αθ τλ ) xa z ak z ah } max ( ) ( ) x (27) where H = NhG( a ) is he oal amoun of efficiency unis of labor available in he economy. Using he expression for za ( ) derived in (26) he manager s problem becomes: 1 θ θ max Bax (1 x) x (28) where B = τλk H / v does no depend on he manager s abiliy. From he firs αθ (1 αθ ) θ order condiion of he previous maximizaion problem we obain ha x = 1 θ for all. Tha is, he effor level devoed o producion is homogeneous across managers and over ime. Noice ha since all managers choose o use he same fracion of ime θ in lobbying aciviies, he fracion of resources ha a manager of abiliy a obains for producion is: 21
z ( a) = a, (29) NM( a ) which is linear in his abiliy level. The oupu produced by a manager of abiliy a in period can be wrien as a funcion of aggregae variables in he following way: y ( a) = λ a(1 θ) 1 θ αθ K H θ N M a (1 αθ ) θ ( ) (30) Noice ha his expression is exacly he same one obained for a decenralized economy where he enrepreneur devoes a fracion x = 1 θ of his ime o producive aciviies. The abiliy hreshold above which an individual becomes an enrepreneur is hus deermined by: τ y ( a) m (31) or, using (30), a mn M( a ) (1 ) K H θ = 1 θ αθ (1 α) θ τ θ λ. (32) 3.2. Leadership s decisions The objecive funcion of he leadership is difficul o assess. Robers and Rodriguez (1997) consider ha he objecive of he leadership (hey refer o i as he cenral planner) is o maximize is own consumpion (unproducive sae consumpion). Brixiová and Bulír (2003) do no specify he leadership s (he ruler, or Pary) objecive funcion. They only sae ha he role of he leadership is o fine is agen, he planner, for no meeing producion arges. In his paper, our objecive is o keep he cenrally planned economy 11 This is a special case of he widely used raio form of he cones success funcion. See Hirshleifer (1989) and Baik (1998) for a comparison wih oher forms. 22
as close as possible o he decenralized framework in order o isolae he effecs of he differences in enrepreneurial aciviy in boh sysems. Therefore, we assume ha he leadership is a benevolen planner whose objecive is o choose a compensaion scheme { m, τ} = 0 in order o maximize a weighed average of individuals discouned uiliy. Furhermore, we assume ha he leadership does no inernalize he effec of lobbying on he growh of enrepreneurial knowledge. Tha is, he leadership akes λ as exogenously given. Le ϕ ( a) denoe he weigh ha he social planner gives o an individual wih enrepreneurial abiliy a. In his paper we assume ha he leadership weighs all individuals equally, so ha ϕ ( a ) = 1 for all a S. Neverheless, we derive he equilibrium condiions under he more general noaion since i is useful in laer sages of he paper. The welfare funcion ha he leadership faces is: ( ) ϕ( ) β ( ) ( ) S = 0 (33) W = N a u c a dg a where c ( a ) is he consumpion level of an individual wih abiliy a in period. As we menioned above, he leadership chooses a compensaion scheme c ( a) = m for individuals who work as laborers, and c ( a) = τ y ( a) for individuals wih abiliy a who work as managers. In our se-up he leadership, by solving he manager s problem, can infer a manager s ype from he amoun of resources ha he receives during he lobbying process. Therefore, given ha a manager s oupu is linear wih respec o his abiliy level, our compensaion scheme is equivalen o one in which a manager s compensaion is a linear funcion of his revealed abiliy. Due o he fac ha individuals 23
do no have incenives o misrepresen heir ype, a manager s compensaion scheme will be a linear funcion of his own abiliy. Le us redefine he compensaion scheme as follows. The leadership assigns resources m ( a ) o an individual of abiliy a such ha: m if a a m ( a) = τ a if a> a (34) where ã is he balanced growh pah hreshold ha separaes managers from workers, m 1 (1 ) = m, and τ τλ (1 θ) θ ( K αθ H αθ N θ M( a ) θ ) =. Using his simplificaion we can wrie he leadership problem as: = 0 ( ) max β Nϕ( a) u c( a) dg( a) m, τ, K+ 1 S s.. [ τ ] N mga ( ) + M( a ) + K (1 δ) K = Y + 1 Y = λ (1 θ) N M( a ) K H 1 θ 1 θ 1 θ αθ (1 α) θ H a = NhGa ( ) = m / τ (35) The objecive funcion in he problem above can, hen, be wrien as: max β N ϕ ( aumdg ) ( ) ( ) ( ) ( ) ( ) 0 \ a ϕ au τ SS adg a + = 1 S + (36) m, τ, K Le ς be he Lagrange muliplier for he period- resource consrain equaion. The firs order condiions for he problem in (35) are: ς = β au ( m ) ϕ( adg ) ( a) + ϕ( au ) ( τ aadg ) ( a) SS \ S aga ( ) + M( a ) (37) g( a ) Y θ(1 α) a β Nu ( m) ϕ( adg ) ( a) ς ( ) (1 ) 0 SS \ NG a θ = τ Ga ( ) M( a ) (38) 24
ς ς Y + 1 = 1 δ + αθ (39) K + 1 + 1 which ogeher wih he leadership s budge consrain in (35), he relaionship a = m / τ, and he equaion for he evoluion of he facor λ characerize he soluion o he leadership s problem. 3.3. Balanced growh in he cenrally planned economy The balanced growh assumpion implies ha he echnology level grows a a consan rae λ = γ(1 θ ) M( a ) µ. 12 All oher variables grow a he rae c η c = +. Given he consan elasiciy of subsiuion assumpion in uiliy, 1/(1 αθ ) (1 λc) 1 he condiions ha characerize equilibrium are consisen wih he balanced growh assumpions. The nex proposiion relaes he equilibrium hreshold of he cenrally planned economy wih he equilibrium hreshold of he decenralized economy. I saes ha he former is higher han he laer, indicaing ha he cenrally planned economy has fewer enrepreneurs han he decenralized economy. Proposiion 3: Le a be he hreshold soluion of he planner s problem. Then a > a. The proof uses he fac ha he erm in brackes in equaion (38) is decreasing and i is equal o zero a ã and ha he firs wo erms in he equaion combined are posiive for 12 Noice ha, given ã, his is he same rae of growh as a decenralized economy wih x = 1 θ. 25
all a a. Therefore, if here is a soluion o he equaion, i has o saisfy a deails of he proof are in he Appendix. > a. The As i can be immediaely seen by looking a he equaions, he soluion o he leadership problem depends on he weighs given o each ype abiliy level. Differen ses of weighs imply differen equilibrium aggregae variables, differen hresholds ã, and differen disribuions of income across agens. Noice ha, given a hreshold ã, he aggregae producion funcion of he cenrally planned economy coincides wih he aggregae producion funcion of he decenralized economy, wih an enrepreneurial effor x = 1 θ. Therefore, he long-run TFP growh rae of he cenrally planned economy is also equal o γ xm( a ) µ. This implies ha here are wo sources of discrepancy beween TFP growh raes of he decenralized and cenrally planned economy. Firs, for any given level of ã he cenrally planned economy has a lower TFP growh due o he fac ha enrepreneurs need o spend a fracion of heir ime lobbying for resources insead of in producive aciviies. Second, a higher level of ã in he cenrally planned economy furher lowers is TFP growh level wih respec o he decenralized economy. In he cenrally planned economy, he hreshold ã is direcly linked o he weighs given o each individual by he leadership. The higher he weigh on low abiliy workers, he higher he hreshold value ã. Therefore, by changing he weighs ha he planner assigns o people wih differen abiliies, we can obain differen levels of ã. In order o isolae he effecs of he wo sources of discrepancy beween he decenralized and he cenrally planned economies, we consider an inermediae sep where he leadership s disribuion scheme mimics he disribuion of resources of he decenralized economy s 26
equilibrium. In his case, he only difference beween boh economies comes from he reversion of producive ime owards lobbying ha managers have o incur in he cenrally planned economy. This exercise isolaes he lobbying effec. We achieve his purpose by choosing weighs ϕ ( a) so ha he equilibrium variables of he cenrally planned economy coincide wih he equilibrium variables of a decenralized economy where enrepreneurs spend he same fracion of heir ime in producion aciviies as in he cenrally planned economy (ha is, x = 1 θ ). The nex proposiion esablishes he se of weighs for which he equilibrium of he cenrally planned economy coincides wih he decenralized equilibrium. In he proposiion we denoe by ν1 θ, for any generic variable ν, he balanced growh pah soluion of a decenralized economy where enrepreneurs spend a fracion x = 1 θ of heir ime in enrepreneurial aciviies. Proposiion 4: Le ν 1 θ denoe any generic variable from he balanced growh pah equilibrium of a decenralized economy where x = 1 θ. Le ĉ1 θ,0 ˆm θ be, and 1,0 respecively, he average consumpion and he average income per person in such equilibrium. Le τ = w1,0cˆ ˆ 1,0 a θ θ 1 θm1 θ,0 and m = w1 θ h. Then he balanced growh pah equilibrium of he decenralized economy wih x = 1 θ is also he balanced growh pah equilibrium of a leadership problem where he leadership weighs individuals of differen abiliies using he weighs: ϕ = 1 u ( m) for a a m 1 θ ϕ( a) = 1 u ( τa) for a> a 1 θ. 27
Noice ha since u < 0, ϕ < ϕ( a) for all a> a. Tha is, in order o mimic he w decenralized equilibrium, he planner has o give higher weighs o managers wih higher abiliy levels. Therefore, assuming ha he leadership reas all individuals equally inroduces inefficiencies in he cenrally planned economy. In he nex secion we parameerize and simulae he model economy and analyze he relaive imporance of such inefficiency. 4. Simulaions In his secion we parameerize he economy and solve for he balanced growh pah in hree scenarios: a decenralized economy, a cenrally planned economy, and a cenrally planned economy wih a planner ha uses he weighs described in proposiion 4. The laer scenario differs from he decenralized economy scenario only in he fracion of ime ha enrepreneurs spend in producive aciviies and, herefore, i isolaes he effec on oupu and TFP growh of he ime spen lobbying for resources. We denoe his scenario as he weighed cenrally planned economy. In order o parameerize he model, we need o choose a funcional form for he disribuion of abiliies across he populaion. We assume ha abiliy levels follow a Pareo disribuion. We pick a Pareo disribuion because i has he desirable propery ha he income disribuion for enrepreneurs implied by he model is also Pareo. Furhermore, exising lieraure repors ha a Pareo disribuion is a good approximaion for he upper ail of he disribuion of income (see for insance, Levy 2003 and Seindl 1965). Given ha in our model all workers earn he same labor income we believe his is a reasonable disribuion o consider. The Pareo disribuion has wo parameers: a 28
locaion parameer, a m, ha deermines he lowes value wih a posiive probabiliy of occuring and a shape parameer, s, ha deermines he hickness of he ail of he disribuion. The densiy funcion is given by: ga ( ) = 0 s sam s 1 a + a < a a a m m. (40) We ake he suppor of abiliies o be [ 1, ) S =, which implies ha a = 1. Deailed and accurae daa on cenrally planned economies are hard o obain. Therefore, as a firs approximaion, we consider parameer values so ha he balanced growh pah of he decenralized economy maches long-run rends for he U.S. economy. We choose a discoun facor β =.95, ineremporal elasiciy of subsiuion of 1.25, which implies σ =.2, and a depreciaion rae of 6 percen, all in line wih he real business cycle lieraure. The res of he parameers are joinly calibraed in order o mach he following long-run feaures of he U.S. economy: a growh rae of oupu per working-age person of 2.0 percen ( η = 1.02 ), a capial share of income of 1/3, a share of employmen in enrepreneurial aciviies of 20 percen and a Gini coefficien for he m disribuion of earnings of.35. 13 Table 2 presens he lis of parameers and heir corresponding values. The Appendix shows in more deail he relaionship beween he daa and he parameers. Given he calibraed parameers, he disribuion of abiliies is ploed in figure 1. Table 3 presens he resuls of he simulaions. The firs wo columns presen he balanced growh pah values for he decenralized and cenrally planned economies. 13 DeNavas-Wal and Cleveland (2002) find a Gini coefficien of household income for 2001 of.466. We adjus his coefficien downwards in order o ge an esimae of he Gini coefficien for individual earnings. 29
Values for he weighed cenrally planned economy are in he hird column. The variables for he decenralized economy are lised only for informaional purposes, since we have parameerized he model so ha he decenralized economy mached he daa perfecly in all he repored dimensions. From he able 4 we observe ha he marke economy has higher TFP and GDP growh han he cenrally planned economy. The lower growh of he cenrally planned economy comes from wo sources: firs, he reducion in he ime ha each enrepreneur spends in enrepreneurial aciviies, due o he need o spend ime lobbying for resources; second, he incenives from greaer redisribuion arising from he desire o rea all individuals equally. We can isolae he firs effec by comparing he decenralized economy wih he weighed-cenralized economy (columns 1 and 3). We observe ha he reducion in he ime spen in enrepreneurial abiliies is responsible for 87 percen of he difference in oupu growh beween he decenralized and he cenrally planned economy. Only 13 percen of he difference is due o he change in he fracion of enrepreneurs in he economy caused by he fac ha he cenralized economy is a more egaliarian regime. This implies ha he inefficiencies associaed wih he ime spen in lobbying aciviies are responsible for he differences in TFP and GDP growh. The lower ime spen by managers in producive aciviies reduces he conribuion o he sock of knowledge and, herefore, i reduces growh raes. Regarding inequaliy differences, noice ha he Gini coefficiens for he decenralized and he weighed cenrally planned economies are he same. Therefore, all he reducion in inequaliy is driven by he leadership s allocaion of 30
income across abiliy levels. Lorenz curves represening earnings disribuion are depiced in figure 2. Gini coefficiens for a large number of counries are repored by Deininger and Squire (1996). Our resuls are consisen wih heir observaion of lower Gini coefficiens in Easern European counries compared o he U.S. (.26 versus.35 in he US). In erms of magniude, he Gini coefficiens in our simulaions are smaller han he ones repored by Deininger and Squire (1996). In erms of our framework, his is an indicaion ha maybe he leadership did no have a compleely egaliarian welfare funcion. Since he resuls on growh are mainly driven by he need for lobbying aciviies, his is no a problem for us. Noice also ha he capial-oupu raio is higher in he cenrally planned economy. The planner supplemens he lower produciviy wih higher levels of capial. 4.1. Sensiiviy analysis In his secion we run some sensiiviy analyses on he free parameers. The mos imporan free parameer is he parameer µ from he evoluion of he produciviy parameer λ. Table 4 presens resuls on TFP and oupu growh as well as he Gini coefficiens for he cenrally planned economy for differen values of he parameer µ. Noice ha since µ is calibraed joinly wih oher parameers, changing µ implies a recalibraion of he whole se of parameers in order for he decenralized economy o mach he long-run rends of he U.S. economy. Table 4 presens he TFP and GDP growh raes as well as he Gini coefficien for he cenrally planned economy under differen values of he parameer µ. Given ha he decenralized economy is calibraed 31
o mach U.S. rends, he values of hese variables will no change wih a change in µ, and are he same as in able 3. We observe ha he TFP growh rae for he cenrally planned economy decreases as µ increases, and i becomes negaive for slighly posiive values of µ. 5. Conclusion In his paper we presen a unified framework for comparing decenralized and cenrally planned economies and we use i o analyze he differen long-run economic performance of he wo ypes of regimes. In our framework, he long-run growh raes of oupu and produciviy are deermined by he growh of he sock of enrepreneurial/managerial knowledge, which in urn depends on he share of he populaion involved in enrepreneurial aciviies and on he ime ha hey spend in hose aciviies. We analyze he effec of wo characerisics of cenrally planned economies on heir growh performance. Firs, in cenrally planned economies facors of producion are disribued by he cenral planner o he firms managers hrough a cones ha uses up some of he managers producive effor. Second, he leadership is egaliarian, in he sense ha i reas individuals wih differen abiliies equally. We show ha hese wo feaures reduce he fracion of people becoming enrepreneurs/managers, as well as heir enrepreneurial effor which, in urn, reduces long-run oupu and TFP growh. We also find ha he cenrally planned economies have lower income inequaliy and slighly higher capial-oupu raios. 32
In his paper we also analyze he effec on economic performance of each of hese characerisics separaely. We find ha he reducion in enrepreneurial effor accouns for abou 85 percen of he decrease in long-run growh raes, whereas he egaliarian leadership accouns for he difference in income inequaliy beween boh regimes. In his paper we ake he sand ha enrepreneurship aciviy is essenial for long-run economic growh. By discouraging enrepreneurial effor in heir counries and closing hemselves off o new ideas and echnologies developed in marke-oriened economies, cenralized economies seriously impaired heir abiliy o susain long-run growh, perhaps conribuing significanly o heir regimes evenual collapse. The framework developed in his paper is quie general and can be used o analyze issues of economic growh oher han hose considered here. Our framework inroduces a channel hrough which enrepreneurial aciviy has long-run economic effecs ha could be used, for example, o sudy he growh effecs of policies ha affec enrepreneurial incenives, such as indusrial regulaion and axaion. This paper is abou long-run rends. Two imporan issues regarding ransiions are no analyzed here. Firs, we do no explain he ransiion from high growh raes in he 1960s o increasingly lower growh raes in he oupu and TFP growh in he 1970s and 1980s ha cenrally planned economies experienced. Inefficiencies buil ino he sysem ha did no allow for he evoluion or implemenaion of new ideas ha naurally come wih free markes and compeiion are probably crucial o his evoluion. Papers like Akeson and Kehoe (1995) and Chu (2001) inroduce such inefficiencies in decenralized economies. Similar echniques could be used in his framework. Second, our paper does 33
no address he issue of ransiioning from one economic regime o he oher. This is he subjec of furher research. 34
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