Entrepreneurship and Productivity: the Slow Growth of the Planned. Economies

Transcription

1 Enrepreneurship and Produciviy: he Slow Growh of he Planned Economies Clausre Bajona a,*, Luis Locay b a Deparmen of Economics, Ryerson Universiy, 350 Vicoria Sree, Torono, ON M5B 2K3, Canada b Deparmen of Economics, Universiy of Miami, 5250 Universiy Drive, Coral Gables, FL 33146, USA Absrac: Trends in gross domesic produc (GDP) and oal facor produciviy (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 managerial 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 managerial effor, which in urn reduces long-run oupu and TFP growh. Furhermore, we find ha cenrally planned economies have lower income inequaliy and slighly higher capial-oupu raios, which is consisen wih hese counries experiences. JEL codes: O4, P5 Key words: managerial knowledge, produciviy, growh, economic sysems * Corresponding auhor. Fax: address: cbajona@miami.edu 1

2 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). Table 1 shows real per capia growh raes for several socialis counries during he poswar period. By he 1980s he Sovie Union s growh rae, compued using boh Wesern esimaes of Sovie GNP and official (Sovie) figures of ne maerial produc (NMP), was less han half ha of he U.S. and falling. 1 The growh experience of Easern European counries mimics ha of he Sovie Union, bu a even lower raes. For he case of Cuba, Madrid-Aris (1997) esimaes Cuba s growh rae of gross maerial produc (GMP) per capia in he period o be 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. 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, 2

3 and 0.11 percen in he period Using Wesern daa Easerly and Fisher (1995) obain similar resuls, wih TFP growh urning negaive a -0.2 percen for he period For Cuba, Madrid-Aris (1997) finds ha TFP growh wen from 1.0 percen during , o 0.8 percen in , and hen fell sharply o -1.7 percen during While i is easy o hink of reasons why cenrally planned economies should be less producive han marke-oriened ones, he apparen convergence of hese counries o unusually low long-run growh raes is harder o explain. In his paper we analyze he effec of cenral planning on long-run balanced growh pahs. We focus on wo main characerisics of cenrally planned economies ha differeniae hem from decenralized economies: (i) he lack of decenralized markes for producive inpus, wih he leadership (or cenral planner) acing as he supply mechanism for enerprises (Robers, 1990), and (ii) he pursui of policies by he leadership ha resul in a more egaliarian disribuion of income. We consider an endogenous growh framework where he TFP level is a funcion of he sock of managerial (enrepreneurial) knowledge in he economy which, in urn, is a funcion of he overall managerial effor. We adap he model of enrepreneurship in Murphy, Scheifler, and Vishny (1991), which in urn builds on ha of Lucas (1978). 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. In he decenralized framework, he resources ha each enrepreneur ges are deermined by he marke. 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 1 NMP does no include consumer services. 3

4 inpus for heir enerprises. This reduces he amoun of ime devoed o producive aciviies and, hus, reduces 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 sock of managerial knowledge. We call his mechanism he lobbying effec. Furhermore, as cenralized economies end o seek a more egaliarian disribuion of income, he behavior of individuals is disored furher by reducing heir incenives o become enrepreneurs, reducing managerial effor even more. We call his effec he redisribuion effec. Our work is relaed o papers in he lieraure ha deal wih he growh paerns of cenrally planned economies. Robers and Rodriguez (1997) analyzes he high growh raes achieved by cenrally planned economies in he iniial periods. They model he leadership as a self-ineresed cenral planner who owns all capial and maximizes a discouned sream of unproducive sae consumpion. Brixiová and Bulíř (2003) explain he growh slowdown of he cenrally planned economies as a failure o provide incenives for eliciing high effor from managers of enerprises. These papers differ from ours in several imporan aspecs. Firs, hey focus on differen sources of inefficiency creaed by he leadership. Second, and more imporanly, he differences in growh raes beween decenralized and cenralized economies are simply emporary phenomenon of he ransiion o new seady saes. Boh papers are silen abou possible long run discrepancies among decenralized and cenrally planned economies. 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 4

5 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. We conclude in secion The Economy Under Decenralized Decision-Making This secion inroduces he basic framework 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, ha is consan over ime. 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 +. The disribuion funcion is exogenously given and does no change over ime. 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. Following Lucas (1978), we model enrepreneurs as managers of a producive echnology ha uses capial, raw labor, and he enrepreneur s effor as inpus. Managerial effor is given by x a where x is he ime he manager spends in producive aciviies, a is he enrepreneur s enrepreneurial abiliy, and is he efficiency unis of enrepreneurship per uni of ime devoed o enrepreneurial aciviy. The laer is 5

6 exogenously given and common o all enrepreneurs. The producion funcion faced by an enrepreneur of abiliy a in period is given by: 1 α 1 α ( ) = λ( ) y a x a k n, (1) where k is he amoun of capial rened by he enrepreneur, n is he number of workers he enrepreneur employs, and λ is he sock of managerial knowledge (discussed below). The parameers α and saisfy α, (0,1). Noice ha his producion funcion exhibis consan reurns o scale in managerial effor, capial, and labor, bu decreasing reurns in capial and labor alone. In our formulaion, as in Lucas (1978), he enrepreneur does no own he capial nor have any specific venure ha needs o be financed. The enrepreneur is jus a manager whose reurn o managerial effor is equal o he residual profis of operaing he producive echnology. Therefore, each period enrepreneurs face he saic problem of maximizing period reurns o managerial effor. Le r be he renal rae of capial and w be he wage paid o workers. The enrepreneur chooses how much ime o spend in producive aciviies and how much capial and raw labor o hire in order o maximize profis, π ( a). Formally, he enrepreneur solves he problem: { ( ) ( ) } 1 α 1 α λ π ( a) = max x a k n wn rk x, n, k s.. 0 x 1. (2) In he decenralized economy resources are supplied in a compeiive marke, and here is no benefi from lobbying. Therefore, x = 1 for all and a. Le κ ( a) = k( a) / n( a) be he capial-labor raio employed by an enrepreneur of abiliy a. From he firs order condiions on he enrepreneur s problem we obain: 6

7 α w κ( a) = κ. (3) 1 α r Noice ha his capial-labor raio depends only on he economy s wage-renal raio and no on he enrepreneur s abiliy. Therefore, all enrepreneurs use he same capial-labor raio in any given period. From here, we obain he amoun of capial and labor hired by each enrepreneur: k ( a) = λ aκ Δ 1/(1 ) 1 α n a = Δ 1/(1 ) α ( ) λ aκ, (4) α where Δ = ( α / ) ((1 α)/ ) r w α is a funcion of he inpu prices. The oupu and profis produced by an enrepreneur of abiliy a are given by: y a 1/(1 ) ( ) = λ aδ (5) and π ( a) = (1 ) y ( a). (6) Noice ha he resources used and oupu produced by an enrepreneur of abiliy a relaive o an enrepreneur of abiliy a are given by: y( a) k( a) n( a) a = = = y ( a ) k ( a ) n ( a ) a. (7) Tha is, he quaniy of oupu produced by a firm is direcly relaed o he abiliy level of is manager. Individuals in his economy derive uiliy from consumpion of he economy s single good. Their preferences are represened wih a CES period uiliy funcion uc () = ( c σ 1)/ σ. Every period hey choose heir occupaion (worker or enrepreneur), consumpion, and savings in order o maximize he presen discouned value of heir 7

8 uiliy. All savings in he economy are done by accumulaing capial. The problem faced by an individual wih abiliy a is: e, c, b+ 1 = 0 max β uc ( ( a)) b = π s.. c ( a) b ( a) e ( a) (1 e ) w (1 r ) b ( a), (8) 0 e 1 where c is consumpion, b is savings, b r is he ineres rae, e is he fracion of ime devoed o each occupaion in period, and β ( 0,1) is he discoun facor. From he firs order condiions of he consumer we obain: c ( a) = β + c ( a) + 1 b ( 1 r + 1) 1/( σ 1). (9) This 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. The occupaional choice of he individual is sraighforward: a every period an individual of abiliy a chooses o be a worker ( e = 0 ) or an enrepreneur ( e = 1) according o which aciviy yields he highes income. 2 Le a be he abiliy of an individual in period who is indifferen beween being an enrepreneur or a worker. Given ha enrepreneurs profis are an increasing funcion of heir abiliy, all individuals wih abiliy level below he hreshold a become workers and all individuals wih abiliy level above he hreshold become enrepreneurs. Using (6) he hreshold a can be wrien as: 8

9 w a = 1/(1 ) (1 λ ) Δ. (10) Given he hreshold a, he oal supply of laborers in period is equal o NG( a ). By aggregaing producion and demand for inpus over all enrepreneurs we obain he o be he se of aggregae oupu and inpu demands. Le us define S = { a A a a } abiliy levels of pracicing enrepreneurs and M ( a ) = adg( a) as he average enrepreneurial abiliy of pracicing enrepreneurs. By inegraing over all enrepreneurs, he demands for raw labor and capial a period are given by: and he level of oupu is given by: ( ) ( ) L = Nλ Δ M a S d 1/(1 ) α K = Nλ Δ M a κ κ d 1/(1 ) 1 α, (11) Y = Δ M( a ) N. (12) 1/(1 ) λ The single good produced in he economy is used for boh consumpion and invesmen in new capial. The supply of capial is given by: s K = N b( a) dg( a). (13) S Non-arbirage opporuniies imply ha he reurns on savings have o be equal o he renal rae of capial, ne of depreciaion: r = r δ. (14) b In equilibrium boh he labor and he capial markes clear: L d = NG( a ), (15) 2 Individuals ha are indifferen beween becoming workers or enrepreneurs may spli heir ime among boh aciviies. They represen a se of measure zero and, herefore, heir decision does no affec our 9

10 and K d = K. (16) s The 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, (17) where C = N c ( a) dg( a) is he economy s aggregae consumpion. S Finally, we need o explain how he sock of managerial knowledge λ changes over ime. Following Murphy, Scheifler, and Vishny (1991), he change in he level of he sock of managerial knowledge depends on curren enrepreneurial pracice. 3 In paricular, we assume ha he parameer λ depends on he mean managerial effor of he enire populaion, wih workers receiving zero weigh because hey devoe no ime o enrepreneurial aciviies. 4 Formally, λ 1 λ = adg ( a + γλ ) μλ S, (18) where γ is a parameer and μ is he rae of depreciaion of managerial knowledge. Wih his formulaion, given a disribuion of abiliy Ga, ( ) λ will grow more rapidly he greaer he fracion of he populaion ha are enrepreneurs (he smaller is a ). Enrepreneurial aciviy provides a posiive echnological exernaliy in his model, generaing perpeual growh. resuls. For simpliciy, here we assume ha hey decide o become full-ime enrepreneurs ( e = 1 ). 3 In Murphy, Scheifler, and Vishny (1991) λ akes on he value of he previous period s bes pracice, which is simply he abiliy of he enrepreneur wih highes abiliy. 4 An alernaive formulaion would be a ( dga Ga ) λ 1 λ = γλ ( ) 1 ( ) + μλ S. Here he rae of growh of λ depends on he mean managerial effor of enrepreneurs only. 10

11 Definiion 1. Given a disribuion of iniial capial socks, { k 0 ( a ) }, a compeiive equilibrium for he economy described above is a se of sequences: consumpion, savings, and occupaional choice for each abiliy level for each period, { c ( a), b 1( a), e( a) } prices, { b,, } r r w, a hreshold separaing workers from enrepreneurs, { } +, a, enrepreneurial choices, { y ( a), k ( a), n ( a), x ( a )}, and echnology levels, { λ } ha: (i) Given prices and echnology levels, { c ( a), b 1( a), e( a) } problem (8)., such + solve he consumer s (ii) Given prices and echnology levels, enrepreneurial choices { ( ), ( ), ( ), ( )} y a k a n a x a solve he profi maximizaion problem (2). (iii) (iv) (v) Given prices and echnology levels, a solves (10). Feasibiliy condiions (15)-(17) are saisfied. The echnology level λ evolves according o he law of moion in (18). The se of equaions ha characerize equilibrium for his economy is lised in he Appendix. The nex proposiion derives properies of he occupaional hreshold a. I saes ha, given our assumpions on funcional forms, he value of he occupaional hreshold is consan over ime, and i depends only on he disribuion of abiliies and he inpu shares in producion. 11

12 Proposiion 1. For any disribuion of abiliies G( a ) saisfying he assumpions described above, he occupaional hreshold is unique and consan over ime. I is defined implicily by he equaion: ag ( a ) (1 α) =. (19) M( a ) 1 Proof: The equaion follows from (10), (11) and (15). Exisence and uniqueness follows from he fac ha he lef hand side is coninuous and sricly increasing in a, akes he value 0 for a = inf S and converges o infiniy as a converges o sup S. The resul obained in proposiion 1 highly simplifies he soluion of he model. Even hough his model involves heerogeneous agens, for any given occupaional hreshold a he 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. Therefore, afer solving for a using (19), solving for he aggregae variables of he model reduces o solving a represenaive agen problem. The nex proposiion saes his resul formally. The proof can be found in he Appendix. Proposiion 2. Assume ha here exiss an equilibrium of our model economy and le a be ha equilibrium s occupaional hreshold. Then, he equilibrium prices and aggregae variables of our model economy are also he equilibrium soluion of an economy wih he same characerisics bu wih a represenaive consumer and a single producer (who 12

13 akes he evoluion of λ as exogenously given and behaves compeiively) ha uses he echnology α 1 α = Y A K L, (20) where A λ ( M( a) N ) 1 =. From he firs order condiions of he represenaive consumer s problem we obain an expression of he renal raes of capial and labor in erms of he aggregae variables: r = α AK H α 1 (1 α ) α (1 α ) 1 = (1 α ), w AK H (21) where H = NG( a ). This formulaion will be useful in comparing he soluion of he decenralized economy o he cenrally planned economy ha we describe in secion 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 equilibrium condiions lised in he Appendix, in a balanced growh pah produciviy grows a a rae λ = γ M( a ) μ, wih λ (1 ) = + λ λ0, whereas aggregae oupu, consumpion, capial and wage raes grow a he rae ( ) 1/(1 α ) η = 1+ λ 1. Noice ha boh growh raes depend on he abiliy hreshold a and on he efficiency parameer. 13

14 Given he naure of our producion funcions, he balanced growh pah can be solved analyically as a funcion of he equilibrium hreshold. The ineres rae in he balanced growh pah is given by: b r 1 σ (1 + η) = 1, (22) β and he wage rae is w (1 ) = + η w0, where b w 0 1/(1 ) α α α M a ( ) (1 )/(1 ) /(1 ) α = (1 α)(1 + η) Ga ( ) r0, (23) and r 0 = r + δ. The res of he equilibrium variables can be easily derived as funcions of he ineres rae and he wage by using he equilibrium condiions lised in he Appendix 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 (20) and comparing he value of he log of oupu beween wo consecuive periods, we obain he growh accouning equaion: y+ 1 y = λ+ 1 λ + (1 α)( N+ 1 N) + α( K+ 1 K), (24) where ν = logν for any generic variable ν. The righ hand side of he equaion shows he conribuion of changes in oal facor produciviy, labor, and capial, o oupu growh. We observe ha each percenage increase in he labor force conribues 1 α percenage poins o oupu growh. The 14

15 corresponding number for capial is α. Noice ha he weighs corresponding o he growh raes of capial and he labor force add up o one, jus as if he aggregae producion funcion exhibied consan reurns o scale in capial and labor. The erm in brackes on he righ hand side of (24) represens growh in oal facor produciviy. Along a balanced growh pah his erm becomes γ M( a ) μ, which is increasing in managerial effor and decreasing in he value of he abiliy hreshold a. We can conclude, herefore, ha raising enrepreneurial aciviy by eiher increasing he managerial effor of each enrepreneur or by increasing he fracion of he populaion ha become enrepreneurs, increases growh. 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, is no enough o achieve efficiency. One difficuly is ha he op leadership has o delegae much of he enrepreneurial and managerial funcions o ohers (even more so for he op leader). In paricular, he leadership has he responsibiliy of disribuing resources among managers, whose managerial abiliy is hard o assess. Furhermore, he leadership of cenrally planned economies ends o pursue policies ha resul in more egaliarian disribuions of 15

16 income. 5 In wha follows we modify he framework of he previous secion in order o accoun for hese wo feaures of cenrally planned economies. The basic 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 difference beween boh arrangemens is he inroducion of he leadership in he cenrally planned economy. 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. 6 Therefore, in each period individuals consume all he income disribued o hem by he leadership. The iming of he decision making in he 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. The srucure of 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 oupu y in period receives 5 I does no maer for our purposes wheher a more egaliarian sociey was he leadership s ulimae aim, or simply a means by which o mainain poliical suppor. 6 Given ha here is no uncerainy in his model and he leadership is a benevolen planner, his assumpion is no resricive. Robers and Rodriguez (1997) sae ha savings in cenrally planned economies were mainly used o finance he purchase of expensive consumer durables and goods appearing unexpecedly on he marke, insead of a consumpion smoohing device. Furhermore, any savings were done hrough sae banks, which disribued he capial among he sae firms. 16

17 compensaion m = τ y. 7 Furhermore, we assume he exisence of a perfec commimen mechanism, so ha he leadership canno change previously announced policies. 8 Once he compensaion scheme is announced individuals make heir occupaional choices and managers decide how much of each inpu o hire and how much ime o spend in lobbying aciviies Individuals decisions Given our assumpions on borrowing and lending, individuals face a saic occupaional decision every period. As in he decenralized economy, individuals who become workers devoe heir uni of ime o 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. Sudies of managemen in he USSR during he socialis period emphasize he procuremen of inpus as he managers main worry. Two feaures of he sysem conribued o his. Firs, he need of allocaion orders in order o be eniled o receive inpus. Berliner (1957) characerizes he procuremen of hese documens as he focus of much of he aciviy of managemen (p.22). Allocaion 7 This compensaion scheme 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. 8 I is well known ha commimen is a problem in any framework ha involves governmen policy in an ineremporal seing. We make he assumpion in order o avoid ime-inconsisency problems. A possible moivaion is o assume ha failure o deliver pre-announced compensaions would cause revol, poenially leading o he fall of he governmen. 17

18 orders were disribued according o he firm s annual economic plan which, in urn, was deermined hrough a long bargaining process beween managers and governmen officials. According o Berliner (1999), during he monhs when he annual economic plans were designed (he firs hree monhs of he year) managers descended on Moscow in grea profusion working o bea ou more favorable condiions for heir enerprises. Managemen s influence wih minisry officials wen a long way in geing plan assignmens and inpu auhorizaions ha were favorable o he enerprise. (p. 250). Second, here was a perpeual shorage of supplies (Berliner 1957, p. 24) ha implied ha even he possession of an allocaion order did no guaranee ha he inpus would be delivered. Furher bargaining and he exensive use of personal influence (Berliner 1976, p 72) was needed in order o ensure a flow of resources o a manager s enerprise. In our model, he lobbying efficiency of a manager depends on he fracion of he ime he spends lobbying, as well as on his abiliy, and on he oal lobbying efficiency in he economy. We assume ha he more able managers are also beer lobbyiss, which implies ha he disribuion of resources among managers in he cenrally planned economy is very similar o he one in he decenralized economy. 9 Le za ( ) be he fracion of he available capial and raw labor in a given period obained by a manager wih abiliy level a, who spends 1 x of his ime in lobbying aciviies. Then: (1 x) a za ( ) =, (25) v 9 A more general version of he model which disinguishes beween managerial and lobbying abiliies is presened in he appendix. 18

19 where v= N (1 x( a)) adg( a) is he oal efficiency unis of lobbying. 10 Here we S assume ha xa ( ) = 1 for all laborers. 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: where 1 α { ( ) [ ] [ ] (1 α ) τλ x a z a K z a H } max ( ) ( ), (26) x H is he amoun of labor available in he economy. Using he expression for za ( ) derived in (25) he manager s problem becomes: 1 max Bax (1 x) x s.. 0 x 1, (27) where B = K H v. The soluion o his problem is x = 1 for all. 1 α (1 α ) τλ / Tha is, he effor level devoed o producion is homogeneous across managers and over ime. Therefore, he income received by a manager wih abiliy a depends linearly on his abiliy level and i is given by m ( a) (1 ) 1 = Ba. Given he compensaion scheme designed by he leadership, here is also an occupaional hreshold in he cenrally planned economy, a, so ha all individuals wih abiliy levels above he hreshold become managers. The hreshold is deermined by he abiliy level ha receives he same income in any of he wo occupaional choices, and i is implicily defined by he equaion: m 1 = Ba (1 ). (28) 10 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. 19

20 Noice ha since all managers choose o use he same fracion of ime in lobbying aciviies, he fracion of resources ha a manager of abiliy a obains for producion is: a z ( 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: α (1 α) 1 1 = λa, (30) y ( a) (1 ) K H N M( a) where H = NG( a) is consan over ime. Using his expression we can rewrie (28) as a ( M( a )) m N = 1 1 α (1 α) τ(1 ) λk H. (31) Noice ha under his disribuion scheme he resources received by an enrepreneur of abiliy a relaive o he resources received by an enrepreneur of abiliy a as well as heir relaive level of oupu saisfy y ( a) / y ( a ) = z ( a) / z ( a ) = a/ a, which is exacly he same raio as in he decenralized economy. Therefore, he leadership in his framework disribues resources among enrepreneurs efficienly: i does no value relaive enrepreneurial abiliy differenly han he marke. Redisribuion in he cenrally planned economy akes place beween workers and enrepreneurs, bu no wihin enrepreneurs. This resul depends crucially on he fac ha we do no disinguish beween managerial and lobbying abiliies. 11 A more generalized framework ha allowed for hese wo abiliies o differ would inroduce a new inefficiency in he 20

21 cenrally planned economy: misallocaion of resources across managers wih differen managerial abiliies. In paricular, high abiliy managers wih low lobbying skills would receive less resources han in he efficien allocaion. Recen lieraure suggess ha his misallocaion of resources has poenially large effecs on TFP (see, for insance, Hsieh and Klenow 2007, Resuccia and Rogerson 2007, and he sudies cied here in). For simpliciy, we absrac from his ype of inefficiency in he paper and we ouline a more general framework in he las par of he appendix Leadership s decisions We model he leadership as a planner whose objecive is o choose a compensaion scheme {, } 0 m τ = in order o maximize a social welfare funcion where each person is given equal weigh, regardless of heir level of abiliy. Furhermore, we assume ha he leadership does no inernalize he effec of lobbying on he growh of managerial knowledge. Tha is, he leadership akes λ as exogenously given. The leadership s social welfare funcion is: ( ) β ( ) ( ) S = 0, (32) W = N u c a dg a where c ( a ) is he consumpion level of an individual wih abiliy a in period, This welfare funcion reflecs our assumpion of leadership ha behaves as if i was egaliarian, since i equally weighs all individuals in he economy, independenly of heir abiliy. 11 We hank an anonymous referee for poining his ou o us. 21

22 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 abiliy 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 do no have incenives o misrepresen heir abiliy, a manager s compensaion is 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) =, (33) τ a if a > a where a is he hreshold ha separaes managers from workers, m = m, and ( K H N M a ) τ = τ λ. Using his simplificaion we can wrie he 1 1 (1 ) (1 ) α α ( ) leadership s problem as: m, τ, K+ 1 S = 0 ( ) max β Nu m ( a) dg( a) s.. [ τ ] N mg( a ) + M( a ) + K (1 δ) K = Y + 1 Y = λ (1 ) N M( a ) K H α (1 α) H a = NG( a ) = m / τ. (34) Noice ha in his se-up he leadership does no sor ou people ino workers and managers. The leadership, hough, akes ino accoun ha people s occupaional 22

23 decisions are deermined by he payoff scheme ha i implemens, as saed by he las consrain. The objecive funcion in he problem above can, hen, be wrien as: max β N u ( m ) ( ) ( ) ( ) 0 G a + u τ S a dg a = m, τ, K + 1. (35) Le ς be he Lagrange muliplier for he period- resource consrain equaion. The firs order condiions for he problem in (34) are: β au ( m) G( a) + u ( τa) adg( a) S ς =, (36) ag( a) + M( a) ga ( ) Y (1 α) a β Nu ( m) G( a) ς NG( a) (1 ) = 0, (37) τ Ga ( ) M( a) ς ς Y + 1 = 1 δ + α, (38) + 1 K+ 1 which ogeher wih he leadership s budge consrain in (34), he relaionship a = m / τ, and he equaion for he evoluion of he facor λ, characerize he soluion o he leadership s problem. The nex proposiion compares he equilibrium hreshold levels of he decenralized and he cenrally planned economies, a and a, respecively. I saes ha a any poin in ime he hreshold level for he cenrally planned economy is higher han he hreshold level in he decenralized economy, indicaing ha he cenrally planned economy has fewer managers han he decenralized economy. Proposiion 3: Le { a } denoe he sequence of equilibrium hreshold levels of he cenrally planned economy and a be he equilibrium hreshold level of he decenralized economy. Then a > a. 23

24 The proof relies on he fac ha he erm in parenheses in equaion (37) is decreasing and i is equal o zero for a posiive for all a = a. The combinaion of he firs wo erms in he equaion is a. Therefore, if here is a soluion o he equaion, i has o saisfy a > a. The deails of he proof are in he Appendix Balanced growh in he cenrally planned economy The balanced growh assumpion implies ha he echnology level grows a a consan 1/(1 α ) rae λ = γ(1 ) M( a) μ. All oher variables grow a he rae η = (1 + λ ) c The long run growh rae of he cenrally planned economy differs from he growh rae of he decenralized economy in wo aspecs: a new erm, 1, and a differen hreshold level a. The former is linked o he fac ha enrepreneurs need o spend a fracion of heir ime lobbying for resources (he lobbying effec ), while he laer is driven by he differences beween compensaion schemes in boh economies (he redisribuion effec ). Boh differences produce a lower growh rae in he cenrally planned economy. In he nex secion we address he quesion of isolaing hese wo effecs. We consruc a weighed cenrally planned economy ha does no have a redisribuion effec and, herefore, all is differences from he decenralized economy are aribued o he lobbying effec. The main inuiion for his consrucion comes from he fac ha he occupaional hreshold a is direcly linked o he weigh ha he leadership gives o c c 12 Given he consan elasiciy of subsiuion assumpion in uiliy, he condiions ha characerize equilibrium are consisen wih he balanced growh assumpions. 24

25 individuals of differen abiliy. Therefore, he key is o find a suiable se of weighs for which in equilibrium m / τ = a A weighed cenrally planned economy Le us consider a version of he cenrally planned economy where he leadership weighs individuals differenly depending on heir abiliies. Le ϕ ( a) denoe he weigh ha he leadership gives o an individual wih enrepreneurial abiliy a. The welfare funcion ha he leadership faces is now: Condiions (36) and (37) now become: ( ) ϕ( ) β ( ) ( ) S = 0. W = N a u c a dg a β au ( m) ϕ( a) dg( a) + ϕ( a) u ( τ ) ( ) S\ S a adg a S ς =, (39) ag( a) + M( a) ga ( ) Y (1 α) a β Nu ( m) ϕ( a) dg( a) ς ( ) (1 ) 0 S\ S NG a =. (40) τ Ga ( ) Ma ( ) The wo previous equaions show ha he hresholds a are direcly linked o he weighs given o each individual by he leadership. Inuiively, he higher he weigh given o low abiliy individuals, he higher he compensaion level given o workers and, herefore, he higher he hreshold values a. By changing he weighs ha he planner assigns o people wih differen abiliies, we can obain differen hreshold values. The nex proposiion derives a se of weighs under which he hreshold values of he cenrally planned economy coincide wih he hreshold value of he decenralized economy. Under his specific se of weighs, he leadership s disribuion scheme mimics he equilibrium 25

26 disribuion of income of a modified decenralized economy wih efficiency parameer ˆ = (1 ). In his case, he only difference beween he wo economies comes from he reversion of producive ime owards lobbying ha managers have o incur in he cenrally planned economy, hus isolaing he lobbying effec. Proposiion 4: Consider a modified decenralized economy where one uni of enrepreneurial ime ranslaes ino ˆ = (1 ) efficiency unis of managerial effor. Le ν denoe a generic variable from he balanced growh pah equilibrium of such economy. Le ĉ 0 and ˆm 0 be, respecively, he average consumpion and he average income per person in such equilibrium. Le τ = wcˆ ˆ 0 0am 0and m= w0 and define he weighs ϕ( a) as: 1 u ( m) ϕm for a a ϕ( a) = 1 u ( τ a) for a> a. Then he balanced growh pah of he cenrally planned economy wih weighs ϕ ( a) coincides wih he balanced growh pah of he modified decenralized economy. Noice ha since u < 0, ϕ < ϕ( a) for all a > a. Tha is, in such an environmen he w planner has o give higher weighs o managers wih higher abiliy levels. Any se of weighs ha is more redisribuive implies a higher hreshold level, a. 4. Simulaions In his secion we parameerize he economy and solve for is balanced growh pah under hree scenarios: a decenralized economy, a cenrally planned economy, and a weighed 26

27 cenrally planned economy where he planner uses he weighs described in proposiion 4. The laer scenario is inroduced in order o isolae he lobbying effec. 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, he 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 locaion parameer, a m, ha deermines he lowes value wih a posiive probabiliy of occurring 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. (41) 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, we consider parameer values so ha he balanced growh pah of he decenralized economy maches long-run rends for he U.S. economy. We normalize =1. 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 exising lieraure. The res of he parameers are joinly chosen in order o mach he following long-run feaures of he U.S. economy: a growh rae of oupu per working-age person of m 27

28 2 percen ( η =.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 disribuion of earnings of 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 model s parameerizaion, 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. 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 Table 3 we observe ha he marke economy has higher TFP and GDP growh han he cenrally planned economy, wih differences on he order of 4. 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; and, second, he incenives from greaer redisribuion ha resul from reaing all individuals equally. We can derive he magniude of he lobbying effec by comparing hese economies wih he weighed cenrally planned economy (column 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 economies. Only 13 percen of he difference is due o he change in he fracion of 13 We adjus he Gini coefficien for household labor earnings in Díaz-Giménez e al. (1997) o a model where he firs 80 percen of he populaion (workers) are idenical. The resuling value is.46. We furher adjus his coefficien downwards in order o ge an esimae of he Gini coefficien for individual labor earnings. 28

29 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 mos of he differences in TFP and GDP growh beween our decenralized and cenrally planned economies. The lower ime spen by managers in producive aciviies reduces heir conribuion o he sock of managerial knowledge and, herefore, i reduces growh raes. Regarding differences in labor earnings inequaliy, 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 income across abiliy levels. Lorenz curves represening he disribuion of labor earnings are depiced in Figure 2. Income Gini coefficiens for a large number of counries are repored by Deininger and Squire (1996). 14 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 U.S.). Regarding magniudes, he Gini coefficiens in our simulaions are smaller han he ones repored by Deininger and Squire (1996). In he conex of our framework, his may be an indicaion ha he leadership of acual cenrally planned economies did no behave according o a compleely egaliarian welfare funcion. Noice also ha he capial-oupu raio is higher in he cenrally planned economy, as he planner supplemens he lower produciviy wih higher levels of capial. This resul is also consisen wih evidence from socialis economies. In his exercise we have parameerized he economy using US daa and assuming ha here is no redisribuion of earnings in he decenralized economy. In doing his we are 14 Díaz-Giménea e al. (1997) repor a high correlaion beween labor earnings and income, wih he disribuion of labor earnings being more unequal han he disribuion of income. 29

30 underesimaing he dispersion of he disribuion of abiliies, since redisribuion schemes reduce he Gini coefficien. 15 In he nex secion we address his issue by performing a sensiiviy analysis exercise on he shape parameer s of he Pareo disribuion, which deermines he dispersion of he disribuion Sensiiviy analysis The mos imporan free parameer in our parameerizaion exercise is he parameer μ ha appears in he law of moion of he sock of managerial knowledge λ and ha specifies he depreciaion of managerial knowledge: λ λ λ ( γ M a μ) = + 1 ( ). 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. 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. Given ha he decenralized economy is calibraed o mach U.S. rends, he values of hese variables will no change wih a change in μ, and are he same as in Table 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. In paricular, for slighly posiive values of μ long run TFP and GDP growh raes become negaive. Convergence o such growh raes is no susainable, which is a possible explanaion of he reason why cenrally planned regimes have been abandoned by mos counries. 15 We hank an anonymous referee for making his suggesion o us. 30

31 Anoher imporan parameer of he model is he shape parameer s, which deermines he dispersion of he disribuion of abiliies. A higher dispersion of abiliies makes redisribuion more imporan, since i increases he difference beween he abiliy hresholds in boh economies ( a and a ). In order o undersand he quaniaive effecs of his parameer, we reparameerize he model using a shape parameer of 1.2 and 1.1 (compared o he 1.35 used in he original parameerizaion), which imply Gini coefficiens on labor earnings of.49 and.79 respecively (40 and 125 percen higher han in he original parameerizaion). We obain ha he ime spen in lobbying changes o 60 and 51 percen respecively, wih he lobbying effec being responsible for 83 and 79 percen (respecively ) of he decrease in oupu. We observe ha hese numbers, even hough hey are smaller han he original ones, are sill in he 80 percen range. 5. Conclusion In his paper we presen a 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 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 leadership o he firms managers hrough a cones ha uses up some 31

32 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. Our model also predics ha he cenrally planned economies should have lower income inequaliy and slighly higher capial-oupu raios, boh feaures consisen wih he experiences of hese regimes. We also analyze he effec on economic performance of each of hese wo 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 enrepreneurial/managerial aciviy is essenial for long-run economic growh. By reducing enrepreneurial effor in heir counries and closing hemselves off o new ideas and echnologies developed in marke-oriened economies, cenrally planned economies seriously impaired heir abiliy o susain longrun growh, conribuing perhaps 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 of oupu 32

33 and TFP in he 1960s o increasingly lower growh raes in he 1970s and 1980s experienced by cenrally planned economies. Inefficiencies buil ino he sysem ha did no allow for he 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 no address he issue of ransiioning from one economic regime o he oher. This is he subjec of furher research. 33

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