Can Time and Markets Eliminate Costly Land Ownership Inequality?*

Transcription

1 Public Disclosure Auhorized Public Disclosure Auhorized Public Disclosure Auhorized Public Disclosure Auhorized Can Time and Markes Eliminae Cosly Land Ownership Inequaliy?* Michael R. Carer Universiy of Wisconsin-Madison USA and Frederic Zimmerman Universiy of Washingon USA April 2000 Paper prepared for he Annual Bank Conference on Developmen Economics April 2000 * This paper assembles and summarizes a number of he auhors wriings. As such, i is indebed o a long lis of individuals and insiuions who have suppored us over ime. Paricular hanks are due o he John D. and Caherine T. MacArhur Foundaion and o he IRIS research program a he Universiy of Maryland. An earlier version of his paper was presened o he conference on Asse Disribuion, Povery and Economic Growh, Brasilia, July 1998.

2 Can Time and Markes Eliminae Cosly Land Ownership Inequaliy? In no region of he world has land ownership inequaliy been sarker and more persisen han in Lain America. The Barraclough sudies of he 1960s (summarized in Barraclough 1967), exhausively documened his persisen saus quo. Wha Coles (1994) calls he land reform period of Lain American agriculural policy was inended as (or, more cynically, inended o appear as) a fronal assaul on wha was perceived as an economically, socially and poliically cosly inequaliy. Times of course change, and irrespecive of wheher we have winessed he deah of land reform as convenionally known (see Lipon, 1994 versus Lehman, 1978), here can be lile doub ha agriculural policy regimes across Lain America have shifed o a more open and liberal sance. New markes, echnologies and expors have accompanied his opening, and propery righs and land markes have in many cases been secured and de-regulaed in an effor o secure invesmen incenives and promoe efficiency-seeking ransacions even as fiscal auseriy has overseen he demise of public agriculural banks and exension services. The impac of hese changes on land ownership srucure (and on he old agrarian quesion abou he fae of he peasanry) has been ambiguous. An early opimism ha he fiscal exhausion of he inervenionis sae would generae less disored prices and open he space for he less well-off o paricipae direcly in he benefis of growh (see de Janvry and Sadoule 1993), has given way o a more sanguine view of he consrains ha limi he paricipaion of he peasanry in hese new economic opporuniies. Sudies of agro-expor booms in Chile, Guaemala and Paraguay (summarized in Carer, Barham and Mesbah, 1995 and Carer and Barham, 1996) idenify a pervasive effec of capial consrains on he paricipaion of he peasanry, leading eiher o wha in Chile has been called an exclusionary growh rajecory, or o growh ha is mued in is impacs on he income and wellbeing of he less well-off. Agains his backdrop of old quesions and new realiies, we urn in his paper o dynamic models of savings and asse accumulaion o see wha we know and can say a a heoreical level concerning he pos-liberalizaion persisence of economically cosly land ownership inequaliy. More specifically, we ask if ime and land asse markes are allies in he search for wha Birdsall e al. (forhcoming) call inequaliy-reducing growh sraegies. Geing he answer righ o his quesion is vial from a policy perspecive. In Mexico, Honduras, and Nicaragua, he answer would speak direcly o concerns abou he shor and medium erm disribuional consequences of recen reforms ha have liberalized land law and opened up he land marke in agrarian reform secors. In Brazil, Colombia and ha mos srucurally Lain American of African counries, Souh Africa, acive effors are underway o acively uilize he land marke as par of negoiaed or marke-assised land reform programs. In hese counries as well, a correc undersanding of ime and markes is vial o he success of hese programs. This paper s heoreical exploraion of ime, he marke and he agrarian quesion is organized ino hree secions. The firs pus forward a single period producion model ha highlighs he forces ha shape producion and land use decisions which are imporan par of he asse value of land, specifically he ineracions beween informaionally-consrained labor and capial markes. In order o capure he wealh heerogeneiy ha ress a he core of he agrarian

3 quesion, he model is analyzed over a wo-dimensional endowmen space ha highlighs wha migh be ermed (endogenous) class differences in he use and producive reurns o land. The paper s second secion hen presens Carer and Zimmerman s (forhcoming) analysis savings and asse accumulaion in an inegaliarian agrarian economy ha is buil upon he base of ha model. Their numerical analysis of he resuling dynamic, general equilibrium model finds ha indeed ime and markes seadily erode he laifundia secor in his model, despie he barriers ha confron land accumulaion by low wealh agens. However, convergence o a more egaliarian economy is boh slow and cosly in economic erms. Moreover, his convergence akes place in an economy which has been shorn of he risk ha many auhors (e.g., Braverman and Sigliz, 1989) have hypohesized blun he accumulaion of he peasanry. To gain insigh on his problem, Secion 3 hen presens resuls from Zimmerman and Carer s (1999) dynamic programming analysis of he impac of boh producion risk and endogenous asse price risk on consumpion smoohing and asse accumulaion decisions. Calibraed on he risky environmen of Wes Africa, his second dynamic analysis issues a srong cauionary noe abou he abiliy of ime and he marke o eliminae cosly asse inequaliy. Finally, secion 4 summarizes he paper s implicaions for research, policy and poliics. Secion 1 Producion and Accumulaion Incenives in a Single Period Model of an Inegaliarian Agrarian Economy This secion lays he groundwork for our exploraion of he persisence of inequaliy by laying ou a saic model ha capures imporan feaures of echnology and labor and capial markes ha have been hypohesized o shape he compeiiveness of differen classes of producers and he evoluion of Lain American agrarian srucure (e.g., see Sco, 1985). As a prelude o he laer dynamic analysis of he land accumulaion and srucural evoluion quesion, his secion also uses his saic framework o derive clues abou he impac of hese feaures on he accumulaion incenives of he differen economic classes implied by he model. 1.1 Producion and Class in an Inegaliarian Agrarian Economy Given endowmens of land (T), Labor (L 0 ), and money (M), we assume ha each agen aemps o maximize household income defined as: d s π { p Q - w L - F P f - 1[z + irb] } + { wφ( L )} + irs} (1) c { where he firs erm in curly brackes gives he ne-income from agriculural producion, he second erm gives labor marke earnings, and he hird gives reurns o money invesed in a bank over he producion cycle. Agriculural oupu is produced wih a simple Cobb-Douglas echnology, α α α Q = DF T L (2) 2

4 where F measures inpus purchased a a price P f, T is he land sock, and L is labor measured in qualiy-adjused, efficiency unis. Efficiency labor is produced according o he following echnology: h h d d d L = L + λ γ ( T, L ) L ] + [1 λ][ ν( L ) + γ L ] (3) [ 0 where L h is family labor devoed o home producion, L d is hours of hired labor and he endogenous indicaor variable λ akes he value of 1 if he household uses informal, family labor supervision and equals one if he agen formally supervises is labor force wih hired supervisors. The employmen funcion, φ(l s ) gives days employed as a funcion of days of labor supplied o s s s he off-farm job marke. We assume ha φ ( L ) L as L 0, and ha 0 < φ < 1 o capure he noion ha employmen becomes increasingly difficul o obain as increased desire o sell labor forces one o search for employmen in he slack season. Maximizaion of (1) is furher consrained by an ex ane working capial consrain: d s wl + Pf F + Pc R0 M S + wφ( L )+1[B - z] (4) which simply says ha he agen needs sufficien cash on hand o finance cash coss of producion plus family subsisence over he rainy season (P x R 0 ). 1 Working capial can be obained from money ha is no saved (M-S), from conemporaneous off-farm wage earnings, and from he ne proceeds of any loans aken ou by he household, l[b-z], where B is he gross loan amoun, z is a fixed ransacion cos and l is a indicaor aking he value of one if B is posiive. Finally, each agen faces a borrowing ceiling ied o he amoun of land owned, B βt, (5) and he following miscellaneous non-negaiviy resricions: h h d ( L 0 L L ), S, L, B 0 (6) The agens objecive is hus o maximize (1) subjec o (2)-(6) and we denoe he opimum value funcion corresponding o his problem as π * ( T, M ) o emphasize is dependence on endowmens. This income maximizaion problem gives prominence o he inrinsic (asymmeric informaion-based) capial and labor marke imperfecions ha have been exensively discussed in he conex of developing counry agriculure. The working capial consrain (3) makes he specificaion of he rules of access o capial of primary imporance. While some would argue ha because of asymmeric informaion, small farmers are compleely raioned ou of credi 1 Alhough his consumpion requiremen consrains farmers in heir use of money for producion, we have adoped he conservaive assumpion ha i does no bind on he ineremporal accumulaion problem: households can choose o spend up o heir full agriculural income acquiring land. In he numerical parameerizaion of his model, he wage is high enough so ha even a full ime wage worker can mee he subsisence requiremen. 3

5 markes (e.g., see Eswaran and Kowal, 1986 and Carer, 1988), we more conservaively assume ha all agens have equal access o credi a a given marke rae of ineres. Borrowers do, however, face a fixed ransacions cos, z, ha is associaed wih he cash and opporuniy coss of loan applicaion, invesigaion and approval. The fixiy of z makes small loans unaracive for all agens (rich or poor). Noe ha because of hese ransacions coss and he consequen relucance of some agens o borrow, he shadow price of he working capial consrain (3) which we denoe as µ will endogenously vary over he endowmen space even hough here is a paramerically given marke rae of ineres. The second feaure of he producion problem is ha oupu depends on inpus of labor effor, no jus labor ime. The non-conracabiliy of labor effor in spaially disperse, biologically based producion process has a long hisory in agriculural economics (e.g., see Brewser, 1950), and we follow Bowles (1985) in specifying labor exracion echnologies (2) ha ransform labor power or ime ino labor effor. Family labor may be used for supervision, bu consisen wih he findings of Frisvold (1994), he efficacy of family labor supervision diminishes as farm size grows and family labor becomes spread oo hinly over a large area. h Specifically we assume ha γ ( T, L ) < 1and ha γ T < 0. Because of he diminishing efficacy of informal, family labor supervision, larger farmers are hus likely o swich o hierarchical supervisory echnology, hereby releasing he farm-size consrain on labor exracion, bu adding significanly o labor coss (Bowles, 1985; Carer and Kalfayan, 1989). 2 Like hired labor supervised informally, hierarchically supervised hired labor is never more producive han family labor ( γ < 0 1) and we assume furher assume ha he supervisory coss, ν ( L d ), conains boh a fixed and a variable componen. As wih he shadow price of capial, he combined effecs of his labor marke specificaion is o make he effecive or shadow price of labor endogenous o he individual s choices and, ulimaely, heir endowmens. The end resul is an analogue o he Chayanovian world in which he opporuniy cos of labor is subjecively (or endogenously) deermined. While he more recen lieraure on household models has ends o characerize an endogenous shadow price of labor as reflecing a non-seperarabiliy beween consumpion and producion decisions (e.g., see Singh, Squire and Srauss, 1986), i resuls here, as in hose household models, from he fac ha labor markes are hin or oherwise imperfec. Maximizaion problem (1) admis a variey of soluion regimes, depending on which consrains bind a he opimum. The labor and capial marke imperfecions ha lie a he hear of he producion model creae he differeniaed shadow prices for capial and labor for each of hese regimes. Because hese marginal shadow prices guide variable inpu choice, hey shape he marginal income ha an agen would receive from an incremenal increases in eiher land or money endowmens. An agen wih access o effecively cheap labor and capial will obviously culivae an incremenal uni of land more inensively, and realize greaer income increases wih i, han would an agen wih correspondingly higher priced variable facors of producion. Oher 2 In addiion, agens wishing o hire ou heir labor mus pay a search cos in erms of ime ha is relaed o he amoun of ime hey wish o sell. Wihou his assumpion, he shadow price of labor would be consan for households ha do no hire in labor. Wih his assumpion, he shadow price of labor for non-labor hiring households increases wih farm size and decreases wih family size similar o a Chayanovian specificaion. 4

6 hings equal and leaving aside for he momen he sraegic complexiies of dynamically raional decisionmaking we migh expec he firs agen o be willing o pay more han he high cos second agen for he incremenal uni of land. There is, however, no easy way of unambiguously deermining which agens and classes have access o he cheapes facors of producion. The labor marke failures end o advanage agens wih low land endowmens. I is precisely his privileged access o cheap family labor ha led Chayanov and laer day advocaes of family labor farms, o posulae he long erm sabiliy of peasan farming. However, sanding agains his Chayanovian advanage are he fixed ransacions cos in he capial marke which end o increase he shadow price of capial for smaller scale producers. Such counervailing disadvanages seem o underlie he view of Panaik (1979) who dispues he noion ha peasan povery and weak labor marke opporuniies suffice o make small-scale producers for long erm expansion and survival. 1.2 Insighs from he producion model abou he economics of accumulaion in inegaliarian agrarian economies One way o explore hese counervailing marke failures and aggregae heir cross-cuing economic impacs is o examine he marginal ne presen producion value (NPPV) of land defined as: = 1 ρ = [ ( T, M )]/(1 + µ ( T, M )) (8) where = π * ( T, M ) T and he discoun rae, µ is he shadow price of he capial consrain given in expression (3) above. Noe ha his expression will no in general be independen of relaive facor prices and echnology, as hese wo hings effecively shape how cosly any paricular marke failure is. As wrien, expression (8) assumes ha prices and echnologies persis indefiniely ino he fuure. Using he numerical specificaion of he producion model deailed in Carer and Zimmerman (1998) and he prices from he final period of he dynamic simulaion o be discussed below, Figure 1 graphs expression (8) evaluaed over he same endowmen or sae space defined by he asse variables T and M. Reflecing he Chayanovian advanage of small scale producers, he ne presen producion value of land is very high for very small land endowmens regardless of he money endowmen. However, a land-poor agen wih lile financial wealh who ried o accumulae land would quickly run ino he rench ha cus across he NPPV surface. This rench corresponds o a band of capial-consrained classes. For agens in he rench, he shadow price of capial is exremely high (as hey neiher have he funds o self-finance producion, nor is i worh heir while o borrow given ransacions coss), and heir resuling facor inensiies and produciviies are low. Assuming a marke price above he level of he rench (which i is in he dynamic simulaion below), any agen raversing he rench hrough land accumulaion will no only have o sacrifice curren consumpion, hey will also have o sacrifice some fuure income as well given ha he land price will exceed he NPPV of he land obained. 5

7 Figure 1: Ne Presen Producion Value of Land This rench, and he ineracing marke imperfecions ha underlie i, hus sand as nonrivial barriers o land accumulaion by low wealh agens and o he eliminaion of economically cosly asse inequaliy. A bes sraegies o raverse he rench, or o circumnavigae i, may ake subsanial ime and sacrifice of consumpion. Wheher or no agens will find i worhwhile o underake such sacrifice requires proper specificaion of he dynamic choice problem o which we now urn. Secion 2 Time and he Persisence of Cosly Inequaliy in an Economy wihou Risk Is ime a powerful enough alley o permi low wealh agens o breakdown a cosly, inegaliarian land ownership srucure in he face of he ineracing muliple marke imperfecions? To gain insigh on his quesion, his secion uses he saic producion srucure deailed in he prior secion as he base for a dynamic model of accumulaion and srucural evoluion. The emerging lieraure on dynamic models of wealh disribuion has also begun o explore similar issues. Aghion and Bolon (1997), for example, develop a model in which a lucraive (bu risky) aciviy is available o hose who can finance he invesmen coss. Since he rich are more likely o have a larger porion of he cos of capial, hey are more likely o be able o borrow he remainder a a lower ineres rae. While he rich hus ge richer iniially, he cos of capial o he poor declines, and he disribuion of wealh can acually become more equal 6

8 over ime. 3 Banerjee and Newman (1991; 1993) presen models in which agens have a choice of occupaions, ranging from subsisence reniers o labor-hiring enrepreneurs. The choice each agen makes depends eiher on capial endowmens (Banerjee and Newman, 1993) or on willingness o bear risk (Banerjee and Newman, 1991). Because boh of hese facors are assumed o depend on inheriance, hese models creae an ineremporal link beween curren income and fuure producion ha ends o perpeuae inequaliy. Similarly, Galor and Zeira (1993) allow agens o inves in educaion, a lumpy invesmen wih a high reurn. Because of capial marke imperfecions, educaional invesmen depends on iniial wealh endowmen, and he curren wealh disribuion has an effec on boh fuure wealh disribuions and presen and fuure aggregae oupu. These models reveal ha a financial marke imperfecion can creae a link beween he srucure of he economy and is long erm performance, even when i is possible for agens o accumulae he asses for which here are imperfec markes. Several of he auhors sugges policy implicaions along he lines of asse-redisribuion or ax policy ha can improve economic performance, alhough he policy implicaions are no always clear. However, a major shorcoming of his lieraure is ha he accumulaion decisions of he agens (or lineage dynasies) are no ineremporally raional. In Banerjee and Newman (1991; 1993) agens bequess are governed no by he effec of he ransfer on children's uiliy, bu on a warm glow ha parens feel from giving. Parens may herefore over- or under-endow children relaive o wha heir accumulaion decisions would have been for hemselves had hey lived longer. Similarly, Pikey (1997) assumes ha bequess are a fixed fracion of income, while Aghion and Bolon (1997) don' allow accumulaion a all. Moreover, he models are no equipped o explore he poenially significan effecs of he changes in equilibrium prices. Ye as endowmens change and some facors become more or less scarce, he prices of hese and oher facors are bound o change in response. Full ineremporal raionaliy would require ha agens recognize and accoun for his endogenous evoluion in facor prices as hey make accumulaion decisions. 2.1 A Dynamic Programming Model of Land Accumulaion and he Agrarian Quesion In order o more fully explore he incenives o use ineremporal accumulaion o work around imperfec financial markes, Carer and Zimmerman (forhcoming) analyze he following infinie horizon problem: maxu s.. 0 ( c) = = 0 δ u( c P T, p) (9) c + ( M + 1 M ) + ( T + 1 T ) P T * π ( M, T, L 0 p ) ( ) 3 Pikey (1997) models a relaed scenario under which a high probabiliy of projec failure and scan aggregae working capial can rap he economy in a siuaion in which high iniial ineres raes raion ou a large proporion of he populaion and aggregae growh is oo low o ever build up sufficien capial o lower he ineres rae. 7

9 where c is consumpion in period, L 0 is he fixed family labor sock, he accumulable asses T (land), M (money) are he sae variables, P T is he (endogenous) asse price of land and p is he vecor of endogenous non-land facor prices. The erms c, P T and p represen sreams of hese variables ino he fuure. The prices are expeced fuure prices. In addiion o hese endogenous prices, here is one imporan difference beween (9) and he canonical Ramsey opimal savings problem. Whereas he righ hand side of he budge consrain for he Ramsey problem is linear and addiively separable in asses (e.g., i would be M + PT T + wl 0 in he curren 3 asse model), here he reurns o any paricular asse combinaion are given by he generally non-linear and * non-separable value funcion, π ( M, T, L0 p ) ha is defined by opimal resource allocaion in he face of imperfec capial and labor markes. The heoreical challenge is hus o merge a non-separable income generaion-process wih a model of ineremporal decision-making ha is fully faihful o he raionaliy of agen behavior and expecaions. The approach o be aken here is similar o a muli-period CGE model excep ha asse accumulaion is ineremporally raional a he household level and all agens hold raional expecaions abou fuure price rajecories. Because we model producion decisions o be separable from consumpion and accumulaion decisions, we can spli each ime period or year ino wo seasons: A producion season in which shor erm variable facors are allocaed o producion; and, a pos-producion consumpion and accumulaion season. A he beginning of each producion season, agens have predeermined (bu ulimaely endogenous) endowmens of land and money. They maximize profis hrough borrowing, labor allocaion and variable inpu ( ferilizer ) decisions. In so doing, hey deermine aggregae demand and supply for facors and goods. Following a sandard Walrasian âonnemen process, he producion season model ieraes on he model s endogenous facor prices (for labor and ferilizer) unil agens choices are muually consisen in he sense ha supply equals demand in inpu markes. Producion occurs, compleing he producion season. Once incomes have been realized, agens make consumpion and accumulaion decisions according o opimizaion problem (9). Choices in his season depend on boh he curren land price and on he sequence of fuure prices for land and he variable facors of producion. Iniially agens are given a se of arbirary (bu reasonable) expecaions for he fuure price sequences. Condiional on hose fuure price expecaions, a pos-harves season âonnemen process is used o adjus conemporaneous land price so ha he land marke clears in every period based on he ne demands for land defined by he soluion o (9). Once ha markeclearing price is found, consumpion and accumulaion decisions are made and agens holdings of land and money holdings are updaed accordingly. The economy hen eners a new producion period. Repeiion of his process for n periods creaes an n-period hisory ha is condiional on he iniial expecaions abou he fuure price sequences. 4 4 Noe however ha he marke clearing prices ha emerge each period over he course of he n-period hisory may no correspond wih he prices ha were expeced for ha period according o he iniial expecaions used o generae he sequence. I is par of he compuaional challenge and he mehodological conribuion of his paper o assure ha hey do. To implemen fully dynamically raional behavior and expecaions, he full n-period hisory is hen iself ieraed. The sequence of equilibrium asse and facor prices ha emerged in he firs ieraion of he n- period hisory is used as he base for he price expecaions for he second ieraion. More generally, hisory k begins wih price expecaions buil around he sequence of equilibrium prices generaed by hisory k-1. This ieraive 8

10 Corresponding o he infinie-horizon problem (1) is he rue value funcion, * J ( T, M ) = { T max + 1, M + 1 { u( c ) + } * δ J ( T + 1, M + 1 )} (10) which expresses direcly he radeoffs beween curren consumpion and he value of accumulaing he sae variables, land and money. Undersanding how he value of J * (T,M) changes over is domain helps in undersanding he srucural evoluion generaed by he model's muliple marke imperfecions. Like he ne presen producion value (NPPV) measure (8) examined in he previous secion, he rue value funcion is defined over he endowmen or sae space. Bu whereas he NPPV measure capures he value of accumulaing land a he margin and holding jus ha incremen forever, he rue dynamic value of accumulaing land supplemens he valuaion of his direc benefi flow wih he sraegic value of land: having more land makes i easier o acquire ye more land. When reurns o land are consan his disincion is unimpressive. However, in a model of muliple marke imperfecions, in which he NPPV of land is highly non-linear as in Figure 1, his sraegic componen of he dynamic value funcion can be imporan. Agens may highly value land whose marginal NPPV is low because i pus hem closer o a land-holding size where accessing capial markes become feasible and high marginal reurns climb sharply. Because of he muliple non-lineariies of his model, he value funcion is complex. If here were no capial marke imperfecions in he model, hen he holding of money socks would no impinge on producion decisions, and he value funcion would be addiively separable in is argumens: J(T,M) = J 1 (T) + J 2 (M). Furher, if here were no labor marke imperfecions, hen he firs derivaive of J 1 wih respec o T would be coninuous and monoonic. These modificaions would conver he problem ino an analogue o he classical Ramsey problem discussed in Secion 2 and would lead o an analyically racable value funcion. Accumulaion rajecories for all agen would become sraighforward. However, under he specified marke imperfecions, he value funcion is analyically inracable, and numerical mehods are necessary o characerize i (see Carer and Zimmerman, forhcoming for compuaional deails) Dynamic Class Sraegies and he Erosion of Land Ownership Inequaliy In order o explore he dynamics of asse inequaliy, we chose echnology and asse disribuions parameers inended o represen he inegaliarian economies of Lain America. Sensiiviy esing was underaken o insure ha he resuls obained were no an arifac of he paricular numerical values ha were chosen. The model was run for 50 periods, creaing a 50 year, dynamic general equilibrium hisory for his economy. The successive soluions oward a raional expecaions equilibrium in prices converged in 5 ieraions of he 50 year hisory. In he final ieraion, he mean absolue deviaion of prices from expecaions was 0.005%. Over he process coninues unil a hisory is reached whose sequence of endogenously realized land and facor prices is arbirarily close o he expecaions upon which he hisory was condiioned. This ieraive approach o raional expecaions is similar o he approach in Imrohoroglu, Imrohoroglu and Joines (1993). 9

11 course of he hisory, he equilibrium wage and ferilizer price increase in he firs 25 periods, wih he ferilizer price sabilizing and he wage dropping off slighly hereafer. The general increase in hese facor prices can be aribued o he more efficien use of labor and ferilizer as land is redisribued by he marke. The wage ebbs somewha laer in he model as more of he large farms ener less labor-inensive forms of producion. As would be expeced in a dynamic model he price of land an asse ha can be coslessly sored across periods is relaively sable over ime a abou 7000 unis of money per manzana. As Carer and Zimmerman (forhcoming) show, a class map can be derived ha idenifies hose regions of he endowmen space ha correspond o each of he possible soluion regimes for he producion period problem (1). An analogue mapping from iniial endowmens o behavior exiss for he dynamic rajecories of accumulaion and consumpion. Figure 2 porrays his dynamic class map. Each arrow summarizes he accumulaion hisory for a paricular agen, wih he beginning poin of he arrow fixed a he agen s iniial endowmen posiion, and he endpoin signifying he agen s porfolio holding of land and money in year 50. Arrows are shown only for a subse of agens in he model and have been seleced o capure he full range of he endowmen space from which agens are pulled ono similar accumulaion rajecories. Class I, he Laifundisas, are eniced by he favorable marke price for land o sell off large quaniies of land over he 5 decades of simulaed hisory, boosing boh heir consumpion and money holdings along he way. Class II is comprised of a class of persisen capialized family farmers. Over ime, hey modesly adjus heir land holdings and build-up sufficien funds o inernally finance he producion process. The hird and final dynamic class is comprised of agens who were eiher iniially asseless, or whose land holdings were below abou 11 manzanas. Over 5 decades of simulaed hisory hese agens move ofen dramaically so oward he asse levels of he persisen capialis family farmers. The specific, year-by-year rajecory of he land and money accumulaion is more complex han Figure 2 shows, however. Agens in his group confron he brun of he labor and capial marke imperfecions. Dependen on he labor marke for a large porion of heir livelihood, and wih capial needs oo small o make i worh heir while o pay he fixed coss associaed wih borrowing, hese agens mus devise a way o expand heir holdings, while mainaining some minimal level of self-finance for he producion hey do have, while no sacrificing oo much of curren consumpion. These Class III agens slowly accumulae land over he firs several years, drawing down any iniial money endowmen o aid in land purchase and defense of heir consumpion sandard. Sill selling a large porion of heir labor ime on he marke, hese agens use heir wage earnings in par o mee he up-fron coss of producion. 10

12 Figure 2: Dynamic Class Map of Accumulaion Regimes 10 5 Money (log scale) Regime III Regime I Regime II Land (log scale) Afer he firs few years of land accumulaion, hese agens arrive a farms sizes beyond which hey can no longer self-finance producion. By year 15 of he simulaion, mos of hese agens are capial-consrained. Because of heir undercapialized producion processes, he ne presen producion value of land (equaion 8 above) o hese agens falls drasically. In erms of Figure 1 above, hese agens find hemselves in he rench ha cus across asse space. Despie facing land prices well in excess of heir marginal ne presen producion value of land, Group III agens coninue o accumulae land, hough hey move ono a balanced accumulaion rajecory in which hey acquire boh land and money. Sill by he end of he simulaion, nearly half of Class III agens remain capial consrained, hough moderaely so, as hey work heir way ou of he rench. The oher half of he Class III agens have, by hisory s end, reached an economic posiion where hey can self-finance a producion process which equaes he shadow price of he capial consrain o he marke rae of ineres. In addiion o is social imporance o be discussed below, he (dynamically raional) behavior of Class III farmers illusraes he value-added of he dynamic modeling sraegy developed here. The saic, ne presen value of land measure (equaion 8 and Figure 1) would indicae ha agens would sop shor of accumulaion decisions ha moved hem ino he rench in he ne-presen-value of land surface. The fac ha hey do move ino and slowly across he rench in he dynamic programming problem indicaes ha in an environmen of muliple marke imperfecions, asse accumulaion has no only an immediae income value, bu also has a longer erm sraegic value as i moves he agen oward a porfolio mix and scale which will permi him or her o circumven marke imperfecions. Alhough his evoluion is of course raional on he 11

13 par of he accumulaing household, i may mean a loss o sociey as he household s producion becomes emporarily consrained by a shorage of imporan facors. 2.3 Coss and persisence of asse inequaliy As seen in Figure 2 above, over he 50 years of simulaed agrarian hisory here is a srong endency oward an egaliarian land disribuion as all agens converge oward a single holding size, irrespecive of heir iniial endowmen. Figure 3 graphs a single, summary inequaliy measure he raio of he land of he op 20% o ha of he boom 40% over he simulaion period. As can be seen, land inequaliy by his measure has nearly evaporaed by he final year, declining from 230 o 1.0. This finding suggess ha ime and iner-emporal choice suffice o dampen he endowmen sensiiviy in an agrarian economy wih he sors of muliple marke imperfecions highlighed in he agrarian insiuions lieraure. Lef o is own devices, he marke redresses inequaliies in he land disribuion, even in he presence of muliple facor marke imperfecions which, as discussed earlier, place significan barriers in he way of land accumulaion by low wealh agens. Figure 3: The Dynamic Cos and Persisence of Asse Inequaliy Index of Oupu Inequaliy (righ scale) Oupu (lef scale) Raio of Landholding of Top 20% o Boom 40% Time 12

14 This marke-driven redisribuion is no wihou a cos, however. Oupu is considerably lower in he earlier periods han i would be under an egaliarian land disribuion. The oupu index, also shown in Figure 3, rises seadily over ime as he land disribuion slowly becomes more equal. By he end of he simulaion, he more egaliarian economy produces nearly 50% more oupu off he same aggregae land-labor endowmen. The presen value of he cumulaive oupu cos of inequaliy over he 50 years is 2 ½ imes he oal oupu of he firs period. A governmen-led redisribuion early on would herefore generae a considerable social surplus. Such findings provide an imporan numerical calibraion of he heoreical observaions of Bardhan, Bowles and Ginis (1998) and ohers, who argue ha equiy and efficiency need no be subsiues in social policy. Secion 3 Time and he Persisence of Cosly Inequaliy under Risk and Subsisence Consrains The resuls in he prior secion sugges ha he ime is indeed an ally of equaliy as agens over ime are able o circumven he saic accumulaion barriers creaed by muliple marke failures and he economy moves oward greaer land ownership equaliy. However, he process is slow and he magniude of he accumulaed coss suggess ha well-designed redisribuive policies could poenially dominae he laissez faire operaion of he asse marke. Moreover, i should be noed ha hese resuls are, if anyhing, biased in favor of he dynamic efficiency of asse markes. The model boh ignores ransacions coss in he land marke and, more significanly, he impac of risk on desired porfolio mix ha less well-off agens migh desire o hold. The model also ignores subsisence consrains and hence he feasibiliy of he consumpion rajecories employed by iniially low wealh agens. As Carer and Zimmerman (forhcoming) repor, in he early periods of heir dynamic simulaion models, low wealh agens are saving and invesing nearly a hird of heir oal income, implying low raes of consumpion. To gain purchase on he ime, markes and asse inequaliy under risk and subsisence consrains, we urn o he dynamic sochasic programming analysis presened in Zimmerman and Carer (1999). 3.1 A Dynamic Model of Consumpion Smoohing and Asse Accumulaion Each household i in a village economy enjoys specific iniial asse endowmens of land, T i0, and grain, M i0. Following he realizaion of is income, he household mus in each period choose a level of consumpion, as well as accruals o is asse socks. Over ime, hese choices generae an infinie vecor of he choice variable consumpion, saring in period 0 (denoed c i0 ), and infinie vecors of he sae variables, saring in period 1 (T i1, M i1 ), wih T i0 and M i0 given as he iniial endowmens. Household decision-making is assumed o be ineremporally raional in he sense ha hese vecors are chosen o solve he following dynamic choice problem: 13

15 max E0 { ci0, T i1, M 1} = 1 δ u( ci ) Ω0 (11) where Ω 0 represens he household s informaion se a ime 0, including full informaion over he disribuion of producion shocks, and he join disribuion of hese shocks wih he endogenous land asse price. Household uiliy for he -h period is given by he following uiliy funcion: (c i /R) ε if c i R and c is R For all s {1,2,...-1} ε < 1 u(c i ) = (12) 0, oherwise Noe ha as specified, if consumpion in any period falls below a subsisence minimum, R, he household suffers an irreversible loss of producive capaciy ha permanenly reduces is capaciy for fuure uiliy. This formulaion follows Rosenzweig and Wolpin (1993), and is a simplificaion of he discussion of his issue found in Dasgupa (1993). 5 Household income in period is given by: F(T i, M i, θ i,θ v ) = θ i θ v D (T i ) σ + µm i (13) Where µ is he rae of reurn on grain socks, θ i and θ v are idiosyncraic and covariae producion shocks; D is a land produciviy parameer, and σ is an oupu elasiciy parameer. To capure in a simple way he classic Chayanovian noion ha households wih lesser land endowmens end o culivae heir land more inensively because of imperfecly markeable family labor, we assume ha his oupu elasiciy is less han uniy. Given ha land is economically scarce, his assumpion of diminishing reurns o land (holding family labor fixed) generaes a srucural specific asse scarciy and creaes incenives for land ransfers beween households wih greaer and less land endowmens. Noe ha by adding covariae shocks and boh producive and non-producive asses, (13) generalizes Deaon s (1991) model (where in our noaion income is generaed according o θ i + µm i ), and Rosenzweig and Wolpin s (1993) model (where income is generaed according o θ i D (T i ) σ ). 6 5 One can imagine a subler relaionship beween consumpion (or nuriion) and produciviy. A household who is facing a subsisence shorfall in year 1, would, for example, have diminished labor capaciy in year 2. However, if he household s asses were such ha in year 1 i fell ino a subsisence shorfall, hen in year 2, wih lower labor capaciy, i would be in even greaer danger of facing a subsisence shorfall. Is labor capaciy would be hen even lower ye in year 3. In his fashion he household would be almos sure o lose is enire labor endowmen over a period of several years. The formulaion adoped here is herefore a simplificaion of his process, and a no unreasonable one in he conex of he dynamic nuriion-produciviy lieraure. 6 In pracice, many asses beside land and grain are available, including livesock, cash, equipmen, labor power, and human capial. Land and grain are chosen because hey are a he exremes of he disribuion in erms of fungibiliy, riskiness of yield and produciviy. The rae of reurn on grain in his model is assumed o be zero, wih cerainy. In pracice, grain sorage is subjec o losses due o pess or hef ha make he reurn on sored grain negaive and variable, bu our assumpion of a sable, zero reurn on grain is moivaed by he abiliy of households o sore cash as well as grain. 14

16 The household s consumpion and asse accumulaion choices each period are hus consrained by he following budge consrain: c F(T i, M i,θ i,θ v ) - P T (T i+1 - T i ) - (M i+1 - M i ) (14) and non-negaiviy resricions (borrowing consrains) where P T is he endogenous land price ha adjuss o clear he village marke in every period. Noe ha as described above, he wo asses, T and M, are disinguished boh by wheher heir reurns are sochasic, and by wheher hey are subjec o price risk in heir conversion o consumable goods. Expression (14) also reflecs an assumpion of auarchic consumpion smoohing (i.e., agens do no have recourse o insurance nor o durable cusomary social srucure ha enforces cusomary reciprociy arrangemens). In order o endogenize asse prices (and he covariance of asse prices wih producion shocks) and fully analyze he dynamic problem defined by (10)-(14), Zimmerman and Carer (1999) urn o numerical dynamic programming mehods. For he purposes of numerical soluion, a sylized village of 100 households was creaed, wihin which he producive-asse (land) marke clears endogenously, generaing a land price. Each household is endowed wih land and grain a he beginning of he simulaion according o empirically observed asse disribuions in Burkina Faso. Each period of he simulaion is characerized by a producion cycle in which households realized producion according o (13) and an asse-adjusmen and consumpion cycle in which households solved he opimizaion problem (10) by allocaing available resources o consumpion and o land and grain accumulaion or deaccumulaion. This simulaion was repeaed for 35 periods, hereby creaing a ime series of endogenous prices. Agens in he model are endowed wih raional beliefs, meaning ha hey correcly know he mean and firs momens of he disribuions of he sochasic variables. As in he Carer and Zimmerman work described above, raional beliefs were achieved in he model by an ieraive mehod. We urn now o consider heir main resuls. 3.2 Consumpion, Income and Asse Smoohing under Opimal Porfolio Managemen Saring from an iniial disribuion of agens across he wo dimensional asse space, numerical analysis of he model developed in he prior secion reveals ha each agen graviaes owards one of hree ypes of porfolio sraegies. Each sraegy is characerized by a paern of shor-erm asse managemen ha is followed in he wake of realized shocks, and by a long run equilibrium porfolio posiion: i.e., a grain-land combinaion o which he household reurns following shor erm adjusmens o shocks. The firs of he porfolio sraegies is simply he collapse o a zero wealh posiion, subsisence crisis and he suffering of he permanen uiliy loss described above. 7 The second is a defensive porfolio sraegy characerized by conservaive, relaively low-yielding long-run equilibrium porfolio (i.e., income smoohing) and a paern of shor-erm asse managemen ha we will call asse smoohing or asse proecion. The hird is an enrepreneurial sraegy characerized by a relaively high yielding porfolio and a more convenional paern of liquidaing asses o buffer shocks and smooh consumpion. 7 The origin is an absorbing sae because a his poin agens have no income o allocae o asse invesmen. 15

17 As analyzed in deail by Zimmerman and Carer (1999), he defensive porfolio sraegy is characerized by boh a much lower porfolio value han he enrepreneurial sraegy and by a less producive porfolio composiion. Alhough he maximum aainable expeced reurn is higher for lower wealh agens, 8 he expeced rae of reurn for he poorer agens who pursue he defensive sraegy (5.3%) is acually lower han ha for he wealhier agens who pursue he enrepreneurial sraegy (5.9%). Indeed, he lower wealh households who opimally follow he defensive sraegy pay an 18% premium (in erms of foregone rae of reurn on wealh), a figure ha dwarfs he 0.4% premium paid by wealhier households. This 18% premium is a sark indicaor of poorer households willingness o pay for insurance, and is in line wih empirical sudies ha have ried o measure he insurance premia implici in he behavior of low wealh agrarian households. 9 While income and consumpion are smooher for he poor who pursue he defenisve sraegy han for he rich, as measured by he sandard deviaion of he realized annual levels, income for he poor is very much smooher (he sandard deviaion of income for he poor is abou one-sixh ha of he rich), consumpion for he poor is only somewha smooher (he sandard deviaion of consumpion for he poor is abou one-half ha of he rich). Indeed, he coefficien of variaion of consumpion reveals ha afer adjusing for average consumpion levels, he poor have more variable consumpion sreams han he rich, even hough heir income sreams are more sable by he coefficien of variaion of income measure. These resuls reveal ha he poor are using consumpion o buffer asses in he wake of shocks no he oher way around. These resuls go agains he common percepion ha agens wih concave uiliy would wan o smooh consumpion o he greaes exen possible. In his dynamic model, given he hrea o fuure labor produciviy posed by leing consumpion fall below subsisence, he poor do no smooh consumpion as much as possible, bu raher vary consumpion o mainain asses. Agens who pursue his defensive sraegy experience coefficiens of variaion of 0.7% and 1.3% in heir socks of land and grain, respecively, while he coefficien of variaion of consumpion is 13.5%. By conras, for he wealhier agens away from he subsisence hrea, he coefficiens of variaion in asse socks are roughly 10 and 50 imes higher han for poorer agens, while he coefficien of variaion of consumpion is of comparable magniude. Graphically, his poin is brough ou in Figures 3 and 4, where he disincive buffering sraegies ha characerize he wo sraegies come ou clearly. The wealhier agens have boh greaer asse movemens as well as more symmerical ones: poorer agens allow grain socks o vary slighly, bu here is no visible movemen in land socks over he enire 250-period simulaion. 8 This maximum rae of reurn is wha a risk neural agen would aain by holding a porfolio comprised enirely of land in he case of low wealh agens. 9 For example, empirical resuls from von Braun, e al. (1989) sugges ha he conservaive adopion of risky, nonradiional expor crops by small-scale Guaemalan vegeable producers coss hese producers as much as 75% of income. Rosenzweig and Binswanger (1993), who find ha he poor forego more poenial income due o a safer invesmen sraegy han do he rich. Moreover, he order of magniude of he loss o he poor is he same. 16

18 Income and Consumpion Under Opimal Sable Sraegies Enrepreneurial 6000 Income and Consumpion (Log Scale) Consumpion Income Defensive Time Figure 3: Income and Consumpion under Opimal Porfolios 9000 Asse Movemens around Seady-Sae Porfolios over 250 periods error bars a sandard deviaions Grain Land Figure 4: Asse Movemens around Seady-Sae Porfolios The failure of he poor o smooh consumpion may seem a firs couner-inuiive, especially in he conex of a risk-managemen lieraure ha ofen describes iself as a consumpion-smoohing lieraure. Consumpion smoohing is of course only one possible implicaion of dynamic uiliy maximizaion under risk as shown by his model and by he nuriional findings cied by Drèze and Sen (1989) ha...he reducion of food consumpion 17

19 ends o be an early response o he hrea of enilemen failure, apparenly moivaed, a leas parly, by he preservaion of producive asses. Such findings suggess ha lieraure's emphasis on consumpion-smoohing, as opposed o asse-proecion, migh no be capuring he full dynamic sory of risk managemen especially for poor agens. In he conex of he model developed here, i is worh sressing ha he low wealh, defensive porfolio emerges as a sable sraegy despie he fac ha individuals in low wealh posiions expec higher reurns from he accumulaion of addiional unis of producive land a he margin. Despie heir seeming echnologically-based compeiive advanage in he land marke, here are wo economic forces ha lead hese individuals cling o a conservaive, graininensive porfolio. The firs is simply ha shifing wealh from land o grain serves o smooh income, since he reurns o land are subjec o yield risk. The second reasons resuls from a more suble inerplay beween covarian risk, endogenous asse prices and subsisence consrains. As deailed above, he defensive porfolio sraegy is disinguished from he enrepreneurial sraegy no only by is ex ane porfolio composiion, bu also by is disincive paern of ex pos behavior in he wake of realized shocks. 10 While income-smoohing moives migh explain he firs, i canno accoun for he second. If here were no asse price risk (i.e., no chance ha he price of land relaive o consumable foodsuffs would deeriorae), poor and rich agens would be equally inclined o use he producive asse as a buffer, since here would be no reason o buffer wih an unproducive asse, and he poor would accumulae asses o he level of he rich. If asse price risk did exis bu were no endogenous, hen for low levels of exogenous asse price risk, holding he producive asse as a buffer would dominae he unproducive asse for all agens. For high levels of exogenous asse price risk, he unproducive asse would dominae for all agens. In eiher case agens would migrae from one sable opimal sraegy o he oher. Only for some range of asse price risk in beween would here be muliple equilibria. Endogenizing asse price risk as in his model assures no only ha he asse price risk is realisic, bu also allows for he asse price risk o be endogenously placed in ha inermediae range ha drives he muliple sable equilibria. To see why he endogenous price risk enails he muliple sable equilibria, i is useful o hink of he asse-price-risk wedge beween he producive and non-producive asse as reflecing he value of asse-based insurance. As wih any kind of insurance, his one is in shor supply: if everyone ries o buffer consumpion agains covarian income shocks wih ransacions in he producive asse marke, hen covariance beween land price and producion would climb, and he producive asse loses is value as a buffer. Land, in oher words, can only be effecively used by some subse of agens o smooh consumpion. This insurance mus herefore be raioned, and he raioning mechanism is quaniaive i is he degree of covarian price variaion of he producive asse. Since richer people are farher from a subsisence crisis, hey are more willing bear some degree of asse price risk, and so hey are beer able o afford his form of insurance, and are more likely o buffer consumpion wih producive asses. 10 Such resuls underscore he poin made by Eswaran and Kowal (1990) ha credi-consrained households are more likely o pursue safer, less producive porfolios han non-credi-consrained households. 18

20 This model hus accouns for he emergence and sabiliy of a low wealh defensive porfolio sraegy in erms of covarian risk, endogenous asse prices and subsisence consrains. While oher explanaions of such behavior have been advanced, hey are no as general or as complee in heir endogenizaion of he elemens of he explanaions. For example, Morduch (1994, 1995) has suggesed ha a defensive porfolio sraegy could derive from he poor having worse access o consumpion insurance han do he rich. If such sraified access o insurance does exis, hen i would end o reinforce he resuls presened here. Moreover, differenial access o formal or informal insurance is predicaed on heir ownership of asses, which, as expressed here, arises ou of a dynamically endogenous accumulaion process. 3.3 The Micawber Threshold and he Reproducion of Inequaliy Our reliance upon numerical dynamic programming mehods permis us o no only idenify asse posiions and sraegies ha are locally sable (as, say, Ray and Sreufer, 1992 do), bu also o show ha hey each draw in agens from meaningfully large porions of he asse space. Figure 5 shows he acual accumulaion rajecories of agens over he course of he enire simulaion. As can be seen, he rajecories of all of he agens can be grouped ino hree classes of movemens. Firs, agens in he lower lef porion of he asse space sock ou over he course of he simulaion. Noe ha even agens who begin he simulaion wih lile land bu wih grain socks several imes he subsisence minimum evenually draw hem down and sock ou Grain Land Figure 5: Evoluion of Individual Porfolios 19