The Persistence of Inferior Cultural-Institutional Conventions

Transcription

1 Amercan Economc Revew: Papers & Proceedngs 203, 03(3): 7 The Persstence of Inferor Cultural-Insttutonal Conventons By Maranna Belloc and Samuel Bowles* Economc nsttutons and cultures (ncludng socal norms) are often dynamcally complementary, meanng that the persstence of each s facltated by the presence of the other. The term feudal socety, for example, refers jontly to the economc relatonshp of lord and serf and to the norms of subordnaton and recprocty that both contrbuted to the smooth functonng of the system and that were ts cultural expresson. Ths complementarty provdes one mechansm for the long-term persstence of partcular confguratons of cultures and nsttutons. Gven the nsttutonal relatonshp of serf to lord (to contnue the example), adoptng the culturally prescrbed norms of subordnaton and recprocty was a best response for ndvduals n the two classes, respectvely. And gven ths culture of subordnaton and recprocty, conformng to the nsttutonal arrangements defnng serf and lord was also a best response. We refer to ths par of mutual best responses as a cultural-nsttutonal conventon. Otherwse smlar populatons wth dfferng recent hstores may exhbt dfferng conventons: free ctes coexstng wth feudal manors n Germany and elsewhere durng the thrteenth to ffteenth centures, for example. Hstorans and socal scentsts have long asked why some cultural-nsttutonal conventons appear ndependently multple tmes n human hstory and persst over long perods monogamy, markets, and prmogenture, for example whle others rarely emerge, and when they do tend to be short * Belloc: Sapenza Unversty of Rome, va del Castro Laurenzano 9, 006, Rome, Italy (e-mal: maranna. belloc@unroma.t); Bowles: Santa Fe Insttute, 399 Hyde Park Rd., Santa Fe, NM (e-mal: bowles@santafe. edu). Acknowledgments: Thanks to the Santa Fe Insttute Behavoral Scences program for support of ths work, and to Quamrul Ashraf, Roy Cerquet, Sung-Ha Hwang, Suresh Nadu, and Peyton Young for comments. An onlne Appendx provdes dervatons and proofs of the man results, and addtonal ctatons to the lterature. To vew addtonal materals, and author dsclosure statement(s),vst the artcle page at lved (Parsons 964). In reply, some economsts smply extend nvsble hand arguments to the selecton of nsttutons. Thus Olver Wllamson (985, p. 394) wrtes that vable modes of economc organzaton ordnarly possess an effcency advantage. The mechansms that would account for ths felctous result, however, have remaned elusve, and evdence of endurng nsttutonal falure s wdespread. Accounts of socally dysfunctonal but endurng cultural practces suggest that nvsble hand arguments work no better when appled to cultures (Edgerton 992). I. Why Do Inferor Cultures and Insttutons Endure? Gven that culture and nsttutons are often mplcated n explanng endurng poverty (e.g., Clark 2007; Acemoglu and Robnson 202) a pressng queston s: what accounts for the persstence of cultural-nsttutonal conventons that are nferor n the sense that almost everyone could be made better off under an alternatve set of techncally feasble confguratons? Cultural nerta s sometmes sad to be the result of the transmsson of learned behavors from parent to chld; but for plausble degrees of transmsson ths process alone would result not n persstence but n the dsspaton of cultural dfferences between populatons n a matter of just a few generatons (see onlne Appendx). Moreover, n lght of recent hstory, persstence cannot be an ntrnsc characterstc of ether culture or nsttutons. Examples nclude the precptous demse of such well defended nsttutons as Communst Party rule n many countres and of aparthed n South Afrca and the extraordnarly rapd spread or retreat of cultural practces such as female gental cuttng n parts of Afrca and the use of honorfc pronouns n many European languages. A more plausble answer proposed n a varety of models and documented wth hstorcal and contemporary examples s that a P ndd

2 2 AEA PAPERS AND PROCEEDINGS MAY 203 concentraton of poltcal power allows favored groups to command a larger slce by means of polces that result n a smaller pe (Sokoloff and Engerman 2000; Acemoglu 2003). The hypothess that Pareto-domnated allocatons are mplemented as part of a strategy of dstrbuton s readly motvated by problems of commtment. For example, an elte may resst movng to a Pareto-superor conventon because there s no way that noneltes can commt to not explotng the nstablty of that superor conventon n order to ntroduce a further transton under whch the elte would lose. But there s another way that nferor culturalnsttutonal conventons may persst ndefntely, one that reles on strategc complementarty rather than cultural transmsson across generatons or elte power. If ndvdual conformty to the status quo nsttutons and cultural norms s a mutual best response, and f ndvduals update ther behavors noncooperatvely, an nferor conventon can persst smply because t s evolutonarly stable by dnt of ts beng a mutual best response (Young 998). Ths bottom-up mechansm for cultural-nsttutonal persstence s complementary to the top-down models just mentoned. But the mechansms accountng for persstence are dametrcally opposte. In the top-down models, nsttutons persst because eltes are organzed and powerful enough to mplement allocatons that lmt the clams of others. In our bottom-up model, nferor cultural-nsttutonal conventons persst because nobody s organzed n that sense, and the actons of ndvduals n conformng to or devatng from the status quo nsttuton and cultural norm are entrely decentralzed. There are other ways n whch our approach s dstnct. Frst, we explctly model the nteractons of cultures and nsttutons and ther coevoluton rather than treatng nsttutonal or cultural dynamcs n solaton. Second, we consder large populatons wthout poltcal dfferentaton, so that no sngle actor (for example, an elte ) has any apprecable nfluence on outcomes. Thrd, both the persstence of cultural-nsttutonal conventons and transtons between them are captured n the same model, wthout the nterventon of exogenous changes. Fnally, n contrast to many of the classcal game theoretc treatments, our agents, whle strategc, have lmted cogntve capactes, updatng ther culture and nsttutons on the bass of past dstrbuton of nsttutonal and cultural trats n the populaton rather than foresght. Whether these dfferenta specfca of our model are taken to be features rather than bugs wll, of course, depend on the questons at hand. But we thnk that the resultng model provdes nsghts complementary to the top-down approach n the understandng of such durable nsttutons as land tenure, nhertance systems, and property rghts more generally, as well as employment contracts and martal practces. It also provdes mportant nsghts nto bottom-up cultural-nsttutonal tppng events resultng n rapd transtons. An example s the end of aparthed n South Afrca: ndvdual frms and trade unons were prvately workng out the terms of a nonracal order years before the rulng Natonal Party freed Nelson Mandela and conceded nonracal electons (Wood 2000). II. A Bottom-up Model of Cultural-Insttutonal Persstence and Innovaton We study the evolutonary dynamcs of culture and nsttutons n an economy wth two classes. These are large subpopulatons whose z members are pared randomly to nteract n a noncooperatve game governed by a set of nsttutons. The classes may be employees and employers, sharecroppng farmers and landlords, slaves and slave owners, ndependent farmers and government offcals, and so on. As these examples suggest, these class relatons are asymmetrc. The alternatve economc nsttutons governng relatons between the classes are one of two contracts, whch are mplemented by the members of the second class (whom we call the Bs) n each of the pars just mentoned. The frst class (the As) may adopt two alternatve socal norms. To represent the complementarty between cultures and nsttutons and the possblty of the persstence of nferor culturalnsttutonal conventons, we assume that some contract-norms matches are more productve than others and can be Pareto-ranked. For concreteness, thnk of a somewhat dealzed rendton of the nsttutonal structure and culture of two frms, Volkswagen and Fat (Jürgens 2002; Nut 20). In the former, an nsttutonal structure based on a works-councl and comanagement matches wth a work force wth norms of cooperaton wth management, resultng n hgh levels of productvty and, as P ndd 2

3 VOL. 03 NO. 3 the persstence of nferor cultural-nsttutonal conventons 3 0 π 00 π 0 = 0 π 0 = 0 0 ϕ * Fracton of members of class adoptng norm (or contract) a result, mutual gans. In the latter, a top-down management structure s matched wth an oppostonal workers culture resultng n reduced productvty. What s mportant for our model s not only that the dealzed Volkswagen match Pareto-domnates the Fat match, but that the two matches are best responses for owners and workers alke. Gven the oppostonal culture of Fat s workers, the owners would do even worse f they mplemented a comanagement structure; a mltant oppostonal culture would not beneft Volkswagen s workers; and so on. We ndex contracts and norms by j = 0, and classes by = A, B, and represent the payoffs to the four possble cultural-nsttutonal matches as π > π 00 > π 0 = π 0 = 0 for both classes, where, for example, π 0 s the payoff of an ndvdual n class mplementng contract (adoptng norm ) when hs partner from the other class adopts norm 0 (mplements contract 0), and payoffs are normalzed so that the two msmatches are zero. Expected payoffs for members of class mplementng contract j (or adoptng norm j) are gven by v j = ( ϕ ) π j 0 + ϕ π j, where ϕ denotes the fracton of ndvduals n the other class ( ) who mplemented contract (adopted norm ) n the prevous perod. Expected payoffs lnes are shown n Fgure. The state space for ths process (shown n Fgure 2) s all possble combnatons of the number of ndvduals n the two classes, respectvely, adoptng norm and mplementng contract, (z ϕ * A, z ϕ * B ). The two matches wth nonzero payoffs are Pareto-ranked Nash equlbra, and n the Markov process that 0 π Fgure. Expected Payoffs of Members of Class v v Bs mplementng contract {0, z} {z, z} zϕ * B {0, 0} represents ths model the states (denoted {0, 0} and {z, z}) n whch all members of both classes adopt one or the other of these two profles are absorbng when all ndvduals best respond. Followng matchng, members of each class have the opportunty to update ther contracts and norms. To ensure that the process s acyclc, we let the revson process be asynchronous (as n Bnmore, Samuelson, and Young 2003) wth all members of one class updatng frst, followed by updatng of the other class. When revsng ther contracts and norms, best respondng ndvduals maxmze ther expected payoffs based on the dstrbuton of, respectvely, norms and contracts n the sub-populaton wth whch they are matched n the prevous perod. But ndvduals are boundedly ratonal, and wth probablty σ > 0 they adopt the norms or nsttutons that are not the best response, wth s strctly decreasng n both the cost of devatng from the best response and the agents degree of ratonalty (defned below). Followng Blume (2003), the probablty of devatng from the best response when the populaton s at {0, 0} s: () σ ( Δ 0, β) = _, wth = A, B, + e β Δ 0 where Δ 0 2 = π 00 π 0 s the cost of devaton from the status quo culture or nsttuton at {0, 0}. We nterpret β as a measure of ratonalty 4 3 z ϕ * A As adoptng norm Fgure 2. State Space and Transtons {z, 0} P ndd 3

4 4 AEA PAPERS AND PROCEEDINGS MAY 203 because the larger s β, the smaller the probablty that the ndvdual wll devate from the best response. When β = 0 the agent randomzes between the two alternatves, and as β goes to nfnty, the ndvdual never devates. Of course, ndvduals may have noneconomc reasons to devate from the status quo even n the absence of cogntve falures; so, strctly speakng, β measures the degree to whch agents maxmze ther expected payoffs. For suffcently ratonal agents, once a populaton s n the neghborhood of ether of the two absorbng states, the assocated conventon may persst over very long perods. The reason s that, for suffcently large populatons and suffcently ratonal ndvduals, the expected watng tme for a realzaton of suffcent nonbest responses to tp the process from the neghborhood of one conventon to the basn of attracton of the other wll be very prolonged. Cultural-nsttutonal conventons are perpetuated n every perod; nerta s not nvolved, as ndvduals have just a sngle-perod memory. III. Impedments to Pareto-Improvng Cultural and Insttutonal Change To study transtons from the nferor {0, 0} to the superor {z, z} conventon, we frst determne the mnmum numbers of devant members of each class, such that wth suffcently ratonal agents, the populaton wll enter the basn of attracton of the superor conventon. The basn of attracton of a state s the set of states from whch, for the above dynamcs and suffcently ratonal agents, the revson process we have just descrbed leads to that state. For suffcently ratonal ndvduals, begnnng near the conventon {0, 0} the state followng updatng wll almost always le wthn quadrant n Fgure 2 and, because agents have just a one-perod memory, even an unlkely substantal excurson away from the conventon wll have no lastng effect. But suppose that, from the ntal state {0, 0}, z ϕ * B of the Bs devate from the status quo nsttuton and offer contract nstead of best respondng wth contract 0, where z ϕ * B s the smallest number such that the As best response s to swtch to norm and ϕ * B = Δ 0 A /( Δ 0 A + Δ A ). (See Fgure. Snce z s large we may avod notatonal clutter by abstractng from nteger consderatons.) In response, each A wll adopt norms wth probablty σ. But as β goes to nfnty σ goes to zero, so there exsts some fnte β such ˆ that for β > ˆ β, as a result of the As updatng, wth vrtual certanty we wll have z ϕ A z ϕ * A, where z ϕ * A s the smallest number such that the Bs best response s to swtch to contract ( wth ϕ * A = Δ 0 B / ( Δ 0 B B + Δ )). When ths occurs, the populaton wll be n the set of states for whch both classes best responses wll lead to {z, z}. Thus, the mnmum number of Bs mplementng contracts suffcent to escape from the nferor conventon s z ϕ * B. Analogous reasonng apples to the mnmum number of nnovatng A members, z ϕ * A, suffcent to nduce a transton to {z, z}. It follows that from the ntal state {0, 0}, the basn of attracton of the superor conventon s composed of quadrants 2, 3, and 4 n Fgure 2. Because devatons from the best response contract or socal norm are ndependent, expected watng tmes for a transton from one absorbng state to the other nduced by each of the classes, respectvely, are approxmated by the nverse of the probablty that n a gven perod the number of devants of that class wll be suffcent to enter the basn of attracton of the other conventon. For large populatons and suffcent ratonalty, ths probablty s approxmated by P, the lkelhood that exactly the mnmum number of nnovators n class (z ϕ * ) wll occur (Bnmore, Samuelson, and Young 2003). Our results are not affected by takng account of the probablty that larger than mnmal numbers devate: (2) P = ( z z ϕ * ) ( σ ) z ϕ * ( σ ) z z ϕ *, = A, B. Hence, the expected watng tme for a transton s the nverse of the probablty that the number of nnovators n at least one class wll be suffcent to tp the populaton to the basn of attracton of {z, z}, that s, (3) E[ W ] = ( P A + P B P A P B ). V. Dscusson Equatons (2) and (3) gve us four results applcable equally to ether of the two classes (proofs n the onlne Appendx). Frst, culture- or nsttuton-based techncal change may accelerate transtons by makng an alternatve conventon more productve relatve to the P ndd 4

5 VOL. 03 NO. 3 the persstence of nferor cultural-nsttutonal conventons 5 status quo. We fnd that for suffcently ratonal agents, because both of the crtcal fractons requred for a transton from {0, 0} to {z, z} ϕ * A and ϕ * B are decreasng n the productvty advantage of the superor conventon ( Δ ), the expected watng tme for a transton (E[ W ] gven by (3)) s decreasng n the superorty of the Pareto-domnant conventon. Our evolutonary dynamc thus favors superor cultural-nsttutonal confguratons. But, second, because devatons from the status quo are less lkely the greater s the degree of ndvdual ratonalty, the expected watng tme for a transton s ncreasng n β. Then, for suffcently ratonal agents, a cultural-nsttutonal conventon can last vrtually forever even f there exsts an alternatve Pareto-superor conventon. There s no nvsble hand for cultural-nsttutonal confguratons, at least not on hstorcally relevant tme scales. Thrd, the greater s the cost of devatng from the nferor culture or nsttuton ( Δ 0 ), the longer wll be the expected watng tme for a transton to the superor conventon. Ths unsurprsng result has a somewhat unexpected mplcaton (Belloc and Bowles 202): because the gans from trade ncrease the payoffs for the approprate contract-norm match at both cultural-nsttutonal nexuses, a shft from autarchy to free trade wll ncrease the costs of devatng and, hence, wll delay a transton away from the Pareto-nferor conventon. Trade lberalzaton, thus, does not favor cultural-nsttutonal convergence to superor confguratons. Fourth, because transtons requre extreme realzatons of the sum of devatons relatve to populaton sze, for suffcently ratonal ndvduals, the expected watng tme for a transton s ncreasng n the group sze (z). Extendng the model to allow the upper B class to be less numerous ( z A > z B ), most of the transtons wll be nduced by the nnovatons by members of the elte. But ths unsurprsng result hstory tends to be drven by the elte s unrelated to the fact that smaller groups may more readly coordnate ther actons n producng the publc good represented by a transton n whch ther members do better. The result occurs because the extreme realzaton of the number of nnovators requred to nduce a transton s more lkely the smaller s the populaton sze. From the above result t follows that, by relaxng the ultra-ndvdualsm of the model and allowng for collectve acton, the expected watng tme for a transton wll vary wth the degree to whch a socety s ndvdualst or collectvst n the terms of Gref (994). We use these terms to mean that n an ndvdualst socety the acton of one person does not affect the other ndvduals actons unless the acton alters the ncentves facng the others. For example, f one member of a famly devates from the status quo, ths has no effect on other famly members actons unless t changes ther expected payoffs. By contrast, n a collectvst socety ndvduals sometmes act n groups, such that f one brother devates all of the sblngs wll also devate. In a collectvst socety the effectve populaton sze s less than the census sze, and the expected watng tme for a transton s correspondngly reduced. To provde a smple llustraton, suppose n our model that employees (As) work n frms of sze n A and that all employees n a gven frm ether conform to the status quo (best respond), or they jontly devate. Effectve populaton sze n ths case s not z A but nstead z A / n A. Worker-nduced transtons wll be correspondngly accelerated. REFERENCES Acemoglu, Daron Why Not a Poltcal Coase Theorem? Socal Conflct, Commtment, and Poltcs. Journal of Comparatve Economcs 3 (4): Acemoglu, Daron, and James A. Robnson Why Natons Fal: The Orgns of Power, Prosperty, and Poverty. New York: Crown Busness. Belloc, Maranna, and Samuel Bowles Cultural-Insttutonal Persstence under Internatonal Trade and Factor Moblty. Unpublshed. Bnmore, Ken, Larry Samuelson, and Peyton Young Equlbrum Selecton n Barganng Models. Games and Economc Behavor 45 (2): Blume, Lawrence E How Nose Matters. Games and Economc Behavor 44 (2): Clark, Gregory A Farewell to Alms. Prnceton: Prnceton Unversty Press. Edgerton, Robert B Sck Socetes. New York: The Free Press. Gref, Avner Cultural Belefs and the Organzaton of Socety: A Hstorcal and P ndd 5

6 6 AEA PAPERS AND PROCEEDINGS MAY 203 Theoretcal Reflecton on Collectvst and Indvdualst Socetes. Journal of Poltcal Economy 02 (5): Jürgens, Ulrch Corporate Governance, Innovaton and Economc Performance. Berln: Socal Scence Research Center Berln (WBZ). Nut, D. Maro. 20. Industral Relatons at FIAT: Dr. Marchonne s Class War. Transfer: European Revew of Labour and Research 7 (2): Parsons, Talcott Evolutonary Unversals n Socety. Amercan Socologcal Revew 29 (3): Sokoloff, Kenneth L., and Stanley L. Engerman Insttutons, Factor Endowments, and Paths of Development n the New World. Journal of Economc Perspectves 4 (3): Wllamson, Olver 985. The Economc Insttutons of Captalsm: Frms, Markets, Relatonal Contractng. New York: Free Press. Wood, Elsabeth Jean Forgng Democracy from Below: Insurgent Transtons n South Afrca and El Salvador. Cambrdge: Cambrdge Unversty Press. Young, H. Peyton Indvdual Strategy and Socal Structure: An Evolutonary Theory of Insttutons. Prnceton: Prnceton Unversty Press. P ndd 6

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