Land Trade and Development: A Market Design Approach

Transcription

1 July 2017 Land Trade and Development: A Market Desgn Approach Gharad Bryan, Jonathan de Qudt, Tom Wlkenng, Ntn Yadav

2 Impressum: CESfo Workng Papers ISSN (electronc verson) Publsher and dstrbutor: Munch Socety for the Promoton of Economc Research CESfo GmbH The nternatonal platform of Ludwgs Maxmlans Unversty s Center for Economc Studes and the fo Insttute Poschngerstr. 5, Munch, Germany Telephone +49 (0) , Telefax +49 (0) , emal offce@cesfo.de Edtors: Clemens Fuest, Olver Falck, Jasmn Gröschl group.org/wp An electronc verson of the paper may be downloaded from the SSRN webste: from the RePEc webste: from the CESfo webste: group.org/wp

3 CESfo Workng Paper No Category 9: Resource and Envronment Economcs Land Trade and Development: A Market Desgn Approach Abstract Small farms and fragmented plots are hallmarks of agrculture n less-developed countres, and there s evdence of hgh returns to land consoldaton and reallocaton. Complementartes, holdout and asymmetrc nformaton mean that prvate trade wll be slow to reallocate land, and mply that market desgn has the potental to contrbute to the development process. Complexty concerns are, however, paramount. We present results from a framed feld experment wth Kenyan farmers, comparng the performance of several contnuous-tme land exchanges. Farmers are able to acheve hgh degrees of effcency, and to comprehend and gan from a relatvely complcated package exchange. JEL-Codes: D470, C930, O130, Q150. Keywords: market desgn, feld experments, economc development, land trade. Gharad Bryan Department of Economcs London School of Economcs London / Unted Kngdom G.T.Bryan@lse.ac.uk Tom Wlkenng Department of Economcs Unversty of Melbourne Australa Vctora, 3010 tom.wlkenng@unmelb.edu.au Jonathan de Qudt Insttute for Internatonal Economc Studes (IIES), Stockholm Unversty Stockholm / Sweden jonathan.dequdt@es.su.se Ntn Yadav Bran, Mnd and Markets Laboratory Unversty of Melbourne Australa Vctora, 3010 ntn.yadav@rmt.edu.au July 4, 2017 We thank Abhjeet Anand for hs help n programmng the expermental nterfaces. We thank Jacob K. Goeree and Luke Lndsay for useful comments and thank Charles R. Plott for early dscussons of contnuous tme package auctons related to the Electronc BushBroker Exchange. We also thank Nkhl Ravchandar, Ruth Wambua, Mercy Musya, Kenneth Okumu, and Paulne Wanjer for help n managng the experments n Kenya. We thank semnar partcpants at the AEA, LSE, Monash, Queensland Unversty of Technology, and Manchester Unversty for helpful comments. We gratefully acknowledge the fnancal support of the Centre for Market Desgn at the Unversty of Melbourne Faculty, the ARC Dscovery Early Career Research Award DE , and STICERD. de Qudt acknowledges fnancal support from Handelsbanken s Research Foundatons, grant no: B :1.

4 Increasng agrcultural labor productvty s key to reducng cross country ncome dfferences. Ths s because poor countres are relatvely less productve n agrculture, and allocate relatvely more workers to t. Recent work supports the conjecture that neffcent land allocaton reduces agrcultural productvty n the developng world: labor productvty ncreases wth farm sze, but poor countres have smaller, more fragmented, farms (Adamopoulos and Restucca 2014; Al et al. 2015; Dennger et al. 2016); optmal farm sze has ncreased wth mechanzaton, yet farms reman smaller than optmal (Foster and Rosenzweg 2011); and despte mportant heterogenety n farmer productvty, there s almost no correlaton between farmer productvty and land holdng (Restucca 2016). 1 Improvng the allocaton of land requres understandng why t does not currently flow to ts most productve use. Whle a great deal of work has nvestgated the role of property rghts n allowng trade (for a revew see Besley et al. 2010), lttle work n economcs consders how the market for land should be desgned. We argue that effcent trade requres both secure property rghts and a careful desgn of the market mechansm, and we take some steps toward understandng the desgn problem. We take nspraton from Goeree and Lndsay (2016), who study a house reallocaton problem. They propose, and expermentally verfy, that a package market can help overcome an exposure problem that arses n two-sded settngs that nvolve reallocaton. 2 We adapt ther approach, and demonstrate smlar results n our settng: Kenyan farmers are able to understand and beneft from a package market despte ts apparent complexty. Formal emprcal evdence shows that, even n the presence of secure property rghts, uncoordnated land markets may take decades to reach effcency. Bleakley and Ferre (2014) study land openngs on the Georga Fronter. In the early 19th century, land was allocated to settlers accordng to lottery. Allocated plots were of arbtrary szes that were unlkely to be optmal n all (or any) locatons. Bleakley and Ferre show that 80 years later, plot sze correlates nearly one-to-one wth the ntal allocaton, and that the correlaton does not dsappear untl 150 years have passed. These results show two thngs: frst, that the correlaton eventually dsappears mples that the ntal allocaton was not 1 Some of these results may seem at odds wth the known nverse relatonshp between farm sze and output per hectare (see, e.g., Dennger and Feder (2001)). There are several key dfferences. Frst, we are nterested n labor productvty, envsagng a potental move of labor out of agrculture, whle much of the lterature s concerned wth land productvty, presumably assumng that the populaton n agrculture s fxed. Second, the advent of mechanzaton seems to have removed the nverse plot sze productvty relatonshp n Inda, and the exstence of mechanzaton may tself be endogenous to the sze of plots. 2 As frst explored n Goeree and Lndsay (2016), and explaned more fully below, the exposure problem arses f a chan of trades that leads to an effcent outcome ncludes an negatve surplus ntermedate trade. We beleve ths to be one of several mportant constrants n our settng. A package market s one n whch a trade can propose a set of trades. For example, a bdder can specfy that she s wllng to sell a specfc plot f and only f she s able to buy a specfc plot. 2

5 optmal; and second, that plot sze perssts shows that, even n the presence of strong property rghts (the US), uncoordnated land trade s a very slow route to effcency. Anecdotal evdence from land consoldaton programs also suggests that formal property rghts are nsuffcent to allow consoldaton. Throughout Europe, agrculture was, at some pont, charactersed by severe fragmentaton. 3 At least snce the 18th century, ths fragmentaton has been mtgated va government programs. 4 The Dansh program s of partcular nterest. A group from the land offce would work wth a vllage for about 4 years to generate a plan for the reallocaton of land. 5 After ths, contracts of sale were drawn up and executed smultaneously and voluntarly. Fgure 1 shows the change n land structure n one vllage. The change s strkng n lght of two observatons: frst, Denmark s nsttutons allowed free trade of land n the absence of the program; second, trade n the program was voluntary; hence every land owner weakly preferred the new allocaton. These two facts mply that farmers wanted to defragment ther land, but were unable to do so wthout a coordnatng mechansm. Theory also mples that uncoordnated land consoldaton s dffcult. Frst, gven ncreasng returns at the plot level, uncoordnated land markets are lkely to be thn because the most advantageous trades wll be those that create contguous plots, and so effcent trade s concentrated among neghbours. Ths thnness s predcted to mpede trade n the presence of two-sded prvate nformaton. Second, farmers who are proactve n defragmentng land may be subject to exposure rsk. Suppose that t s optmal to hold two contguous plots, and a farmer starts wth two fragmented plots. Defragmentaton requres two smple trades. If the frst trade must take place at a loss and the second trade cannot be guaranteed to take place, perhaps because of holdout, then tradng s rsky and may not occur. 6 Fnally, the effcent set of trades s lkely to be complex. Effcent trades often nvolve multple partes n a chan, and there are many possble trades and tradng mechansms that could be used. 7 Theoretcally, a centralzed market desgn can mtgate these problems n a tmely and 3 Land s fragmented f farmers own multple small noncontguous plots. 4 For a revew see 5 See Hartvgsen (2014) for a revew of the nsttutons used n Denmark. 6 Goeree and Lndsay (2016) s the frst paper that we are aware of to pont out ths form of exposure n two-sde reallocaton problems. Exposure also arses n one-sded settngs where objects are complements. See, for example, Rassent et al. (1982), Brunner et al. (2010), Goeree and Holt (2010), and Chernomaz and Levn (2012) for package desgns amed at mtgatng exposure n one-sded settngs. 7 An addtonal ssue arses f there s asymmetrc nformaton about the qualty of land. Whle we do not drectly address ths problem, we beleve that t can be partally mtgated by ntally exchangng leases (potentally wth an opton to buy) so that purchasng farmers have the ablty to learn about land qualty. 3

6 apoltcal manner. 8 In partcular, a package exchange wth XOR bddng 9 that allows for suffcently complex packages: () ncreases market thckness by allowng farmers to bd on multple consoldated farms ndependent of ther ntal allocaton; () removes the exposure problem by allowng all trades to take place at once; and () reduces complexty, because both chans and tradng rules are defned by the aucton envronment. 10 Packages may also releve credt constrans as buyng can be made condtonal on sellng. A gudng prncpal of market desgn s that mechansms work best when they are talored to the needs of partcpants. A frst step n desgnng a mechansm for rural land trade s to understand whether the target populaton small holder farmers wth lttle formal educton s able to trade effcently usng potentally complex market mechansms. 11 Toward ths am, we desgned a smple land tradng envronment, and mplemented a framed feld experment n rural Kenya. The envronment has several features that mrror mportant aspects of the land tradng problem. Frst, there are ncreasng returns at the plot level, so defragmentng land s effcent. Second, both farmers and land are heterogeneous n ther productvty, and a complementarty means that effcency s reached when hgh productvty farmers farm more productve land. We are thus able to study the ablty of dfferent market desgns to acheve two goals: effcent land defragmentaton; and effcent sortng of land. Thrd, there s a potental for exposure rsk n our envronment. We mplemented three dfferent market mechansms that are based on the package market desgn of Goeree and Lndsay (2016). 12 We based our mechansms on a preexstng format for two reasons. Frst, the land defragmentaton problem we study and the house reallocaton problem that they study share the smlarty that many partcpants 8 We see the hstorcal land consoldaton programs as akn to the comparatve hearngs dscussed n the market desgn lterature on spectrum auctons (Mlgrom 2004). Even f these nsttutons allocate goods effcently (whch s debatable), they are costly, tme consumng and open to poltcal ntrgue. 9 XOR denotes exclusve or,.e. partcpants can submt multple bds smultaneously, at most one of whch wll be accepted. 10 Whle there has been consderable recent work on package auctons, package exchanges have attracted much less attenton. Combnatoral exchanges have been explored n the context of arport take-off and landng slots (Rassent et al. 1982; Grether et al. 1989; Balakrshnan 2007), natve vegetaton offset permts (Nemes et al. 2008), polluton permts (Fne et al. 2017), housng (Goeree and Lndsay 2016) and the reallocaton of spectrum (Mlgrom and Segal 2017; Mlgrom (2017)). For a revew of the lterature see Mlgrom (2007) and Loertscher et al. (2015). 11 Feld evdence on the extent to whch ndvduals n developng countres are able to trade effcently n markets s mxed. See Bulte et al. (2013), Fala (2015) and Haushofer and Zurlnden (2013) for expermental studes related to market effcency n a developng country context. 12 The algorthm we use s near dentcal to the one n Goeree and Lndsay (2016) except that we mpose XOR bddng whereas they use endogenous cash and holdng constrants. Our strcter set of constrants s due to the complementarty that exsts across plots of land; t ensures that a bdder doesn t defragment land wth one wnnng bd and then break up ther land holdngs wth another. Our desgns also dffer n that we allow communcaton n all treatments and use a dfferent vsualzaton scheme. 4

7 are lkely to want to move locatons rather than ncrease or decrease holdngs. Gven that ther mechansm can elmnate the exposure problem nherent n reallocaton and was expermentally valdated, t was a natural mechansm to explore. Second, we are nterested n the ssue of complexty and ts nteracton wth our target populaton who may have low numeracy and lteracy sklls. By usng a parallel treatment structure, ther experment gves us a natural benchmark for the complexty tradeoff n a more tradtonal subject pool. In our frst treatment, farmers were able to trade sngle plots of land n a contnuous double aucton, wth a broker who facltated communcaton (CDA-Broker). Communcaton was allowed because exchange n Kenya s often done through drect blateral barganng and we are nterested n market desgns that can act alongsde exstng nsttutons. Our second treatment was dentcal to the frst, except that farmers could also specfy swaps that s they could offer to buy (or sell) one plot condtonal on sellng (or buyng) another plot (CDA-Swap). We allow cash to be offered or demanded as part of the swap. Our fnal treatment (CDA-Package) was the same as CDA-Swap, except that farmers could also make package offers, wth a maxmum of two buys and two sells. That s, they could offer to buy two plots, offer to sell two plots, and offer to sell (or buy) up to two plots condtonal on buyng (or sellng) up to two plots. 13 We show several results. Frst, effcency s hgh. Farmers were able to extract more than 70% of the avalable effcency gans across all treatments, and there are very few nstances of losses. We beleve ths s an mportant result, t demonstrates that our target sample are able to understand the market and to trade. Second, as conjectured, the more complcated CDA-Package mechansm acheves hgher effcency, extractng 8 percentage ponts more surplus than CDA-Broker. Ths shows that our subjects are able to make use of a market desgn that one may conjecture s too complex. Across treatments, farmers extract most of the gans from defragmentaton, but less of the gans from sortng. CDA-Package does better overall because t mproves sortng. Thrd, we fnd that farmers are able to mtgate exposure rsk. Wthn a sesson, half the auctons featured tght credt constrants, and half lax credt constrants. Credt constrants heghten the exposure problem by preventng subjects from recevng the full value of land sold early n a chan, and we conjectured ths would reduce effcency. We fnd no statstcal evdence that credt constrants reduced effcency. 13 In our context, larger packages (for example sell 3 and buy 3) have no theoretcal value, because t s always optmal for each farmer to own exactly two plots. We chose to constran our package market followng the prncpal that desgns should be as smple as possble, but not smpler. Ths aphorsm s often attrbuted to Albert Ensten and s hghlghted as a feature of good desgn by Bchler and Goeree (2017). 5

8 Fourth, we show that farmers earnngs are strongly correlated wth ther Shapley value. We see ths as evdence that tradng dd not ncrease nequalty, a key concern n our settng. From a theoretcal perspectve, exposure may lead to an asymmetrc dvson of surplus, even f t does not create neffcency. 14 To evaluate whether ths occurs n our data we requre a predcton for how surplus would be dvded f barganng was effcent and egaltaran; the Shapley value provdes such a benchmark. We fnd a remarkably strong correlaton between Shapley value and the ex-post dvson of surplus, regardless of treatment. Ths tght connecton between behavor and the leadng cooperatve soluton suggests that nformal nsttutons may be mportant n our settng, and that nterventons that can be overlad atop these nsttutons may be partcularly successful. 15 Taken together, these results suggest that formal market nsttutons can play an mportant role n mprovng land allocaton, and that complex desgns such as package exchanges can be used effectvely n a development context. Our results also hghlght the potental complementarty between formal mechansms and current practces. 1 Expermental Desgn 1.1 Overvew We conducted 48 expermental sessons, each consstng of 6 farmers who played 8 auctons. Farmers were recruted by takng a census of two vllages n Kambu County, Kenya, and nvtng ndvduals who dentfed as farmers, owned land, and were between 18 and 55 years of age. Approxmately 70 per cent of nvtees attended. Two ntal plots showed that females were more lkely to attend, so males were oversampled, wth a target nvtaton rate of 60% males. At the begnnng of each sesson, farmers were randomly assgned a computer and an enumerator, and read nstructons n ther preferred language (Englsh, Swahl, or Gkuyu). The enumerator remaned wth hs or her assgned farmer for the duraton of the experment, and also acted as a bd assstant. 16 After readng the nstructons, the 14 Ths s seen n Collns and Isaac (2012), who use a laboratory experment to study a land assembly problem. Across ther treatments surplus dvson s asymmetrc: buyers receve only a small porton of the fnal surplus when trade s successful. 15 A caveat s that the stakes n our experment are much smaller than the value of land. If barganng outcomes are supported by repeated game consderatons, the temptaton to devate s lkely to be much greater n real land auctons, and nformal nsttutons may break down. 16 Bd assstants are a common feature of real-lfe combnatoral auctons when the target populaton may have dffculty wth the nterface, and have been used, for nstance, n the aucton of slot machnes and tax medallons n Australa. To reduce the nfluence that an ndvdual bd assstant mght have on the experment, we recruted extra bd assstants (16 total) and randomzed bd assstants across treatments. 6

9 bd assstant s role was to answer any questons about the tradng rules, calculate the surplus from any trade upon request, and nput bds nto the system. Enumerators also recorded earnngs n each aucton, and whether subjects communcated. 17 Enumerators were gven three days tranng on the mechancs of the game pror to the frst sesson. We were clear wth the enumerators that they were not to suggest partcular trades to farmers, and enumerators dd not fnancally beneft from farmer performance. After the nstructons, farmers partcpated n one 15 mnute practce aucton n whch they were encouraged to make bds usng the mechansm assgned to ther sesson. In the sessons that allowed for packages, enumerators encouraged ther farmers to use all possble package structures and to make multple bds. Farmers then partcpated n 8 auctons, each lastng 10 mnutes. As dscussed n the nterface secton, subjects could see ther current allocaton and bds on ther screen, and a centralzed screen showed the plots for whch there were actve bds. An addtonal enumerator was avalable n each sesson to act as a broker. The broker would take oral messages between farmers, but was explctly told not to actvely organze trades. 18 Farmers had a 30 mnute break after the fourth aucton, and were fed a lght snack. At the end of the experment, farmers were pad for all 8 auctons va moble payment. The exchange rate was 20 ponts to 1 shllng. An experment lasted about 3.5 hours, and farmers receved shllngs on average. Ths was roughly 1.5 days wage for the represented populaton. 1.2 Aucton Envronment Producton Functons Our envronment was desgned to study two ssues: de-fragmentaton; and farmer sortng. Fragmentaton occurs f plots are not contguous, and s conjectured to reduce effcency. An effectve market desgn should be able to de-fragment an allocaton, and allow land to flow to the most productve farmer, leadng to effcent sortng. In each sesson, 6 farmers traded 12 plots of land located on a smplfed map. The map s presented n Fgure 2. Each farmer was ntally allocated two plots. There were two dmensons of heterogenety. Frst, there were three land types: blue land was the most productve, red the second most and green the least. Second, there were three farmer types: hgh productvty, medum productvty and low productvty. In all sessons there 17 In practce there was communcaton for all subjects n all sessons. 18 We allow for oral communcaton n ths experment snce we are nterested n developng exchanges that can be used n conjuncton wth current nsttutons. Gven that communcaton s a feature n our target envronment we consder t an mportant part of our desgn. 7

10 were two of each type of farmer. Panel A of Fgure 3, shows total proft for each farmer and land combnaton. A hgh productvty farmer always earned twce as much as a low productvty farmer, and a medum productvty farmer earned one and a half tmes as much. Red land was twce as productve as green land, and blue land was one and a half tmes as productve. Ths setup creates a complementarty. For example, the gan from movng from green to blue land was 200 for a hgh type, but only 100 for a low type. Hence, effcency requred the hgh type farmers to farm the blue land, the medum type farmers to farm the red land, and the low type farmers to farm the green land. There was also a bonus for operatng adjacent plots, and a cost from operatng too many plots. A farmer who operated two adjacent plots of the same colour receved a 20% bonus, as shown n Panel B of Fgure 3. A farmer who operated more than two plots, earned only the profts of the two most proftable. The adjacency bonus allows for an ncrease n productvty from de-fragmentaton. The complementarty allows us to study sortng. The fact that a thrd plot s not productve allows us to ntroduce a complementarty, but avod a stuaton n whch effcency requres all land to be held by the most productve farmer. It also allows us to ntroduce exposure rsk wth a smple to explan producton functon. We explaned the two-plot restrcton as a span of control constrant, a farmer smply does not have enough tme to tend to more than two plots. The maps and producton functons remaned constant across all auctons. All players knew ther own producton functon and that there were three types of farmers. However, detals of the other two producton functons, and the assgnment of types to subjects, was not revealed. Subjects knew whch plots were owned by whch subjects The Intal Allocaton of Land We conjectured that the the ntal allocaton of plots would affect the ease of achevng defragmentaton and effcent sortng. To study ths ssue, we created eght dfferent ntal land allocatons, whch are shown n Fgure 4. In each map, players 1 & 2 are hgh types, players 3 & 4 are medum types and players 5 & 6 are low types. The maps are symmetrc wthn player type. That s, players 1 & 2 are nterchangeable, players 3 & 4 are nterchangeable, and players 5 & 6 are nterchangeable. The allocatons are ordered accordng to our pre-expermental assessment of how dffcult t would be to reach full effcency. We consdered four dmensons of dffculty. Frst, for each player, we determned how many CDA-Broker trades were necessary to get to ther effcent allocaton. 19 Second, we consdered how many farmers would need to be 19 Note that f an allocaton requred two CDA-Broker trades, t requred only one CDA-Swap trade. If an allocaton requres four CDA-Broker trades, t requres two CDA-Swap trades or one CDA-Package trade. 8

11 nvolved n any effcent CDA-Swap trade. Thrd, we consdered whether money was requred to reach an effcent outcome. Fnally, we consdered strategc ssues, for example the extent to whch one farmer could holdup another farmer. Map 1 was thought to be the smplest. For each player, reachng effcency requres only one CDA-Swap, and only two partcpants are nvolved n each trade. No money s requred, because all effcent trades ncrease all partcpants surpluses equally. Map 2 s smlar to Map 1, but money s requred because effcent trade reduced land value for some farmers. For example, players 1 and 3 must swap land, but ths wll reduce farmer 3 s output and so she must be compensated. Map 3 s smlar to Map 1, and n prncple requres no money. However, players 2, 4 and 6 mght have a strategc motve to holdout and explot the weak barganng postons of players 1, 3, and 5. Map 4 can be solved wth only one CDA-Swap per player, but those trades requre a chan of 3 partcpants. Money s requred, but there s no strategc ssue. Map 5 was thought to be more complex than Map 4, and requres two CDA-Swap trades or one CDA-Package trade by each player to reach the effcent allocaton. Each of those trades nvolves only two players, money s requred and there does not appear to be a strategc ssue. Map 6 agan requres two CDA-Swap trades, but n ths case, some of those trades requre a 3 person chan. Agan, money s requred and ther does s not obvous strategc ssue. Map 7 s smlar to Map 6 but appears to have a holdout problem; player 6, for example, may not wsh to sell. Fnally, we judged map 8 to be the most dffcult. It requres two CDA-Swap trades per player and some of those trades requre a chan of 4 players. It should be noted that n comng to our ex-ante assessment of dffculty we tred to determne how hard t would be to reach full effcency. We dd not consder whether ntal allocatons dffered n the ease wth whch partal effcency could be acheved. We return to ths pont n Secton 2.4. In rankng ntal allocatons, our goal was to generated a varety of maps and allow emprcal evaluaton the conjecture that ntal allocaton matters. We show below that ntal allocatons do matter, and beleve that there may be nterestng work to do n formalzng the ntutons presented n ths secton Tradng Mechansms We consder three tradng mechansms based on the contnuous double aucton and the package market of Goeree and Lndsay (2016): a smple CDA-Broker mechansm where farmers can communcate va the broker but can place only buy or sell orders to the market, a CDA-Swap mechansm where subjects can place buy orders, sell orders, or package orders consstng of one sale and one purchase, and a CDA-Package mechansm where 9

12 subjects can place buy orders of up to two unts, sell orders of up to two unts, and package orders consstng of up to two buy orders and up to two sell orders. Communcaton through the broker s avalable n all three mechansms. Wnner determnaton and surplus dvson are as outlned n Goeree and Lndsay (2016) wth some modfcatons to mpose XOR bddng. Let the set of farmers, F, be ndexed by {1,..., 6} and the set of plots, L, be ndexed by l {1,..., 12}. Farmers submt orders o = (m, x) consstng of the mnmum amount of money they must receve, m, and a vector of demanded plots, x { 1, 0, 1} 12. A negatve number ndcates that a farmer s offerng money or tryng to sell a plot, whle a postve number ndcates that a farmer must receve money, or wants to buy a plot. For nstance, an order ( 500, 1, 0,..., 0 ) ndcates that a farmer s wllng to pay up to 500 ponts to acqure plot 1, whle an order (0, 1, 1, 0,..., 0 ) mples that the farmer s wllng to buy plot 1 and sell plot 2, as long as he pays no money. Orders placed by a farmer must be legal. Denote the plots owned by farmer at tme t as ω t {0, 1} 12 and denote the cash of farmer at tme t as c t. A bd (m, x) s legal f at the tme of placng the order, c t + m 0 and ωt + x contans only zeros and ones. A bd s thus legal f the farmer has more cash than the amount of money he offers, he sells only land that he owns, and he buys only land that he does not own. Orders placed by a farmer are also restrcted by the mechansm used n each treatment, as outlned above. Legal orders are sent to the order book n the order that they arrve, and transactons occur any tme there exsts a set of legal orders where: () supply equals or exceeds demand for all plots; () only a sngle order s used for each farmer; and () the total amount of money offered s not postve. Formally, let O t denote the legal orders n the order book at tme t, and ndex ts elements o j = (m j, x j ), by j = {1,..., O t }. Let d = {0, 1} Ot be a vector of orders from the order book, where d j = 1 f an order j s wnnng and d j = 0 otherwse. Let O t be the actve orders of farmer and let W = {o j O t d j = 1} be the orders of farmer that are wnnng. At each tme t we fnd: subject to V max d m j d j j x l j d j 0 l L, and j W 1 F. 10

13 Trade s trggered f V When a transacton s trggered, we return plots that were not demanded to ther orgnal owners, and transfer all other plots accordng to the set of wnnng orders. If there s a postve surplus (.e., V > 0), we dvde the remanng surplus amongst the wnnng farmers as follows: let W = {o j O t d j = 1} be the set of wnnng orders and Ŵ = {o j O t o j O t, W = 1} be the set of all orders made by the wnnng farmers. Lkewse, denote the set of orders made by non-wnners by NW = O t \ Ŵ. Let p {0,..., 10000} 12 be a vector of (nteger) prces, and denote the surplus generated by order j at prces p as s j (p) = m j p x j. 21 As s standard n these problems, we fnd the set of prces that lexcographcally maxmzes the mnmum surplus of wnnng farmers, subject to the revealed preference constrants of the losng orders. 22 The revealed preference constrants ensure that a losng farmer would not prefer to have won once the surplus s reallocated gven the nformaton that was submtted to the market. Fndng these prces s equvalent to solvng: subject to: mn p ( ) 2 d j s j (p) V W j s j (p) 0 o j W, s j (p) 0 o j NW, and d j s j (p) = V. j Each wnner pays or receves p x j and losng farmers pay and receve nothng. In the case of tes, we use the frst soluton found by the solver Note that the restrcton to legal trades ensures that there s no short sellng, and that all budget constrants are met. We handle these on the clent sde to mnmze the computaton tme requred to solve the wnner allocaton problem, and to make farmers aware of attempted bds that could not be exercsed. Relatve to Goeree and Lndsay (2016), the addtonal cardnalty constrant prevents more than one order from a farmer beng used n each transacton. Ths constrant ensures that orders submtted by each farmer are consdered XOR. Further, we only use the bds of non-wnners to set prces, whle Goeree and Lndsay (2016) use all non-wnnng bds. Ths change avods a stuaton that can arse n our settng, where bdders mpose revealed preference constrants on themselves, and reduce ther own surplus. 21 We use nteger prces n the experment n the range of 1 and so that trade prces are smlar to ones that farmers are lkely to encounter when tradng n Kenya Shllngs on a day-to-day bass. 22 See Kwasnca et al. (2005) for a broader dscusson of revealed preference constrants. 23 The underlyng algorthms were wrtten n Mnznc, a free open-source constrant modellng language, and solved usng GECODE (Nethercote et al. 2007; Stuckey et al. 2014). In general, the wnner determnaton problem could be solved n under 200 mllseconds for order books contanng under 100 legal orders. 11

14 As can be seen n the optmzaton rule above, lexcographcally maxmzng the mnmum surplus s equvalent to mnmzng the squared dfference between the surplus of each wnner and the equal splt subject to an addtonal constrant that all surplus s allocated. We explan our surplus dvson rule usng ths logc. Farmers are told that we try to splt the surplus as evenly as possble between the farmers but that we want to make sure that farmers who do not trade are not dsadvantaged. In tranng our enumerators we gave two man examples one where there s a sngle buy order and a sngle sell order and where the surplus s dvded equally, and one where there are two buy orders and a sngle sell order and where the non-wnnng buy order pns down prces. After a transacton s trggered, all non-wnnng orders made by farmers n the wnnng coalton become nactve, and we allow farmers to renew any legal orders f they wsh. Orders that are made llegal (for nstance, orders that contan sale offers of objects no longer owned) are hdden from a farmer s offer book, but can be renewed f later transactons make them legal. Farmers have the ablty to wthdraw legal orders at any tme Interfaces All bds were entered through a computer nterface. The nterface dsplayed the farmer s valuatons and current allocaton on a geospatal map as n Panel (a) of Fgure 2, and provded a calculator that could be used to determne the value of dfferent allocatons. Players (or ther bddng assstant) could clck on sets of plots on the map (dependng on the treatment) and enter a wllngness to pay, or wllngness to accept to make the trade. Only legal bds were accepted by the computer. The nterface also showed a lst of all current bds placed by the farmer. In addton to the ndvdual nterfaces, a projector showed a map whch ndcated who owned each plot of land and when a plot of land was offered for sale, or had an offer to purchase. Combnatoral bds showed up on the projected nterface as separate components. A screenshot of the ndvdual and projected nterfaces s shown n Fgure 5. The surplus dvson rule was slghtly slower, but usually completed n under 600 mllseconds. To ensure that the system was able to contnue n real tme, we bult tmeouts nto the surplus dvson rule that would end the solver and consume all the surplus f no soluton was found n 10 seconds. Ths crcumvented problems that occur f prces aren t fully pnned down by orders. In practce, the tmeouts were never trggered. 12

15 1.2.5 Cash Constrants and Exposure Rsk Exposure rsk exsts f reachng an effcent allocaton requres at least one farmer to make a loss on an ntermedate trade. Ths may dscourage all trade f future transactons that compensate for the loss cannot be commtted to. In practce, subsequent trades may not occur, ether because of strategc holdup, or because of changes of crcumstance. To see that ntermedate trades may lead to losses, consder a stuaton wth ntal allocaton blue lots red lots, and the effcent allocaton blue lots red lots. Intally the land values are 720, 525 and 525 for 1, 3 and 4 respectvely; after trade they are 960, 540 and 540. Thus, there exsts a sequence of trades that s mutually benefcal. Gettng to effcency, however, requres ntermedate trades that create losses. If 1 frst buys from 3, he holds three plots and cannot farm them all. After ths ntermedate trade hs landholdng s stll worth 720, whle farmer 3 s value has decreased to 225. Snce the surplus from ths trade s negatve (-300), someone must make a loss. Alternatvely, f 1 frst sells to 3, 1 s land value decreases to 300 whle 3 s ncreases to 540. The net gan s negatve (-285), and agan someone must make a loss. There are three reasons why smple trades (.e. a sale and purchase of one plot) may have negatve surplus n our settng. Frst, as n the example, a purchased plot may not be farmed, because the buyer now has three plots. In ths case output s lost untl the buyer sells a plot. Second, the buyer may produce less from the purchased plot than the seller, because of type productvty dfferences. Ths would occur, for example, when a hgh type farmer owns low type land. Effcency requres that ths land be sold to a low type farmer, and that the hgh type farmer later acqure hgh type land. But, the ntal sale reduces total output. Thrd, the trade mght break up a prevously consoldated set of plots. Ths would occur, for example, f a hgh type farmer owned two adjacent medum type plots. Effcency requres that the hgh type farmer sell these plots and acqure hgh type plots. Any smple trade would requre frst that the adjacency bonus be lost. We ntroduced an addtonal expermental feature, cash constrants, to ncrease the lkelhood that trade creates exposure rsk. In half of all auctons, farmers started wth 13

16 cash of 750. Ths s enough money to nduce any farmer to sell any sngle plot. In partcular, t would be suffcent to compensate a hgh productvty farmer wth two adjacent hgh qualty plots for sellng one. 24 In the other half, the cash endowment was 250. Ths s not enough to compensate all farmers for all effcency ncreasng smple trades. For example, effcency requres a medum type farmer who owns two consoldated hgh qualty plots to sell to a hgh type farmer. Ths trade reduces the medum types output by 460. Wth only 250 n cash, the hgh type farmer cannot fully compensate the medum type farmer for ths loss n output Treatment Randomzaton We played 48 sessons n total. Each sesson conssted of 8 auctons, and was assgned to one tradng mechansm: CDA-Broker, CDA-Swap, or CDA-Package. In each sesson, the frst four auctons had the same cash treatment and, the second four the alternatve cash treatment. Hence, each sesson could be assgned to one of sx possble treatments: {BrokerLH, BrokerHL, SwapLH, SwapHL, PackageLH, PackageHL} where BrokerLH denotes a CDA-Broker treatment that plays low cash for the frst four auctons and then hgh cash for the last four. These treatments were block randomzed. The set of 48 sessons was dvded nto 8 blocks, each consstng of 6 consecutve sessons. Each of the 6 treatments was then randomly assgned to one of the sessons wthn each block. Each lab sesson requred one lead enumerator to ntroduce the envronment and mplement the computer programs, 6 bddng assstants, and one broker. Two labs (labeled red and black) ran n parallel, each playng one sesson n the mornng and one n the afternoon. Lead enumerators were assgned to a specfc lab (red or black) and stayed n that lab throughout. Bddng assstants were randomly assgned to a specfc farmer and lab (e.g. farmer 4 red) on a sesson by sesson bass. Brokers were also randomly assgned on a sesson by sesson bass. Because subjects arrved slowly over tme (t was hard to get farmers to all arrve at 9am), the frst sesson of the day alternated between the red and black lab. The frst 6 farmers to arrve were randomly assgned to a player number between 1 and 6, and then played n the lab that was operatng the frst sesson. The next sx farmers to arrve were smlarly assgned a player number, and played n the second lab. Each farmer played four auctons as ther ntal player number, and was then moved to a dfferent player number. Ths was done such that every subject had an equal chance of beng assgned to play one of the sx possble sequences {HM; HL; MH; ML; LH; LM}. 24 The land value before a sale s 960. after a sale hs land value would be 400. Thus, the dfference s 560. If ths farmer were offered 750 to make ths trade she would be wllng. 14

17 Fnally, the 8 maps dsplayed n Fgure 4 were assgned to sessons. Every sesson played every map, and they were played n one of 8 orders. These orders were devsed to mnmze orderng effects: we wanted to have dffculty approxmately even across the sesson to mnmze the mpact of learnng. To assgn orders to sessons, we frst randomly permuted the 8 map orders as shown n Fgure 6. We then assgned map orders 1 to 6 to the sessons n block 1 (n order), orders 2 to 7 to block 2 (n order), etc. Overall, ths method gves assgnment to the man aucton and cash treatments that are orthogonal to the other elements of the desgn, as well as maps that are assgned orthogonally to the treatments and also randomly across tme and sesson. We also have balance across all man elements of the expermental desgn. 2 Results 2.1 Data Overvew and Summary Statstcs Table 1 provdes summary statstcs for our sample. Despte oversamplng men, we had nearly 60% female partcpants, lkely reflectng greater avalablty durng daytme hours. Recall that each of these partcpants ndcated that they own land, and are responsble for farmng decsons on that land. Average age was 43 years, and the average attendee had about 12 years of school, ndcatng that our sample was slghtly better educated than antcpated. Most farmers owned very lttle land (just less than 1 acre), and one plot on average. Ths low ownershp of plots lkely reflects the fact that many women own a small fracton of the famly land. Very few of the farmers had ever traded land. As dscussed n the desgn secton, we provded enumerators wth 3 days of tranng pror to the start of the experment; where they learned how to use the nterface, how to calculate payoffs, how to place bds, and how prces were set. In the tranng sessons, enumerators also practced gvng nstructons to each other. Despte ths tranng, our lead enumerators rased concerns that the other enumerators dd not fully understand the rules of the more complcated package exchanges. These concerns dmnshed as the experment progressed. As the enumerators were responsble for translatng the nstructons and teachng farmers, t s lkely that farmers dd not fully understand the mechansms n the early sessons. Lookng at the data, the frst two sessons n each treatment accounted for 43% of auctons where effcency was n the bottom decle, and accounted for 63% of auctons where effcency was negatve. Fgures 7a and 7b show the evoluton of effcency overtme, broken down by treatment. 25 Fgure 7a shows that there s 25 Effcency s formally defned below. 15

18 a marked mprovement n effcency over tme for all treatments, but that ths s much stronger for the more complcated package treatments. Ths makes sense f enumerators found those treatments dffcult to explan. Fgure 7b s the same as Fgure 7a but a lnear ft s added to the data after block one. Ths fgure shows that, after removng block one, learnng s even across the three treatments. Gven these observatons we dsplay all our results n three ways. Frst, we use all the data and no tme trends. Second, we present results that exclude the frst block. Thrd, n our preferred specfcaton, we also nclude a lnear tme trend. In all specfcatons we nclude block (strata) fxed effects, as well as controls for the gender composton of the sesson, and the dentfy of the lab (red or black). Unless otherwse stated, we analyze the data at the aucton level, wth errors clustered at the sesson level. Summary fgures quoted n-text are from our preferred specfcaton. We lost one sesson due to the accdental reformattng of the server computers. 26 We also drop one sesson where the wrong mechansm was used, and two auctons where the wrong confguraton was used. In total our data conssts of 46 sessons, 366 auctons, 276 farmers, and 2196 farmer-aucton observatons. 2.2 Effcency We begn our analyss by studyng how much of the gans from trade was captured by farmers. In each aucton, we calculate: where s f nal s optmal Effcency = n =1 ( n =1 ( s f nal s optmal ) s ntal s ntal ), (1) s fnal surplus generated by farmer, s ntal s farmer s ntal surplus, and s the surplus farmer would generated at the optmum. Effcences are bounded above by 1, and are the proporton of possble gans realzed n a gven aucton. Result 1 Average effcency s 70 percent or hgher. The CDA-Package mechansm acheves 8 percentage ponts more effcency than the CDA-Broker mechansm. Support for Result 1 s gven n Fgure 8a and Table 2. Fgure 8a shows average effcency and 95% confdence ntervals, for each of the three market mechansms. As can be 26 Our experments took place n a vllage where there was no nternet access and we used two laptops as servers. Followng the last sesson, these laptops were confused by staff wth the computers we used as clents and the hard drves were formatted n order to reuse the machnes for other projects. The last sesson run was not backed up. 16

19 seen, average effcency s hgh under all three mechansms, wth an average effcency rate 70% or hgher n all treatments. The CDA-Broker mechansm has the lowest average effcency of 70%. Ths effcency s hgh relatve to the work of Goeree and Lndsay (2016) who document poor performance of a CDA n a house aucton wth exposure rsk. As ndcated n the ntroducton, a major dfference n our desgns s that we allow for communcaton through a broker, potentally allowng farmers to mtgate exposure rsk through nformal agreements. 27 To see how communcaton nfluenced trade, we look at the transacton level data. In our plots, deals negotated through the broker typcally led to smultaneous buy and sell bds at the arranged prce. Such bds regster n the system as havng no surplus to dvde (.e., V = 0). We use the proporton of trades wth zero surplus as a measure of brokered transactons. Fgure 8b shows that a very hgh proporton of trades are brokered, and that the proporton of brokered transactons declnes as the avalable package sze grows. 37% of transactons n the CDA-Broker treatment are brokered, whle brokered transactons account for 20% of transactons n the CDA-Swap mechansm, and just 16% of transactons n the CDA-Package auctons. All these dfferences are sgnfcant n an OLS regresson wth errors clustered at the sesson level (p-value <.01 for all comparsons). Our data thus suggests partal substtuton between communcaton and formal package mechansms. Table 2 reports coeffcents from an OLS regresson wth effcency on the left hand sde, and the mechansms on the rght. CDA-Broker s the left out. Our preferred specfcaton s (5), whch controls for block fxed effects and tme trends, and leaves out the frst block, as dscussed above. In ths specfcaton, the CDA-Package mechansm has sgnfcantly hgher effcency than the CDA-Broker mechansm. From a base of 70% effcency, the CDA-Package mechansm ncreases effcency by 8 percentage ponts, or 11%. Effcency s 4 percentage ponts (6%) hgher n CDA-Swap than CDA-Broker, but the dfference s not sgnfcant. As dscussed above, we also changed the amount of cash that farmers started wth. Ths was desgned to alter the degree of exposure rsk. Regardless of the specfcaton, the low-cash treatment does not statstcally sgnfcantly alter effcency, and ths lack of mpact does not depend on the treatment. Ths results suggest that farmers were able to deal effectvely wth the greater exposure rsk that comes from a tghter cash constrant, although t should be noted that we have low power to detect nteracton effects. 27 We also had a dfferent value structure and use a shared graphcal vsualzaton of open trades. 17

20 2.3 Fragmentaton and Sortng We next ask how the dfferent treatments performed at the two separate tasks of defragmentaton and sortng. For a gven allocaton of land, let y denote the value assocated wth farmer s two best plots (gnorng consoldaton bonuses), and let c {0, 1} ndcate whether these plots are fragmented (c = 0) or consoldated (c = 1). Based on the producton functon used n the experment, t follows that the total proft on farmer s land s s := ( c )y. After some algebra, the change n surplus from a farmer s ntal allocaton to ther fnal allocaton can be rewrtten as: s f nal [ s ntal = 0.2 ] c f nal c ntal y ntal }{{} Defragmentaton ( + ) [ ] c f nal y f nal y ntal. }{{} Sortng We nterpret the frst term as the change n surplus due to defragmentaton and the second term as the change n surplus due to sortng. 28 Aggregatng over the sx farmers, and normalzng by the maxmum change n socal surplus, we calculate a defragmentaton and sortng measure for each aucton: [ Defragmentaton abs = n =1 0.2 c f nal ] c ntal y ntal [ ] =1 n s optmal s ntal ( ) [ ] Sortng abs = n = c f nal y f nal y ntal [ ] =1 n s optmal. s ntal Note that, by constructon, Effcency = Defragmentaton abs + Sortng abs. Fgure 9 shows these measures, frst for a hypothetcal case where full effcency occurs n each aucton, and then for each of the three treatments. Lookng frst at the full effcency case, note that defragmentaton accounts for 73 percent of the avalable gans, whle sortng accounts for only 27 percent. The lower potental gan from sortng s due to our selecton of ntal allocatons: two of our easest maps (Map 1 and Map 3) had no gans from sortng, whle two of the remanng maps (Map 2 and Map 4) had only small gans. The fgure shows that farmers were able to capture most of the avalable gans from 28 Due to the multplcatve nature of the adjacency bonus, a farmer who both consoldates land and sorts to hgher qualty land wll get a larger adjacency bonus then one who retans her lower qualty land. Ths mples that there s not a perfect separaton between the gans from defragmentaton and the gans from sortng. The decomposton we have chosen holds the qualty of land fxed at the ntal allocaton for the purpose of calculatng defragmentaton and assgns the addtonal gans and losses to sortng. The results n the analyss below are robust to alternatve decompostons and to specfcatons that count the number of fragmented lots rather than weghtng them by ther value. 18

21 defragmentaton, and ths does not depend on the aucton format. In contrast, farmers extracted only a small percentage of the avalable gans from sortng, and the CDA-Package treatment performed sgnfcantly better n ths regard. To further understand defragmentaton and sortng rates across the treatments, we renormalze our defragmentaton and sortng measures so that they are bounded above by one. For defragmentaton, we calculate: and for sortng, we calculate: [ Defragmentaton = N =1 0.2 c f nal Sortng = N =1 ( ] c ntal N =1 0.2 [ 1 c ntal c f nal ) [ y f nal N =1 ( ) [ y optmal y ntal ] y ntal, (2) ] y ntal ]. (3) y ntal Note that the sortng measure s not defned n Maps 1 and 3 because all farmers start wth ther effcent land types. We thus drop these observatons. Result 2 Defragmentaton rates are over 80% n all three aucton formats, wth no statstcally sgnfcant dfference between treatments. The treatments are less successful overall at mprovng sortng. The CDA-Broker treatment realzes only 35% of potental gans from sortng. However, the CDA-Package treatment mproved sortng by 16 percentage ponts (48%) n our preferred specfcaton. CDA-Swap mproved sortng by 4 percentage ponts (not sgnfcant). Table 3 reports the mpact of our treatments on defragmentaton. The defragmentaton rate s surprsngly hgh n the CDA-broker treatment, suggestng that subjects are effectve at agglomeratng land, even n mechansms that do not allow for packages. Somewhat surprsngly, the CDA-Swap mechansm has a smlar defragmentaton rate. The CDA- Package aucton acheves slghtly more defragmentaton than the other two treatments, but the dfferences are not statstcally sgnfcant. Table 4 reports the treatment effects for sortng. As can be seen from the control group means, the CDA-Broker mechansm mproved sortng by only 35% of the optmum. 29 Rel- 29 There are a number of reasons why defragmentaton may be easer for farmers to accomplsh then effcent reallocaton. Frst, from the standpont of mechansm desgn, defragmentaton shares smlartes wth the partnershp dssoluton problem of Cramton et al. (1987) n the sense that both partes n a swap act as both a buyer and a seller and own a share of the effcent allocaton. In such settngs (and n contrast to the blateral tradng settng of Myerson and Satterthwate (1983)) t s often possble to nduce effcent trade wthout generatng a budget defct (Loertscher and Waser 2017). Second, emprcally, farmers often worked towards defragmentng land frst and then tred to move to more effcent lots. Ths orderng of 19