WPS8343 Policy Research Working Paper 8343 The Role of Social Ties in Factor Allocation Ulrik Beck Benedikte Bjerge Marcel Fafchamps Development Economics Vice Presidency Strategy and Operations Team February 2018 Policy Research Working Paper 8343 Abstract This paper investigates whether social structure helps or introduced. Land transfers lead to a more equal distribution hinders factor allocation using unusually rich data from The of land and to more comparable factor ratios across house- Gambia. Evidence indicates that land available for cultiva- holds in general. But equalizing transfers of land are not tion is allocated unequally across households; and that factor more likely within ethnic or kinship groups. In conclusion, transfers are more common between neighbors, co-ethnics, ethnic and kinship divisions do not hinder land and labor and kinship related households. Does this lead to the con- transfers in a way that contributes to aggregate factor inequal- clusion that land inequality is due to flows of land between ity. Labor transfers do not equilibrate factor ratios across households being impeded by social divisions? To answer households. But it cannot be ruled out that they serve a ben- this question, a novel methodology that approaches exhaus- eficial role, e.g., to deal with unanticipated health shocks. tive data on dyadic flows from an aggregate point of view is This paper is a product of the Strategy and Operations Team, Development Economics Vice Presidency. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The authors may be contacted at urb@dors.dk. The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent. Produced by the Research Support Team The Role of Social Ties in Factor Allocation∗ Ulrik Beck Benedikte Bjerge Marcel Fafchamps Keywords: social networks; allocative efficiency; land markets; factor markets JEL codes: C21, D85, O12 ∗ Ulrik Beck (corresponding author) is a senior economist at the Danish Economic Councils, Copenhagen, Denmark; his email address is urb@dors.dk. Benedikte Bjerge is an economic consultant; her email address is benediktebjerge@gmail.com. Marcel Fafchamps is a senior fellow at the Freeman Spogli Institute for Interna- tional Studies, Stanford University, Stanford, USA; his email address is fafchamp@stanford.edu. We benefitted from comments from seminar participants at the Universities of Oxford, UC-Berkeley, Paris 1, Gothenburg and the Goethe University in Frankfurt, as well as conference participants at the CSAE conference 2014, the International Economic Association’s World Congress 2014 and the Nordic Conference in Development Eco- nomics 2015. The authors also thank Dany Jaimovich, Thomas Markussen, Carol Newman, John Rand, M˚ ans S¨oderbom and Finn Tarp and three anonymous referees for their very valuable comments. Finally, we thank Jean-Louis Arcand and Dany Jaimovich for making the Gambia Networks Data 2009 available to us. Much attention has been devoted to identifying the sources of friction responsible for inefficient or inequitable economic outcomes. One particular area of investigation is the extent to which exchange is shaped by important aspects of social structure such as caste, ethnicity, kinship, and family ties. Examples of issues to which this approach has been applied include informal insurance (e.g., Townsend, 1994; Fafchamps and Lund, 2003; Fafchamps and Gubert, 2007; Attanasio et al., 2012; Mazzocco and Saini, 2012), labor markets (e.g., Granovetter, 1995; Topa, 2001), and international trade (e.g., Rauch, 2001; Rauch and Casella, 2003; Chaney, 2014, among others). While the literature has been successful at documenting important sources of friction, demon- strating that these frictions are responsible for aggregate misallocation has proved more diffi- cult. The reason is that there typically exist many different ways of achieving an efficient or equitable outcome. The fact that social structure precludes or impedes some of these ways is not sufficient to demonstrate that it affects the final outcome. To illustrate the problem, consider an exchange economy with N economic agents, each en- dowed with a vector of goods. Achieving allocative efficiency requires goods to flow between agents. Let the flows between pairs of agents be represented as network links. The number of possible links between N individuals is N (N − 1)/2 and the number of possible network configurations is 2N (N −1)/2 . For instance, if N = 10, there are 45 possible links and more than 35 trillion network configurations. If one drops, say, 25 of these links because they are impeded by social structure, this still leaves 33 million possible network configurations – many of which can achieve efficiency, depending on the structure of the remaining network and the distribution of endowments. This shows that while friction can distort resource allocation, proving that it actually does is considerably more complicated. To demonstrate that misallo- cation arises because of a specific aspect of social structure, it is necessary to consider social links, pairwise flows, and aggregate allocation simultaneously. With a few exceptions (e.g., La Ferrara 2003 on credit and (e.g. Sadoulet et al., 1997; Holden and Ghebru, 2005; Macours et al., 2010) on land markets),1 this has seldom been done. The purpose of this paper is twofold: to present a methodology that can identify whether resource misallocation is due to specific restrictions to flows between agents or groups of agents; 2 and to illustrate its usefulness with an example that is relevant for development policy. The proposed method is potentially applicable to a wide range of questions. Its main use is to investigate whether a particular dimension of social structure may be involved in resource misallocation. It does so by checking that the pattern of flows across agents is consistent with the existence of frictions associated with a particular social structure. If no evidence is found, it implies that this particular aspect of social structure could not have caused the misallocation.2 The methodology is implemented by focusing on land allocation in village economies. Factor markets in developing countries are plagued by incomplete information and unclear property rights that lead to high transaction costs and are thought to hinder the allocation of productive factors (de Janvry et al., 1991; Pender and Fafchamps, 2005; Otsuka, 2007). Pre-existing social networks are thought to play an important role in alleviating these issues by increasing trust, decreasing information asymmetries, and reducing transaction costs. Such markets are thus a good test case for the methodology presented here. Land ownership is notoriously unequal in many agrarian societies. At the same time, tra- ditional agricultural systems are often characterized by decreasing returns to scale beyond a minimum scale of operations (see Ali and Deininger (2015) for an excellent recent review of the literature). A more efficient and equitable allocation of cultivated acreage thus requires temporary transfers of land from land-rich to land-poor farming households. It is also well known that homophily and discrimination are common in market and non-market exchange: many people prefer to trade and exchange favors with people who are socially proximate. The question therefore arises of whether homophily and discrimination contribute to the unequal allocation of cultivated acreage. Access to agricultural land is a sensitive political issue in many developing countries because it is a major determinant of household welfare. Whenever access to land is impeded – or perceived to be impeded – by ethnic and other social divides, this can lead to violence, as has been seen in a number of developing countries. Identifying the dimensions of social structure that contribute to unequal access to land can thus make a valuable contribution to conflict prevention. The empirical analysis takes advantage of an unusually rich dataset on land and labor trans- 3 actions in the rural Gambia. Land usage rights in rural Gambia are vested in the hands of the descendants of the ancestral settlers, and thus the distribution of land ownership rights is highly unequal. This results in an abundant practice of land exchange between households whereby temporary land usage rights are transferred on an annual basis. This makes The Gambia a suitable candidate for testing how pre-existing networks in the form of ethnicity, kinship and geographical proximity affect the efficiency properties of temporary land trans- fers. The data covers all pairwise transfers of agricultural land and labor in 50 rural Gambian villages, together with information on pre-existing social links between each pair of house- holds. The focus is exclusively on the factor transfers themselves, not on the form (e.g., gift, rental, sharecropping) or motivation (e.g., reciprocity, self-interest) of the transactions – these are examined in detail, for the dataset at hand, by Jaimovich (2011), Jaimovich (2015) and Beck and Bjerge (2017). The methodology of this paper is based on flows only and the main results of the paper do not depend on the underlying mechanism behind these flows. Land ownership and cultivated acreage are unequally distributed across farmers, with system- atic differences between ethnic groups. Further, transfers of temporary usage rights over land are more common between neighbors or family related households. A prima facie, evidence thus suggests the presence of frictions between non-neighbors and unrelated households. But do these frictions contribute to aggregate inequality in cultivated acreage? There is no evidence that ethnic or kinship groupings distort land transfers away from an equal distribution of land. In other words, the data rejects the idea that preferential ex- change between certain farmers contributes to land inequality. The main reason seems to be that a small number of land-rich households transfer land to non co-ethnic farmers in their village, and these transfers are sufficient to compensate for the abundance of small land transfers between socially proximate households. These findings are in agreement with the anthropological and historical literature about land settlement in sub-Saharan Africa, which emphasizes the redistributive role of pioneer lineages who control the village land that their ancestors cleared, but who welcome newcomers into their community with transfers of usage rights over land (Platteau, 1992). The paper contributes to the literature in several different ways. The first contribution is 4 methodological. There can be many ways by which goods can end up in the right hands by travelling along pre-existing social ties. The proposed method empirically resolves this difficulty by approaching exhaustive data on dyadic flows from an aggregate point of view. This method is applicable well beyond factor markets in developing countries. It is potentially applicable to research questions as diverse as gravity models and international trade; labor markets; value chains; favor exchange; electrical power grid and diffusion of information on social networks. As argued more in detail in the appendix, all these questions have in common that flows take place on a network of links that are partially shaped by the geographical and social context. The same question arises in all of them: do restrictions on flows potentially imposed by social structure lead to an inefficient or inequitable allocation of resources, as evi- denced by unequal marginal productivities or utilities – or ratios thereof? The main constraint to the applicability of the method is the availability of exhaustive information about dyadic flows, and sufficiently detailed information about social structure. While such datasets have largely been lacking in the past, they are becoming increasingly available. The methodology can also be applied to study whether differences in prices, costs, access or opportunities are due to social, geographical, or regulatory obstacles to exchange. The empirical application presented in this paper illustrates how the method can be used to identify situations in which social structure is an obstacle to an efficient or equitable resource allocation. Second, the paper contributes to the empirical literature on the importance of pre-existing social networks for offsetting the negative effects of market imperfections. There is some evi- dence to this effect – but perhaps not as much as anticipated, based on the existing literature. Third, this paper provides empirical evidence on the efficiency properties of social networks in The Gambia, a country that is fairly representative of West African rural institutions. If pre-existing social networks are important for the selection of trading partners, this has direct implications for the prospects of reducing poverty and inequality as well as economic growth (Holden et al., 2009). This issue is particularly important in West Africa where access to land is an increasing concern as land scarcity increases due to population growth (World Bank, 2005). Land ownership is unequally distributed within villages of the Gambia, with some systematic advantage to members of the majority ethnic group in each village. Land transfers 5 serve a modest but significant role in equalizing factor allocations between households, and they do so in a way that appears unimpeded by ethnic and kinship divisions. Geographi- cal proximity, in contrast, appears to have a factor equalizing effect over and above that of village-level equalization. The paper is organized as follows. Section 1 provides an overview of the conceptial framework of the paper. Section 2 presents the methodology and articulates a novel testing strategy aimed at identifying the role of social ties in shaping transfers. The section starts by showing how the method works for a single good. It is then illustrated how it can be applied to study allocative efficiency in factors of production. The rest of the paper applies this this method to agrarian factor markets in The Gambia. Section 3 describes the land tenure system in rural Gambia and the data used in the empirical analysis. In Section 4 the the testing strategy is applied to the data and main results of the empirical analysis are presented. Section 5 discusses alternative interpretations of the empirical findings and provides a number of robustness checks. Section 6 concludes. 1 Conceptual framework In this paper, a method for testing whether misallocation of resources can be ascribed to frictions to the flow of goods that are associated with a particular aspect of social structure is proposed and tested. Much attention has been devoted to test whether goods or services flow less freely between certain econonomic agents than others. Studies using data at the plant- level have documented how misallocations of input factors contribute to differences in total factor productivity across countries (Alfaro et al., 2008; Hsieh and Klenow, 2009; Midrigan and Xu, 2014). Frictions have also been documented between individuals. In a meta analysis of controlled experiments in 10 countries, Riach and Rich (2002) note that ”significant, persistent and pervasive levels of discrimination have been found against non-whites and women in labour, housing and product markets”. Experimental evidence of labor market discrimination is also reported by Bertrand and Mullainathan (2004), Goldin and Rouse (2000), and Carlsson and Rooth (2007), among others. In the same vein, Edelman et al. (2017) find that white 6 landlords of a well-known online platform are less likely to rent to black tenants. Hanson and Hawley (2011) report similar evidence in the housing market. Fafchamps and Gubert (2007) find that risk-sharing transfers occur primarily between neighbors and relatives. While this body of work provides compelling evidence of frictions, it does not by itself imply that discrimination causes misallocation: individuals who are discriminated against by some employers or landlords may find equivalent employment elsewhere. Whether frictions cause misallocation depends on whether they impede flows sufficiently for misallocation to arise. An intuitive way of visualizing the issue is from a high school physics example, namely, communicating vessels.3 Imagine a set of N vessels linked to each other by pipes. Unequal amounts of water are poured in these vessels, with ai denoting the water poured in vessel i. Think of vessels as representing households and water as being any good or service that is exchanged between them, either through market or non-market exchange. Water pipes represent the social structure. Equalization of water levels represents the equalization of marginal productivities or utilities – or of their ratios (see appendix for examples). Physics theory informs us that water levels will be equalized among all communicating vessels. This can be represented formally as a network or graph in which each vessel is a node and each pipe is a link Lij between two nodes i and j . Friction across social groups usually translates into clustering within groups – i.e., more links between group members. Yet, if all vessels are connected either directly or indirectly, they all belong to the same component and water levels will equalize across all of them. In other words, clustering/preferential attachment does not impede equalization. Alternatively, the network may be divided into multiple components, that is, into distinct subsets of nodes that are connected with other nodes in the same component, but not with any node in other components. In that case, water levels will equalize within components but not across components. What this example shows is that equalization of levels cannot be predicted by clustering: links (and hence flows) may be more frequent within certain subsets of the network, e.g., between co-ethnic nodes; but all nodes within the same component have equal access to water. It is only when social structure precludes flows between components that access can be unequal. 7 Even in this case, however, water level equalization can occur if the water endowment of each component is proportional to their number of nodes. It follows that level equalization depends both on the distribution of initial endowments and on aggregate properties of the network – in this simple case, its partition into distinct components. Local network properties like clustering/preferential attachment have little predictive power. Similar conclusions apply to other distributive networks. This example can be amended to allow only some of the water to go through individual pipes.4 Let sij ≥ 0 be the maximum amount of water that can flow from i to j , and let S ≡ [sij ] denote the matrix of all sij . If there is no pipe between i and j , sij = 0. When flows are constrained, it is difficult to determine a priori whether equalization can be achieved within components or even between any pair of nodes i and j . In particular, it is not possible to predict whether equalization will be achieved between any pair of nodes i and j simply from knowing their local properties sij , ai and aj . Even if i and j are not connected (sij = 0), water may flow between them through other nodes, equalizing water levels between them. In contrast, even when the connection between the two nodes is sufficient to equally share their initial endowments ai and aj , flows to and from other nodes may prevent pairwise equalization between them.5 Hence it is not because flows are restricted between i and j that equalization cannot be achieved, and it is not because flows between i and j are less constrained that equalization will be achieved between them. The same reasoning applies to other distributed networks, e.g., electric power grid, value chains, gravity models, and the like.6 Several lessons can be drawn from the above discussion. First, observing that individual flows are shaped by local social structure does not imply that allocation is unequal. The reverse is also true: the fact that social structure does not shape flows does not imply equal access – there can be obstacles to flows that are not correlated with social structure. Finally, observing that social structure shapes individual flows and that allocation is unequal does not, by itself, imply that one causes the other. To address the latter issue a methodology that identifies situations in which the pre-existing social structure is responsible for unequal allocation is proposed. 8 2 Testing strategy Given that the method is applied to land and labor transfers later in the paper, the testing strategy is framed in terms of factors of production. But it is in principle applicable to any good or service, and to any flows – whether they take place in a centralized manner, or through decentralized market or non-market exchange. Consider an economy with N farming households observed during a single cropping season. Each household starts the season with ai units of a single factor of production, say land. N The total supply of a in the economy is denoted A ≡ i=1 ai . Each agent shares the same production function q (xi ) where xi denotes the land available for cultivation by agent i. It is assumed that q (xi ) exhibits decreasing returns to scale in xi .7 The efficient factor allocation A is to set xi = a = N to equalize the allocation of land across households. In the absence of frictions, this allocation can be expected to be realized through mutually beneficial exchange.8 Given these assumptions, failure to equalize land across households signals the presence of frictions. The object of interest is to what extent the failure to achieve an efficient allocation is associated with specific aspects of observable social structure. Let li be the net amount of a that is transferred out by household i. Allocative efficiency requires that households have an equal amounts of land after transfers, i.e., that ai − li = a which implies that li = ai − a for all i. A regression of the following form can be employed to investigate whether the average factor transfer is efficiency-enhancing: li = α0 + α1 (ai − a) + ui (1) Allocative efficiency requires α1 = 1. Land transfers are efficiency-enhancing if 0 < α < 1. This occurs when, on average, land-rich households transfer land out and land-poor households receive land transfers. While easily implementable, regression (1) does not allow testing the effect of pre-existing networks on the efficiency properties of factor transfers. To do so, the analysis is moved to the dyadic level, i.e., the pairwise level. Factor transfers between households can be represented 9 by a weighted directed graph in which agents are nodes and transfers are links. Let wij denote a net transfer of a from agent i to agent j with wji = −wij by definition. Let the transfer matrix W ≡ [wij ] denote the set of all pairwise transfers. Simple accounting implies that transfers satisfy: xi = ai − wij j =i xi = A i subject to feasibility conditions of the form: xi ≥ 0 for all i Let W ∗ denote a transfer matrix that satisfies the feasibility conditions and achieves efficiency, i.e., such that xi = a for all i. Call such matrices efficient. There is a very large number of efficient matrices W ∗ , which means that the specific factor transfers that are needed to achieve efficiency are undetermined. The reason is simple. Say that a necessary condition for efficiency is that i transfers 3 units of land to others. This can be achieved in a myriad of ways, e.g., by giving 1 to j and 2 to k , or 1.5 to j and 1.5 to k , or 3 to m, etc. Testing aggregate allocative efficiency While it is not possible to determine which specific trades take place without introducing additional assumptions,9 it is possible to provide some characterization of average trade flows if they serve to improve allocative efficiency within a village v with average landholdings av and population Nv . The logic is best illustrated with an example. Starting from an unequal factor distribution in village v , allocative efficiency requires that those with an above-average endowment transfer out ai − av and that those with a below-average endowment receive in av − ai .10 Although there are many transfers wij that can achieve this result, allocative efficiency requires that, for each i, the sum of i’s out-transfers satisfies j wij = ai − av . Similarly, the sum of in-transfers 10 is j wij = av − aj . Thus if all net transfers wij in village v are observed, a regression of the following form can be estimated: ai − a a − aj wij = α0 + α1 + α2 + uij (2) Nv Nv over all Nv (Nv − 1) dyads. Since wij = −wji by construction, it follows that α0 = 0 and α1 = α2 always. If land transfers achieve an efficient allocation, it must be that α1 = 1 = α2 . Simulation results detailed in the appendix confirm this property. The appendix also shows that α1 provides an estimate of how far actual transfers are from efficient transfers: for any set of ∗ that are multiplied by a shrinking factor τ < 1 such that w = τ w ∗ , efficient transfers wij ij ij then α1 = τ = α2 . Hence the closer α1 is to zero, the less efficiency gains are achieved by land transfers. Testing group-wise efficiency Now suppose that transfers can only take place between certain pairs of nodes – e.g., because social ties are needed to mitigate information asymmetries and enforcement problems. To fix ideas, let S ≡ [sij ] denote, as before, the set of maximum socially feasible flows such that: |wij | ≤ sij for all ij (3) S is not observed directly. Instead, pre-existing social links thought to reduce frictions are used as proxy variables for sij : if the absence of a particular type of social link between i and j precludes factor transfers, then one can expect wij = sij = 0. Can efficiency be achieved? This depends on whether there exists an efficient transfer matrix W ∗ that satisfies the set of constraints (3). If such a matrix exists, allocative efficiency can be achieved even though transfers can only occur along existing social ties. If it does not, restrictions imposed by matrix S prevent allocative efficiency from being reached – unless aggregate land endowments happen to be identical across groups. 11 As discussed earlier, allocative efficiency may be prevented when the network is segmented into distinct components. Formally, this means that the set of nodes N can be partitioned into mutually exclusive sets {N1 , ...Np } such that (1) there is a path in S leading from any node in Nk to any other node in Nk ; and (2) there is no path in S leading from a node in Nk to a node in Nm=k . In this case, allocative efficiency is only possible within each component. It follows that if average factor endowments are identical across components, allocative efficiency can be achieved since it does not require flows across components. If average endowments vary across components, however, allocative efficiency is precluded since it requires flows between components. In this case, applying model (2) separately to each component yields: ai − ak ak − aj wij = α0 + α3 Dij + α4 Dji + uij (4) Nk Nk 1 where Nk is the size of the component k , ak ≡ Nk i∈Nk ai is the average endowment in component k , and Dij = 1 if i and j belong to the same component k and 0 otherwise. As before, α0 = 0 and α3 = α4 always. Allocative efficiency within components requires α3 = 1 = α4 , and the magnitude of α3 captures the extent to which transfers achieve within- component equalization of land available for cultivation. See the appendix for illustrative examples. An extreme case of this is when transfers are only possible across pairs of agents – e.g., between neighbors or between brothers. In this case, the regression model simplifies to: ai − aj wij = α0 + α5 Lij + uij (5) 2 where Lij = 1 if there is a direct link between i and j in S , and 0 otherwise. If allocative efficiency is only achieved across isolated linked pairs of agents, then α0 = 0 and α5 = 1. An illustration is provided in the appendix. 12 Testing social structure To investigate the role of social structure in allocative efficiency, we combine the estimation of individual models (2), (4) and (5) with various joint models discussed below. As long as aver- age factor endowments differ between social groups, the same method applies. From model (2) an estimate α1 of how far transfers are from being allocatively efficient on average is obtained; if α1 < 0 it means that transfers move land allocation away from efficiency. Comparing α1 to α3 in model (4), shows whether more efficiency is achieved within components than in aggregate. If α3 > α1 , this indicates that the lack of social links between components hinders aggregate efficiency. Similarly, if α5 > α1 , more efficiency gain is achieved within pairs than in aggregate. In all these cases, identification requires average factor endowments to differ across social groupings. Indeed, when average endowments are identical across groupings, no flow is required for efficiency and thus restrictions on flows have no identifiable effect on aggregate efficiency. Results can be further refined by estimating joint models of the form: ai − av av − aj wij = α0 + α1 + α2 Nv Nv ai − ak ak − aj +α3 Dij + α4 Dij + uij (6) Nk Nk ai − av av − aj ai − aj wij = α0 + α1 + α2 + α5 Lij + uij (7) Nv Nv 2 ai −av av −aj In model (6), two types of differences can arise between Nv and Nv on the one hand, ai −ak ak −aj and Nk Dij and Nk Dij on the other: av = ak ; and Dij = 0 for some pairs. If average endowments differ across components, convergence towards the village average can take the allocation of land away from allocative efficiency within components. This results in α3 = α4 < 0 while at the same time the estimates of α1 and α2 in (6) are larger than in (2). In contrast, if transfers serve to equalize land within components more than across components, then α3 = α4 > 0 and α1 and α2 tend to zero. 13 A similar reasoning applies to (7): if improvements in allocative efficiency are achieved solely through transfers across linked pairs, α1 and α2 tend to zero while α5 remains positive. In contrast, if individual pairwise links place no restrictions on aggregate efficiency gains means that that α5 tends to zero while α1 = α2 > 0. Extensions To explain the testing strategy the focus has been on a simple case in which returns to scale are decreasing and there is a single traded factor. The advantage is that this case closely resembles the communicating vessels example: allocative efficiency requires land equalization, and the role of social structure can be investigated by testing whether transfers equalize land available for cultivation across all households, or within components, or across individually linked pairs. Before taking this testing strategy to the data, however, a natural question to ask is whether assuming decreasing returns to scale and a single traded factor makes sense for the context of the current study. While the data at hand does not contain specific information about yields, it is well known that, in the kind of traditional farming area under study, yields fall with farm size. This has been well documented in the literature (e.g. Ali and Deininger 2015).11 Hence it is not unreasonable to assume that returns to farm size are decreasing for the purpose of this study. As documented in the next section, trade in labor is much less prevalent than land transfers, suggesting that, at least as a first approximation, assuming a single traded factor is not entirely unreasonable either. What cannot be ruled out is that farmers differ in terms of productivity – e.g., because of differences in agricultural knowledge, business acumen, or household labor mobilization. So far, a maintained assumption has been that all households share the same decreasing returns to scale production function q (xi ). In this case, allocative efficiency requires equalization of land across all farms. If households differ in productivity, however, land equalization is no longer efficient. The method can nonetheless be applied if productivity differences across farmers are multiplicative (i.e., Hicks-neutral). In this case, allocative efficiency requires equalization of factor ratios. In the appendix, it is shown how models (2), (4), (5), (6) and (7) can be modified for this case by replacing the land endowment ai with factor ratios throughout.12 14 3 Data To illustrate the testing strategy outlined in the previous section, a a unique dataset, the Gambia Networks Data 2009, is used, which were collected in six out of eight Local Govern- ment areas between February and May 2009. A sample of 60 villages was randomly selected among villages with between 300 and 1000 inhabitants in the 2003 census. Restricting the sample to small villages is motivated by the desire to obtain complete dyadic data on factor transfers for each entire village. Collecting similar data in larger villages would have been impractical. For more detailed information on the data collection strategy, see Jaimovich (2015). The sample is representative of smaller villages of The Gambia, which account for 20 percent of villages in the country (Arcand and Jaimovich, 2014). Data was collected on each household in each village using a structured group interview approach. Information is available on the land ai and labor li endowments of each household, as well as on all land and labor transactions wij within each village for an entire agricultural year. The data also contains information on pre-existing social links. Six villages are dropped from the analysis presented here because of missing household-level information. Given that the empirical focus is on factor transfers in agriculture, three semi- urban villages are dropped13 and the analysis is restricted to households whose main activity is farming.14 The sample used for the empirical analysis consists of 1,625 households across 50 villages, corresponding to 54,144 within-village dyads. Descriptive statistics paint a picture typical of rural Gambia.15 Rural villages in The Gambia are organized around compounds. A compound is a group of buildings, used for housing, storage and other purposes, that are located in relative prox- imity to each other, typically around a central courtyard. Most often, a compound has a single household head that makes decisions regarding production and other daily activities. Sometimes a compound has several decision makers. In such cases, independent production units (dabadas ) can exist within the compound and independent consumption and cooking units (sinkiros) can exist within a single compound or within a single dabada (von Braun and Webb, 1989; Webb, 1989). Since the interest is in production decisions, the dabada is used as 15 the unit of observation. If several dabadas reside within the same compound, the data contain information about the social links between them. Fourteen percent of household heads in the sample are not heads of the compound in which they live. Endowments and transfers of land and labor In The Gambia, all land is nominally owned by the state, but usage rights are determined by the indigenous land tenure system (Freudenberger, 2000). Two principal types of usage rights exist, which are referred to as primary and secondary. A household with primary rights over a plot of land can not only decide which crops to grow but also whether to lend all or some of the land to another farmer – in which case this farmer gains secondary rights over that land. A household with secondary rights over a plot has full control over its agricultural management while they maintain secondary rights over it. Landless and land-poor households can obtain secondary usage-rights to land in two ways (Freudenberger, 2000). First, households with surplus land have a moral obligation to transfer secondary rights over some of it to those in need. The village chief, in particular, often has a land reserve from which he can allocate land to households in need. Second, usage rights over land can be accessed through market-based transactions such as land rental. Sharecropping is not a common practice in The Gambia.16 The questionnaire was designed to capture both monetary and non-monetary transfers of secondary usage rights. In practice, most transfers are non-monetary, although small payments in cash, kola nuts, or labor services sometimes are made to mark the fact that the secondary user continues to recognize the primary rights of the owner over the land (Eastman, 1990; Freudenberger, 2000; Jaimovich, 2011). This practice is common in African land tenure systems (e.g., Platteau 1992) and is confirmed by field observations made during the survey. Secondary usage rights are temporary in nature. Plots are borrowed on an annual or seasonal basis (Chavas et al., 2005). This means that households with few or no primary usage rights to land must secure or renew secondary usage rights every year. The overwhelming majority of land transfers recorded in the survey relate to annual or seasonal usage rights. 16 Table 1: Descriptive statistics on land and labor Mean Std. Dev. Have primary usage rights to land 81.9% Land owned with official rights (hectares) 10.5 24.5 Gini coefficient of land owned 0.52 Ratio of land share to population share of main ethnic group 1.2 Land-labor ratio (hectares land per active worker) 2.76 7.39 Participates in land transfers 45.2% Land transfer (hectares) 1.04 2.83 Land transfer (% of donors’ land endowment)* 37.6% 0.307 Number of working adults 5.4 10.4 Participates in labor transfers (within the village) 54.4% Labor transfer (days) 5.3 15.4 * Conditional on transferring out land. Excludes observations where the donor is also a receiver. Source: Author’s own calculations on the Gambia Networks Data 2009. 82 percent of farming household have some primary usage rights to land and their average land holding is 10.5 hectares per household (see table 1). The distribution of primary usage rights is highly unequal, however, with some households having less than 0.5 hectares and others more than 100 hectares. The Gini coefficient of primary land rights, averaged over the 50 villages, is 0.52 and the share of land in the hands of the 10% most land-rich households is 34% on average. This unequal distribution is partly a result of the process of village settlement – which, in the case of much of sub-Saharan Africa, tend to be relatively recent.17 According to African customs, village founders acquire primary usage rights over the land they clear. Upon their death, these rights are passed on to their descendants. As the village grows by attracting new members from other lineages and ethnic groups, descendants of the village founders tend to retain rights over more of the village land. The unequal ownership of land is reflected in the social structure: members of the founder lineages have intermarried and tend to belong to the same ethnic group. Therefore, owners of much of the land tend to come from the same ethnic group and to all be related to each other: a village’s main ethnic group typically own more land than its share of the population – the ratio between the two exceeds 1 on average (see table 1). Similarly, households in the village’s largest kinship group on average own more than three times more land that households outside that group. There is therefore much scope for increasing allocative efficiency by transferring secondary land usage rights from descendants of the village founders to relative newcomers. 17 Efficiency-enhancing transfers of land should thus flow primarily from founder lineages to other ethnic and kinship groups. It is nonetheless unclear whether moral obligations to transfer usage rights to land-poor households are sufficiently strong to extend across ethnic and kinship lines. The dataset also contains information about labor endowments. Households have an average of 5.4 working-age adults. The corresponding land–labor ratio is 2.8 hectares per working adult on average among the farming households in the sample. While this indicates that land is relatively abundant on average, land endowments are inequitably distributed, so that the median land–labor ratio is 1 hectare per working adult. These observations form the main motivation for the empirical investigation: the settlement history of Gambian villages has generated a highly unequal distribution of primary land rights that partly coincides with ethnic and kinship divides. Hence the main research question of this paper: are transfers of secondary land rights hindered by social structure, thereby hindering allocative efficiency? Descriptive statistics on participation in land and labor transfers, in the sample as a whole, and separately by land–labor ratios are provided in table 2. Around 45 percent of households engage in land transfers, and households that export land typically transfer land to more than one household. Land transfers amount to 38 percent of the initial land endowments of the land-exporting households. At the receiving end, 36 percent of landless households in the sample receive secondary land rights from other households.18 A large proportion of households participate in labor transfers (54 percent). But the average household head only spends 5.4 days working on someone else’s farm. This is small compared to land transfers, which amount to more than one hectare of land per household, or around 10 percent of their average land endowment. One possible interpretation, often proposed in the literature (e.g., Ali and Deininger 2015) is that transaction costs are higher for labor than land transfers – possibly because of supervision difficulties.19 For this reason, labor markets in subsistence agriculture are very thin throughout most of West Africa (Otsuka, 2007; Holden et al., 2009).20 Since land transfers by definition take place before labor transfers, transfers 18 Table 2: Land and labor market participation rates by initial land–labor ratios All Landless 0.1-0.6 ha/w 0.6-1.6 ha/w 1.6-3.0 ha/w 3.0 ha/w Land transfers: Participates 45.2 36.1 42.4 41.1 53.8 56.5 Land sender 21.0 2.0 14.9 19.0 30.1 40.5 Land receiver 28.9 35.7 33.3 26.2 30.5 21.4 Labor transfers: Participates 54.4 42.5 49.8 56.6 64.3 57.5 Labor sender 36.9 30.6 34.1 39.5 43.6 34.7 Labor receiver 32.3 23.8 27.5 30.6 41.0 39.8 Observations 1,625 294 255 516 266 294 Note: ha/w corresponds to the number of hectares per working adult. Source: Author’s own calculations on the Gambia Networks Data 2009. of secondary land rights serve to reduce differences in land-labor ratios across households ex ante, so as to obviate the need for ex post adjustment through labor transactions. As a result, the primary role of labor transactions is to deal with shocks in household manpower availability, e.g., through illness. A cursory look at the data reveals that, as anticipated, households with a higher initial land–labor ratio are more likely to transfer-out land and less likely to transfer-in land. The same pattern is not evident for labor: land abundant households are not more likely to transfer in labor, suggesting that labor transfers do not serve to equalize land-labor ratios across households. For these reasons, the empirical analysis is largely focused on transfers of secondary land rights. Social proximity The focus is on dimensions of social structure that have been widely discussed in the literature. Ethnicity is included because ethnic fractionalization has been shown to be associated with aggregate outcomes (e.g., Alesina et al., 2003, 2016) as well as with frictions and discrimination (e.g., Riach and Rich, 2002, and the other references listed in Section 2). We include kinship and family ties because they have long been suspected of being a source of market inefficiency and inequality (e.g., La Ferrara, 2003). Frictions caused by distance have also long been documented (e.g., Ravallion, 1986; Fafchamps and Gubert, 2007). These aspects of social 19 Table 3: Descriptive statistics on ethnicity and kinship links Mean Ethnicity: Mandinka 54.1% Ethnicity: Fula 18.6% Ethnicity: Wollof 10.1% Ethnicity: Jola 6.5% Ethnicity: Sererr 5.6% Household head has family links in the village 85.0% Wife of household head has family links in the village 50.8% Household have marriage links in the village 64.2% Household has family links in the village 95.8% Observations 1,625 Source: Author’s own calculations on the Gambia Networks Data 2009. structure may also be more amenable to policy interventions aimed at reducing discriminatory behavior. In contrast, it is unlikely that it is possible to ever totally eliminate idiosyncratic obstacles to trade due to, say, enmity between individuals. The data contain information on three distinct aspects of pre-existing social structure: eth- nicity, kinship (family ties), and geographical proximity. This data is used to construct two group-wise Dij and two pairwise Lij variables. The sample is representative of the ethnic diversity in The Gambia. The largest ethnic group (Mandinka) accounts for 54.1 percent of households in the sample (see table 3). Four other ethnic groups each account for at least 5 percent of the households.21 Since, by definition, ethnicity is shared by all the members of E equal to 1 if i and j share the same a group, it is captured using a group-wise variable Dij ethnicity. In this case, each ethnic group forms a component. Kinship, in contrast, defines a symmetric network in which a link LK ij between two households i and j is defined to exist if they are related, either through the household head, the wife(s) of the head, or through marriage. Unlike in other African contexts (e.g., Barr et al., 2012), kinship networks are relatively dense in the sample. 85 percent of household heads and 51 percent of their wives have relatives in the village (see table 3). Similarly, 64 percent of households have marriage ties in the village. In total, 95.8 percent of households have at least one of these kinds of links. This means that the largest component of the kinship network is often large: in the majority of villages, most (though not all) households are connected, directly or indirectly, through consanguinity and marriage, and thus belong to the same 20 K. network component. Component membership defines a second group-wise variable Dij The dataset also contains information on whether two households reside in neighboring com- pounds. This information is used to define a pairwise variable LD ij equal to 1 if i and j are neighbors, and 0 otherwise. Given that households live relatively close to each other, there D is not is no natural partition of households into components, and a group-wise variable Dij defined. Data on geographical proximity were only collected in 25 of the villages, containing 624 households in total. In the reduced sample on which proximity data is available, almost 10 percent of the households are compound neighbors. Kinship, ethnicity, and geographical distance are the dimensions of social proximity for which there is data available. They offer the advantage of being immutable or pre-determined and are thus reasonably exogenous to the factor transfers taking place within an agricultural sea- son. Nonetheless, factor transfers between two households are often embedded in long-term relationships of favor exchange that are not observed. From the available literature, it is likely that these favor exchange relationships are shaped, as least partially, by kinship, ethnicity, and geographical distance. If gift exchange transcends pre-determined social categories such that they do not matter, this will show up in the analysis as zero α3 , α4 and α5 coefficients on network regressors. Even in this case, gift exchange may still not achieve efficiency. For in- stance, even if people choose their network links so as to maximize gains from factor exchange, they may not be able to sustain a number of links that is sufficient to ensure equalization of factor endowments or factor ratios in all circumstances. This situation will manifest itself in the form of α1 and α2 being less than 1. These observations form the basis for the testing strategy. The network structure of the data give rise to two potential problems to identification of the α parameters. First, in order to seperate out the effects of different pre-existing networks, sufficient variation between different network measures is needed to avoid multicollinearity. A second potential identification issue relates to the need for multiple components within each village to identify component effects. In order to check this, the mean and range of the share of households who belong to the largest and second largest components of ethnicity and family ties were calculated (see appendix S2.2 for statistics and additional discussion). 21 Link correlations are sufficiently low as to not to present a problem for identification. While some villages do not contribute to the identification of component parameters, many villages consist of multiple components and this generates sufficient variation to estimate component parameters. 4 Empirical results Before launching into the estimation of the model, the available evidence regarding the re- distribution of land among farming households through transfers is considered. The Gini coefficient on after-transfer household land is 0.47, compared to 0.52 for before-transfer land endowments. More than 75 percent of villages have a more equal factor distribution after land transfers than before. The proportion of after-transfer land in the hands of the 10% most land-rich households is 31% – down from 34% on average. Land transfers also tend to equalize differences in endowments across ethnic groups: after transfers, the largest ethnic group controls 1.12 times more land than members of other ethnic groups, compared to 1.2 before transfers. To conclude, transfers have, on average, an equalizing effect on the allocation of cultivable land. But the distribution of land after transfers remains fairly unequal. As initial check on the idea that inequality is mitigated by social structure, a set of regressions of village-level land inequality on measures of social network density are estimated (Table 4). To facilitate interpretation, network density is normalized by its standard deviation. Inequal- ity measures are calculated both before and after land transfers. The results show a negative association between village network density and land inequality before transfers: more so- cially connected villages are more equal both before and after land transfers. This is true for both the kinship network as well as neighbor links, but this association does not hold for the ethnic components. This is somewhat surprising discussed in more length in connection to the link-level analysis. The effects are qualitatively unchanged if instead inequality after land transfers is considered, although the significance level is reduced.22 The estimated coef- ficients are small, but economically meaningful: a one standard deviation increase in either the kinship or neighbor density measure is associated with a decrease in the Gini coefficient 22 Table 4: Village land inequality and social network density (1) (2) (3) (4) (5) (6) Before land transfers After land transfers Kinship Ethnicity Neighbor Kinship Ethnicity Neighbor Density / SD -0.068*** -0.019 -0.107** -0.038* 0.005 -0.071* (0.021) (0.023) (0.041) (0.020) (0.020) (0.035) Constant 0.645*** 0.572*** 0.662*** 0.542*** 0.457*** 0.557*** (0.043) (0.066) (0.077) (0.041) (0.059) (0.066) Observations 50 50 24 50 50 24 Note: The dependent variable is the Gini coefficients in land in each village. It varies between zero and one. Source: Author’s own calculations on the Gambia Networks Data 2009. Table 5: Land transfers and social proximity (1) (2) (3) (4) (5) Ethnic component 0.000 -0.001 (0.001) (0.005) Family component -0.005 -0.002 (0.008) (0.009) Family link 0.045*** 0.045*** (0.009) (0.010) Neighbor link 0.035*** 0.026** (0.011) (0.010) Constant 0.037*** 0.041*** 0.031*** 0.023*** 0.020** (0.006) (0.008) (0.005) (0.004) (0.007) Observations 54,144 54,144 54,144 21,266 21,266 Note: The dependent variable is the absolute amount of land transferred from i to j measured in hectares. Standard errors clustered by village are shown in parentheses. *** p<0.01, ** p<0.05, * p<0.1 Source: Author’s own calculations on the Gambia Networks Data 2009. of between four and eleven points, depending on the network density measure used. Whether land transfers are more common between socially proximate households is also in- vestigated. To this effect |wij | is regressed on the five measures of social proximity described E , membership in the same kinship component D K , being directly earlier: co-ethnicity Dij ij related LK D E K ij , and being neighbors Lij . Results show that Dij and Dij do not predict land transfers, but LK D ij and Lij do, suggesting homophily in land transactions along those two dimensions (see table 5).23 The situation can thus be summarized as follows: an essential resource is not allocated eq- uitably between small producers, a situation there are reasons to suspect is inefficient; the 23 dominant ethnic group in a village owns more land; inequality in land and factor ratios is lower in more socially connected villages; and farmers who are neighbors or directly related share more land with each other. To many, this type of evidence is a smoking gun suggesting that preferential transfers between members of the land-rich dominant ethnic group contribute to the unequal land allocation. The purpose of the testing strategy is to put this reasoning to the test. First, the the various models outlined in section 2 on land transfers alone are estimated. The main reason for focusing on land is that, as noted above, land transfers are much more important than labor transfers in terms of the proportion of traded factors. A fair approximation of the data is that land transfers are used to determine the size of one’s farm ex ante, while labor transfers are used to deal with temporary surpluses and deficits in labor ex post – e.g., in response to unforeseen shocks in the production process (Fafchamps, 1993). To verify the robustness of the findings, in the next sub-section we replicate the analysis in terms of land–labor ratio. As discussed in the conceptual section and demonstrated in the appendix, the methodology can similarly be applied using land-labor ratios in lieu of land endowments to allow for possible trade in labor. Land transfers First, whether land transfers eliminate differences in land endowments is tested. This is achieved by estimating the simplest model (2). The average land endowment a is calculated as the sum of all land endowments divided by the number of households in the village.24 Since the regression is dyadic, standard errors must be corrected for non-independence across observations. To deal with this issue, standard errors are clustered at the village level. This allows for any correlation structure between errors within each village, including the type of network error correlation discussed in Fafchamps and Gubert (2007). The fact that α1 is positive and statistically significant imply that land abundant farmers on average transfer out land, while land-poor households import land from others (see table 6). But these transfers are not sufficient to equalize land across households within each village: 24 Table 6: One factor model: Do social components equalize farm size? (1) (2) (3) (4) (5) Regressor Coefficient Ethnicity Kinship Ethnicity Kinship (ai −a) Nv α1 0.024** 0.032*** 0.0510*** (0.009) (0.011) (0.016) (a−aj ) Nv α2 0.024** 0.032*** 0.051*** (0.009) (0.011) (0.016) (ai −ak ) Nv Dij α3 0.015** 0.017** -0.009* -0.029*** (0.006) (0.007) (0.005) (0.010) (ak −aj ) Nv Dij α4 0.015** 0.017** -0.009* -0.029*** (0.006) (0.007) (0.005) (0.010) Constant α0 0 0 0 0 0 Observations 54,144 54,144 54,144 54,144 54,144 Note: The dependent variable is the amount of land transferred from i to j measured in hectares. Standard errors clustered by village are shown in parentheses. *** p<0.01, ** p<0.05, * p<0.1 Source: Author’s own calculations on the Gambia Networks Data 2009. the test α1 = α2 = 1 is strongly rejected with p < 0.0001. This particular finding is vulnerable to measurement error in ai , which is expected to generate attenuation bias. It follows that α1 and α1 should probably best be seen as as a lower bound on the true coefficients. Still, point estimates are only a small percentage what would be required for land equalization, suggesting that attenuation bias is unlikely to account for the rejection of perfect equalization. Next, whether there are more equalizing land transfers between members of the same ethnic E and D K , respectively. Estimation group or kinship component is examined, i.e., for Dij ij results for regression model (4) indicate that transfers achieve less equalization of land area within ethnic groups (table 6, column 2) or kinship components (table 6, column 3) than they achieve across the villages as a whole: α3 < α1 in both cases. This is a first indication that land transfers do not operate primarily within ethnic or kinship groupings. In Columns 4 and 5, both sets of regressors are combined and estimate the joint model (6), repeated here for convenience: 25 ai − av av − aj wij = α0 + α1 + α2 Nv Nv ai − ak ak − aj +α3 Dij + α4 Dij + uij (8) Nk Nk Positive coefficient estimates for α1 (and α2 ) are obtained but negative coefficient estimates for α3 (and α4 ). As shown in the simulation results presented in the appendix, this outcome arises when transfers serve to equalize land across the whole village.25 This confirms that there is no more land equalization within ethnic or kinship groups than across the entire village. In other words, ethnicity and kinship are not what drives the lack of land equalization in the village. This is consistent with Arcand and Jaimovich (2014) who also conclude that ethnic divisions do not reduce land transfers in the Gambia Networks Data 2009. One possible interpretation of these findings is that lineage heads, who are entrusted with the land of their lineage, choose to co-opt newcomers into the village by granting them sec- ondary or temporary rights on land. Since these newcomers often are from a different ethnic and kinship group, this means that sizable land transfers take place across ethnic and kin- ship boundaries. If land transfers from these outliers are ignored, more evidence of land equalization within ethnic and kinship groups may be found. To verify this interpretation, the regressions are estimated without land-rich outliers. In ak − aj )/Nk below practice, outliers are winsorized by replacing values of (ai − ak )/Nk and (¯ the first percentile and above the 99th percentile with the value of the first and the 99th percentile, respectively. Two findings come out of this exercise (see appendix S2.3). First, when estimating regression model (4) (columns 1 and 2), point estimates for α3 and α4 increase markedly: they more than double for ethnicity and nearly double for kinship. This suggests that, when transfers from outliers are omitted from the analysis, the rest of the transfers within co-ethnic or kin farmers serve a more effective role in within-group land equalization. However, when model (6) is estimated, again negative estimates for α3 and α4 (albeit not significantly so in the case of co-ethnicity) and positive estimates for α1 and α2 are found. This indicates that the negative coefficients found in Table 6 are not purely due to large land 26 Table 7: One factor model: Do direct links equalize farm size? (1) (2) (3) (4) Regressor Coefficient Kinshipy Kinship Neighbor Neighbor (ai −a) Nv α1 0.021** 0.025 (0.010) (0.022) (a−aj ) Nv α2 0.021** 0.025 (0.010) (0.022) (ai −aj ) 2 Lij α5 0.002** 0.001 0.007* 0.005* (0.001) (0.001) (0.004) (0.003) Constant α0 0 0 0 0 Observations 54,144 54,144 21,266 21,266 Note: The dependent variable is the amount of land transferred from i to j measured in hectares. Standard errors clustered by village are shown in parentheses.*** p<0.01, ** p<0.05, * p<0.1 Source: Author’s own calculations on the Gambia Networks Data 2009. owners: even smaller land owners share land across ethnic or kinship boundaries. Next, direct kinship links between households LK ij are introduced, and model (5) is estimated. Results show that α5 is positive and statistically significant, suggesting that land transfers between directly related households tend to equalize their respective land areas (see column 1 of Table 7). The point estimate is very small, however: approximately 0.2% of the transfers that would be necessary to equalize landholdings between related households. Once village ai −av av −aj regressors Nv and Nv are added, the finding disappears, as shown in column 2. Again, the interpretation is that land transfers are better predicted by differences from the village average than by pairwise differences across related households. In the last two columns of Table 7 geographical proximity LD ij is considered. As explained earlier, data on compound neighbors only exist for a subset of households, hence the drop in the total number of observations. When the only regressor is the pairwise land difference between neighbors, a positive and significant α5 estimate is found, suggesting that land trans- fers between neighbors on average go in the direction of equalizing their respective land areas. ai −av Unlike in the case of related households, this finding survives adding village regressors Nv av −aj and Nv : point estimates for α1 and α2 remain large and comparable to those obtained in column 2, but they are not statistically significant. In contrast, α5 remains statistically signif- icant, weakly suggesting that land transfers serve more the role of land equalization between 27 neighbors than land equalization within the village. It is not possible, however, to reject the hypothesis that α1 and α2 are equal to the estimates reported in column 2. Furthermore, point estimates remain well below 1 throughout, indicating that perfect equalization is far from achieved. To conclude, land transfers on average go in the direction of equalizing land across all house- holds in the village, although the effect is small in magnitude – a result that is in agreement with the earlier finding that the Gini coefficient of land drops from 0.52 to 0.47 after trans- fers, a modest improvement. There is no evidence that there is more equalization of land area within ethnic or kinship group than across the village as a whole. This finding remains even when large landowners, whose social role includes welcoming newcomers into the village by offering them some land to cultivate on a temporary basis, are removed. This implies that land transfers generally occur across ethnic and kinship boundaries. When close links between neighbors and between directly related households are considered, we find evidence that land transfers go in the direction of equalizing landholdings between them. But for direct kinship links, the effect disappears once village-level regressors are included. In contrast, there is evi- idence that land transfers between neighbors serve to equalize their respective landholdings over and above their role in equalizing landholdings at the village level. Coefficient estimates are well below 1 in all cases, however, indicating that equalization is far from achieved in any of the considered cases. Factor ratios As explained in the conceptual section, land equalization need not be efficient if farmers differ in productivity. If productivity differences are Hicks-neutral and labor is tradable, however, factor ratios should be equalized across farms. To investigate this possibility, a test is performed of whether land transfers serve to equalize the land-labor ratio ri across farms and, more importantly, whether social structure is an impediment to such equalization at the village level. To this effect the same analysis using land-labor ratios ri in lieu of land endowments ai is performed. 28 Table 8: Two factor model: Do social components equalize farm size? (1) (2) (3) (4) (5) Regressor Coefficient Ethnicity Kinship Ethnicity Kinship (r−r) Nv α1 0.065*** 0.089*** 0.152*** (0.021) (0.029) (0.037) (r−rj ) Nv α2 0.065*** 0.089*** 0.152*** (0.021) (0.029) (0.037) (ri −rk ) Nv Dij α3 0.037*** 0.045*** -0.026* -0.090*** (0.013) (0.015) (0.013) (0.023) (rk −rj ) Nv Dij α4 0.037*** 0.045*** -0.026* -0.090*** (0.013) (0.015) (0.013) (0.023) Constant α0 0 0 0 0 0 Observations 54,144 54,144 54,144 54,144 54,144 Note: The dependent variable is the amount of land transferred from i to j measured in hectares. Standard errors clustered by village are shown in parentheses.*** p<0.01, ** p<0.05, * p<0.1 Source: Author’s own calculations on the Gambia Networks Data 2009. The first set of results is presented in Table 8, which mirrors Table 6. Results are qualitatively similar, but point estimates are larger – albeit still well below 1. As before, equalization within villages trumps equalization within ethnic or kinship groups: point estimates α3 and ri −rv rv −rj α4 become negative once village level regressors Nv and Nv are included. In results not shown here to save space, the winsorization exercise conducted on the one factor model is repeated. Results are qualitatively identical, albeit with larger point estimates. Table 9 mirrors Table 7, with the inclusion of direct kinship or neighbor links between household pairs. Results are again similar to those presented earlier. To conclude, results regarding factor ratio equalization are quite similar to those of land equalization: land transfers on average go in the direction of factor ratio equalization but fall far short of achieving it in full. We do not, however, find that this failure is driven by a propensity to equalize factor ratios primarily within ethnic or kinship groups, or between directly related households. There is, however, some evidence that neighbors share land to even out their factor ratio differences over and above what is explained by village-wide equalization. 29 Table 9: Two factor model: Do direct links equalize farm size? (1) (2) (3) (4) Regressor Coefficient Kinship Kinship Neighbor Neighbor (r−r) Nv α1 0.061** 0.058 (0.023) (0.070) (r−rj ) Nv α2 0.061** 0.058 (0.023) (0.070) (ri −rj ) 2 Lij α5 0.005** 0.002 0.017* 0.014* (0.002) (0.003) (0.010) (0.008) Constant α0 0 0 0 0 Observations 54,144 54,144 21,266 21,266 Note: The dependent variable is the amount of land transferred from i to j measured in hectares. Standard errors clustered by village are shown in parentheses.*** p<0.01, ** p<0.05, * p<0.1 Source: Author’s own calculations on the Gambia Networks Data 2009. Labor transfers Land transfers are not the only margin that can be used to equalize factor ratios across households. Another option is to adjust the amount of labor during the cropping season. To formally examine this, labor transfers of household heads is used as dependent variable wij and estimate a model of the form: (ri − r) (r − rj ) wij = β0 + β1 + β2 + uij (9) Nv Nv This model can be extended similarly to models (4) and (5). Labor transfers that improve allocative efficiency requires negative parameter estimates: labor l should on average to flow from agents with a low land-labor endowment ratios ri to agents with high land-labor ratios relative to the village average r. There is no evidence that labor transfers equalize factor ratios: The only parameter of statistical significance is the kinshop link parameter, and it is of the opposite sign (positive), than what is required for family links to positively impact the factor-equalizing properties of labor transfers (table 10). These findings suggest that labor transfers do not help equalize ex ante factor ratios in the studied villages. Given the timing of labor transfers – i.e., after cultivation rights have been allocated and planting has begun – the logical conclusion is that labor transfers primarily serve as an ex post adjustment to labor 30 Table 10: Do labor transfers equalize farm size? (1) (2) (3) (4) (5) Regressor Coefficient Ethnicity Kinship Kinship Neighbor ( r −r ) NV α1 0.000 (0.000) (r−rj ) Nv α2 0.000 (0.000) (ri −rk ) Nv Dij α3 0.000 0.000 (0.000) (0.000) (rk −rj ) Nv Dij α4 0.000 0.000 (0.000) (0.000) (ri −rj ) 2 Lij α5 0.005** -0.000 (0.001) (0.000) Constant α0 0 0 0 0 0 Observations 54,144 54,144 54,144 54,144 21,266 Note: The dependent variable is the amount of household head labor transfered from j to i, measured in working days. Standard errors clustered by village are shown in parantheses. *** p<0.01, ** p<0.05, * p<0.1 Source: Author’s own calculations on the Gambia Networks Data 2009. shocks.26 If labor transfers are only used as an ex post adjustment to labor shocks during peak sea- son, cultivated land can be taken as pre-determined at the time these transfer takes place. Given this, it may be useful to reestimate model (9) using land-labor ratios calculated using cultivated land in lieu of owned land.27 Results are very similar to those reported in Table 10. 5 Discussion This paper has examined whether social structure affects the equalization of factors and factor ratios across farming households. With some additional assumptions, the absence of equalization can be seen as implying a failure to allocate factors of production efficiently. How convincing is this conclusion? As noted in the conceptual section, whether or not inequality in cultivated acreage or factor ratios signals allocative inefficiency hinges on two maintained assumptions that cannot be substantiated with the data at hand: decreasing returns to scale; 31 and unobserved productivity differences. These are discussed in turn. The possible existence of increasing returns to scale in tropical farming cannot be ruled out, and indeed a number of tropical countries have (or have had) large successful commercial farms – including Liberia, which lies in West Africa like The Gambia. These commercial farms, however, rely on technological and organizational innovations that are out of the reach of the predominantly illiterate farmers residing in the study villages. Successful use of animal traction requires a minimum scale of production, but this scale is well within the realm of the smallholder farmers in our study. Using a simple replication argument, one may conclude that traditional farming is characterized by constant returns to scale in land and labor. While this argument is not without merit, it is widely recognized that hired labor is subject to various moral hazard considerations which create a wedge between the productivity of labor on one’s own farm or someone else’s. This particularly true in West Africa because agrarian sharing norms tend to delegitimate efforts to hire large number of agricultural laborers (Platteau et al., 1998). In the context of our study population, decreasing returns to scale thus are a reasonable assumption, substantiated by much existing data on smallholder farming in African and elsewhere (e.g., Deininger and Feder 2000, Ali and Deininger 2015). To circumvent the possible existence of unobserved productivity differences, the methodology was applied to factor ratios which, if productivity differences are Hicks-neutral, should be equalized to achieve allocative efficiency. Land transfers do not equalize ex ante land-labor ratios, and labor transfers do not equalize ex ante or ex post factor ratios. The conclusion that follows from this evidence is that factors of production are not efficiently allocated so as to match possible Hicks-neutral differences in productivity across farmers. There remains the possibility that productivity differences across farmers are factor-biased. If some farmers have a higher land productivity than others28 , they can be expected to have a higher land-labor ratio. The authors of this paper suspect that unobservable productivity differences matter more in modern agriculture, and less in traditional subsistence agriculture which is fairly undifferentiated and follows simple heuristic rules of behavior. In the study area, factor-biased productivity differences would have to be large to explain a Gini coefficient of 0.47 in land available for cultivation – given how thin agricultural labor markets are in the 32 study area. Furthermore, unless land and labor are near perfect substitutes in production – which is unlikely – much larger labor transactions from land-poor to land-rich (and presumably highly productive) farmers should be observed. However, this is not what is observed with the current data: labor flows hardly respond to differences in ex ante or ex post factor ratios. Finally, Chavas et al. (2005) find evidence that technical inefficiency among Gambian farmers is modest and that differences in factor mix are not driven by technological differences. The authors nonetheless find substantial allocative inefficiency in farm input allocation, which motivates the focus of the present paper. While these arguments militate against the idea that productivity differences account for the data, it cannot be fully ruled out. To provide evidence about the possible extent of the issue, regression models (2), (4) and (5) are reestimated with additional controls for possible differences in factor-biased productivity across farmers. The main findings of the models do not change when household characteristics are included (see appendix S2.4 for results and further discussion). In sum, the evidence fails to provide support for the conjecture that productivity differences are the primary driver of variation in land endowment across households in the study area. 6 Conclusion In this paper, it was examined whether observable dimensions of social structure hinder or facilitate factor equalization in the rural Gambia. Land ownership is highly unequal in the surveyed villages in spite of being populated by largely illiterate smallholders practicing a traditional form of agriculture. Furthermore, labor transactions, though common, only represent a small share of total available labor. In this context, factor transactions can improve the efficiency of factor allocation by reducing disparities in factor usage and factor ratios across farms. In village economies it is common to observe that many economic transactions take place along more socially proximate households. This is also what we find in the data at hand. This suggests that it is easier to equalize factor allocations within social groupings or between 33 kin and neighbors. The question that is investigated is whether frictions in factor transfers restrict factor equalization across socially distant households and groups. To our knowledge, this paper constitutes the first attempt to formally investigate this issue at the level of the aggregate village economy. We introduce a novel way of testing whether social and geographical distance reduces the likelihood of equalizing factor transfers. The data requirements for this approach are severe: information on factor endowments, exhaustive pairwise information about factor transfers, and data on relevant aspects of the social structure is needed. Using such data for a large number of villages in The Gambia, the approach is implemented empirically. The results support the hypothesis that land transfers lead to a more equal distribution of land and to more comparable factor ratios across farms. But complete equalization is far from achieved. Contrary to expectations, equalizing transfers of land are not more likely within ethnic groups or kinship groups – if anything, the opposite result is found. This finding survives when land transfers originating from a small number of households with large landholdings, whose social role is to welcome newcomers with some land, are omitted. There is also some evidence that land transfers between neighbors perform a factor-equalizing function over and above that occurring at the village-level, suggesting that land-poor households may benefit from proximity to land-rich households. In contrast, there is no evidence that labor transfers serve to equalize factor allocation, either ex ante or ex post. Their role is probably to deal with unanticipated shocks – on which there is no information available in the dataset at hand. The methodology presented in this paper has many other potential applications to study the extent to which the absence of equalization – e.g., in prices, costs, access, or opportunities – is due to preferential linking or its converse, discrimination. A number of these examples are presented in the appendix. The method requires extensive information about dyadics flows and sufficient information about social structure. Until not so long ago this type of information would have been hard to come by. Today, however, exhaustive datasets on flows and links are becoming more commonly available, extending the relevance of the method. 34 The method has some inherent limitations, at least in its current form. The focus is on flows and obstacles to flows, not on the form that flows take (e.g., market or non-market exchange) or on the motivation for these flows (e.g., mutual assistance or self-interest). For instance, the empirical results do not imply that the perceived motive for land transfers is to equalize factor ratios or to increase efficiency. It is more likely that transfers are seen as a way of helping poor households and are given out of a sense of civic duty (Beck and Bjerge, 2017),29 or because it is more cost-effective to transfer land to a poor household ex ante rather than transfer food and cash ex post (Fafchamps 1992). No matter the intent behind land transfers, the end result is the same: transferring land to a land-poor household leads to a more egalitarian allocation of factors which, in a world of decreasing returns to scale, increases allocative efficiency. 35 Notes 1 La Ferrara (2003) studies the role of kinship networks in credit in Ghana. She finds that two third of the amounts borrowed come from potential kinsmen and that family structure helps enforce these loans, thereby improving the efficient allocation of funds within kin groups. Sadoulet et al. (1997) compare land contracts between kin related and non-kin related households and find that the former are more efficient. Holden and Ghebru (2005) show that tenants in communities with a larger share of contracts between kin related households face lower access constraints to the land market. More recently, Macours et al. (2010) finds that insecurity of property rights in the Dominican Republic reduces rental activity, and causes the tenancy market to match up along socio-economic lines. None of these authors use the general approach suggested here. 2 Unlike causal inference based on experimental evidence, the method presented in this paper does not aim to test one specific cause. Rather it tests for the presence of a flow pattern that would have to be present for a particular type of social-structure-driven friction to cause resource misallocation. 3 Similar examples can be found in Temperley (1981) and Foulds (1992). 4 To take another example, an electrical power grid may be interconnected, but the flow of power between different points is often restricted by technological constraints. If one segment of the grid fails, it may not be possible to channel enough current from the rest of the grid to avoid a loss of service, resulting in a power outage. 5 To illustrate, consider a network with three nodes {1, 2, 3} arranged in a line, with s12 = 1 and s23 = 1. Endowments are {0, 2, 2}. Consider nodes 1 and 2 first. Water equalization implies a transfer of 1 from node 2 to node 1, which is feasible since s12 = 1. Suppose this takes place. Node 1 now has 1 unit of water, and so does node 2. Now consider nodes 2 and 3: equalization between them leads to a transfer of 0.5 units of water from node 3 to node 2, who now has 1.5 units of water. Since 1 unit of water has already been transferred from 2 to 1, further water equalization between them is impossible, and the final allocation is {1, 1.5, 1.5}: there is no water level equalization between 1 and 2 even though s12 is large enough to equalize their respective endowments. 6 e and Kranton (2007) provide other examples in risk sharing games on networks. Bramoull´ 7 This assumption is discussed in more detail later. 8 The reallocation of land among households can be organized in a variety of market (e.g., sale, rental or sharecropping) and non-market ways (gift exchange, exchange of usage rights or squatting). Since the focus is on allocative efficiency, only the transfers themselves are considered in this paper, not the mechanisms by which land is transferred and the gains from trade shared between households. 9 E.g., one could ask which transfer matrix W minimizes the number of separate transfers needed to achieve 36 efficiency. Since it is unclear how these trades could be implemented in a decentralized manner, it is not discussed further. 10 Let N1 and N2 denote the number of agents with an above and below average endowment, i.e., with ai − av > 0 and aj − av < 0, respectively. The N − N1 − N2 others have an allocatively efficient endowment such that ak = av . Allocative efficiency requires that N1 agents collectively transfer out i∈N1 ai − av and N2 agents collectively transfer in j ∈N2 av − aj . 11 The few cases of increasing returns to farm size that have been documented in the literature seem to coincide with large differences in technological know-how between farmers, and may in fact signal high returns to human capital combined with the presence of readily available technological innovations. See also Allen and Lueck (1998) and Deininger and Feder (2001). For The Gambia, see Kargbo (1983)and von Braun and Webb (1989). 12 The appendix also contains an in-depth discussion of other possible models and their predictions regarding efficiency-enhancing reallocation of factors. 13 In terms of network activity, 2 percent of the households in the semi-urban villages participate in the land market, while 10 percent participate in the labor market. The main reason for the absence of land sharing is probably the very small landholdings in these areas (0.24 hectares per household compared to 10.28 in the rural villages), and the much higher availability of employment opportunities outside the village. 14 ¯ and r Village level averages such as a ¯ are calculated for farmers only. 15 See appendix S2.1 for additional discussion and descriptive statistics 16 Dey (1982) describes how donor-supported sharecropping schemes in The Gambia were unsuccessful and quickly abandoned. 17 It is estimated that a hundred years ago, Africa had less than 100 million inhabitants, possibly as few as 50 million. This compares to the current population of approximately 1 billion. The offshoot of this reality is that the majority of African villages in existence today were probably created in the last century (See Arcand and Jaimovich, 2014, for more detail on the case of Gambia). 18 The 2 percent of landless households who transfer out land also transfer land in – and thus end up with a nonnegative amount of land. 19 The relatively small geographical size of the villages means that soil quality is fairly uniform within each village. Hence information asymmetries and moral hazard are probably less severe in land transactions than in labor transactions. 20 Seasonal migrant workers typically referred to as ‘strange farmers’ were a relatively common phenomenon in rural Gambia in the past (Swindell, 1987). They were not commonly found in the studied villages in 2009, 37 however, and they do not appear in the data. 21 Using the Herfindahl index to measure ethnic diversity, ethnic fragmentation inside villages ranges from 0 (completely homogeneous) to 0.84, with a mean of 0.28. 22 This is perhaps not surprising: the same underlying factors that facilitate short-term land transfers may also facilitate permanent land transfers between households – e.g., through inheritance and transfers inter vivos at the time of marriage. 23 Virtually identical results are obtained if the dependent variable is replaced by a dummy equal to 1 is |wij | > 0 and 0 otherwise. 24 The dataset also includes information about land transfers to and from households outside the village. To ¯. avoid biasing the testing strategy, these transfers are netted out before calculating a 25 Point estimates α3 and α4 turn negative in this case because average land endowments differ across ethnic groups, and land equalization within the village means moving away from land equalization within ethnic or kinship groupings. 26 Results of the combined models (6) and (7) are not shown in order to save space. Results closely resemble the reported results: Labor does not appear to play a factor-equalizing role. 27 ˜ a i ≡ i ˜ In results not shown here, this possibility was investigated by defining r li ˜i is the land in the where a hands of farmer i after all land transfers have taken place. If labor transfers serve to equalize factor rations ˜ ex post, labor should on average flow from agents with a low r ˜ i to those with a high r i relative to the village ¯. average r 28 And land and labor are strong substitutes, i.e., the elasticity of substitution between them is more than 1. If the production function is (approximately) Cobb-Douglas, factor-specific productivity shifters factor out of the land and labor aggregates and are observationally equivalent to Hicks-neutral productivity differences. 29 Using the same dataset, Jaimovich (2011) finds that differences in realized income inequality across villages are correlated with transfers of inputs and credit - though not of land. 38 References Alesina, A., Devleeschauwer, A., Easterly, W., Kurlat, S., and Wacziarg, R. (2003). Fraction- alization. Journal of Economic growth, 8(2):155–194. Alesina, A., Michalopoulos, S., and Papaioannou, E. (2016). Ethnic inequality. Journal of Political Economy, 124(2):428–488. Alfaro, L., Charlton, A., and Kanczuk, F. (2008). Plant-size distribution and cross-country income differences. Technical report, National Bureau of Economic Research. Ali, D. A. and Deininger, K. (2015). Is there a farm size–productivity relationship in african agriculture? evidence from rwanda. Land Economics, 91(2):317–343. Allen, D. W. and Lueck, D. (1998). The nature of the farm*. The Journal of Law and Economics, 41(2):343–386. Arcand, J.-L. and Jaimovich, D. (2014). Does ethnic diversity decrease economic interactions? evidence from exchange networks in rural gambia. MPRA Paper No. 60497. Attanasio, O., Barr, A., Cardenas, J. C., Genicot, G., and Meghir, C. (2012). Risk Pooling, Risk Preferences, and Social Networks. American Economic Journal: Applied Economics, 4(2):134–167. Bank, A. D. (2005). Appraisal report: farmer managed rice project. Agricultural and Rural Development Department, Central and West Regions, African Development Bank Group. Tunis, Tunisia. Barr, A., Dekker, M., and Fafchamps, M. (2012). Who shares risk with whom under different enforcement mechanisms? Economic Development and Cultural Change, 10(4):677–706. Beck, U. and Bjerge, B. (2017). Pro-poor land transfers and the importance of land abundance and ethnicity in the gambia. World Development, 99:122–140. Bertrand, M. and Mullainathan, S. (2004). Are emily and greg more employable than lakisha and jamal? a field experiment on labor market discrimination. The American Economic Review, 94(4):991–1013. 39 e, Y. and Kranton, R. (2007). Risk-sharing networks. Journal of Economic Behavior Bramoull´ & Organization, 64(3):275–294. Carlsson, M. and Rooth, D.-O. (2007). Evidence of ethnic discrimination in the swedish labor market using experimental data. Labour Economics, 14(4):716–729. Chaney, T. (2014). The Network Structure of International Trade. American Economic Review, 104(11):3600–3634. Chavas, J.-P., Petrie, R., and Roth, M. (2005). Farm household production efficiency: Evi- dence from the gambia. American Journal of Agricultural Economics, 87:160–179. de Janvry, A., Fafchamps, M., and Sadoulet, E. (1991). Peasant household behaviour with missing markets: Some paradoxes explained. The Economic Journal, 101:1400–1417. Deininger, K. and Feder, G. (2001). Land institutions and land markets. Handbook of agri- cultural economics, 1:288–331. Dey, J. (1982). Development planning in The Gambia: The gap between planners’ and farmers’ perceptions, expectations and objectives. World Development, 10(5):377–396. Eastman, C. (1990). Gambian usufruct tenure. help or hindrance to agricultural production? Land Use Policy, 7(1):27–40. Edelman, B., Luca, M., and Svirsky, D. (2017). Racial discrimination in the sharing economy: Evidence from a field experiment. American Economic Journal: Applied Economics, 9(2):1– 22. Fafchamps, M. (1993). Sequential labor decisions under uncertainty: An estimable household model of west-african farmers. Econometrica, 61(5):pp. 1173–1197. Fafchamps, M. and Gubert, F. (2007). The formation of risk sharing networks. Journal of Development Economics, 83:326–350. Fafchamps, M. and Lund, S. (2003). Risk-sharing networks in rural philippines. Journal of Development Economics, 71:261–287. 40 Foulds, L. R. (1992). Graph Theory Applications. Springer-Verlag. Freudenberger, M. S. (2000). Tenure and natural resources in the gambia: Summary of research findings and policy options. Land Tenure Center. University of Wisconsin-Madison. Working paper no. 40. Goldin, C. and Rouse, C. (2000). Orchestrating impartiality: The impact of” blind” auditions on female musicians. The American Economic Review, 90(4):715. Granovetter, M. (1995). Getting a job: A study of contacts and careers. University of Chicago Press. Hanson, A. and Hawley, Z. (2011). Do landlords discriminate in the rental housing mar- ket? evidence from an internet field experiment in us cities. Journal of Urban Economics, 70(2):99–114. Holden, S. and Ghebru, H. (2005). Kinship transaction costs and land rental market par- ticipation. Department of Economics and Resource Management. Norwegian University of Life Sciences. Holden, S. T., Otsuka, K., and Place, F., editors (2009). The Emergence of Land Markets in Africa: Impacts on Poverty, Equity, and Efficiency. Washington, DC: Resources for the Future. Hsieh, C.-T. and Klenow, P. J. (2009). Misallocation and manufacturing tfp in china and india. The Quarterly journal of economics, 124(4):1403–1448. Jaimovich, D. (2011). Macrostructure and microstructure: Evidence from overlapping village networks in the gambia. MPRA paper 38932, University of Munich. Jaimovich, D. (2015). Missing links, missing markets: Evidence of the transformation process in the economic networks of gambian villages. World Development, 66:645–664. Kargbo, A. (1983). n Economic Analysis of Rice Production Systems and Production Orga- nization of Rice Farmers in the Gambia. PhD thesis. 41 La Ferrara, E. (2003). Kin groups and reciprocity: A model of credit transactions in ghana. The American Economic Review, 93(5):1730–1751. Macours, K., Janvry, A. d., and Sadoulet, E. (2010). Insecurity of property rights and social matching in the tenancy market. European Economic Review, 54(7):880–899. Mazzocco, M. and Saini, S. (2012). Testing efficiency risk sharing with heterogeneous risk preferences. American Economic Review, 1:428–468. Midrigan, V. and Xu, D. Y. (2014). Finance and misallocation: Evidence from plant-level data. The American Economic Review, 104(2):422–458. Otsuka, K. (2007). Efficiency and equity effects of land markets. Handbook of Agricultural Economics, 3:2671–2703. Pender, J. and Fafchamps, M. (2005). Land lease markets and agricultural efficiency in ethiopia. Journal of African Economies, 15(2):251–284. Platteau, J.-P. (1992). Land reform and structural adjustment in sub-saharan africa: contro- versies and guidelines. Technical Report 107, FAO. Platteau, J.-P., Hayami, Y., and Dasgupta, P. (1998). Resource endowments and agricultural development: Africa versus asia. In The institutional foundations of East Asian economic development, pages 357–412. Springer. Rauch, J. E. (2001). Business and social networks in international trade. Journal of Economic Literature, 39(4):1177–1203. Rauch, J. E. and Casella, A. (2003). Overcoming Informational Barriers to International Resource Allocation: Prices and Ties. The Economic Journal, 113(484):21–42. Ravallion, M. (1986). Testing market integration. American Journal of Agricultural Eco- nomics, 68(1):102–109. Riach, P. A. and Rich, J. (2002). Field experiments of discrimination in the market place. The economic journal, 112(483). 42 Sadoulet, E., de Janvry, A., and Fukui, S. (1997). The meaning of kinship in sharecropping contracts. American Journal of Agricultural Economics, 79(2):394–407. Swindell, K. (1987). Family farms and migrant labour: The strange farmers of the gambia. Canadian Journal of African Studies, 12(1):3–17. Temperley, H. N. (1981). Graph Theory and Applications. Ellis Horwood Limited. The Gambia Bureau of Statistics (GBOS) (2008). Population and housing census 2003 - volume 6: Housing and household characteristics. Technical report, The Gambia Bureau of Statistics (GBOS). The Gambia Bureau of Statistics (GBOS) (2011). The gambia multiple indicator cluster survey 2010, final report. Technical report, The Gambia Bureau of Statistics. Topa, G. (2001). Social interactions, local spillovers and unemployment. The Review of Economic Studies, 68(2):261–295. Townsend, R. M. (1994). Risk and insurance in village india. Econometrica: Journal of the Econometric Society, pages 539–591. von Braun, J. and Webb, P. J. R. (1989). The impact of new crop technology on the agri- cultural division of labor in a west african setting. Economic Development and Cultural Change, 37:513–534. Webb, P. (1989). Intrahousehold decisionmaking and resource control: The effects of rice commercialization in west africa. Technical report, International Food Policy Research Institute. 43 S1 Appendix: Extended conceptual section In this appendix, the modeling and testing strategy, which is adopted in the main paper, is extended. First, the models that make predictions at odds with the data are discussed. Then, it is considered what happens if there are two factors of production. Finally, the testable implications of unobserved heterogeneity are examined. To conclude, a summary of the lessons learned from this discussion is included. Some production function/transaction costs configurations make factor allocation predictions that cannot be tested by the data at hand. Nonetheless, an important and empirically relevant subset that makes testable predictions regarding the reallocation of factors between farmers is identified. For these configurations, the proposed method can be applied to test whether efficiency-enhancing factor transfers are shaped by the structure of social networks. S1.1 Constant and increasing returns to scale If the single-factor production function exhibits constant returns to scale in xi , any allocation of factors across households is efficient. Given this, there should not be factor transfers if, as is likely, there are any transaction costs in transferring factors across households. Since factor transfers are observed in the data, this is not considered further. Similarly, increasing returns to scale implies the concentration of all factors into a single production unit, which is not what is observed either. Hence, it is ignored here. S1.2 Two factor models Assume two factors of production, say, x and y . The production function is now of the form q (xi , yi ) where yi is a second factor of production. Each agent is endowed with a factor vector {ai , li } while the agent’s factor usage is denoted {xi , yi }. The total supply of factors in the N N economy is denoted A ≡ i=1 ai and L ≡ i=1 li . Allocative efficiency again depends on whether production is characterized by decreasing, constant, or increasing returns to scale. If the function q (xi , yi ) has increasing returns to scale 44 in x and y , the efficient allocation of factors is to have a single production unit concentrating all available factors – e.g., a plantation. Since this is not what is observed in the data, this is not considered further. With constant returns to scale, there is no specific efficient scale of production. But efficiency requires equal marginal rates of substitution between factors across households: ∂q (xi ,yi ) ∂q (xj ,yj ) ∂xi ∂xj ∂q (xi ,yi ) = ∂q (xj ,yj ) for all i and j (S1.1) ∂yi ∂yj If it is further assumed that the production function is homothetic in x and y , an efficient factor allocation must satisfy:30 xi xj = = r for all i and j (S1.2) yi yj A where r ≡ L is the average factor ratio in the economy. Hence, for transfers of factors across households to improve production efficiency, they must flow so as to equalize factor ratios across all households in a given village.31 This observation provides a partial characterization of factor transfers that can be used to ai test the role of social networks. Agents that have a factor ratio endowment ri ≡ li ¯ should >r on average transfer out part of their ai endowment such that their factor usage ratio xi /yi is equal to r. This can be tested by estimating a regression model of the form: ri − r r − rj wij = α0 + α1 + α2 + uij (S1.3) Nv Nv where wij as before denotes out-transfers of a. If factor transfers improve allocative efficiency it should be the case that α1 > 0 and α2 > 0: on average, factor a flows from agents relatively rich in that factor to agents poor in that factor.32 Limits to transfers imposed by social matrix Scannowbeimposed. The testing logic remains the same as before. If transfers are not feasible across components, factor ratios should 45 converge within components only. The estimating equation becomes: ri − r r − rj wij = α0 + α1 + α2 Nv Nv ri − rk rk − rj +α3 Dij + α4 Dij + uij (S1.4) Nk Nk i∈Nk ai where rk ≡ li . The testing strategy is similar as before: if factors only flow within i∈Nk components of the social network, α1 = α2 = 0 and α3 > 0 and α4 > 0 is expected. Other regression models presented in the conceptual Section similarly extend to this case, and need not be discussed further. If returns to scale are decreasing, allocative efficiency requires that: ∂q (xi , yi ) ∂q (xj , yj ) = for all i and j ∂xi ∂xj ∂q (xi , yi ) ∂q (xj , yj ) = for all i and j ∂yi ∂yj which implies that each household should use the same quantity of x and y . This also implies that: ∂q (xi ,yi ) ∂q (xj ,yj ) ∂xi ∂xj ∂q (xi ,yi ) = ∂q (xj ,yj ) for all i and j (S1.5) ∂yi ∂yj and hence efficiency requires an equalization of factor ratios across farms, as in the CRS case. Thus, for the DRS case, there are two available testing strategies: to apply model (2) to an individual factor; or to apply model (S1.3) to factor ratios. Both strategies should yield similar results in the DRS case. In the CRS case, only model (S1.3) can be used; model (2) is not identified since farm size is undetermined. S1.3 Unobserved heterogeneity Identifying efficiency-enhancing factor flows is more difficult if agents differ in unobserved productivity – or, equivalently, in an unobserved fixed factor (e.g., management capacity). In an efficient allocation, more productive agents attract more factors of production for the marginal productivity of factors to be equalized across agents. If it is not known who is more 46 productive, whether the absolute allocation of factors is efficient cannot be tested. To illustrate the difficulty, let the production of agent i be written θi q (xi ) where θi denote the total factor productivity of agent i and xi is a single factor of production.33 With decreasing returns to scale,34 allocative efficiency requires that: ∂q (xi ) ∂q (xj ) θi = θj for all i and j ∂xi ∂xj This implies that xi > xj if θi > θj : more productive agents use more x. Since θi is not observed, identification fails in all the regression models discussed so far: without knowing who is most productive, it is not possible to test whether the allocation of the single factor xi across farmers is efficient. By extension, the same conclusion applies in the CRS case if there are two factors of production but only one is traded. Some identification can be recovered if not one but two traded factors, x and y , are observed. The production function is now of the form θi q (xi , yi ), and DRS in x and y is still assumed.35 Allocative efficiency now requires that: ∂q (xi , yi ) ∂q (xj , yj ) θi = θj for all i and j ∂xi ∂xj ∂q (xi , yi ) ∂q (xj , yj ) θi = θj for all i and j ∂yi ∂yj which yields the same expression (S1.1). If the production function is homothetic in x and y , an efficient factor allocation still must satisfy (S1.2): factors should flow so as to equilibrate factor ratios among agents. It follows that, unless factor endowments are perfectly correlated with productivity differen- ai tials, on average agents with ri ≡ li ¯ should transfer out some of their excess factors to >r others, and vice versa. In the conceptual section, this property holds exactly for each farmer; here it only holds on average, and requires that factor endowments and productivity not be strongly positively correlated.36 With these assumptions, it is possible to apply the same test- ing strategy as that outlined above. The strategy requires a strong maintained assumption about the distribution of factors and productivity. But the assumption is fairly reasonable in 47 the context of the data at hand, where land is mostly inherited from the household’s lineage and its manpower endowment largely depends on where the household is in its life cycle. There is no compelling reason to expect these exogenous factors to be strongly positively correlated with θi , even if some correlation may be present. Moreover, given the low technological level of the study population, it is unlikely that productivity differentials differ massively among them – or at least not as much as the very large differentials in land endowment. Hence it is not entirely unreasonable to give this approach a try. S1.4 Summary To summarize, a method for testing the role of social network structure in improving the efficiency of factor allocation in farming villages is devised. This method does not work if production exhibits increasing returns to scale, or if constant returns to scale are combined with unobserved heterogeneity in productivity: in these cases, all factors should go to a single producer – which is not what is observed in the data. The method also fails when unobserved heterogeneity is combined with decreasing returns to scale and a single traded factor. In this case, it is not possible to empirically characterize the efficient allocation of factors without information on individual heterogeneity, and hence it is not possible to test test whether factor transfers serve to improve efficiency. There remain several cases in which the efficient allocation of factors can be characterized, either in absolute terms or in terms of factor ratios. In these cases, the characterization can be used as basis for a test of the role of social network structure in permitting or curtailing efficiency gains in factor allocation. Table S1.1 lists all the various configurations and their predictions. The testable cases include: decreasing returns to scale (DRS) with one traded factor and no unobserved heterogeneity; and DRS with two traded factors, with or without unobserved heterogeneity. In the first case, efficiency can be characterized in absolute terms and model (2) serve as starting point for our testing strategy. In the second case, efficiency can be characterized in terms of factor ratios and construct a testing strategy based on factor ratios. The latter method also applies to the CRS case with two factors but no unobserved heterogeneity, even if one factor is de facto not traded. 48 Table S1.1: Summary table of model predictions Case Hetero- No. of No. of Returns Prediction of factor structure across Model(s) geneity? factors traded to scale? farms factors 1 NO 1 1 DRS Equality of factors. (2), (5)-(8) 2 NO 1 1 CRS Undetermined. If any tc, no trade. Ruled out 3 NO 2 1 DRS Unidentified. - 4 NO 2 1 CRS Equality of factor ratios. Cultivated land (11), (12) is multiple of ex ante labor. 49 5 NO 2 2 DRS Equality of both factors. (5)-(8), (11), (12) 6 NO 2 2 CRS Equality of factor ratios. If any tc, trade (11), (12) only in factor with lowest tc. 7 YES 1 1 DRS Unidentified. - 8 YES 1 1 CRS One plantation. Ruled out 9 YES 2 1 DRS Unidentified. - 10 YES 2 1 CRS Unidentified. - 11 YES 2 2 DRS If θ is not strongly correlated with r: (11), (12) Equality of factor ratios. 12 YES 2 2 CRS One plantation. Ruled out Source: Summary of authors’ discussion in the appendix. S2 Appendix: Additional tables S2.1 Descriptive statistics The largest households in the sample have more than 50 members, but they only account for 0.01 percent of the total sample (table S2.1). These large households arise as the result of polygamous marriages, which are frequent in the data: fifty percent of household heads have more than one wife. The household head is on average 54 years of age. Sample households are predominately headed by poorly educated men: only 8.7 percent have any formal education and nearly half are illiterate; the rest have received Koranic education providing basic literacy in Arabic. The high incidence of polygamy, low education level, and advanced age of household heads are unusual compared to other parts of Africa. But they tally with what is known about The Gambia. According to the nationally representative Multiple Indicator Cluster Survey (MICS) from 2010, 41 percent of women aged 14-49 are in a polygamous marriage. More than two-thirds of the women aged 14-49 are currently married (The Gambia Bureau of Statistics (GBOS), 2011). MICS also reports that 68.4 percent of household heads have no education. This share is higher in the dataset at hand due to the rural nature of the sample. The official report on the 2003 Gambian census, which constitutes the sampling frame for the survey, lists the mean age of household heads to be 46 (The Gambia Bureau of Statistics (GBOS), 2008) In the analysis, the number of working adults available to the household for work on the farm is taken as pre-determined, and the focus is on factor transfers made during a single cropping season. The average monetary income per capita is 2,750 Gambian Dalasis a year, which is equivalent to 282 USD a year in PPP terms.37 The share of monetary income that comes from crop sales is 16 percent, which appears low but is probably due to the fact that crops are mostly consumed or bartered and, as a result, their contribution to income is under-reported. More than 45 percent of households receive remittances, reflecting a substantial incidence of migration abroad and to urban centers in The Gambia.38 50 Table S2.1: Household-level descriptive statistics Mean Std. Dev. Household size 14.1 15.0 Age of head 54.3 16.2 Female headed household 5.7% Head has some formal education 8.7% Head is illiterate 48.9% Income per capita (in 2009 PPP US$) 282 285 Share of income from crop sales 16.1% 0.271 Receive remittances 45.5% Relative wealth level (=1 (low), 2, 3 or 4 (high)) 1.75 0.81 Observations 1,625 Source: Author’s own calculations on the Gambia Networks Data 2009. S2.2 Multicollinearity and overlap statistics To check whether multicollinearity may be a problem, the correlation between network mea- sures is reported in the top panel of table S2.2. Correlation coefficients are all below 0.2, which alleviates this concern. At first glance, these coefficients may seem low: Wouldn’t fam- ily and ethnicity links be expected to coincide? To answer this question, overlap statistics are investigated (see the lower panel of table S2.2). These show that while 90.2 percent of family links are between co-ethnics, only 16.9 percent of co-ethnics belong to the same family: many households share an ethnicity without having close family ties. This therefore shows that link correlations are sufficiently low as to not to present a problem for identification. A second potential identification issue relates to the need for multiple components within each village to identify component effects. In order to check this, the mean and range of the share of households who belong to the largest and second largest components of ethnicity and family ties are reported in table S2.3. Village networks are characterized by so-called giant components, an attribute found in almost all types of network data. On average, 79.6 and 88.3 percent of households belong to the largest ethnicity or family component in their village. There is, however, considerable variation across villages, as the size of the largest component ranges from around 32 percent for ethnicity and 28 percent for family to 100 percent. Thus while some villages do not contribute to the identification of component parameters, many villages consist of multiple components and this generates sufficient variation to estimate 51 Table S2.2: Correlation and overlap between network types Ethnicity Family Neighbor Correlation coefficients Family 0.17 Neighbor 0.04 0.18 Overlap, percent of column type links Ethnicity 90.2 76.8 Family 16.9 32.7 Neighbor 10.3 22.4 The overlap statistics show the percent of column links that overlap with a row link. For example, 90.2 percent of family links are between co-ethnics but only 16.9 percent of co-ethnics belong to the same family. Source: Author’s own calculations on the Gambia Networks Data 2009. Table S2.3: Component size information Ethnicity Family Largest component, in percent of households Mean 79.6% 88.3% Range [32.2-100.0% ] [28.1-100.0% ] Second-largest component, percent of households Mean 13.6% 8.2% Range [0-48.1% ] [0-39.2% ] Observations 50 50 The table shows the mean and range of the percentage of households who belong to the two largest components in each village. Source: Author’s own calculations on the Gambia Networks Data 2009. component parameters. 52 S2.3 Robustness to outliers of component results Table S2.4: Robustness to outliers of component results (1) (2) (3) (4) Regressor Coefficient Ethnicity Kinship Ethnicity Kinship (ai −a) Nv α1 0.046** 0.083*** (0.021) (0.024) (a−aj ) Nv α 2 0.046** 0.083*** (0.021) (0.024) (ai −ak ) Nv Dij α3 0.038*** 0.032*** -0.004 -0.043*** (0.012) (0.011) (0.017) (0.016) (ak −aj ) Nv Dij α4 0.038*** 0.032*** -0.004 -0.043*** (0.012) (0.011) (0.017) (0.016) Constant α0 0 0 0 0 Outlier method Winsorization Winsorization Winsorization Winsorization Observations 54,144 54,144 54,144 54,144 Note: The dependent variable is the amount of land transferred from i to j measured in hectares. Standard errors clustered by village are shown in parentheses. *** p<0.01, ** p<0.05, * p<0.1 Source: Author’s own calculations on the Gambia Networks Data 2009. S2.4 Including controls in the one factor model Village fixed effects can control for possible differences in land quality across villages. However, in the dyadic system that we estimate where wij = −wji , village fixed effects are perfectly collinear with the main variables of interest and differences across villages are de facto already accounted for. The territory of each individual village is fairly small so that within-village differences in land quality are likely to be small. Household-specific controls are added to proxy for differences in farm management and labor supervision capabilities between farmers (table S2.5). The list of controls, which is limited by the available data, is household size; age of the household head; literacy of the household head; whether the household head has any formal education; whether the household head is female; a dummy for whether the household receives remittances; and a wealth-level indicator. These controls are included for both the sending and receiving household. If village fixed effects and household controls capture part of the variation in land and labor productivity, transfers should respond more closely to the model, and thus the earlier estimates should increase. The main findings of the one factor 53 model do not change when household characteristics are included, and point estimates are comparable in magnitude to those reported earlier (table S2.5). This is also the case when the controls are added to the two-factor model (results not shown).39 Table S2.5: Including controls in the one-factor model (1) (2) (3) (4) (5) Regressor Coefficient Ethnicity Kinship Kinship Neighbor (ai −a) Nv α1 0.023** (0.009) (a−aj ) Nv α2 0.023** (0.009) (ai −ak ) Nv Dij α3 0.014** 0.016** (0.006) (0.007) (ak −aj ) Nv Dij α4 0.014** 0.016** (0.006) (0.007) (ai −aj ) 2 Lij α5 0.002** 0.007* (0.001) (0.004) Constant α0 0 0 0 0 0 Controls YES YES YES YES YES Observations 54,144 54,144 54,144 54,144 21,266 Note: The dependent variable is the amount of land transferred from i to j measured in hectares. Standard errors clustered by village are shown in parentheses.*** p<0.01, ** p<0.05, * p<0.1 Source: Author’s own calculations on the Gambia Networks Data 2009. 54 S2 Appendix: Simulations The purpose of this Appendix is to demonstrate the validity of the testing strategy using simulations.We simulate an economy with a single asset a shared unequally among N farm- ers divided into two unequal-size groups or components. We also generate undirected links between pairs of farmers, with a random probability of linking p. We generate three types e such that every farmer has a ≡ a/N cultivated of transfers: globally efficient transfers wij g aj acreage; group efficient transfers wij such that each farmer in group k has ak = j ∈k Nk ; d partially equalizing cultivated acreage between pairs of farmers. To and dyadic transfers wij e illustrate the fact that efficiency does not require many pairwise transfers, we construct wij g and wij so as to occur only over a small number of dyads – 95% of dyads have no transfers. To e and w g by a fraction simulate inefficient aggregate or group-wise transfers, we multiply wij ij d , dyadic efficiency is achieved for farmers that have a single link. τ < 1.40 In the case of wij Many farmers have more than one link, however. Because they must share land with several others, pairwise efficiency cannot be achieved with each of them since farmers cannot transfers out more than their land endowment ai .41 Simulation results are presented in Tables S1.1-S1.3. We simulate 30 villages each with N = 20 farmers. In the main simulations, farmers are sorted by land endowment and divided into two groups, one with rich farmers and one with poor farmers. The two groups have size N1 = 11 and N2 = 9. We also simulate what happens when the two groups have similar endowment – more about this later. We set the linking probability p = 0.1, and the shrinking parameter τ = 0.3. Villages differ systematically in total land endowment but there is no land transfer between villages. In all the reported regressions standard errors are clustered at the village level. e . The first five columns present Table S3.1 presents results for village-efficient transfers wij results when the two groups have sharply different endowments. Column 1 report estimates from regression model (2). The estimated values of α1 and α2 are identically 1 while α0 is e is replaced with ‘shrunk’ identically 0, as predicted. In column 2, the dependent variable wij e . Coefficient estimates α and α are equal 0.3, the value of the shrinking transfers τ wij 1 2 55 Table S3.1: Simulation results. Dependent variable is simulated village-efficient transfers (1) (2)(3) (4) (5) (6) (7) Endowment: Endowment: Split according to rich and poor Similar across groups Regressor Coefficient wij wij ∗ τ wij wij wij wij wij (ai −a) Nv α1 1.00*** 0.30*** 1.24*** 1.02*** (0.00) (0.00) (0.02) (0.07) (a−aj ) Nv α2 1.00*** 0.30*** 1.24*** 1.02*** (0.00) (0.00) (0.02) (0.07) (ai −ak ) Nv Dij α3 0.11*** -0.54*** 0.48*** -0.03 (0.02) (0.02) (0.03) (0.07) (ak −aj ) Nv Dij α4 0.11*** -0.54*** 0.48*** -0.03 (0.02) (0.02) (0.03) (0.07) (ai −aj ) 2 Lij α5 0.08*** -0.03 0.02 (0.02) (0.02) (0.02) Constant α0 0 0 0 0 0 0 0 Observations 11,400 11,400 11,400 11,400 11,400 11,400 11,400 Note: Standard errors clustered by village are shown in parantheses. *** p<0.01, ** p<0.05, * p<0.1 e on deviations from group average ai −ak av −ak parameter. In column 3 we regress wij Nk and Nk . Estimated coefficients are close to 0, although not identically so: village-wide land redistri- bution achieves a modicum of within-group redistribution as well, and this is what is picked e is regressed on the average dyadic difference ai −aj up by α3 and α4 . In column 4 wij 2 . The e , in this coefficient estimate α5 captures whatever dyadic redistribution is generated by wij case 10%. In column 5 we estimate model (6). We find that α3 and α4 are both negative while α1 and α2 are larger than 1. The first result arises because transfers that are village-efficient take cultivated acreage away from what would be group efficient: since the two groups have different land endowments, achieving group efficiency would take farmers away from village efficiency. To cast more light on this finding, we present in columns 6 and 7 simulation results in which the two groups are equal in terms of land endowment. Columns 6 and 7 duplicate columns 3 and 5, respectively. The only difference is in ak . In column 6 we find ai −ak av −ak that Nk Dij and Nk Dij predict village-efficient transfers much better than when groups have very different land endowments: α3 and α4 are nearly equal to 0.5. This is not surprising: ai −ak av −ak since ak is now close to av , the main difference between the Nk Dij and Nk Dij terms 56 Table S3.2: Simulation results. Dependent variable is simulated group-efficient transfers (1) (3) (2) (4) (5) (6) (7) Endowment: Endowment: Split according to rich and poor Similar across groups Regressor Coefficient wij wij ∗ τ wij wij wij wij wij (ai −a) Nv α1 0.40*** -0.00 0.96*** 0.00 (0.02) (0.01) (0.01) (0.02) (a−aj ) Nv α2 0.40*** -0.00 0.96*** 0.00 (0.02) (0.01) (0.01) (0.02) (ai −ak ) Nv Dij α3 1.00*** 0.30*** 1.00*** 1.00*** (0.00) (0.00) (0.00) (0.00) (ak −aj ) Nv Dij α4 1.00*** 0.30*** 1.00*** 1.00*** (0.00) (0.00) (0.00) (0.00) (ai −aj ) 2 Lij α5 0.04*** 0.00 -0.00 (0.01) (0.01) (0.02) Constant α0 0 0 0 0 0 0 0 Observations 11,400 11,400 11,400 11,400 11,400 11,400 11,400 Note: Standard errors clustered by village are shown in parantheses. *** p<0.01, ** p<0.05, * p<0.1 ai −av av −av and the Nv and Nv is Dij , which is 0 when i and j do not belong to the same group. ai −ak av −ak Given that the groups are of roughly equal size, it means that Nk Dij and Nk Dij cannot predict any transfer between individuals in different groups. Hence the coefficient estimates. ai −av This is confirmed in column 7 where we combine both sets of terms, and where Nv and av −av ai −ak av −ak Nv get coefficients clost to 1 and Nk Dij and Nk Dij have coefficients that are small in magnitude and not statistically significant. g In Table S3.2 we present similar results for group-efficient transfers wij . In column 1, we obtain estimated coefficients α3 and α4 that are equal to 1, as predicted. In column 2, we g shrink wij to 30% of its original value. Coefficient estimates shrink by the same amount, as g it should be. In column 3 we regress wij on deviations from village average. Estimates for α1 and α2 are positive and significant. This is because within-group land redistribution does ai −aj improve village-wide efficiency, although by much less than 100%. In column 4 we use 2 as sole regressor. The estimated coefficient α5 is small by slightly above 0, capturing the fact that some of the gain in group-wide efficiency is achieved through transfers between linked farmers. When we include all regressors, we again find α3 = α4 = 1 as in column 1. 57 Table S3.3: Simulation results. Dependent variable is simulated dyadic transfers (1) (2) (3) (4) (5) Regressor Coefficient wij wij ∗ τ wij wij wij (ai −a) Nv α1 0.44*** -0.01 (0.03) (0.01) (a−aj ) Nv α2 0.44*** -0.01 (0.03) (0.01) (ai −ak ) Nv Dij α3 0.23*** 0.02 (0.03) (0.02) (ak −aj ) Nv Dij α4 0.23*** 0.02 (0.03) (0.02) (ai −aj ) 2 Lij α5 0.49*** 0.15*** 0.49*** (0.03) (0.01) (0.03) Constant α0 0 0 0 0 0 Observations 11,400 11,400 11,400 11,400 11,400 Note: Standard errors clustered by village are shown in parantheses. *** p<0.01, ** p<0.05, * p<0.1 In columns 6 and 7 we again consider groups with similar land endowments. In this case, group-efficient redistribution can achieve close to village-wide efficiency, as indicated by the α1 and α2 estimates reported in column 6. When we combine both sets of terms in column ai −av av −av 7, α3 and α4 take value 1 while α1 and α2 become 0. This is because Nv and Nv are incapable of predicting why transfers only take place within groups. d . Column 1 shows that, on Table S3.3 presents equivalent results for dyadic transfers wij d eliminate 53% of the ai −aj average, wij 2 difference across all linked dyads. As explained earlier, full pairwise efficiency is not achievable when farmers have more than one link on d by a factor average, and have to accommodate multiple redistribution needs. Shrinking wij τ reduces the α5 coefficient accordingly (see column 2), as expected. From column 3 we d transfers cause a sizeable reduction in factor allocation inefficiency: the conclude that wij gain is equivalent to what 45% of what is generated by village-efficient transfers. In column 4 we similarly note a reduction in within-group inefficiency, but the gain is much smaller since, as we have explained above, dyadic links are uncorrelated with group membership, and within-group efficiency would not eliminate across-group endowment differences. When we combine all regressors in column 5, results are dominated by α5 – the other coefficients are much smaller in magnitude. 58 To summarize, by estimating the different regression models discussed in Section 2, we have been able to estimate not only to what extent transfers on average increase efficiency in village-wide, group-wide or pairwise allocation of land, but also whether transfers are more common within groups or across linked dyads and whether group membership and dyadic links affect efficiency. 59 S3 Appendix: General applicability of the method The methodology presented in this paper was developed to address a specific research question about factor markets in the Gambia. But its applicability is much more general. Much of economics is interested in allocative processes, e.g., the allocation of factors of pro- duction to their best use, as in this paper – but also the allocation of jobs to workers, the allocation of capital to firms, the allocation of goods to consumers, or the allocation of infor- mation within organizations. Some of these allocative processes rely on markets; others take place within hierarchical organizations; others yet involve non-market transactions among economic agents, such as favor exchange or informal risk sharing. The efficiency and equity of allocative processes are typically hindered by frictions in peer- to-peer flows. Economists have identified many sources of friction. Some are due to pure transaction costs (e.g., transport, handling, information processing). Others result from infor- mation asymmetries, imperfect enforcement of contracts, or ineffective protection of property rights. Others yet arise from the social structure within which transactions take place, and combine elements of discrimination, variation in search costs, homophilous socialization, and other forms of preferential treatment reserved to socially proximate individuals. Much work has been devoted to documenting and studying individual sources of friction. The purpose of our methodology is to test whether a hypothesized friction – for instance due to a particular aspect of social structure – can be responsible for observed inefficiency or inequity. The key idea is that all allocation processes can be represented as flows on a graph or network. This is true irrespective of how the process is organized – e.g., through a decentralized market or through hierarchical assignment. Friction impedes or restricts flows between certain links. Suppose we observe various predictors of link-specific frictions. Our methodology aims to rule out certain types of frictions as potentially responsible for unsatisfactory allocation. The logic of our approach is based on communicating vessels: if flows are impeded between different segments of the network but not within them, we should observe equalization of levels within these segments but not across them. The analogy with flows between communicating 60 vessels is particularly useful because the efficiency or equity of an allocative process requires the equalization of some relevant expression across economic agents. Here are some examples: • Factor markets : In this paper, we argued that, under plausible conditions, if farmers all have the same inherent productivity efficiency in factor allocation is achieved by equalizing factor usage across them. In Appendix B, we demonstrate that, under suitable conditions, if farmers have different productivity, factor ratios should be equalized across farms. See the references listed in the text. • Welfare : If individuals have the same marginal utility of income function, equalization of welfare among them requires equalization of expenditures. • Risk sharing : Efficient risk sharing within a group requires that ratios of marginal utilities between any pair of individuals be equalized across states of the world. • Consumption goods : Efficient allocation of consumption goods among consumers in a given time and location requires that the ratio of marginal utilities for any pair of con- sumed goods should be equalized across consumers. Efficient allocation of a particular good across locations at a given time requires that prices net of transport costs should be equalized across locations (i.e., market price integration). Equitable allocation of goods requires that two consumers should have the same likelihood of being assigned a particular good (i.e., equal opportunity). • Intertemporal allocation : Efficient allocation of capital across economic agents requires that the marginal utility of funds be equalized across them. Efficient allocation of capital across investors or firms requires that the marginal return to capital be equalized across them. • Job markets : Efficient allocation of workers across jobs requires that the marginal pro- ductivity of any two equally productive workers should be equalized across jobs and firms. Equitable worker compensation requires that wages should be equalized between any two equally productive workers (i.e. no wage discrimination). Equitable allocation 61 of jobs requires that two equally productive workers should have an equal probability of finding a job suited to their qualification (i.e., equal opportunity). • International trade: Gravity models have been used to study the pairwise restrictions in trade flows imposed by physical barriers or regulation. These studies can be comple- mented using the method presented here to identify determinants of aggregate efficiency that allow for re-exporting and other indirect flows. All these examples have in common that efficiency or equity in allocation requires (1) flows to take place on a (2) potentially large network in order to (3) equalize a particular object or concept – e.g., factor usage, expenditure, ratio of utilities, assignment probability. They also all share the feature that (4) flows between certain node pairs may be impeded or restricted. Given the right data, all these cases are amenable to our methodology to investigate which friction or flow impediment is not responsible for the failure to equalize. 62