Testing Lin's social capital theory in an informal African urban economy

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Introduction

Though social capital refers to a variety of social dimensions (norms, trust, networks), it may be more fruitful for empirical analysis to 'step back from grandiose approaches' and focus instead on the specific social components of social capital, such as social networks (Durlauf and Fafchamps, 2004: 46, 57). Actually, the role of social networks in markets and economic action, outcomes and institutions is widely acknowledged and has been studied for decades by social scientists, particularly sociologists [START_REF] Granovetter | Economic action and social structure: The problem of embeddedness[END_REF][START_REF] Coleman | Social capital in the creation of human capital[END_REF]. Economists have also recently begun to address this issue, in particular by demonstrating the role of social networks in market efficiency (reduction of transaction costs, enforcement of contract; [START_REF] Greif | Contract enforceability and economic institutions in early trade: The Maghribi traders' coalition[END_REF][START_REF] Kranton | Reciprocal exchange: a self-sustaining system[END_REF]. In the current framework of states and modern institutional failure in Africa, social networks and personal relations inevitably play an important part in structuring economic activities, particularly for micro and small-enterprises (MSE) within informal economies. They may facilitate access to a range of useful resources for entrepreneurs, for example information, ideas and knowledge (about markets, activities, and skills) or financial and material support (particularly in times of crisis). This is of particular significance in the case of MSE insofar as it tends to compensate for the weakness of the internal resources of small firms.

There are two interrelated perspectives in studies of contemporary social networks in African urban informal economies and MSE [START_REF] Barr | The functional diversity and spillover effects of social capital[END_REF][START_REF] Knorringa | Social capital for industrial development: operationalizing the concept[END_REF]. The first relates to the analysis of interfirm networks in industrial sectors or clusters in developing countries [START_REF] Mccormick | African enterprises clusters and industrialization: Theory and reality[END_REF][START_REF] Brautigam | Substituting for the state: Institutions and industrial development in Eastern Nigeria[END_REF], Meagher, 2007). The second is based on literature in the field of social capital and focuses on the social networks in which entrepreneurs are engaged. It attempts to evaluate their nature, role and impact on entrepreneurial success and economic performance. Yet surprisingly, this perspective remains relatively undeveloped since most of the empirical literature that studies individual social capital in developing countries focuses on households rather than entrepreneurs, particularly in rural areas (see [START_REF] Durlauf | Social capital[END_REF]. There is a common distinction in social capital literature between bonding, bridging and linking social capital [START_REF] Woolcock | The place of social capital in Understanding Social and Economic Outcomes[END_REF].

Bonding ties refers to relations between community members and close friends (generally strong ties, such as those developed in family or ethnic groups), whereas bridging ones refers to generalized social relationships across groups (and so generally weak ties). Linking social capital serves to describe the ties that connect individuals to people or groups in position of political and financial power. This last dimension of social networks is directly inspired from the 'social resources' or 'social capital theory' elaborated by Nan [START_REF] Lin | Social networks and status attainment[END_REF]Lin ( , 2001)). Lin argues that the social status of network members is a predictor of the quality of resources There have as yet been very few investigations that focus on the role of this dimension of social capital in the performance of African MSEs. This paper aims to fill this gap by analyzing and evaluating its economic impact on MSEs in the informal economy of Bobo-Dioulasso (the second largest city of Burkina Faso). We suggest an approach based on the notion of 'ego-centred network' derived from the Social Network Analysis (SNA) research tradition [START_REF] Wasserman | Social network analysis. Method and applications[END_REF]). An 'ego-centred' (or 'personal') network is defined as one actor's set of connections with others [START_REF] Wellman | The network is personal: Introduction to a special issue of Social Networks[END_REF]. This perspective is particularly relevant to the study of informal entrepreneurs' social networks that are often composed of a mixture of business, friendship and kinship ties. A network is thus defined as entrepreneurs' regular social relations conveying essential resources for the current exploitation of their activity. This approach implies a description of the configuration of social networks according to three salient dimensions: network structure (size, density), the content of ties (strength, social role, exchanged resources), and obviously the attributes of members (sociodemographic, social status, professional occupation). Since this requires specific data concerning personal networks [START_REF] Wellman | The network is personal: Introduction to a special issue of Social Networks[END_REF], we conducted an original survey of a representative sample of 317 entrepreneurs between February and July 2007. In addition to sociodemographic and economic data, personal networks data were collected for a sub-sample of 278 entrepreneurs. This part of the questionnaire is based on an adaptation of the multiple names generators method (Fischer, 1982;Burt, 1984;[START_REF] Campbell | Name generators in surveys of personal networks[END_REF][START_REF] Marsden | Recent developments in network measurement[END_REF]. The explanatory power of this approach derives from its ability to produce rich statistical information about the complex nature of informal entrepreneurs' networks, especially with regard to the attributes of network members. Thanks to this approach, descriptive statistics and earning functions can be used to discuss Lin's hypothesis about access to social capital and to assess and discuss Lin's prominent social capital proposition about its individual return.

The remainder of the paper is organized as follows. Following a brief overview of entrepreneur's social networks in African MSE, section two provides a definition of the egocentred network framework. Section three reviews Lin's social capital theory and its relevance to an African urban informal economy. Data and survey methodology, particularly the multiple name generators instrument, are discussed in section four. Section five explores the configuration of members' attributes in entrepreneurs' networks, and tests its potential effects on economic outcomes. Finally, a discussion is presented in section six.

Entrepreneurs' social networks in African MSE: an 'ego-centred network' framework

Interfirm networks in industrial clusters

Studies of inter-firms networks aim to analyze the role of industrial clusters in African industrialization and development, and the determinants of their success or failure [START_REF] Mccormick | African enterprises clusters and industrialization: Theory and reality[END_REF]. The core idea is that industrial inter-firms networks tend to favour different clustering gains called collective efficiency [START_REF] Schmitz | Collective efficiency: Growth path for small-scale industry[END_REF]. [START_REF] Nadvi | Industrial clusters in less developed countries: Review of experiences and research agenda[END_REF] argue that dense cooperative networks embedded in local socio-cultural relations favour collective efficiency. [START_REF] Brautigam | Substituting for the state: Institutions and industrial development in Eastern Nigeria[END_REF]Brautigam ( , 2003) ) demonstrates the positive role of ethnic business networks in the development of international relations with Asian firms in Nigerian and Mauritian industrial clusters. Conversely [START_REF] Meagher | Social capital, social liabilities, and political capital: social networks and informal manufacturing in Nigeria[END_REF]Meagher ( , 2007) ) argues that in times of economic crisis, increasing competition and state neglect, social networks and their organizational capacity tend to be disintegrated or fragmented. Such effects may cause the (Nigeria). By analysing the role of social networks in strengthening industrial clusters, this first perspective is connected with the second concerning entrepreneurs' social networks. However, while the first is mostly based on meso and sectoral level analysis, the second focuses on individual firms and entrepreneurs.

Entrepreneurs' social networks

Research that focuses on entrepreneurs' social networks seeks to identify the nature and types of social networks used by entrepreneurs (not only for clustered enterprises). It evaluates their role and impact on entrepreneurial success and economic performance. Most studies in this area use social capital approaches [START_REF] Fafchamps | Ethnicity and credit in African manufacturing[END_REF]Minten, 2001, 2002;[START_REF] Barr | The functional diversity and spillover effects of social capital[END_REF].

Networks and social relations are seen as a form of social capital that is useful for reducing transaction costs in a context of imperfect markets ('flea market') and modern institutional failure. From an empirical standpoint, such research work generally suggests that social networks have a strong and significant positive impact on entrepreneurs' economic performance. Such is the case for instance of agricultural traders in Madagascar, Benin and Malawi [START_REF] Fafchamps | Ethnicity and credit in African manufacturing[END_REF]Minten, 2001, 2002). Nevertheless, in her study of the Ghanaian manufacturing sector, [START_REF] Barr | The functional diversity and spillover effects of social capital[END_REF] also insists that small entrepreneurs appear to be characterized by 'solidarity networks' that reduce income variability but which have little impact on economic performance. Within this framework, social network capital has been essentially analysed in two ways. The first is the entrepreneur membership of various (formal or informal) organizations, groups, and communities (business communities or ethnic groups for example, see [START_REF] Fafchamps | Ethnicity and credit in African manufacturing[END_REF][START_REF] Knorringa | Social capital for industrial development: operationalizing the concept[END_REF]. However, as shown by most qualitative surveys, these perspectives are likely to overlook the less formalized relations developed outside organizations and social groups, which have an important role, particularly in the formation of [START_REF] Lyon | Trust, networks and norms: The creation of social capital in agricultural economies in Ghana[END_REF][START_REF] Lourenço-Lindell | Walking the Tight Rope: Informal Livelihoods and Social Networks in a West African City[END_REF]. The second type of analysis focuses on entrepreneurs' inter-personal relationships, especially business relationships [START_REF] Fafchamps | Ethnicity and credit in African manufacturing[END_REF]Minten, 2001, 2002;[START_REF] Barr | The functional diversity and spillover effects of social capital[END_REF]. It is measured in concrete terms by the number of contacts that a firm owner tends to maintain with some category of agents in the market sphere (relations with suppliers, customers, other traders), and sometimes outside the market sphere (such as relations with bankers, public servants or politicians; see [START_REF] Barr | The functional diversity and spillover effects of social capital[END_REF]. These quantitative studies provide useful general insights into social networks and African entrepreneurial dynamics (see section 3). However, these measures essentially depend on the size of the network ('number' of contacts) and provide very little qualitative information concerning the complex nature of social networks and their members. These measures may remove personalized relations from their social context. Of course, the social category of contacts carries some information but herein lies another limit. These categories are predefined, and there is therefore an element of risk in predicting which type of social group is useful for entrepreneurs before having demonstrated it. In addition, important ties maintained by entrepreneurs outside these categories could be overlooked.

The ego-centred network framework

The use of SNA to study economic action, outcomes and institutions has undergone considerable expansion since [START_REF] Granovetter | Economic action and social structure: The problem of embeddedness[END_REF] seminal paper on 'structural embeddedness'. Generally speaking, social relations between individuals are commonly viewed in this framework as interpersonal experience (each agent knows the relevant characteristics of other agents) based on interactions that enable the transmission of resources.

A social network is therefore merely an aggregation of social relations. SNA rests on two methodological corpuses. First of all, social networks are defined from a socio-centred standpoint as finite sets of actors and the relations between them (Wasserman and Faust, 1994: 20). These are known as 'whole' or 'complete' networks' 1 . The second defines social [START_REF] Wellman | The network is personal: Introduction to a special issue of Social Networks[END_REF]). An 'ego-centred' (or 'personal') network is defined as one actor's set of relations with others. It is composed of a focal actor (named ego), a set of ego's direct social contacts (named alters) and the ties between them (see figure 3, section 4). This perspective proposes a kind of 'enriched individualism' and uses networks to unpack the social context in which individuals (assumed to be independent of each other) are embedded [START_REF] Knox | Social networks and the study of relations: networks as method, metaphor and form[END_REF]. It is particularly appropriate for analyzing the networks of agents, the composition of which is diversified and not limited by some geographical, organizational or community boundaries. It is thus particularly relevant for the analysis of urban African informal entrepreneurs' networks, which are often composed of a blend of business, friendship and kinship ties. Furthermore, rather than focusing on ties with some specific social category, an entrepreneur's social network directly refers, in our approach, to the regular social relations that convey useful resources for the current exploitation of their activities (both tangible and intangible). Ego-centred networks of this kind can be described by three salient dimensions: the content of ties, network structure and the attributes of members. In order to analyse and discuss Lin's social capital theory [START_REF] Lin | Social networks and status attainment[END_REF](Lin, , 2001)), the focus here is on members' attributes in an entrepreneur's social network. We then need to clarify how this network dimension is related to economic outcomes, both theoretically and empirically.

Lin's social capital theory and alters attributes in entrepreneurs' network

Lin's social capital (resources) theory [START_REF] Lin | Social networks and status attainment[END_REF](Lin, , 2001) can be considered as the most significant approach for studying alters' attributes. Lin's thesis is that social resources exert an important and significant effect on the realization of individual instrumental actions. The theory is based on a hierarchical vision of social structure in which the positions of agents are ranked according to their resources proxied by social status, wealth, and power. Structure 8 therefore has a 'pyramidal shape in terms of accessibility and control of such resources', implying an advantage for those nearer the top (Lin, 1999: 470). The theory concludes with three chief propositions [START_REF] Lin | Social networks and status attainment[END_REF](Lin, , 2001; see figure 1): (i) the 'social capital proposition': access to better social resources enables more efficient instrumental actions; (ii) the 'strength of position proposition': the initial social position influences access to social resources and their use; (iii) the 'strength of ties proposition': weak ties tend more than strong ties to give access to better social resources. The first proposition concerns the individual return of social capital and the two others pertains to access to social capital. Return of social capital can be investigated using two approaches: 'contact resources' and 'network resources' [START_REF] Lin | Social networks and status attainment[END_REF](Lin, , 2001;;[START_REF] Lai | Network resources, contact resources, and status attainment[END_REF]. The first one is based on the social status of a contact mobilized for a particular, and punctual, instrumental action ('mobilized social capital'; [START_REF] Lin | Social networks and status attainment[END_REF]Lin, , 2001). The second one focuses 'on the networks an ego routinely maintains and the configuration of the members' resources characteristics (for example, diversity and range of resources)' (Lai et al, 1998:161). Here it is the general configuration of the network that contributes to the success of instrumental actions. Social capital then represents the accessible resources used for a regular action ('accessed social capital'; [START_REF] Lin | Social networks and status attainment[END_REF]Lin, , 2001) ) 2 . Several empirical investigations of the relationship between social capital and individual social status attainment have tended to corroborate Lin's propositions, especially regarding the job-search process, except for the 'strength of ties proposition', which appears to be more ambiguous (see Lin, 1999: 74).

In the economic literature, this approach refers to the notion of 'linking social capital' [START_REF] Woolcock | The place of social capital in Understanding Social and Economic Outcomes[END_REF], which describes ties connecting individuals to people or groups in position of political and financial power. The adaptation of this theory in the context of an African informal economy has rarely been the object of empirical analysis and assessment. Notable exception includes [START_REF] Barr | The functional diversity and spillover effects of social capital[END_REF] study of the Ghanaian manufacturing sector. She distinguishes 'solidarity' networks from 'innovative' networks. Solidarity networks tend to be small, dense, locally concentrated and with poorly resourced personal relations (with no access to advantageous economic positions or privileged commercial groups). These networks are very homogeneous in terms of member attributes. Though they reduce risks and incomes variability, they have little impact on economic performance and tend to undermine rather than enhance profits [START_REF] Barr | The functional diversity and spillover effects of social capital[END_REF] 3 . Conversely, innovative networks are wide, geographically dispersed, and significantly more diversified in terms of status of members. They are composed of advantageous ties with privileged access to resources. [START_REF] Meagher | Social capital, social liabilities, and political capital: social networks and informal manufacturing in Nigeria[END_REF] qualitative analysis of Nigerian clusters also distinguishes 'survival' networks from 'accumulation' ones (ties with privileged social classes, civil associations and successful traders, especially international traders). [START_REF] Brautigam | Substituting for the state: Institutions and industrial development in Eastern Nigeria[END_REF]Brautigam ( , 2003) ) arrives at a similar typology in her studies of the role of 'ethnic business networks' in cluster dynamics in Nigeria and Mauritius. Conversely, some qualitative studies also indicate that relationships with the most powerful actors may lead to unequal exchange relations of subordination and domination [START_REF] Lomnitz | Informal exchange networks in formal systems: A theoretical model[END_REF][START_REF] Lourenço-Lindell | Walking the Tight Rope: Informal Livelihoods and Social Networks in a West African City[END_REF]2002[START_REF] Meagher | Social capital, social liabilities, and political capital: social networks and informal manufacturing in Nigeria[END_REF].

These results tend to confirm the prominent proposition of Lin's social capital theory: the core determinants of the positive impact of networks on economic performance include the heterogeneity of alters' attributes and the access to high social positions (access to better social resources). However, in order to avoid an overly restrictive hierarchical vision of social structure it is important to consider some other attributes. We therefore also integrate horizontal dimensions referring to the professional and socio-demographic characteristics of alters (box and circle in figure 2). Actually, professional cohesion or similarity (as between ego and a3, a4 and a5) may improve entrepreneur's efficiency (or conversely professional heterogeneity may increase the probability of accessing a range of useful resources).

Regarding sociodemographic characteristics of alters, the homophilous dimension of social ties (as between ego and a2) reveals the social homogeneity of a given network, or its level of social closure, which may affect entrepreneurs' performances.

Finally, note that though not econometrically tested, the two other propositions outlined by Lin regarding access to social capital will also be briefly commented through descriptive statistics.

Data and method

The data

The data were collected in the informal economy of Bobo-Dioulasso in Burkina Faso, which is one of the poorest countries in the world. In 2007, real GNI per capita was estimated at US$ 2003). The importance of the informal economy in this country matches regional tendencies (Brillaud et al., 2004). In Bobo-Dioulasso, it represents 49.5 per cent of local value added and 68.2 per cent of employment (Fauré, Soulama, et al., 2000).

Between February and July 2007 we conducted a survey on a representative sample of 317 entrepreneurs. Firstly, sociodemographic and economic data were collected, focusing in particular on features, type of activity, employment, economic capital and outcomes.

Secondly, the statistical information was completed several weeks later by collecting personal network data on a sub-sample of 278 entrepreneurs. The boundaries of the informal economy were empirically defined according to ILO's criteria (size of the activity and official registration) (OIT, 1993) plus an accountancy criterion. The sample is representatively distributed by economic sectors (production, trade and services) and sub-sectors, and by geographical area, from the results of the last exhaustive census of economic activities carried out in Bobo-Dioulasso (Fauré and Soulama., 2000). Among this sample, fourteen entrepreneurs have undergone an in-depth interview in 2008. Interviews were based on lifestories method: entrepreneurs tell their professional careers and the history of their businesses is embedded in this whole story. During interviews, reminder questions about the access to external resources have been used to identify the medium of access (such as social relations).

In this paper, this qualitative material will only be used to illuminate the discussion of results.

The multiple names generators instrument

There are different instruments for the collection of personal networks data (Marsden, 2005, Wasserman and[START_REF] Wasserman | Social network analysis. Method and applications[END_REF]. The name generators method is the most commonly used in the field of entrepreneurship in industrialized countries [START_REF] Hoang | Network-based research in entrepreneurship: A critical review[END_REF][START_REF] Greve | Social networks and entrepreneurship[END_REF] (vi) financial backing (as support in times of crisis, or for an investment, through loan or gift); and (vii) contact for recruitment (access to employment). Lastly, a 'contextual name generator' was inserted. This refers to important support relations at the moment of business start-up, which are invariably active in entrepreneurs' networks. In order to limit the duration of interviews, the number of alters cited for each generator was restricted to three (two for the second generator) 6 . Furthermore, in addition to the eight generators, a final name eliciting question was added for additional important contacts that may have been forgotten. occupation and their sector of activity. This information was then ranked in classifications of professions and social status 8 . For the social status classification, level of schooling and other proxies of alter's wealth were used, such as means of transport (vehicle, moped, cycle) and residential status (owner, tenants, family yard). As an example taken from our database, figure 3 illustrates the rich data provided by the names generators instrument for the purposes of describing entrepreneurs' personal networks, especially alters' attributes.

Measurement of alters' attributes

The 'network resources' approach associated with the multiple names generators method provides a variety of possibilities for measuring the composition of networks 9 . Our analysis of alters' attributes in entrepreneurs' personal networks focuses on three different aspects. In line with [START_REF] Lin | Social networks and status attainment[END_REF]Lin ( , 2001)), the first is social status. Compared to ego, we distinguish alters enjoying an intermediate status and alters enjoying a higher status. The first are principally business owners of the upper part of the informal sector (as wealthy merchants) and of the small and medium-sized formal enterprises (especially in building trade) (65%), workers and non qualified employees in the private formal sector (notably in building industry, transport and services) (15%), and minor public officials (public sector employees) (12%). The second are mostly top-ranking civil servants and intellectual and intermediary professionals in public sector (47%), business owners, senior executives, managers and officers in formal enterprises of the private sector (36%) and in NGOs (14%) 10 . Secondly, we also consider the professional occupation of the network's members through the proportion of alters belonging to the same profession as the ego. Thirdly, we consider the sociodemographic similarity between the ego and his alters (homophily or, conversely, heterophily). This similarity is evaluated considering four sociodemographic characteristics (age group, ethnicity, religion, and geographical location). Ties are considered heterophilic if alters are different from egos for at least three of these four characteristics. activities than in production and other services 12 . However, the production sector is the most important in terms of employment and wage distribution.

Some comments about Lin's 'strength of ties' and 'strength of position' propositions

The total rows and columns of tables 1 and 2 give a very interesting insight into the average nature of entrepreneurs' social network and ties in our sample. However, we focus our comments on Lin's (2001) 'strength of ties' and 'strength of position' propositions.

Firstly, at ties level, we combine alters attributes and the characteristics of ties (content and strength of ties) to broach Lin's 'strength of ties proposition'. the creation of activity, reciprocity and trust intensity) are not significantly linked with access to higher-status alters. Furthermore, close friendship ties are significantly linked with higher status individuals. These observations corroborate the difficulty to empirically observe the 'strength of ties proposition' [START_REF] Lin | Social networks and status attainment[END_REF]. Concerning alters' professional occupation, table 1 indicates that relations developed in the same profession as the ego are often business ties of partnership. Finally, socio-demographic heterophily is obviously negatively linked with the different aspects of ties' strength.

Secondly, at entrepreneurs' personal networks level, alters' attributes can be crossed with entrepreneurs' (firms) characteristics. In order to proxy the initial social status of ego, we introduce entrepreneurs' level of education, their former professional status and the level of their start-up capital. These variables are useful to broach Lin's 'strength of position proposition'. Table 2 reveals that the most highly educated entrepreneurs are embedded in networks with a significantly larger proportion of alters enjoying higher social status.

Entrepreneurs' former professional status shows that the higher it is the higher their probability to reach high social status alters. As a consequence, their networks are also more diversified in terms of the socio-demographic characteristics of alters (more heterophile) and less professionally homogenous. Start-up capital leads to the same kind of conclusions. Thus, these descriptive results are in line with the 'strength of positions' hypothesis. In other respects, entrepreneurs from Mossi ethnicity are less often than others linked to alters enjoying higher status. Geo-ethnic historical oppositions may explain this fact (see [START_REF] Savonnet-Guyot | Etat et sociétés au Burkina[END_REF]. Owners' age and experience appear to be important characteristics in accessing alters with higher social statuses. Sectoral specificities also appear. The networks of production entrepreneurs prove to be 'poor' regarding alters statuses.

Testing Lin's 'social capital proposition' on informal entrepreneur's economic outcomes

We are now in a position to assess the relevance of the attributes of network members as a predictor of entrepreneurs' economic outcomes. Ordinary least squares (OLS) regression was used to investigate the extent to which inputs, business and entrepreneurs characteristics, but also and especially member's attributes of entrepreneurs' network, help to predict informal business earnings. Regression coefficients give the change in earnings corresponding to a unit change in the appropriate explanatory variable, which is conditional on the other variables remaining constant. We may therefore assess the impact of social networks on economic performance, whatever the value of other explanatory variables.

Regarding Two blocks of predictors were implemented, that is. usual predictor variables of informal earnings (inputs, business and entrepreneurs characteristics) and predictor variables standing for alters' attributes of entrepreneur networks. With respect to the usual independent variables in the model, the following remarks can be made. Firstly, capital input is a monetary estimation of the value of the machinery, tools, equipment and stocks owned by entrepreneurs at the time of the survey. Labour input is measured by the monthly monetary value of wages paid to business employees, whatever their status. The effective contribution of labour to earnings may thus be more easily appreciated, since the usual 'number of employees' variable is likely to suffer from serious productivity bias. Secondly, business characteristics capture the impact on earnings of engaging in retail trade or catering activities. It also considers the alleged positive impact of administrative registration, pluriactivity and the favourable economic situation during the present year. Thirdly, entrepreneurs' characteristics include variables that describe the human capital of entrepreneurs (primary education and on-the-job experience), entrepreneurial behaviour (demand anticipation), gender, ethnic group and membership of a professional organisation. The second block aims to introduce information about entrepreneurs' social networks as predictors of earnings. In doing so, we will be able to test the impact of the attributes of network members on earnings, ceteris paribus. We therefore introduce four additional variables in the model in order to describe the network of an ego in relation to the attributes of his alters. The first two variables in this block measure the proportion of network members who enjoy an intermediate or higher status than the ego.

The third variable measures the professional homogeneity of ego's network through the proportion of intra-profession ties. Finally, the fourth variable considers the sociodemographic opening of the ego's network (its heterophily) by pointing out the proportion of heterophilic ties (regarding age group, ethnicity, religion, and geographical proximity) in the ego's network. (2) for independent workers, log(labour monthly input) is standardized to 3.17 for continuity purpose ; (3) dummy variable, 0 = other activities ; (4) dummy variable ; (5) dummy variable, 1 = activities that have experienced a favourable economic situation this year ; (6) dummy variable, 1 = entrepreneurs conducting their business since at least 5 years ; [START_REF]Standard Classification of Occupations of the OIT (ISCO-88)[END_REF] dummy variable, 1 = female ; (8) dummy variable, 1 = Mossi ; (9) dummy variable, 1 = members of one or several professional organisation ; (10) dummy variable, 0 = entrepreneurs who set the level of their activity only according to placed orders and/or their productive capacities. The reliability of OLS regression parameters may be challenged by potential endogeneity bias, notably with regard to the direction of causality between entrepreneurs' social networks and their economic performances. We therefore test whether our five social networks variables can be regarded as exogenous, by using the standard econometric procedure of instrumental variables and Hausman test. The implemented instruments refer to the network's ties created before the start up of the activity. More precisely, the picked instruments are the number and the proportion of ties created before activity's start-up and among them, the proportion of ties with intermediate status alters, higher status alters, alters in the same profession, and the proportion of heterophilic ties 13 . Sargan tests of overidentifying restrictions are also presented in table 3. It confirms the validity of our instruments. Hausman tests indicate that the exogeneity of our network variables can not be statistically rejected, except for the regression on sales turnover. Thus, parameters estimates shown for sales turnover in table 3 have been computed through IV (2 SLS) regression.

The results of regressions are shown in table 3 14 . Means and standard deviations are presented in table A.2, in the appendix. The three modelizations significantly predict sales turnover (F(19, 231) = 16.56, p < .01, adjusted R² = .537), value added (F(19, 250) = 17.17, p < .01, adjusted R² = .520) and earnings (F(19, 250) = 8.04, p < .01, adjusted R² = .320). The standardized estimated coefficients for significant network variables demonstrate their important part in entrepreneurs' economic outcomes. Actually, their magnitudes appear to be comparable to that of basic predictors such as capital input or favourable economic situation.

Discussion

The most important result of this paper is that the proportion of alters enjoying an intermediate status in the social network of entrepreneurs has a strong and significant positive impact on all economic outcomes in the informal economy of Bobo-Dioulasso. Conversely, the proportion of alters with a high social status has no significant impact. This issue is of particular interest since it partly contradicts Lin's social capital proposition [START_REF] Lin | Social networks and status attainment[END_REF](Lin, , 2001)). So, why are these intermediate status alters so valuable compared to higher status ones? The main explanation rests on the idea that the resources owned by intermediate status alters are particularly useful for entrepreneurs in the urban African informal economy.

As intermediate status alters are mostly rather 'well-off' business owners, the argument must actually be especially relevant for business relationships. This is, for example, the case for supplier relationships. The organisation and dynamics of large formal private firms rarely come up to informal activities' expectations. These last require a high degree of flexibility for their economic transactions because of the uncertainty which characterizes an informal economy in a context of economic crisis. It is thus more useful and easy to work with informal or small and medium-size formal suppliers. The analysis of life-stories that we have collected reveals that access to important resources, such as supplier credit, is easier with this kind of suppliers. For example, a garment seller told us that he has no difficulties to obtain credit with his supplier who is an important informal garment wholesaler in the central marketplace, while a wood joiner and a specialist in metal fittings express difficulties to obtain credit with some formal enterprises, because the times for payment required by suppliers are not compatible with the extended times for payment that they have to afford to their clients. Moreover, regarding clientele, the capture of a middle class clientele may also represent a crucial determinant of business success as it constitutes a more reliable clientele (creditworthy) than the informal population and a more accessible one than the upper class (who seeks for better quality products). Last but not least, as wealthy merchants are well represented among intermediate status alters, it is important to remember that they historically constitute a group of financial, political and social power in the city (Fauré and Labazée, 2002).

Another aspect of the value of intermediate status alters relates to their approachability, notably concerning the access to 'social' resources. Considering the high degree of uncertainty of the informal economy, approachability is of the highest importance, as for example, when instant access to financial support is required. In most life-stories that we have collected, we observe that in time of crisis, financial support comes from approachable individuals, notably from entrepreneurs' own household members, rather than from their even more comfortable highest-rank relations. For example, a garment maker explains that the first person from who he receives financial support in time of difficulties is his wife (an administrative secretary in a private formal enterprise) whether than his village relative who is the director of one of the most important national industry in the country. Some kind of autorestriction process prevents entrepreneurs to easily ask help from high status relations (even though they are relatives). Intermediate statuses are also particularly useful for administrative support. Although corruption in Burkina Faso mostly operates hidden in the administrative offices [START_REF] Insd | La pauvreté en[END_REF], it is if need be more useful for informal entrepreneurs to have relations, for example, with the local tax officer (field employee) than with the director of the fiscal administration. Whereas he can directly deal the payment of a 'gift' with the former, it would be difficult to do the same with the latter which is in a position that strongly constrains its possibilities of action. The same kind of argument occurs with any public or private administrative service. Generally speaking, ties with employees are more useful than with executives in the relations with formal organisations and institutions. Life-stories back up this conclusion in many aspects like for example in relations with formal banks or institutions of micro finance (IMF). For example, a restaurant owner explains how she obtained five important credits from an IMF thanks to four regular customers who were employed in that bank (counter-clerks, secretaries, etc.). Without them, she would never have known how to complete her file credit application and how to manage her bank account to expose her restaurant's financial health. Social approachability is thus of the highest importance in access to social support. Furthermore, social ties with intermediate status alters are less asymmetrical than with higher status ones. Qualitative studies have tended to emphasize that relations with the most powerful actors may lead to unequal relations of subordination and domination [START_REF] Lomnitz | Informal exchange networks in formal systems: A theoretical model[END_REF][START_REF] Lourenço-Lindell | Walking the Tight Rope: Informal Livelihoods and Social Networks in a West African City[END_REF]Meagher, 2005[START_REF] Meagher | Social capital, social liabilities, and political capital: social networks and informal manufacturing in Nigeria[END_REF]. As Lomnitz (1988: 48) suggests: 'The symmetry of the relationship depends on social distance: the closer the social relation, the greater the confianza and consequently the balance of the exchange'. When the differential of power between the two partners is important, reciprocity tends to be transformed into a 'patron-client' relation. Thus, when ego's capacity of reciprocity is limited, whether he does without help or returns the offered resources through demonstrations of gratitude and loyalty. In other words, social distance between partners favours subordination.

The significant negative effect of the sociodemographic heterophily of networks is another aspect of the importance of social proximity. This result differs from [START_REF] Barr | The functional diversity and spillover effects of social capital[END_REF] conclusion. Rather than constituting a strong social constraint impeding entrepreneurial agency, homophily seems to favour the trust required to develop economic activities.

Regarding professional homogeneity, we find no evidence of its impact on economic outcomes. Thus, social diversification, often praised as a core determinant of performance, does not appear to be of great relevance here.

We have shown that intermediate status alters are extremely valuable contacts in their selves, but they may also be valuable regarding the contacts they give access to. One might consider that such relations hold an intermediary position within the local social structure (between informal entrepreneurs and the top of the social scale). Thus, they hold a particularly strategic position and fill what [START_REF] Burt | Structural holes. The social structure of competition[END_REF] refers to as 'structural holes'. However, it would necessitate some unavailable specific network data to assess this idea 15 . Yet, in their selves, intermediate status alters remain valuable by sparing informal entrepreneurs to have direct asymmetrical relationships with high-rank alters.

The test for endogeneity bias reveals a likely reverse causality between sales turnover and network's configuration. In that case, such result deserves a brief comment as reverse causality would only occur with sales turnover and not with earnings or value added. The joint evolution of business turnover and entrepreneur's network seems actually coherent: Finally, this paper also raises some implications for policy-making. Our results show that in the informal economy of Bobo-Dioulasso, social networks and relations matter for small entrepreneurs, though in highly specific ways. This is of particular importance for policy intervention, since it is important to understand the role of social dynamics in the operation of local markets. To sum up our results, we find that entrepreneurs' personal networks are characterized by social proximity and closeness. Half of all entrepreneur ties concern alters with comparable social status (see table 1). Concerning their economic impact, our results do not indicate the importance of relations with high privileged social status alters but rather with intermediate ones. Herein lies the need for policy intervention. A report of the National Commission for Decentralisation for the local economic growth argues in favour of the connexion between informal sector and large, small and medium-sized enterprises of the formal sector (CND-PDM, 2002: 21). Regarding our results, since intermediate status alters are often business owners of the upper part of the informal sector and of the small and medium-sized formal enterprise, we suggest focusing on the latter rather than on large formal enterprises. In other words, policy intervention has to promote more equitable linkages between formal and informal activities [START_REF] Chen | Rethinking the informal economy: linkages with the formal economy and the formal regulatory environment[END_REF], particularly by facilitating the creation of institutions which might enable the development of equitable market-based relationships (business and professional organizations, but also meeting places such as market-places or trade fairs). Such institutions would all the more be necessary since the access to intermediate status alters is likely to depend on an initial social position (see table 2 about 'strength of position proposition'). Moreover, the importance of entrepreneurs' personal ties with minor civil servants and employees for their relationships with formal organizations and institutions reveals a crucial lack of access to information that policy intervention may fulfill. This points to the necessity of institutions and structures that favour access to information for microentrepreneurs.

To conclude, further investigation on the subject is clearly required, notably regarding dynamic perspectives on social networks [START_REF] Slotte-Kock | Entrepreneurship research on network processes: A review and ways forward[END_REF]. This can be addressed through three distinct but not exclusive methods: the analysis of network formation with complete network data as in risk sharing networks studies [START_REF] Fafchamps | The Formation of Risk Sharing Networks[END_REF], the collection of longitudinal ego-centered network data (it may be for example very fruitful to insert an ego-centred network item into 1-2-3 surveys; [START_REF] Amegashie | La conception et la mise en oeuvre des enquêtes 1-2-3 en UEMOA, les enseignements méthodologiques[END_REF] and the use of qualitative material [START_REF] Durlauf | Social capital[END_REF]

Advice, information and ideas

Usually, entrepreneurs know people they can ask some advices and information to, or with whom they can discuss and share some of their ideas and even some important issues concerning their business. For example ideas about how to improve and enlarge business, ideas about investment and management, or information about markets, suppliers, customers, access to credit, and so on. During the last 12 months, are there any people you have asked advices or information to, or with whom you shared ideas concerning your current business? Please name up to three people with whom you have especially discussed about that kind of things.

Support in administrative or bureaucratic relationships

Within the framework of their business, small entrepreneurs often face some administrative obligations and problems. They have relations with the public authorities, the municipality (Bobo-Dioulasso central town council or town hall of arrondissement), the specialized organizations (as the chamber of commerce, professional associations, labour unions), the tax office, the police, and so on, for example concerning controls and inspections for the payment of taxes, the constitution of files to access public markets, the location of businesses…Generally speaking, in your current business, is there some people you rely on to settle that kind of problems concerning administrative burdens ? Please name up to two of these people.

Regular suppliers (access to goods and raw materials)

Within the framework of your business, regarding the purchase of goods, raw materials and equipments that are essential to your activity's exploitation, do you have personal contacts through which you access suppliers or suppliers with whom you maintained regular relations during the last 12 months? Please name up to three of these people.

Faithful customers or access to customers

Concerning customers, did you have, during the last 12 months, personal contacts which allow you to regularly reach them, to improve your reputation, or do you have "faithful customers" who regularly purchase your goods and/or allow you to reach good markets? Please name up to three of these people.

Cooperation or partnership with other entrepreneurs

Within the framework of their current activity, small entrepreneurs often develop some relations of mutual aid, partnership or cooperation with other entrepreneurs. As for example in the case of breakdowns, or when you do not have the appropriate tool, machine or good; and even when you cooperate in the process of production, the share of markets or the exchange of customers. Who are the entrepreneurs with whom you maintained such kind of relations? Please name up to three of these entrepreneurs with whom you personally and regularly cooperated during the last 12 months.

Financial support

In their current business, small entrepreneurs may face some financial difficulties causing problems to maintain the business and even threatening the activity with closure. Did you recently, during the last year for example, experience some financial difficulties, cash flow problems, or important breakdowns? If yes, how did you overcome such kind of situation? Did you ever asked for financial support to anybody? In addition, some entrepreneurs may decide to invest in new equipments in order to develop their business and workshop, or to replace their machines. Did you ever received financial support for that kind of investment? Finally, when you face that kind of problems, who do you rely on for financial support or help to reach for financing (whether it is gifts, loans or advances)? Please name up to three people to which you regularly asked for financial support during the last 12 months.

Access to employment (contact for recruitment)

Do you have employees, permanent or occasional, wage workers, familial assistant or apprentices? Concerning those hired during the last year, were there personal contacts which served as intermediaries for their recruitment? For example you may have hired them through a family member, a neighbour, a friend, a customer, and so on. Who are these personal regular contacts which have served as intermediaries for your recruitments, or by whom you would pass to recruit somebody for your activity? Please name up to three of these contacts.

Support for business start-up

At the time of your business start-up, did some people support you in such a manner that you consider them as very important for you during this period? If yes, how did they support you? Moral support, financial or material help? For example, how did you constitute your start-up capital? Among these people, with whom you still have been in regular contact during the last 12 months, please name up to three.

Opened question

Looking at the entire name list you have quoted, are there other people who you consider as very important for you in your activity's current exploitation and who do not appear on the list? If yes, how many people did we forget? Please name one of them. Note: * the total percentage exceeds 100% as one tie can be classified in several categories (a parent who is also a customer for example) ; chi-square test has not been computed on shown proportions but on the numbers of each given type of relation in each population.

  relations. His theory covers both the access to social capital and the individual return of social capital. Regarding the last point, Lin considers that access to high social status through a network enables more efficient instrumental action.

  networks composition and content can be computed. From these,

  industrial clusters in African informal economies, such as in the garment and shoe clusters of Igbo communities in Aba

  Figure 1: Lin's theoretical propositions

  Figure 2:Alters' socioeconomic attributes in ego's network

  Bank, 2009) and almost half of its population lives under the poverty line (INSD,

  Main features of the sample 11In Bobo-Dioulasso, as in most informal economies, the dominant form of business is selfemployment. Entrepreneurs are relatively young (35.5 years in average) and their households are composed of 7.5 members on average. Only 26 per cent have an educational level above primary education. In the informal economy, training is essentially provided through traditional on-the-job apprenticeships. Most entrepreneurs follow an informal route (from family assistant to apprentice and then owner). Regarding legality, 11 per cent of enterprises are registered in an official commercial register (mostly trade activities). The localization of economic exchanges confirms the autarkical confinement of informal activities, since it is mainly concentrated in the perimeter of the city for both customers and suppliers. The measure of economic performance reveals that earnings are higher in trade and catering

  endogenous variables, monthly sales turnovers are expressed in Francs CFA and adjusted for seasonal variations. Their logarithms are introduced in the model to lessen the impact of extreme values. Value added is computed on a monthly basis as the difference between sales turnover and intermediate consumptions and raw material expenses. Earnings are computed on a monthly basis as the difference between sales turnover and global monthly expenses, including raw materials and intermediate consumptions, current charges (including wages and rents) and financial and administrative charges. Both value added and earnings are also expressed in francs CFA and their logarithms are introduced in the model.

  the insertion in the local business environment which in turn creates new relations with customers, supplier and partners. Numerous life-stories illustrate this fact, notably in trade activities and production sector were such co-evolution often even started before the creation of present activity.

32 years old; Mossi; Muslim Garment makers 38 years old, Male, Lebanese, Muslim, Superior education, Commercial director of import/export society in textile industry 57 years old, Male, Samo, Muslim, no education, Informal garment maker 21 years old, Male, Mossi, Muslim, primary education, Informal calligrapher 40 years old, Male, Mossi, Muslim, Superior education, Assistant director of Finance in Police School 35 years old, Male, Dioula Muslim, primary education, Informal trader in various commodities 45 years old, Male, Marka, Muslim, Superior Education, Colonel of Army

	Figure 3: case of professional occupation, respondents were asked to give precise descriptions of alters' Informal entrepreneur's ego-centred network (adapted from Burt, 1984: 298)
	Parent,
	F o r Advice and information & Start-up support F o r	Parent, Administrative support
	P P	Close friend; Recruitment information
	e e r RESPONDENT (EGO) Acquaintance; e Faithful Customer & Administrative Support e r
		R e v i e R Acquaintance; Faithful Customer & Administrative Support e Regular Supplier, Business tie; Supplier credit v i e
		w w
		O n l O n l
	y entrepreneurs), respondents were asked to characterize each relation from a social role y
	standpoint (kin, friend, neighbour, business tie, acquaintance). For a representative sub-
	sample of relations (1324), complementary name interpreters focused on the content of ties
	(duration, contact frequency, trust intensity, context of creation), alters' attributes (age,
		14

Once the entire name list had been elicited (1964 names, average network's size of 7.06 names per gender, ethnicity, schooling, occupation, status), and ties between alters

7

. Name interpreters for alters' attributes mainly focused on observable characteristics (sociodemographic characteristics are better informed than alters' attitudes or opinions;

[START_REF] Marsden | Recent developments in network measurement[END_REF]

. In the

  Table1shows that ties with lower-status alters tend more often than not to be long term and strong kinship ties (see trust intensity and reciprocity). Partnership or cooperation relations are more specifically Although strong ties appear to be more important with lower status members, important dimensions of ties' strength (length, including anteriority to

	spatially distant and less frequent.
	F o r
	P
	e
	e r
	R
	e
	v i e
	w
	O n l
	y
	16

developed with alters of comparable status, whereas alters with intermediate status often provide suppliers and financial support ties. Ties with alters enjoying higher status than egos provide significantly more administrative support or loyal clientele. They are also more

Table 1 : Content of ties and alters' attributes (n=1324) *

 1

	Trade networks are

Table 2 : Enterprises / entrepreneurs' characteristics and social networks alters' attributes (N=270) *

 2 The first value in the table shows that the mean proportion of ties with alters whose status is lower than ego's is 14.4 % for entrepreneurs who have at least reach secondary school). Significantly different means are in bold type in the table (independent samples t-tests; sig. 2-tailed at least <.10). Thus, this result also shows that relations with lower status alters are significantly less frequent in the production sector than in others; (1) Start-up capital inferior to the median; (2) Born in Bobo or arrived at the latest at the age of 10 years old. Catering networks are characterized by significant diversity and the high statuses they give access to. The peculiarity of catering activities is not surprising insofar as informal catering is a dynamic sector in the city (see table A.1.) and also a popular meeting place where all social categories, including the highest, meet. In other services, entrepreneurs' networks are remarkable for the proportion of heterophilic relations. The important proportion of low statuses in their networks is consistent with the fact that they run small scale survival activities with low levels of economic performance (table A.1.).

		Proportion of	Proportion of	Proportion of	Proportion of	Proportion of	Proportion of
		lower status relations in	same status relations in	intermediate relations in	higher status relations in	heterophilic relations in	intra-profession	Total
	Characteristics	network	network	network	network	network	relations
	Education
	Secondary and more	.144	.422	.222	.211	.332	.197	.263
	None / Primary	.154	.519	.205	.122	.251	.315	.737
	Former occupation
	Inactive or farmer	.253	.470	.153	.124	.209	.277	.141
	Apprentice -familial assistant (informal sector)	.151	.531	.203	.116	.281	.329	.548
	Employee -Independent (informal sector)	.118	.457	.245	.180	.265	.245	.263
	Employee (formal sector)	.046	.341	.255	.358	.393	.105	.048
	Start-up capital
	Low 1	.193	.537	.168	.102	.281	.307	.500
	High	.110	.451	.250	.188	.263	.260	.500
	Ethnic group
	Mossi	.169	.487	.244	.100	.153	.319	.396
	Other	.140	.498	.186	.175	.350	.261	.604
	Length of presence
	Native from Bobo 2	.161	.525	.176	.138	.274	.291	.448
	Others	.142	.461	.244	.153	.271	.276	.552
	Owner's age
	Less than 25 years	.232	.525	.187	.056	.228	.359	.107
	25 to 35 years	.138	.528	.202	.132	.303	.269	.444
	35 to 45 years	.140	.487	.218	.155	.269	.316	.344
	More than 45 years	.164	.338	.236	.262	.195	.163	.104
	Sector
	Production	.127	.526	.191	.157	.264	.303	.350
	Trade	.143	.545	.240	.072	.216	.433	.300
	Catering	.144	.332	.282	.241	.329	.054	.120
	Other services	.204	.464	.158	.173	.328	.182	.230
	Length of activities
	Less than 5 years	.147	.512	.223	.123	.268	.294	.463
	5 years and more	.158	.474	.189	.178	.279	.273	.537
	Total	.152	.494	.209	.145	.272	.284	-
	Notes: (*)

Table 3 : OLS regression analysis summary for variables predicting value added and earnings; IV (2SLS) regression analysis summary for variables predicting turnover

 3

	Outcome variables :	log (turnover)	log (value added)	log (earnings)
	Predictors 1
	Constant	3.184 (15.11)***	2.835 (15.86)***	3.416 (14.22)***
	Inputs
	Log (capital input)	.135 (2.46)**	.113 (2.11)**	.104 (1.63)*
	Log (labour monthly input) 2	.383 (7.14)***	.494 (9.40)***	.160 (2.56)***
	Business characteristics
	Retail trade 3	.499 (8.29)***	.177 (3.14)***	.176 (2.63)***
	Catering 3	.360 (6.29)***	.250 (4.45)***	.317 (4.74)***
	Pluriactivity 4	.034 (0.76)	.070 (1.61)	.091 (1.76)*
	Administratively registered activity 4	.097 (1.82)*	.116 (2.36)**	.148 (2.55)**
	Favourable economic situation 5	.075 (1.56)	.133 (2.94)***	.153 (2.83)***
	Entrepreneurs characteristics
	Primary education or more	.029 (.64)	.058 (1.31)	.065 (1.22)
	Experience 6	.037 (0.80)	.082 (1.81)*	.097 (1.81)*
	Gender 7	.011 (.20)	-.040 (-.77)	-.028 (-.45)
	Ethnic group 8	-.047 (-.89)	-.053 (-1.10)	-.035 (-.62)
	Professional organisation 9	.085 (1.84)*	.120 (2.66)***	.142 (2.64)***
	Demand anticipation 10	.022 (0.46)	.114 (2.38)**	.158 (2.77)***
	Alters' attributes in entrepreneurs' network
	Proportion of alters enjoying an intermediate status	.205 (3.33)***	.145 (3.13)***	.130 (2.37)**
	Proportion of alters enjoying an higher status	.088 (1.17)	-.037 (-.72)	-.058 (-.94)
	Professional homogeneity	.043 (0.64)	.070 (1.37)	.054 (.88)
	Proportion of heterophilic ties	-.113 (-1.65)*	-.079 (-1.65)*	-.101 (-1.78)*
	Network's size	.067 (1.02)	.032 (.66)	.007 (0.12)
	Number of obs.	251	270	270
	F (sig)	16.56 (.000)	17.17 (.000)	8.04 (.000)
	R²	0.571	0.552	0.366
	Adjusted R²	0.537	0.520	0.320
	Hausman test (p-value)	30.76 (0.031)	18.25 (0.439)	12.49 (0.821)
	Sargan test (p-value)	0.101 (0.750)	0.078 (0.780)	0.393 (0.531)
	Notes : (1) Standardized estimated coefficients are shown, t tests for unstandardized coefficients are in brackets, ***p < .01, **p <
	.05, *p < .1 ;

Table O .A.1 : The names generators

 O like life-stories which allow to analyze the evolution and transformation of social relations and networks during the professional career of micro entrepreneurs.

	Online appendix
	F o r F o r F o r F o r F o r
	P P P P P
	e e e e e
	e r e r e r e r e r
	R R R R R
	e e e e e
	v i e v i e v i e v i e v i e
	w w w w w
	O n l O n l O n l O n l O n l
	y y y y y

Table O .A.2 : Number of alters quoted by entrepreneurs for each names generators N= 278 entrepreneurs (P= 1964 alters)

 O

		No name (%)	Maximum of possible names (%)	Average names quoted	Std. deviation
	Advice, information and ideas	13,3	26,3	1,68	1,006
	Administrative support	48,6	5,0	,56	,590
	Regular suppliers	28,1	5,8	,97	,808
	Faithful customers	7,6	39,6	2,08	,930
	Cooperation or partnership	30,2	6,5	1,03	,872
	Financial support	25,9	10,8	1,16	,934
	Contact for recruitment	40,3	5,4	,86	,870
	Start-up support	28,8	4,7	1,03	,836
	Total	-	-	7,06	2,59

Table O .A.3.: Type of relations in the whole sample of alters (P2) and in the sub-sample (P3)*

 O

		Proportion in P2 (%)	Proportion in P3 (%)
	Close family	13,1	15,5
	Enlarged family	7,7	8,8
	Other kinship relations (ethnic, village)	3,7	4,0
	Close friends	22,3	24,0
	Acquaintances	12,4	11,6
	Neighbors	4,1	3,5
	Labor colleagues	13,8	14,2
	Business ties	57,3	53,4
	Chi-square test for expected values	11.32 (df = 7 ; p = .125)

URL: http://mc.manuscriptcentral.com/fjds Journal of Development Studies

Journal of Development Studies

Note that none of these instrumental variables is significantly correlated with any outcome variable.

The assumptions of linearity, normally distributed errors and uncorrelated errors were checked and met.

It would be an interesting field of investigation, but it necessitates data on alter's ties, through 'second order zone' ego-centered network data, or through 'complete networks' data.

Appendix


A Dicko

B Gilles

F Faure

O Palombi

From Generic to Specific Musculoskeletal Simulations using an Ontology-based Modeling Pipeline

We present a novel pipeline for the construction of biomechanical simulations by combining generic anatomical knowledge with specific data. Based on functional descriptors supplied by the user, the list of the involved anatomical entities (currently bones and muscles) is generated using formal knowledge stored in ontologies, as well as a physical model based on reference geometry and mechanical parameters. This simulation-ready model can then be registered to subject-specific geometry to perform customized simulations.

The user can provide additional specific geometry, such as a simulation mesh, to assemble with the reference geometry. Subject-specific information can also be used to individualize each functional model. The model can then be visualized and animated.

This pipeline dramatically eases the creation of biomechanical models. We detail an example of a musculoskeletal simulation of knee flexion and hip flexion and abduction, based on rigid bones and the Hill muscle model, with subject-specific 3D meshes non-rigidly attached to the simulated bones.

Introduction

The simulation of the human musculoskeletal system is ubiquitous in Biomechanics, Computer Aided Medicine and Computer Graphics. However, many of the models used for these purposes are relatively simple and generic due to the difficulties inherent in their construction. One of the biggest difficulties in the setup of a simulation is to select the relevant anatomical entities: Various bones, muscles, ligaments and organs may have an important role, depending on the phenomenon we want to simulate. This is further complicated by the fact that a plethora of physical parameters are required for correct nu-merical simulation. Moreover, it may be necessary to incorporate additional, subject-specific data.

The work presented here is initially motivated by the need to simulate the interaction of medical devices such as braces with specific human bodies, in order to speed up the design process. Another example is to study how a hip or knee prosthesis interacts with individuals with various morphologies during flexion/extension of the knee or abduction/adduction of the hip. The first step of this approach is to create a biomechanical model of the subject. However, this is a very time-consuming and error-prone task, generally difficult to achieve for a mechanical engineer.

In this paper, we introduce a novel pipeline for tackling this challenge. Our pipeline allows a user to select a set of desired functions to simulate and from this functional description a list of approriate anatomical entities can be constructed. This construction is automated using formal knowledge structured in ontologies. The list of anatomical entities involved in the given function is generated, and a physical model based on reference geometry and mechanical parameters is created. This mechanical model may then be personalized using subject-specific parameters, and registered to subject-specific geometric data such as volumetric images, to create a subject-specific model of a given anatomical function. The simulation of arbitrary biomechanical phenomena being beyond the scope of this work, we focus on producing computer simulations of standard tasks such as walking or sitting. However, the functional nature of our modeling pipeline permits extension to a much wider range of scenarios.

Our pipeline, illustrated in Figure 1.1, is targeted to non-specialists as well as expert users. We show how to generate simulations using standard open source simulation software, and to obtain visually pleasing results. The remainder of the paper is organized as follows. Section 1.2 briefly reviews previous work. The anatomical knowledge base and the modeling pipeline are presented in Section 1.3. A simulation is presented in Section 1.4, and results are finally shown and discussed in Section 1.5.

Related work

The modeling and simulation of the human body has been a subject of much interest. This attention has produced a cornucopia of methods which are as diverse as the subject areas from which they arise: biomechanics, ergonomics, diagnosis, treatment planning, visualization, graphics, robotics, etc. Consequently, a wide variety of models have been proposed which we briefly review below. Symbolic models: The most generic models used to describe the anatomy are ontologies. Ontology can be defined as a structured specification of the concepts and semantic, intelligent relations in a field [DMT07]. Guttierrez Set of involved anatomical entities for the selected function et. al. proposed an ontology of the human shape [GGRT + 07], focusing on its relations with the environment. The anatomical knowledge is the network of relations between entities. An anatomical ontology is a set of taxonomies where anatomical entities are organized as a formal vocabulary. It is organized in data structures easily processed by computers. This data structure contains a list of terms such as femur, psoas, and a list of symbolic relations between this terms describing inheritance or inclusion. The Foundational Model of Anatomy (FMA) [RM03] is a widely accepted ontology of the human anatomy and is generally used to denote and navigate across anatomical structures. One-dimensional representations: The earliest musculoskeletal mathematical model was suggested by Gasser and Hill in 1924 [HG24] to capture global muscle mechanical properties. This model was used to describe the macroscopic relationships between muscle actuation, force-length and veloc-ity [Hil38] , along the muscle path. It was improved by Zajac [Zaj89] to a dimensionless aggregate model which can be scaled to approximate subjectspecific musculo-tendon units. The force components are modeled from the measurement of isolated muscle fibers, which directly reflect the non-linear properties due to the sliding filaments. While the series elastic elements can be grouped with the tendon and removed from the model. Pennation effects are directly included into the model [Lee10]. Schutte improved Zajac's model and added a damping parameter into the force-velocity relationship [Sch93]. Thelen [The03] adjusted the parameters to account for changes in muscle properties that occur with aging. Physical models based on a finer discretization, allowing non uniform deformation along the fiber, have been recently proposed [SKP08].

In computer animation and robotics, skeletons are traditionally simplified into acyclic graphs, called animation skeletons or stick figures, composed of one-dimensional segments (limbs) connected by joints. Skeleton poses are then compactly expressed as a set of rotations along the most relevant joint degrees of freedom (i.e., reduced coordinates), which can be easily manipulated or animated based on real data such as motion capture. Surfacic representations: For visual applications, additional realism can be achieved using a boundary discretization of organs. Procedural methods can then be used to derive organ motion from the pose of an underlying animation skeleton (i.e. Skeleton subspace deformation, also knows as vertex blending or skinning [MTLT88, KCvO07]). Although interior material points are not modeled, physical methods based on shell elements have also been proposed to simulate thin muscles [KHYS02]. Surface bone models have been used to generate more realistic skeleton animations based on possibly cyclic graphs and moving joint centers [SNTH03].

In the context of medical image analysis, subject specific models can be reconstructed using surface models based on the visible organ boundaries [GRP10]. Multiple images of the same subject can be exploited using sophisticated registration techniques [SKMT10]. To fit one dimensional models such as muscle action lines to subject data, post-processing is required to identify a muscle path. A widely used approach is to generate a piecewise line from the muscle cross-section centroids [DLH + 90].

Volumetric representations: Although one-dimensional abstractions are sufficient in many applications, the complex muscle architecture, large muscleto-bone attachment areas, as well as muscle contacts, can only be simulated using three-dimensional models. The most widely used technique is to subdivide organs into elements and to apply continuum mechanics, typically the finite element method (FEM). Chen and Zeltzer in 1992 [CZ92] modeled individual muscles as coarse linear finite elements and applied a Hill-type model to approximate their constitutive behavior. Ng-Thow-Hing in 2001 [NTH01] chose to model muscles as B-spline solids, with embedded Hill-type one dimensional elements. They proposed to simulate skin deformation, and took into account the effect of fat layer, dermal layer, and musculature, in a fi-nite element framework. Blemker and Delp [BD05] developed and evaluated a new formulation for creating three-dimensional finite-element models that represent complex muscle geometry and the variation in moment arms across fibers within a muscle. This 3D muscle model has the advantage to represent complex muscle path motion without via point [DLH + 90] and wrap surface [BAG99], but it is computationally expensive and impractical to use in real-time applications. Teran et .al [TEB + 05] used a finite volume method (FVM) with quasi-incompressible, transversely isotropic, hyperelastic constitutive model to simulate soft tissue contraction and deformation. B-spline solids were used to model fiber directions, and the muscle activation levels were derived from key-frame animations. A framework for the construction of a 3D simulation model based on MRI data has been proposed [ACS + 09], focusing on the hip model subject imposed bone skeletal motion. Lee, Sifakis and Terzopoulos [LST09] introduced one of the most highly detailed biomechanical model of the human upper body composed of a dynamic articulated skeleton, numerous Hill-type muscle actuators which include the forcevelocity relation, and realistic finite element simulation of soft tissues and skin deformation. They used target poses and co-activation as input to compute muscle activation using inverse dynamics. The activation is then used to simulate skeleton dynamics and soft tissue deformation. The skin and underlying soft tissues were also simulated using FEM. In 2011, Stavness et al. [SLPF11] introduced an original 3D dynamic model for jaw-tongue-hyoid complex, consisting of an FEM model of the tongue, rigid jaw, and hyoid structures, Hill-type muscle actuators, constraints for bite contact and the temporomandibular joint.

Accurate musculoskeletal simulations are achievable using these detailed three dimensional representations, but at the cost of computational speed (e.g. the method of [TEB + 05] runs at 4 minutes per frame), making these methods impractical in many real world applications. Moreover, heterogeneous models can not be easily combined or reused in different contexts, as they are not integrated into a common framework allowing for the modular design of simulation scenarios. Interpolation and extrapolation mechanisms are not available to adapt the model complexity and type of representation to application constraints. As a result, subject-specific data such as medical images are currently difficult to exploit. Without a high level multi-model description, it is tedious to produce subject specific simulations, as we need to complete the subject-specific extracted model with additional geometry and parameters not available in the data.

Modeling Framework

Our modeling framework is summarized in Figure 1.1, and this section presents its different modules. The main input is a set of anatomical functions that the user wishes to simulate (e.g. walking). Our system then produces a list of involved anatomical entities and mechanical parameters required for their simulation. A generic model is then be created, which can be complemented with subject-specific information.

Symbolic description of anatomical entities

Biomechanical simulations require an accurate anatomical description. We base our framework on symbolic knowledge of the human body, organized in a widely accepted ontology of human anatomy called Foundational Model of Anatomy (FMA) [RM03]. This ontology describes our body as a set of anatomical entities named classes, and connected by relations. Each class contains data named attributes. The main relations we use are :

• is a : describes each entity as a child of another one. This relation describes the inheritance of property.

Example : The femur is a bone organ • part of : This relation represents each entity as a part of another one and consequently denote the inclusion.

Example : The patella is a part of knee • inserted on : Which is mainly used for the ligaments, muscles, tendons and . . . etc. It describes the fact that one entity is inserted on another one, and then can be used to located one part of our anatomy.

Example : The vastus medialis is inserted on the femur

In order to ease the simulation of anatomical functions, we introduce a new ontology of human body functions consistent with FMA. It consists of a taxonomy of human functions, along with the new relation involved in used to represent that an anatomical entity is involved in a given function.

Example : rectus femoris is involved in knee flexion.

In this example:

• rectus femoris is the anatomical entity (class)

• knee flexion is the biomechanical action or function (class)

• And involved in is the relation between those.

This new ontology, currently consisting of 4200 functions, was created using the Protégé 4.2 software and is stored in OWL format.

Reference model

One key feature of our approach is the coupling of a universal symbolic description of anatomy with numerical data and parameters. For versatility, different levels of coupling are proposed. First, a collection of reference data is associated with entities in the ontology and in a second step, this reference model is enriched with custom data. The first version of our reference model includes:

• Geometry: some template bone and muscle surface meshes. For now, we have chosen to use the commercially available Zygote model as our template for its completeness. It represents an average normal subject. This data collection is easily extendable, and we intend to include more detailed functional information in the future, such as local fiber orientations and rheological properties. Moreover, to make our reference model both generic and parameterizable, we are collecting subject-specific data, to be averaged and integrated into a statistical atlas.

Assembly

Our framework allows the selection of the geometry, functional parameters, and even the nature of the representation (e.g., Hill-derived muscles, surface or volumetric meshes with different discretizations, etc.) as shown in the left of Figure 1.1, among a choice of built-in or external models. Once the selection is achieved, an assembly stage is necessary to connect the anatomical entities and build a fully functional model that can be automatically registered to medical data or simulated. The connections are composed of pairs of matching points (for attachments) or reference frames (for simple joint models). These features can be located with respect to others in hierarchies, as allowed by the mapping components in the SOFA framework [FDD + 12] discussed in Section 1.4. In our prototype, these include the location of joint frames and insertion points with respect to bones, and non-rigid attachment of muscle geometry to the bones. In the future, more general interpolation functions will be implemented. For instance, the way muscle fibers will be embedded into a volumetric mesh, or the repartition of actuation amplitudes in a group of co-actuated muscles.

Registration to subject specific data

We rely on existing registration techniques to fit our generic models to subject-specific data. Registration is a central problem in the computer graphics and image processing communities [ZF03]. It proceeds by iterating two basic steps: first, the distance between the current position of the reference shape and the target is estimated; secondly, this distance is minimized by transforming the reference model. The main difficulties are to find an adequate distance measure that is as-convex-as-possible and a good parameterization of the transformation through the introduction of prior information. This introduced constraints in the deformation mechanism describe the allowed geometric excursion from the reference model. In the context of the musculoskeletal system, articulated bones can undergo large discontinuous displacements, soft tissues are highly deformable and due to shape variability in the population, geometric differences between the reference model and the subject can be relatively large. However, organ topologies, their relative positions and muscle attachment sites are stable in healthy subjects. Moreover, models must remain collision-free. We leverage this knowledge in our reconstruction framework.

The specific registration technique we use here is described in [GRP10]. This technique is well suited to the musculoskeletal system because it decomposes the unknown displacement field into: (a) a global articulated motion of the bones; (b) global bone deformations from a statistical shape model generated from multiple subjects; (c) a locally smooth as-rigid-as-possible deformation field. The additional constraints are the range of motion of joints, the maximum amplitude along each statistical mode, and the stiffness of the as-rigid-as-possible deformation technique (see [GRP10] for details). Given some reference manual segmentations, a prior appearance model, containing image intensities in the neighborhood of organ surfaces, is learned. Maximizing the similarity between this appearance model and the current observed appearance in the subject images, the reference model automatically converges to the target contours, by evolving in the constrained deformation space. In our study, we use T1-weighted MR images of the complete lower limbs, acquired with an isotropic spatial resolution of 1.2mm. Slice-by-slice manual delineation was done once on one dataset (about 15 hours of work) to reconstruct a reference model for automatic registration (about 2 minutes of computation). Our approach is hierarchical: we first register the skeleton, then muscles. Based on comparisons with manual segmentation, the final accuracy of our model is about 1mm. As shown in [GRP10], when target geometric models are available through manual segmentation or other sources, a similar registration procedure can be used to perform surface-to-surface registration. Structures that are not visible or outside the field of view do not undergo image-based constraints; they are automatically extrapolated based on the regularizing internal deformation constraints previously described. Our

Simulation

We rely on a number of simulation techniques tied together using the SOFA framework. Our simulation pipeline is summarized in Figure 1.2. It combines a skeletal dynamics simulation module with Hill-type muscle actuators, and procedural methods for soft tissue deformation. The independent degrees of freedom of our simulation model are the positions and orientations of the bones, while the input parameters are the function actuation levels which can be interactively changed by the user. Skeletal model: Each bone is represented as a rigid body equipped with a center of mass and an inertia matrix. To model joints, frames are rigidly attached to bones using a SOFA RigidMapping component. In most biomechanical frameworks [DLH + 90], bone positions are expressed using reduced coordinates (the classical serial approach of robotics). In contrast with these simplified models, we use world coordinates and stiff penalty forces to enforce soft articular constraints. This allows a simpler handling of kinematic loops (such as the femur/patella/tibia complex), and it is more realistic, since slight translations are present in real biological joints. Note, however, that a traditional robot-like link hierarchy could be applied to the same functional model. Reference joint angle and shift limits, as well as joint stiffnesses are provided by the reference model, although they are easily customizable by the user. Stable bone dynamics with large time steps is achieved using an implicit Euler integration scheme.

Passive soft tissue model: Based on bone positions, we compute the deformation of soft tissue (e.g. skin, muscles) using a classical Skeleton subspace deformation approach [KCvO07]. The transformation of a given soft tissue vertex is computed as a combination of bone transformations. In + 90] accounting for age. Tendon and muscle elasticity is modeled using exponential stress-strain laws followed by linear functions. Active muscle forces are modeled using a stress-strain Gaussian function, based on the actuation level. Dependence on contraction velocity is also taken into account. The macroscopic model is composed of the serial assembly of the tendon elastic component and the muscle component, which is composed of the passive and active units in parallel. In summary, the macroscopic muscle model can be considered as a generalized spring that generates forces on bones at insertion points, based on its internal length, velocity and actuation level. The intrinsic muscle parameters, controlling the shape of strain-stress curves, have been adapted from the OpenSim framework [DLH + 90]. Specifically, they are scaled to fit the subject-specific morphology at the registration stage. In our method muscle paths are automatically deformed using skinning methods as for their external shape so there is no need to add via points and warp surfaces as done in OpenSim [SLDT07].

Results

We present an example of the results obtained using the described framework. As explained, we start by selecting the functions we want to model and simulate. We choose knee flexion and extension, hip adduction, abduction, flexion and extension. Based on this, the output is a lower limb composed by 8 rigid bones linked by 7 joints, 44 muscles actuators (parameters taken from [AWLD10]), 108 muscles and 23 bone geometries as shown on the top of Figure 1.4.

Given this data as input of the simulation pipeline presented in Section 1.2, we obtain a model allowing the realistic simulation of the targeted functions for the reference model, as shown in the bottom of Figure 1.4. The muscles can be controlled using sliders to change the levels of activation, or using an EMG file containing the time varying activation level for each muscle.

In order to simulate the same functions for a specific subject, we register the generic model to the subject-specific MRI data as shown in Figure 1.6. The output of this registration is shown in the top of Figure 1.5. This registered model is used in the same simulation framework. The results are shown on the bottom of Figure 1.5, and a live capture of the modeling an simulation pipeline is available in the accompanying video. These simulations run interactively at 8 frames per second on a computer with a core i7 720qm at 1.60 GHz and an NVidia quadro 1800M graphics board with 1 Gbyte of memory. While not achieving the same level of physical accuracy as detailed Finite Element or Finite Volume simulations, the precision of this simulation is comparable with OpenSim [SLDT07], with subject-specific geometry and improved visual realism.

Conclusion

We have presented a versatile modeling and simulation framework based on ontologies of human anatomy and reference models. By combining novel functional information with efficient registration techniques, our method can produce interactive, subject-specific musculoskeletal simulations. We will use this framework to generate subject-specific biomechanical models interacting with various devices as discussed in the introduction.

This novel approach of anatomical modeling raises new questions. The optimal selection of involved anatomical entities, given a user-specified musculoskeletal function, is an open question. For instance, the muscles directly involved in knee flexion (i.e., 1-ring neighbors in the ontology graph) are:

Cliquez pour modifier le style titre

Cliquez pour modifier le style des sous-titres du masque Biceps femoris long head, Biceps femoris short head, Gastrocnemius lateral head,Gastrocnemius medial head, Gracilis, Sartorius, Semimembranosus, Semitendinosus, as illustrated in Figure 1.7. These entities are not sufficient to create a fully functional model to simulate this function, because some features such as the presence of stabilizing and antagonistic muscles are not automatically present in the output. Some additional knowledge and input is required, such as the concatenation of functions (e.g. muscle flexion and extension) in this example. The automatic completion of models is ongoing work. More accurate, three-dimensional mechanical models such as Finite Element meshes are necessary where accuracy is needed. The associated challenge will be to finely tune each model type and resolution (thus its computational cost) depending on the function of interest, and on the purpose of the simulation.

We believe that by allowing the easy creation of anatomical models combining reference and specific data, our framework opens avenues for new applications of biomechanical simulation, and that it is a significant step toward an anatomical knowledge and modeling system to help users from different domains with various levels of expertise to share, customize and re-use models.

  Fig.1.1 An overview of our modeling framework. On the left, the user input is a list of functions to simulate, optionally complemented with specific data. On the right, the output is a mechanical model ready for simulation. The modeling pipeline uses symbolic knowledge to select anatomical entities to assemble. The final model can be composed of a mix of reference and specific parameters and geometry.

  Fig. 1.2 Overview of our simulation pipeline

  Figure 1.3, point P is associated with each bone in the reference configuration (left). During the simulation, bones are displaced as illustrated in the right of Figure 1.3. If P was moving rigidly with respect to each bone, different target positions would be obtained. In linear blend skinning, the final position of P is obtained by computing the weighted sum of these target positions. The influence of each bone is modulated by its weight function. Weights are computed as a function of the closest distance d i to each bone i. Here we use the function w i (P ) = tan(-d 2 i + π/2), and subsequently normalize the weights to sum up to 1, but other functions are possible. Other techniques such as dual quaternion blending [KCvO07] have been proposed and are applicable in our context. The vertex blending allows to preserve the approximate distances between the muscles, and therefore the fat is implicitly taken into account. The external forces acting on the soft tissue are mapped to the bones using the principle of virtual work (transpose of the Jacobian of the kinematic relationship). Muscle actuation model: In this example, we use the one dimensional Hilltype model proposed by D.G Thelen [The03], which is a variant of the popular Delp model [DLH

  Fig. 1.3 Skinning of a point P of the rectus femoris muscle by the patella, pelvis and femur bones. On the left, the original configuration used to compute the closest distance and the weights. On the right, the deformed configuration where P is computed as a weighted sum of rigidly transformed positions.

  Fig. 1.4 Simulation of the reference model. (a), (b), (c), (d) : mechanical representation of bones, joint, actuator muscle and deformable model. (e), (f), (g), (h) : hip and knee functions.

  Fig. 1.5 Simulation of the subject-specific model. (a), (b), (c), (d) : mechanical representation of bones, joint, actuator muscle and deformable model. (e), (f), (g), (h) : hip and knee functions.

Fig. 1 . 6

 16 Fig. 1.6 Registration of the reference model to the subject-specific data.

Fig. 1 . 7

 17 Fig. 1.7 Partial model obtained with a one-level propagation in the ontology graph from the term "knee flexion"

•

  Active muscle model: one-dimensional muscle paths equipped with functional parameters. Currently, these models are adapted from Opensim [DLH + 90], a widely used framework for musculoskeletal simulation.• Joint and bone model: we have defined joint centres and rotation axes with respect to surface models based on available biomechanical literature. To model bone inertia, an average density is specified.

Ontology-based modeling pipeline