DO FIELD PARTNERS ADD VALUE TO CROWDFUNDED MICROFINANCE? AN INDUSTRY APPROACH

The framework of this study is the ¯eld of crowdfunded micro¯nance that represents a way to scale up ¯nancial access, leveraging digital technology applications. A key element of this value chain is the ¯eld partner, represented by a local Micro¯nance Institution (MFI) that intermediates between the crowdfunding platform and the individual borrowers or group of borrowers. In this context, the main objective of this paper is to measure the ¯nancial and prosocial contributions of ¯eld partners through crowdfunded microloans. Methodologically , this prosocial impact is measured with an innovative approach, by using network theory to describe the supply and value chains that link crowdfunding investors to ¯eld partners and, consequently, to micro-borrowers. The main contribution of this study is the introduction of a global indicator able to quantify the increase of the social impact and the ¯nancial system of a country, coming from the presence of ESG-compliant crowdfunded microloans.


Introduction
Micro¯nance Institutions (hereinafter, MFIs) play the role of lenders for unbanked/ underbanked individuals or groups, getting back lent capital plus an interest rate for their intermediatory risk-taking activity. This allows lots of modest collectives to access entrepreneurship, with a bottom-up impact that fosters the well-known Sustainable Development Goals (SDGs). The increasing awareness of sustainability, especially among young people, led the United Nations member states to promote, in related to such economic sectors. This indicator has the important advantage that it varies from À1 to þ1. On the other hand, the second indicator will be de¯ned as the increase of entropy before and after the inclusion of new micro-borrowers.
The main contribution of this study is the introduction of a global indicator able to measure the¯nancial and prosocial values added by¯eld partners to the economic system of a country through the so-called crowdfunded microloans. The target of this paper can be visualized in Fig. 1.
This study is structured as follows: After this introduction, Section 2 illustrates the consistency between crowdfunded microloans and the SDGs. Section 3 is dedicated to a short revision of the extant literature. Section 4 describes the methodology of the study, and Sec. 5 presents the results. Section 6 contains a critical discussion, before the conclusions summarized in Sec. 7.

Crowdfunded Microloans and the Sustainable Development Goals
Sustainability is based on three main dimensions: economic, social, and environmental (Alsayegh et al. 2020). This established taxonomy is consistent with the Environmental, Social, and Governance (ESG) indicators, with the SDGs, and with a more institutional framework, represented by Political, Economic, Social, Technological, Legal, and Environmental (PESTLE) considerations. The interactions among these three systems are shown in Fig. 2.
ESG parameters represent a complementary representation of the SDGs: Whereas the latter are somewhat wider, the former are increasingly measured by the assessment of ESG-compliant listed¯rms (Antoncic et al. 2020), providing growing benchmarking evidence even for unlisted securities. In this way, ESG evidence from listed MFIs represents a further research stream that may provide a benchmark for less-structured¯eld-partnering MFIs. ESG compliance represents a prerequisite for socially responsible investments.
On a corresponding side, PESTLE analysis represents an institutional framework of macro-environmental factors used in the environmental scanning component of strategic management.   Visconti (2021)] summarizes the correspondence between the 17 Sustainable Development Goals and the characteristics of crowdfunded micro¯nance.

Securitizing Microloans: The Role of Field Partners in the Literature and the Case of Kiva
Financial institutions and funding mechanisms are rapidly evolving. Entrepreneurs are combining equity start-up¯nance (e.g. family and friends, angel investors, venture capitalists, and private equity funds) and then (when they can a®ord it) traditional bank debt, with micro¯nance (Khavul 2010), crowdfunding (Belle°amme et al. 2013), peer-to-peer (P2P) lending, and other¯nancial innovation instruments (Moenningho® & Wieandt 2012). Consequently, micro¯nance, crowdfunding, and peer-to-peer lending provide some excellent examples of new¯nancial alternatives that play a signi¯cant role in the design of new¯nancial products for entrepreneurship in both developed and developing countries. After the boom of micro¯nance, we witness a boost in crowdfunding. It is so interesting to study their interactions (Attuel-Mendes 2016). Crowdfunding and peer-to-peer lending are two of the many FinTech applications [for a taxonomy, see Moro Visconti et al. (2020)] that can evolve incorporating arti¯cial intelligence and machine learning patterns (Allen et al. 2021). In the last decade, the introduction of smartphones combined with key developments in cryptography (blockchains) and arti¯cial intelligence has revolutionized the workings of every¯nance function À À À from payments to credit, and from equity¯nancing to asset management.
As crowdfunding is rapidly spreading across developing economies, it is emerging as a way of allowing individual investors to pool small amounts of money to meet the funding requirements of new and expanding ventures. As a¯nancial innovation, crowdfunding has di®used from an initial launch in several developed economies and is rapidly spreading across developing economies (Kukk & Laidroo 2020).
Kiva, the largest crowdfunding intermediary, is probably the best exponent of using social media to raise¯nancing. Kiva aggregates the funds from individuals and places them as blocks with micro¯nance organizations, which are then responsible for the disbursement and management of the loans to entrepreneurs (Kiva 2020).
In essence, Kiva acts as an online bridging platform between borrowers and lenders. The pro¯les of people from developing countries who are in search of microcredit are posted on Kiva's platform. Lenders browse the di®erent pro¯les and invest money in their preferred projects, according to the characteristics of the loan request and the borrower. On the other hand, borrowers pay interest to the intermediaries of the¯nancing process, referred to as¯eld partners (the MFIs), who are essentially the ones that bear most of the risk. The sponsored MFI pays back Kiva the capital, with no interest charges, softening its cost of collected debt (typically in hard currency, such as the USD).
Every Kiva loan is o®ered by a local partner to a micro-borrower and the MFI partner works with Kiva to get funding for that loan from lenders. The association between a crowdfunded loan and an on-¯eld partner is of great importance since the loan risk is closely correlated to the reputation of the partner. This is why Kiva tries to assign a risk rating to every partner, when possible, following an annual due diligence process.
To mitigate the risk, each borrower is screened by a local Kiva¯eld partner before their application is posted on the Kiva website. This¯eld partner plays a role as a rating agent to look at a variety of factors (such as loan history, village or group reputation, and loan purpose) before deeming a borrower to be creditworthy. Despite these precautions, a variety of factors can result in borrowers defaulting. Digitalization of credit history and big data gathering and processing, even using cloud storage, validating blockchains, and arti¯cial intelligence interpretation, add value to the intermediation chain.
Borrowers who are more intensely monitored by MFIs are more likely to repay crowdfunded loans on time. Monitoring is particularly important in reducing repayment problems of individual loans rather than group-based loans. In this way, crowd-funders are interested in knowing the ability of MFIs to monitor loans through a measure of their prosocial and¯nancial impacts (Berns et al. 2021).
By the end of the month, Kiva generates a bill to charge the¯eld partner for all the collected repayments. Kiva works on a net billing system. Kiva subtracts the number of repayments that a¯eld partner owes to Kiva lenders from the amount that a¯eld partner fundraises for entrepreneurs on Kiva. If the balance is positive, this means that the partner has raised more than they need to repay, and Kiva uses those funds to credit the lender account with the repayments due to them. If the balance is negative, then the partner has to send a payment to Kiva for the balance. As soon as Kiva receives that payment, the organization uses those funds to credit the lender account with the repayments due. Once the repayment is made to the lender, the lender may choose to re-lend the funds, donate them to Kiva's operating expenses, purchase a gift certi¯cate, or withdraw them to be credited to the lender's PayPal account (Moleskis & Canela 2016). Poverty and hunger reduction improves health and well-being.
(4) Quality Education Education is not a direct object of microloans since it does not produce immediate refundable liquidity but can be improved by micro¯nancedriven higher living standards. Education is a key pillar of development, representing a long-term investment that can be partially funded with microloans. (5) Gender Equality Micro¯nance, lending mostly to women (Aggarwal et al. 2015), promotes gender equality. Micro¯nance has a strong gender-e®ective impact. Field partners who are noted for higher social performance because they focus on lending to women, are more likely to see their loans re¯nanced (Dor°eitner et al. 2021 A default occurs when a borrower or a¯eld partner fails to make payments on a loan to the¯eld partner or Kiva, respectively. Kiva¯eld partners screen loan applications before accepting them. Berns et al. (2020) show that crowd-investors use Kiva as a delegated monitoring platform in crowdfunded micro¯nance. The repayments are collected by the¯eld partner and the funds are then funneled back to Kiva lenders. Every step of this digital process is completed online through the Kiva platform. This concept of lending with no expected¯nancial gain, while bearing a default risk, is a distinguishing feature of a handful of online crowdfunding platforms, most notably Kiva. Uddin et al. (2018) consider the Kiva microcredit system, which provides a characterization (rating) of the risk associated with the¯eld partner supporting the loan, but not of the speci¯c borrower who would bene¯t from it. After joining Kiva, MFIs' sustainability improves and interest rates decrease (Luo et al. 2022).

Methodology
Figure 3 describes the value and supply chain that link investors through the crowdfunding platform to the¯eld partners and eventually to micro-borrowers. This is consistent with the social networking \homophily" described by Burtch et al. (2014) that eventually links crowdfunding investors to micro-borrowers through the crowdfunding platform and then the MFI.
This methodology is also consistent with the research question that investigates the value added by¯eld partners through crowdfunded microloans. When analyzing this value, two approaches could be considered: (1) The¯eld partner plays the role of a traditional bank in a syndicated loan, but with the noteworthy di®erences shown in Table 2.
(2) The¯eld partner is an MFI that \securitizes" its microloans, making it possible for potential lenders (or lending groups) to participate in social and sustainable businesses.
This intermediating role of¯eld partners implies important advantages: (i) The principal amount of microloans is granted by the crowd-lenders and so thē eld partner need not put (eventually advance) any money. (ii) In most cases, the (high) interest is only received by the¯eld partner because the lenders only receive the loan principal. (iii) The risk is supported by the¯eld partner but may be minimized by a careful selection of borrowers and the high interest rates applied to compensate for potential insolvency. Despite the reduction of risk, the interest rates continue to be relatively high.
Therefore, the value added by a¯eld partner can be decomposed into the following items: (i) An important increase in the numbers of borrowers and lenders involved in the operation (outreach maximization). (ii) The substitution of the purely banking interest by a mix of¯nancial interest (cashed by the¯eld partner) and \social" interest (morally attributable to crowd-lenders).
Consistently with these premises, this study will measure: (1) the prosocial impact of¯eld partners by scoring its relationship with the SDGs; (2) the purely¯nancial impact of¯eld partners, di®erentiating between individual lending and group lending.
Task #1 will be developed in Sec. 5.1 by using the Pearson correlation coe±cient derived from the regression between the number of microloans per economic sector and the weight of an industry within the SDGs. Task #2 will be described in Sec. 5.2 and will be performed with an innovative network theory application.

Measuring the prosocial impact of¯eld partners
The positive e®ect in an economy of the increase of funded businesses is obvious, as it promotes¯nancial inclusion. However, the in°uence of the \social"¯gurative interests in an economic system is di±cult to measure independently of the fact that the¯eld partner is an MFI, a social business, a school, or a nonpro¯t organization.
A possible methodology to quantify these \social" interests is to estimate the proximity of the¯eld partner's investments to the ful¯llment of the so-called SDGs. This last aspect of¯eld partners' role is reinforced by Internet crowdfunding platforms that catalyze the \social economy".  Table 3 sets a correspondence between the sectors¯nanced by crowdfunded microloans, in a sample of 385 microloans granted by Kiva, with the 17 SDGs.
Kiva has been selected as it represents one of the most important MFIs in the United States microcredit market. In e®ect, the three main MFIs in the United States are the Paci¯c Community Ventures (founded in 1998 to provide microloans in California), CDC Small Business Finance Corp. (founded in 1978, and operates in Arizona, California, and Nevada), and Kiva (founded in 2005, is headquartered in San Francisco). Additionally, Kiva represents the most visited micro¯nance website (with over 10 million visits per year À À À https://www.similarweb.com/it/website/ kiva.org/#tra±c) and is a celebrated nonpro¯t crowdfunding platform. The data have been obtained from the website: https://www.kiva.org/build/data-snapshots, whence the information about the loans granted by Kiva was freely downloaded. Following sampling techniques, we have selected 385 loans granted in the period from 2008 to 2020 as shown in Table 3.
This way, we will be able to quantify the prosocial gains provided by crowdfunded microloans to the added value of an economy.
In Table 3, we have assigned a score to each sector, according to the number of related SDGs. This will allow correlating the percentage of amount (or the number of borrowers) with this novel SDG index, and e®ectively check if there is a positive and prosocial assignment of¯nancial resources to those businesses identi¯ed with the SDGs, then leading to e±ciency. The degree of association is given as usual by the Pearson correlation coe±cient (between À1 and þ1).
The geographical distribution is reported in Table 4.
The results of the regression show that there is no resource assignment according to the association between sectors of the economy and related SDGs. In e®ect, the Pearson correlation coe±cient is very low (r ¼ 0:010610283) and the coe±cient derived from the regression is not signi¯cant at 95% level (p > 0:05).  (6), (8), (9), (12), (17) 6 Wholesale 1 0.26% (12), (13), (17) 3 TOTAL 385 100.00% À À À À À À The Global Commission on Business and Sustainable Development asked Corporate Citizenship to elaborate an analysis of the SDGs by sectors to identify business opportunities and risks (2016). In this report, 10 industry sectors were identi¯ed: oil and gas, basic materials, industrials, consumer goods, healthcare, consumer services, technology, telecommunications, utilities, and¯nancials. These 10 industry sectors were mapped across the primary, secondary, and tertiary sectors of the economy, and classi¯ed according to the following criteria: . sectors with strong linkages to a single SDG; . sectors with linkages to two or more SDGs; . sectors that act as an enabler across all SDGs.
The results are summarized in Table 5.
Unfortunately, this linkage cannot be used for the data obtained from the Kiva website because this nonpro¯t organization uses another classi¯cation of industry sectors, di®erent from that of Table 5. This is the reason why we have used Table 3 instead.
A sector should not be classi¯ed as \good" or \bad" depending on the score which measures its proximity to the 17 SDGs. In e®ect, by assuming the same relative importance to all SDGs, this index simply aims to represent the degree of ful¯llment of the aforementioned objectives when a sector is supported through¯nancing. So, this means that a speci¯c sector will help to satisfy more SDGs than another one.

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It is possible that, in African countries, the scores assigned to Agriculture (6) and Housing (2) re°ect the true preferences of the population as in these countries there is a problem of famine but, taking into account their lifestyle, there is not a problem of housing. However, this could not be the case in Asian countries where the scarcity of houses is an important problem. Then, a possible solution could be to assign a di®erent score to each SDG depending on the speci¯c country and even the time of the analysis. Nevertheless, our aim in this paper has been to propose a general index of closeness.
Considering that all real assignments of loans to industry sectors add value to the prosocial impacts of MFI loans, we are going to present the following approach. Assume that n k loans have been assigned to the kth SDG with a score p k . Thus, the total score of this assignment is P n i¼1 n k p k . Assume now that n k and p k are increasingly ordered giving rise to n 0 k and p 0 k , respectively. Obviously, P n i¼1 n k p k P n i¼1 n 0 k p 0 k , which allows us to construct the ratio r, and then the factor 1 þ r is always greater than 1. Thus, any assignment creates prosocial value for the economy.

Preliminary concepts
In the analysis conducted in the following paragraphs, each link between any two nodes within a network vehiculates either data, money, or both.
. An adjacency matrix is a square matrix whose elements indicate whether any pair of vertices (nodes) are adjacent or not in each network. . A simple network is an undirected graph (with all linking edges being bidirectional) where neither loops (edges from a vertex to itself) nor multiple edges are allowed. In a simple network N, the adjacency matrix A is a square matrix whose elements a ij are 1 (if there is an edge from vertex i to vertex j) or 0 (if there is no edge from i to j). As a consequence, the adjacency matrix of a single network is symmetric and the diagonal is exclusively composed of zeros. . An interesting property of adjacency matrices is the following: If A is the adjacency matrix of an undirected network, then the ði; jÞth element of the power matrix A n gives the number of undirected walks of length n from i to j.
In the next analysis, we will distinguish between traditional and crowdfunded microloans.

Traditional microloans
Traditional microloans (e.g. in the absence of crowdfunding) are represented by individual or group lending. They can be described with network theory, in graphical form, or using adjacency matrices. They are divided into two main categories [individual loans (A) and group lending (B)] and incorporate the risk of default (C).

(A) Case of an individual lending
In a traditional model, the MFI is related to its n micro-borrowers, according to a simpli¯ed radial scheme. Figure 4 is an example of individual lending from the MFI to micro-borrowers who are not connected among them. Speci¯cally, it shows an MFI working with 10 micro-borrowers (from B 0 to B 9 ). This network is easy to monitor by the MFI which acts as a pivoting (central) node, collecting information and intermediating loans.
In this case, by considering that the relationship between each micro-borrower and the MFI is bilateral, the adjacency matrix is reported in Table 6. The adjacency matrix of this undirected (bidirectional) network provides a mathematical description of the links, showing how the network works and how the degrees of each node can be measured.
Tables 6 and 7 represent a sample of how each node's degree can be calculated, mapping the network and providing a basic measure of its properties. Adjacency   matrices also represent a starting point for the interpretation of multilayer networks (mentioned in the discussion as a new research avenue).
The number of ones in the matrix in Table 6 is 20. In general, if the number of micro-borrowers is n, then the number of ones in the adjacency matrix is 2n. Moreover, if n ¼ 2, the number of paths of length 2 is given by the following power matrix: In general, the following law applies:  Case (A) may be compared with a similar one (see Fig. 5) where micro-borrowers coalesce around a group lending platform that is related to the MFI. Group lending can be de¯ned as a lending mechanism that allows a group of individuals (often called a solidarity group) to provide collateral or loan guarantees through a group repayment pledge. The incentive to repay the loan is based on peer pressure: If one group member defaults, the other group members make up the payment amount. This shows the di®erence between individual lending and group lending.
In this case, by considering that the relationship between each micro-borrower and the rest of the micro-borrowers and the MFI is bilateral due to the intermediation role of the group lending node (that intermediates funds and data between each micro-borrower and the MFI), the adjacency matrix is represented in Table 7.
The number of ones in the matrix in Table 7 is 110. In general, if the number of micro-borrowers is n, then the number of ones in the adjacency matrix is ðn þ 1Þ 2 À ðn þ 1Þ ¼ ðn þ 1Þ½ðn þ 1Þ À 1 ¼ nðn þ 1Þ: Let p i be the probability that borrower B i repays 1 EUR. If the amount due by borrower B i is C i , then the probability that this borrower can repay his/her entire debt is p C i i . Therefore, the probability that borrower B i defaults is 1 À p C i i and, consequently, the probability that any of the borrowers composing the group lending can take care of some solidarity payments is ð1 À p C 1 1 Þð1 À p C 2 2 Þ Á Á Á ð1 À p C n n Þ. Finally, the probability that the group lending can take care of some payments is 1 À Q n i¼1 ð1 À p C i i Þ, which represents the solvency added by the group lending.

(C) Risk of default
The default risk is a crucial variable both in traditional micro¯nance schemes (with either individual borrowers or group lending) and when crowdfunded value chains are introduced. Reduction in the risk of default improves loan repayment which, in turn, increases the convergence towards SDGs and the prosocial targets.
Consider a traditional MFI which promotes the potential participation of n micro-borrowers. A measure of the risk of default can be determined by the following expression: where p i is the probability that the ith microloan is repaid by the corresponding borrower. However, in a microloan within a lending group, due to the solidarity among its micro-participants, the probability p i increases until p 0 1 > p i . Therefore, the entropy is now Entropy is the measure of the disorder or randomness of a system. The entropy of a system X with n possible components whose probabilities are p 1 ; p 2 ; . . . ; p n , is given by the following expression: For values of p i high enough, one has H 0 < H, as expected, the risk of default decreases. Consequently, the reduction of the risk of default leads to a diminishing of the interest rate which gives rise to an increase in investments at the micro¯nance level.

Crowdfunded microloans
Crowdfunded microloans represent an \augmented" dimension of traditional microloans, examined above in Sec. 5.2.1.1. Consistently with the basic case, they are divided into two main categories [individual loans (A) and group lending (B)] and incorporate the risk of default (C).
As formerly indicated, in a new conception of micro¯nance, the MFI posts the information about its n micro-borrowers by using a digital platform in such a way that potential micro-lenders can participate as funders of one or more micro-borrowers. This novel¯nancial instrument is called a crowdfunded microloan and the micro-lenders are also called crowd-funders.
In this case, as the MFI acts as a¯nancial intermediary, each microloan needs at least one crowd-funder able to fund the posted micro-project. Therefore, if k denotes the average number of crowd-funders necessary to fund a standard micro-project, the total number of crowd-funders will be kn, where k ¼ kðnÞ > 1 is a function of n.

(A) Case of individual lending and crowdfunding
Crowdfunding digital platforms add value to the whole micro¯nance ecosystem thanks to their networking properties (Possega et al. 2015). Network theory analysis (Barab asi 2016) produces a mathematical measurement of the degree of the nodes (number of links with other nodes), and a consequent estimate of their economic value. The application of this methodology to crowdfunding platforms is innovative. Figure 6 shows a hypothetical example of a crowdfunded microloan, where crowdfunders C 11 , C 12 , and C 13 lend their money to micro-borrower B 1 ; crowd-funders C 21 , C 22 , C 23 , and C 24 lend their money to micro-borrower B 2 ; and crowd-funders C 31 and C 32 lend their money to micro-borrower B 3 . In general, C ij denotes the crowd-funder #j of borrower #i (B i ). As indicated, each micro borrower's project is posted on the lending platform and then potential crowd-funders lend their money for funding this speci¯c project (yellow, green, or blue, respectively). In this network, microborrowers (B 1 , B 2 , and B 3 ) represent again an individual lending target.
Figures 6 and 7 represent hypothetical cases that illustrate our reasoning. In this case, the adjacency matrix is represented in Table 8 (observe that the MFI disappears in this matrix because now it plays the role of an intermediary and, consequently, it does not provide any money or information): In the matrix in Table 8, k ¼ 3, and the number of ones is 54. In general, if the number of micro-borrowers is n, then the number of ones in the adjacency matrix is 2kn 2 . Thus, the multiplier (mÞ of the complexity of the microloan system, in case (A), is m :¼ 2kn 2 2n ¼ kn: In our example, the multiplier is m ¼ 9.

(B) Case of several group lending and crowdfunding
This case is represented in Fig. 7. In this case, the adjacency matrix would be Table 9.
Observe that, in Table 9, the number of ones is 24. In general, if there are h group lenders GL 1 , GL 2 ; . . . ; GL h with n 1 ; n 2 ; . . . ; n h micro-borrowers, then the number of ones in the adjacency matrix is X h j¼1 ½ðn j þ 1Þ 2 À ðn j þ 1Þ ¼ X n j¼1 n j ðn j þ 1Þ: (C) Case of a group lending and crowdfunding In this case, the number of ones in the adjacency matrix can be determined by the same formula as in case (B) in Sec. 5.2.1.1.

(D) Credit risk
Consider a traditional MFI which promotes the potential participation of n micro-borrowers. A measure of the credit risk can be determined again by the entropy of the system which is given by the following expression: where now p i is the probability that the ith microloan is granted by the MFI. It is well known that the entropy represents the uncertainty of a system, in this case, the Table 8. Adjacency matrix corresponding to Fig. 6. Table 9. Adjacency matrix corresponding to Fig. 7. credit risk of the system is composed of the MFI and the group of micro-borrowers. However, in a crowdfunded microloan, there are k crowd-funders for each microloan which makes that the probability p i increases until p 1=k i > p i . Therefore, the entropy is now For values of p i high enough, one has H 00 < H, as expected, the incertitude (credit risk) associated with the system (microloan) decreases as the number of microlenders increases. For example, in the sample of crowdfunded microloans managed by Kiva and described in Sec. 5.1, the average value of k is 21.02. This¯gure supposes a huge increment in the probability of granting a microloan.
As the risk of default is associated with the number of borrowers and the credit risk is linked to the number of lenders, the corresponding results are determined as summarized in Table 10. The risk of default is inversely proportional to the number of borrowers, and the credit risk is inversely proportional to the number of lenders. This is due to diversi¯cation gains that could be acknowledged in the Kiva crowdfunding model. Table 10 illustrates how the risks of default and credit (a®ecting borrowers and lenders, respectively) diminish as the numbers of borrowers and lenders increase. So, it serves to demonstrate that the measure of both risks (according to the above formula) is accurate.

Proposal of a multiplier by¯eld partners in microloans
As previously indicated, the insertion of¯eld partners in crowdfunded microloans supposes an increase in the volume of granted microloans and, consequently, an increment in the volume of business of micro-borrowers. Additionally, through these combined instruments, lots of micro-lenders (crowd-funders) satisfy their need to collaborate in the development of the so-called social economy.
Previous discussions in Sec. 5.1, (C) in Sec. 5.2.1.1, and (D) in Sec. 5.2.1.2 have quanti¯ed the variations of the prosocial impact, risk of default, and credit risk, respectively, associated with the inclusion of¯eld partners in crowdfunded with r being the ratio de¯ned in Sec. 5.1. This indicator will be called the multiplier associated with the presence of a¯eld partner in crowdfunded microloans. A multiplier is fully consistent with the scalable properties of digital crowdfunding platforms.
The multiplier m can be greater than, equal to, or less than 1. Thus, if m > 1, there is value creation; if m ¼ 1, there is no value creation; and,¯nally, if m < 1, there is a loss of value in the involved economy.

Discussion
The most di®used microloans by sector of activity, shown in Table 3, are often related to a higher number of SDGs (Agriculture, Food, Clothing, etc.), even if this is not always the case. Education, transportation, construction, and manufacturing show high SDG scoring with a low number of micro¯nance loans. This could indicate new¯nancing priorities, reducing the information asymmetries that prevent optimal allocation from Kiva sponsors (crowd-funders) to micro-borrowers, as shown in Fig. 3.
Goal setting, consistent with SDG scoring, and coordination (mastered by architectural networking) are e®ective mechanisms to increase prosocial behavior in teams (Chen et al. 2017).
A further purpose of this theoretical paper is to introduce a tool (i.e. an indicator) to measure the value added by a¯eld partner (i.e. a micro¯nance institution) in the economic system where the partner moves on. So, in this context, it does not make sense to test any hypothesis, speci¯cally due to the absence of data on default and credit risks in these contexts.
The¯ndings of this study can be corroborated by consistent literature. Despite the crucial role that¯eld partners play in this sort of microcredit through online platforms, such as Kiva (Gosh & Vachery 2016), there is a lack of speci¯c literature review about it. Mahajan & Srivastava (2019) show that the inexorable rise of the Internet has given traditional microlending facilities a new online platform where people from any part of the world can lend their money to those in need of it. With the risk of default being tremendously high in comparison to tra-ditional¯nancing, there is an utmost need for the platform to be transparent and trustworthy. Mahajan and Srivastava (2019) propose a model which is based on blockchain technology and uses a holistic rating system to rate both the borrower and lender instead of the generally used rating of the MFIs or¯eld partners, which act as intermediaries and have a tie-up with the online peer-to-peer platforms nowadays. Paruthi et al. (2016) specify how highly rated¯eld partners drive more lending activities and how di®erent aspects like gender and other features play a role in lending activities. Moreover, they also outline that team lending behavior is willing to take a greater risk than individuals. Armstrong et al. (2018) show that Kiva plays a connector role in the micro¯nance ecosystem by directly linking funders with borrowers; this type of business model is popularly known as person-to-person lending. The intermediating role of¯eld partners is also explained by Ly & Mason (2012), who show that Kiva assigns a risk rating, from one star to¯ve stars to each of its¯eld partners, considering¯nancial sustainability and reliability. Ibrahim & Verliyantina (2012) illustrate that the role of¯eld workers is to: (1) examine the feasibility of SMEs; (2) calculate the amount of loan required; (3) collect entrepreneur stories, pictures, and loan details and upload them to the system; (4) provide the training and knowledge required by the SME entrepreneur. Galak et al. (2011) show that lenders favor individual borrowers over groups or consortia of borrowers, a pattern consistent with the identi¯able victim e®ect. The discrimination between individual lending and group lending represents a key and trendy distinction in micro¯nance evolution. Field partner risk rating also speaks to the creditworthiness of the borrower, an issue important in person-to-person lending literature.
Other variables such as loan term and¯eld partner risk rating a®ected the loan value. Burtch et al. (2014) show that lenders do prefer culturally similar and geographically proximate borrowers. Choo et al. (2014) show that lending teams are generally more careful in selecting loans by the loan's geo-location, borrower's gender,¯eld partner's reliability, etc. when compared to lenders without team a±liations. Figueroa-Armijos & Berns (2021) show that entrepreneurs using¯eld partner institutions (e.g. micro¯nance institutions) speci¯cally tailored to serve vulnerable populations will be better positioned to garner attention from prosocial crowd-funders.
Third-party actors who endorse the entrepreneurial project provide a valuable asset for both investors and entrepreneurs alike (Massa Saluzzo & Alegre 2021). In our context, they may well be represented by¯eld partners.
This study goes beyond the extant literature since it shows that the value added by¯eld partners in the context of crowdfunded microloans can be divided into their prosocial impact through the ful¯llment of the well-known SDGs and the variations of the risk of default and the credit risk, both considered as the main purely¯nancial parameters associated with the microcredit operations. The novel theoretical model proposed in this study cannot be calibrated due to the absence of data on default and credit risks in these contexts. Of course, both risks can be considered independent.
If this is a concern, we propose to¯nd a more accurate relationship between both risks by using copulas. Whenever data become available, an update of this study will be possible.
A network theory interpretation is original, as it provides mathematical tools for innovative analysis of the relationships described in Figs. 3-7. Frontier research may consider dynamic networks, where the relationships among connected nodes (crowd-funder, their digital platform, the MFI, group lenders or individuals as microborrowers, etc.) change over time.
Furthermore, multilayer networks (Bianconi 2018) where nodes exist in separate layers, representing di®erent forms of interactions, are fully consistent with the main bridging nodes of this case (the crowdfunding platform and the MFI, illustrated in Fig. 3). Multiplex networks (where the bridging nodes coexist) and their evolving dynamics, fostered by digital scalability, may so represent a further analytical tool.
We have wondered whether the gender of crowdfunded micro-borrowers (Strøm et al. 2022) is related to the main features that de¯ne the quality of a microloan: amount, term, number of lenders, repayment system, and period of lenders' recruitment. By using the multinomial logit regression, we have shown that amount, term, repayment method, and recruitment period indicate that women are the best borrowers. These¯ndings provide useful indications to improve¯nancial inclusion and outreach, consistently with the Sustainable Development Goals.
The role of gender in crowdfunding and micro¯nance (Gray & Zhang 2017) deserves, however, further investigation, also considering that most micro¯nance borrowers are women. This could inspire a further research avenue.

Conclusion
This study provides a novel indicator of the value added to the economic system where a¯eld partner (i.e. a micro¯nance institution) is operating. The paper introduces a theoretical model which, unfortunately, cannot be calibrated due to the absence of data on default and credit risks in these contexts. Of course, both risks can be considered independent. If this is a concern, we propose to¯nd a more accurate relationship between both risks by using copulas À À À a multivariate cumulative distribution function. This paper has dealt with crowdfunded microloans where¯eld partners have played the role of agents able to \securitize" microloans. Thus,¯eld partners have been considered the \meeting point" of the converging interests of both microborrowers and micro-crowd-lenders. Thanks to the crowdfunding scheme (exempli¯ed in Fig. 3), micro-borrowers can easily obtain the microloan they need for developing their business initiatives and, in the case of belonging to a group, they can obtain some economic help for repaying their joint microloans.
On the other hand, micro-lenders are people very sensitive to the development of a social economy and share homophily with the ultimate borrowers. Thus, the securitization of microloans facilitates their participation in these \prosocial" initiatives by contributing modest amounts.
The main contribution of this study has been the proposal of a global indicator À À À a multiplier associated with the presence of¯eld partners in crowdfunded microloans À À À which is a function of the variations of social impact, risk of default, and credit risk in microloans funded by a¯eld partner. This indicator so provides a measure of the increase or decrease of the volume of microloans, as a function of the e±ciency of the¯eld partner involved in the crowdfunded microloan.
Network theory analysis, conducted with a graphical representation of the different networks along with a digital supply and value chain, and their adjacency matrices, shows how increased networking À À À linking crowd-funders to microborrowers À À À adds value, especially if the interacting edges between any two nodes vehiculate richer information (thanks to the intermediating role of¯eld partners) and smarter transactions, ignited by the Kiva model.
Considering the political implications,¯eld partners play a decisive role in the progress and fair development of crowdfunded microloans when matching the legitimate interest of both micro-borrowers and micro-lenders. For these reasons, political authorities of undeveloped and developing countries must promote and monitor the activities of these economic agents to guarantee a credit multiplier greater than one. In this way, further research may determine the multipliers associated with¯eld partners operating in speci¯c economic sectors exempli¯ed by the Kiva community.
Financial inclusion externalities suggested by the on-¯eld application of the model proposed in this study can foster ESG adoption, consistently with SDGs. This may ignite a virtuous spiral, where all the involved stakeholders coalesce around win-win targets, with a common aim to combat everywhere poverty and inequalities.