Informed principal and the microcredit market: Is help always bad news?

Informed principal and the microcredit market:

Is help always bad news?

Renaud Bourlès

Anastasia Cozarenco

Dominique Henriet

Xavier Joutard

aEcole Centrale Marseille (Aix-Marseille School of Economics), CNRS and EHESS

bAix-Marseille University (Aix-Marseille School of Economics), CNRS and EHESS

cLyon2 University, GATE - UMR 5824

Preliminary version February 2014

Keywords: microcredit, reversed asymmetric information, looking-glass self, bivariate probit, scor- ing model

JEL Codes: C34, C41, D82, G21

The authors thank Mohamed Belhaj, Sebastian Bervoets, Yann Bramoullé, Habiba Djebbari, Ce- cilia Garcia Penalosa, Marek Hudon, Thierry Magnac, David Martimort, Ariane Szafarz for valu- able comments and discussions. The paper also beneted from discussions at the Ninth CIREQ Ph.D. Students' Conference, Montréal, Canada; CERMi Seminar, Brussels, Belgium; European Doctoral Group in Economics (EDGE), Munich, Germany; Summer School in Development Eco- nomics (IDEAS), Ascea, Italy; 29ème Journées de Microéconomie Appliquée, Brest, France; and GREQAM Lunch Seminar, Aix-Marseille School of Economics, Marseille, France.

1Corresponding author. Address: Centre de la Vieille Charité, 2, rue de la Charité, 13236 Marseille cedex 02, Fance; Phone +33 (0)4 91 14 07 21; Email: anastasia.cozarenco@univ-amu.fr

Abstract

In this paper we analyze how decisions of a micronance institution (MFI) on business train- ing (or help) provision can impact borrowers' behavior. In the theoretical model we assume a situation where the MFI - through help - and the borrower - through eort - can act on the probability of borrower's project to succeed. We show that, in contexts where under symmet- ric information the MFI optimally helps more the borrower with lower probability of success, superior information (when the MFI has better information on probability of success than the borrower) can lead the MFI not to help (or to help less) riskier borrowers. In this last case, because of a "looking-glass self" eect, MFI's choice of help impacts borrower's belief about his risk. We then test this prediction using data from a French MFI. By means of empirical models, taking into account both the credit-granting and the training-granting processes, we analyse how training programs are assigned to dierent borrowers. Conrming our theoretical reasoning, we nd a non-monotonic relationship between the MFI's decision to help and the risk of micro-borrowers. The probability to be helped appears to increase with risk for low-risk borrowers and to decrease for with risk for high-risk borrowers.

1 Introduction

Microcredit is a small-scale nancial tool designed for individuals who are rejected from the classical nancial market.

Micro-borrowers are often unemployed, lacking collateral and any experience in starting a business. After having been widely used and studied in developing countries, microcredit is now largely spreading to developed countries. While its main objective - poverty alleviation - is common for both types of economies, its implementation has several particularities in the developed countries. For example, individual lending is prevalent, loans don't specically target women and there is generally a high government implication through guaranties or subsidies in industrialized economies. Another important characteristic of micronance in the developed countries is the pres- ence of formal business training,

also termed Business Development Services (BDS). European Micronance Institutions (MFIs) have been involved in BDS since their emergence (Lammermann et al., 2007).

Business training refers to dierent kinds of additional non-nancial support services that accom- pany loans. They may consist of dening and developing the business project (studying the prof- itability, setting the commercial strategy and nancing needs, administrative help), information and help to obtain nancing, trainings in accounting, management, marketing, law and the follow-up of the project.

By means of a theoretical model and empirical evidences we study how an MFI assigns borrowers to training programs. We use data on applicants of a French MFI. This MFI faced two types of decisions. First, it approved or rejected applicants for a microcredit. Second, conditionally on loan approval, it assigned some of the borrowers to a training program. We also have information about unpaid installments and defaults of the clients, which we used to assess the riskiness of the borrow- ers. Interestingly, data suggests that individuals assigned to training are not riskier ex-post than individuals without training.This evidence reects two possible scenarios: either training is targeted toward (ex-ante) high-risk individuals and is highly ecient (as ex-post borrowers with training are not riskier than borrowers without training) or training is not targeted exclusively toward high-risk borrowers.

2From this perspective, microcredit can be viewed as a solution to credit rationing occurring on the classical credit market with imperfect information ineciencies. For details on credit rationing see Stiglitz and Weiss (1981).

3Formal business training is provided through special arrangements, conditions or contracts between a business development agency/micronance institution and the entrepreneur (Lammermann et al., 2007). In developing coun- tries training programs that accompany loans are less formal and often consist of social development programs, such as information on health, civil responsibilities and rights, rules and regulations of the bank (McKernan, 2002).

Existing literature is agnostic about the eciency of training in micronance (see for example Kar- lan and Valvidia 2011; Lensink et al. 2011 for developing countries, and Balkenhol and Guézennec 2013; Evans 2011; Edgcomb 2002 for developed countries). Overall, studies in both developed and developing economies fail to corroborate the rst scenario where help is mainly targeted toward the riskiest individuals and is highly ecient. This gives credit to the second scenario, where BDS do not necessarily target only high-risk borrowers.

Consequently, training assignment process appears to be somewhat puzzling and the aim of this paper is to tackle this puzzle. Generally, micro-entrepreneurs need nancing to start-up a business for the rst time in their life. Therefore, they lack the necessary entrepreneurship experience. It is plausible that the micronance institution is better informed than the borrower about the potential success of the project due to its past experience. In this context, the contract oered by the MFI (assignment to a training program or not) can reveal some information to the borrower about his self and impact his actions. This mechanism, termed looking-glass self (Cooley, 1902), provides a rationale to the hypothesis where the MFI having superior information might indeed not target help (or BDS) exclusively toward high risk individuals.

By the same token as Akerlof and Kranton (2005), in our theoretical model, the MFI will not provide training to some borrowers in order to make them exert eort. This is possible due to MFI's superior information about borrower's type. In this context, we are looking for equilibria where help is not necessarily bad news. To do so, we provide a theoretical model where both the MFI - through help - and the borrower - through eort - can impact the probability of success of the project. Borrowers are heterogeneous on their type

which enters the probability of success of the project. The MFI, rst, decides on loan granting and, second, on training assignment. We rst develop a discrete theoretical model to illustrate the main intuitions underlining how MFI's decision on training assignment varies with borrower's type. A more general continuous model is then presented, to illustrate how a continuous level of help varies with a continuous type of the borrower. For both models we rst present a framework under symmetric information where the level of help chosen by the MFI is decreasing with the type of the borrower. Second, we develop a model under reversed asymmetric information where the MFI has information advantage on the type of the borrower. This situation is unarguably plausible on the microcredit marked where the experienced MFI faces an inexperienced borrower. Contrary to the rst-best solution, under re-

4By "type" we mean the intrinsic probability of the borrower to succeed. It can also be interpreted as the risk of the borrower.

versed asymmetric information we show that a non-monotonic relation between help and the type of the borrower may arise. We more precisely show that there exists a Perfect Bayesian Equilibrium where optimal help in a non-monotonic concave function of type (or risk): the optimal level of help is rst increasing with the type of the borrower, and beyond a certain threshold it is decreasing.

We further test for the existence of such a mechanism using data from a French MFI. We develop a credit scoring model using a bivariate probit model where we control for individual unobserved het- erogeneity. We proxy the type of the borrower discussed in the theoretical model by his estimated risk, which is modeled in the rst probit regression. Using the simplest form of non-linearity, by introducing the estimated risk and its square term in the second probit regression for help, we nd that help is rst increasing with borrowers' type and beyond a certain threshold it is decreasing.

The mechanism behind the Perfect Bayesian Equilibrium outlined in the theoretical model seems therefore plausible in real life.

This result, moreover, seems to be robust to the introduction of business cycles, to controlling for selection bias (Heckman, 1979; Boyes et al., 1989) and to the use of the survival time of the loan, instead of borrower's risk, as a measure of risk (Roszbach, 2004).

Our analysis contributes to at least three strands of literature concerning, respectively, the theo- retical eect of reversed asymmetric information, the role of training programs in micronance and the empirics of scoring models.

A person's sense of self, or identity, can aect individual interactions in economics (Akerlof and Kranton, 2000). For instance, Akerlof and Kranton (2005) argue that in labor market a rm might be willing to invest in changing a worker's identity in order to make him exert high eort. The identity issue is highly relevant on the microcredit market. Copisarow (2000) underlines that mi- crocredits psychologically boost borrowers' self-condence and self-esteem by giving them greater control over their lives and expanding their options. Principal's superiority of information approach has been previously assumed in literature in principal-agent models. For instance, in insurance theory, Villeneuve (2000) studies pooling and separating equilibria in the context where the insurer evaluates risk better than its customers. Benabou and Tirole (2003) discuss many situations where the principal might be better informed than the agent (for example at school, in the labor market and family). Concerning help, authors show that it is always bad news in equilibrium.

In contrast

5Other situations where help can be detrimental to the agent are presented by Gilbert and Silvera (1996). Using dierent experiments authors show that help can be used to undermine the beliefs of the observers who might attribute a successful performance to help rather than to performer's abilities.

we will study situations where help is not always bad news for the beneciary. To our best knowl- edge, this paper is the rst one to introduce reversed asymmetric information in micronance.

Our paper also contributes to the literature on the eect of training in micronance. Concerning developing economies, Karlan and Valvidia (2011) study the eect of business training in FINCA- Peru using a randomized control trial. They nd a signicant impact of training on client retention in the MFI, business knowledge improvement but little evidence on the prot or revenues increase.

Lensink et al. (2011) use data for MFIs in 61 emerging and developing countries and show that MFIs providing both nance and business development services have similar performance as MFIs providing no "plus" services. On the other hand, McKernan (2002) nds that noncredit aspects of micronance have positive eects on borrowers' prots. However, these noncredit aspects are composed of group cohesion, joint liability and social development programs which are absent in developed countries. In developed countries, formal impact evaluation of BDS is scarce.

For in- stance in France, business training is recognized as a salient component of French micronance (Observatoire de la Micronance de la Banque de France, 2010). Nevertheless, extensive research on its impact is absent and hardly dissociable from the microcredit itself (Balkenhol and Guézen- nec, 2013). Evans (2011) underlines some positive outcomes for BDS in the framework of Women's Initiative for Self Employment in the United States (US). Nevertheless, the author stresses that few programs are able to meet the demand as they face low budgets, lack sta and adequate products or services. Edgcomb (2002) provides ve case studies for institutions involved in business support services in the US and reports mitigated correlations between training completion and successful entrepreneurship outcomes. Moreover, in the European Union (EU) most micro-entrepreneurs do not consider that they do need BDS and prefer using informal sources of training oered by family, friends or media (Lammermann et al., 2007). Lammermann et al. (2007) additionally highlight that in Europe, one of the main challenges remains the increase of business training eciency. We con- tribute to this literature by providing formal evidence on BDS eciency using data from a French MFI. Whereas, training appears to have no impact on the probability of default of the borrowers, we identify some positive impact on the survival time of the loans.

Our empirical strategy is based on a bivariate probit model where we jointly model two probit equations: the rst one modeling training assignment process and the second one modeling the

6We can, however, report some evidence from training programs in developed countries on the job market. Card et al. (2010) provide a meta-analysis of 97 studies focusing on the eectiveness of labor market programs, mainly in developed countries. Their analysis suggests that public sector employment programs are relatively ineective.

However, job search assistance has some positive impacts, especially in the short run.

probability of default of the borrower. A comparable bivariate probit model has been developed by Boyes et al. (1989) where the two probit equations concern the loan granting process and the default of borrowers. Such a model allows to control for the selection bias (Heckman, 1979). To address selection bias issue in our setting, our paper pioneers the development of a trivariate probit model to test for the robustness of our baseline bivariate probit model. Empirical literature, moreover, argues that despite default some loans may still be protable to the bank which is concerned about the moment when a default occurs rather whether a default occurs. Roszbach (2004) addresses this issue by providing a survival time model. In line with this study, we use an alternative measure of risk in a bivariate mixed model to check for the robustness of our ndings. The originality of our paper consists in the development of formal empirical models, taking into account endogeneity issues, selection bias or the survival time of the loans, to study how an MFI assignes dierent bor- rowers to training programs.

The remainder of the paper is structured as follows. In section 2 we present the theoretical model.

We rst present the discrete type model, followed by continuous type model. Data used to test theoretical results is presented in section 3. In section 4 we present the econometric model which we used to estimate the empirical results presented in section 5. We check for robustness of our results in section 6. Section 7 concludes.

2 Theoretical model

2.1 General framework

The agent, a borrower, has a project for which he needs nancing. He has no collateral and no personal investment. He needs to borrow from the bank the total amount of the project, which we normalize to 1. The project will generate a return, ρ , in case of success and 0 in case of failure.

The principal, an MFI, demands a return of R = 1 + r in case of success with R < ρ , where r is the xed interest rate.

It receives 0 in case of failure. The probability of success (denoted p(θ, e, h) ) depends on the type of the borrower θ , his eort e and the level of help from the MFI h .

We assume the probability of success to be increasing in these three terms. θ can also be interpreted

7A xed interest rate is consistent with data where the MFIs x the same interest rate for all the borrowers.

8In the context of micronance, help may take dierent forms. Generally, microborrowers follow various trainings in accounting or business management which are organized by the MFI or by its partners. From the approach of the literature on double-sided moral hazard (Casamatta, 2003; De Bettignies and Brander, 2007), help may be interpreted as the eort provided be the MFI.

as the intrinsic probability of success, or the ability of the borrower (i.e. p(θ, 0, 0) = θ ). Eort is costly for the borrower and help is costly for the MFI. The respective costs are denoted by ϕ(h) and ψ

(e) (i.e. we allow the cost of eort to be type-dependent). The utility of the MFI is therefore given by

U

= p(θ, e, h)R − ϕ(h) and the utility of the borrower is given by:

U

= p(θ, e, h)(ρ − R) − ψ

(e)

We are going to analyze two information structures. In the rst one, the information is perfect and symmetric: both the borrower and the MFI observe borrower's type θ . The MFI chooses h and the borrower chooses e simultaneously.

Figure 1:

Our aim it to analyze if reversed asymmetric information can lead the MFI not to help the lowest type, i.e. the riskiest borrowers. We will therefore focus on cases where, under perfect information, the MFI provides a level of help decreasing with type. In that sense, absent the looking-glass self eect highlighted earlier, help would then be considered as a bad news for borrowers (as it would reect a low probability of success).

In the second conguration, we will assume reversed asymmetric information, that is a situation where the borrower does not know his type, while the MFI does. In this case, the level of help chosen by the MFI ( h ) also conveys information about borrower's type, that might inuence borrower's behavior. In other terms, observing h , the borrower makes a belief about his type that leads him to some level of eort.

We will show that, in contrast with the symmetric information case, a non-monotonic (concave)

relationship between help and the type of the borrower, can emerge in some Perfect Bayesian

Equilibrium (PBE). The purpose of the empirical section will then be to highlight this peculiar

feature of help.

Figure 2:

2.2 A discrete model

Let us rst give the basic intuitions of our model through a simple discrete model ( e ∈ {0, 1} , h ∈ {0, 1} ) with three types of borrowers: θ ∈ {θ

, θ

, θ

} . Let ∀θ ψ

(0) = 0 , ψ

(1) = ψ , ϕ(0) = 0 and ϕ(1) = ϕ . Borrowers' types are dened by the return on eort and help. We assume that return of eort is increasing with type (that is p(θ, 1, h) − p(θ, 0, h) is increasing with θ , ∀h ) whereas the return on help is decreasing with type (that is p(θ, e, 1) − p(θ, e, 0) is decreasing with θ , ∀e ). For the problem to be pertinent, we assume that contrarily to other types the lowest-type borrowers do not have the incentive to provide eort (whatever the level of help), that is:

p(θ

, 1, h) − p(θ

, 0, h) < ψ

ρ − R < p(θ

, 1, h) − p(θ

, 0, h) ∀h and that the MFI is not interested in helping the highest-type borrowers:

p(θ

, e, 1) − p(θ

, e, 0) > ϕ

R > p(θ

, e, 1) − p(θ

, e, 0) ∀e

Remark 1. This setting leads to a situation where, under symmetric information, the MFI helps the two lowest types: θ

and θ

and does not help the highest type: θ

. Borrowers of types θ

and θ

provide eort but the low type θ

does not.

. Under reversed asymmetric information,the borrower is not aware about his type. Only the MFI

observes the borrower's type. The action played by the MFI (help or not) can therefore convey information to the borrower. The borrower forms beliefs about his type after having observed the level of help chosen by the MFI.

Our aim is to show that there exists a Perfect Bayesian Equilibrium in which help is a concave

function of type, that is in which the MFI only helps borrowers of type θ

. In this case, a borrower

observing that he is not helped, infers he is either of low or high type. Let us note α the probability of the borrower to be θ

when he receives no help from the MFI ((1 − α) is then probability of being θ

). In other words, α represents, in such an equilibrium, the belief of the borrower that he is of high type when he observes that the MFI chooses not to help him. Moreover, in the considered equilibrium, when the borrower observes that the MFI decided to help him he knows with certainty that he is of type θ

. This leads us to the following proposition.

Proposition 1. Under reversed asymmetric information, there exists a PBE where the MFI only helps θ

-type borrowers and all borrowers exert eort, if and only if:

(1 − α)(p(θ

, 1, 0) − p(θ

, 0, 0)) + α(p(θ

, 1, 0) − p(θ

, 0, 0)) ≥ ψ

ρ − R (1)

and

p(θ

, 0, 1) − p(θ

, 1, 0) < ϕ

R (2)

. Condition (1) insures that a borrower observing he is not helped optimally exerts eort, whereas

condition (2) states that the MFI prefers the situation where low-type borrowers exert eort with- out being helped to the one of the equilibrium with symmetric information (where the low-type borrower does not exert eort but receives help).

The intuition behind this result is rather simple. In the highlighted PBE, the MFI uses its superior information to induce the low-type borrowers to exert eort. It does so by pooling them with the highest type borrowers, those for whom eort is the most protable. This is done at the expense of not providing them help which is worth it under equation (2).

2.3 The continuous model

Let us now turn to a more complete model with a continuum of types, levels of eort and levels of help: θ ∈ [0, 1] , e ∈ [0, 1] and h ∈ [0, 1] . In this case, we assume for the sake of simplicity that the impact of help or eort on the probability of success is decreasing with the type of the borrower:

p

< 0 f or j = 2, 3

In the explicit example that we consider in this section, we more precisely assume p (θ, e, h) = θ + (1 − θ) 1

2 (e + h) (3)

which is in line with our denition of θ as the intrinsic probability of success and with the literature on venture capital (Casamatta, 2003), in which eort and help are perfect substitutes considering their impact on the probability of success. Still, consistently with the discrete model above, optimal eort will be increasing in type, due to a "discouragement" eect: a borrower who "realizes" or is led to believe he has a small intrinsic probability of success, will be discouraged to exert eort. This eect will materialize in our model through a type-specic cost of eort. More precisely, we need ψ

(e) to be such that E (θ, h) = arg max

e

[p (θ, e, h) (ρ − R) − ψ (θ, e)] is increasing in θ . One very simple way to model this property that keeps the model tractable is to assume a linear eort with respect to the type of the borrower E (θ, h) = γθ . Taking the probability of success as dened in (3) this can be obtained, for instance, by assuming ψ

(e) =

e

.

Regarding the cost of help incurred by the MFI, a quadratic form ϕ(h) =

(where c is a positive constant) will be enough to insure that optimal help is decreasing with type under symmetric information.

Indeed, under symmetric information, the program of the MFI is then given by:



 

 

h

(θ) = arg max

h∈[0,1]

θ +

(1 − θ) (e + h)

R −

ch

s.t. e = γθ

We have the following remark:

Remark 2. Under symmetric information, the optimal help provided by the MFI is decreasing with the borrower's type:

h

(θ) = R

2c (1 − θ)

. In other words, the MFI provides help to those who need it the most. The optimal help is a de-

creasing ane function of the type.

Let us now turn to the case of reversed asymmetric information. Once again, our aim is to show that (in a situation where help would be decreasing in type under symmetric information), superior information can lead the MFI to follow less the lowest-type borrowers. In the case of a continuum of types, this would correspond to a concave relationship between help and type, i.e. an "exotic"

pooling Perfect Bayesian Equilibrium in which several non adjacent values of θ are associated with the same level of help. Let us show that such an equilibrium is possible.

Consider that help is a concave non monotonic function of type h

(θ) such that, a level of help h is

associated with two possible types θ(h) and θ(h) (except at its maximum). A borrower, observing

a given level of help infers some information about his type. Assuming risk neutrality, the inferred type of the borrower writes:

t

(h) = θ(h)f

(θ(h)) + θ(h)f

θ(h) f

(θ(h)) + f

θ(h)

where f

(x) represents the belief of a borrower type θ on the distribution of types. This will consist in a Perfect Bayesian Equilibrium if the optimal help strategy when the borrower's inferred type is t

(·) is precisely h

(θ) , that is if h

is the solution of:



 

 

h

(θ) = arg max

h∈[0,1]

θ +

(1 − θ) (e + h)

R −

ch

s.t. e = γt

(h)

Proposition 2. There exists a PBE in which help is a concave function of type. It notably involves that borrowers' beliefs are decreasing in types: observing a high level of help is bad news for high-type borrowers but a good news for low-type borrowers.

. To prove the existence of such an equilibrium, we analyze a particular concave help function, sym-

metric with respect to

: h

= σθ(1 − θ) . In this case, the MFI oers the same level of help h to borrowers of type:

θ(h) = 1 2 −

r 1 4 − h

σ and θ(h) = 1 2 +

r 1 4 − h

σ and (type-dependent) distributions of beliefs of the form:

f

(x) = 1 − σ

γ (θ − 1)

x − 1 2

will lead to a Perfect Bayesian Equilibrium. Indeed, we then have the inferred type of the borrower:

t

(h) =

1 − 2 (θ − 1)

1 4 σ γ

−

2

such that the optimal level of help which is solution of



 

 

h∈[0,1]

max θ +

(1 − θ) (e + h)

R −

ch

s.t. e = γt

(h)

writes h(θ) =

θ (1 − θ) which corresponds to the help function h

(θ) with σ =

.

In the highlighted equilibrium, the beliefs of borrowers therefore correspond to distorted uniform

distributions: distorted upward for types θ < 1/2 and distorted downward for types θ > 1/2 . In this setting, for high-type borrowers help is bad news, whereas it is good news for low-type borrowers:

for a given level of help, low-type (resp. high-type) borrowers put more weight on the higher (resp.

lower) corresponding type. This allows the MFI to increase the level of eort provided by lowest- type borrowers, by pooling them with a highest-type borrowers.

The aim of the above argument was to show that there exist Perfect Bayesian Equilibria in which help is a concave function of type of the borrower. There may exist a lot of other PBE in the considered setting and a lot of other settings in which such PBE exist.

Still, we have shown in this theoretical section that, because of superior information, a micro-nance institution might not want to help (or might want to help less) the lowest-type borrowers. This comes from the fact that its help decision conveys information about the ability of the borrower. By pooling the lowest-type borrowers with highest-type borrowers, the MFI uses the so called "looking- glass self eect" to induce them to exert more eort.

In the following we test for the presence of these eects using data from a French MFI. By studying if help is indeed a concave function of borrowers' type (measured by their risk or ex-ante probability of default), we will analyze whether the MFI internalizes the fact that its help decision impacts borrowers' behavior through the "looking-glass self eect".

3 Data

We use data from a French MFI that allows us to model the credit-granting process, the help- granting process and default process. In Table 1 we present the descriptive statistics of our data along with the t-test to compare means between dierent groups. We have individual information on 782 applicants for a business loan

from a French MFI. A large majority of these loans was dedicated to business start-up. The average amount of the approved loans was 8, 900 e, the average interest rate was 4.2%

and the mean maturity was 52 months.

We will use this data in order to study how MFI's decision to help borrowers varies with their risk. In the baseline model we provide a bivariate probit model where help-granting process and default process are jointly modeled to control for endogeneity bias, under unobserved individual heterogeneity assumption. To capture the simplest form of non-monotonicity we introduce in the

9We do not study consumer loans, in contrast with Roszbach (2004).

10The interest rate was xed at 4% per year at the beginning of the period and reached 4.5% at the end of the period of analysis. The interest rate is xed and hence does not depend on borrower's characteristics.

help equation the estimated risk of the borrower and its square term. The risk of the borrowers is estimated using the predicted probability of default for each borrower. The predicted probability of default is modeled in the second probit equation. To better correspond to the theoretical model, we moreover introduce heteroscedasticity in the bivariate probit model. This will account for the theoretical assumption where two dierent individuals observing the same level of help will have dierent inference processes. To check for the robustness of our results, we further introduce in the baseline model business cycles, loan-granting process to control for selection bias, and an alternative measure of risk using information on the survival time of the loans.

One original characteristic of our data consists in information available for both accepted and rejected applicants. 47% of the applicants have been granted a microcredit between May 2008 and May 2011. We note that the proportion of long term unemployed applicants (more than 12 months) is signicantly greater among rejected projects. So is the case for applicants with low personal investment

(lower than 5%), projects in the food and accommodation sector, projects having a larger ratio of gross margin to sales. This last gure may appear surprising at rst sight, yet it suggests that the MFI privileges the amount of sales in the approval process, rather than this ratio.

Finally, accepted applicants come from households with higher incomes on average.

A second decision concerns assignment of accepted applicants to a training program. 55% of the accepted borrowers were assigned to a training program. Helped and not helped borrowers seem to hardly dier with respect to their individual characteristics, according to Table 1. We note that the proportion of long term unemployed individuals is larger for helped borrowers. Moreover, they have larger household incomes and their businesses exhibit larger amounts of assets. Signicant dierences arise for variables concerning other characteristics. Helped individuals are more likely to have other demands and benet from honor loans. This dierentiation is however in line with the context of microcredit where NGOs providing training programs also provide honor loans

and may help project holders to apply for other demands. Hence, the link between the two variables having a honor loan and other demands and the likelihood to be helped is direct.

Interestingly,

11Low personal investment is a dummy taking value 1 if the applicant's personal nancial contribution to the project is lower than 5% of the project size. We take this cut-o because this is the lowest cut-o available in our data, after "No personal investment" and very few individuals provided no personal investment.

12A honor loan is an interest free loan subsidized by the French government for individuals willing to start a business in order to get self-employed. The government delegates the disbursement of these loans to NGOs which may also provide training programs.

13Microcredit disbursement process takes place in several stages. The borrower assigned to a training program gets in touch with the institution in charge of the training. This institution can complete the nancing of the borrower's

Table 1: Descriptive Statistics

Applicants Borrowers

Variables Total GrantedRejected t-test HelpNo help t-test DefaultingPerforming t-test

Granted (%) 0.47

Help (%) 0.26 0.55 0.49 0.57 -0.08

High Risk (%) 0.10 0.22 0.19 0.25 -0.05

Individual Characteristics

Male (%) 0.62 0.61 0.63 -0.02 0.62 0.60 0.02 0.75 0.58 0.17***

Education (# of diplomas) 1.84 1.89 1.80 0.09 1.89 1.89 0.00 1.46 2.01 -0.55***

Single (%) 0.55 0.53 0.57 -0.04 0.50 0.57 -0.07 0.63 0.51 0.13**

Unemployed more than 12 months (%) 0.39 0.33 0.44 -0.11*** 0.37 0.28 0.08* 0.42 0.31 0.11*

Household Characteristics

Household income (kEUR) 1.33 1.49 1.19 0.30*** 1.61 1.33 0.29** 1.11 1.59 -0.49***

Household expenses (kEUR) 0.45 0.45 0.45 -0.01 0.47 0.42 0.06 0.47 0.44 0.03

Business Characteristics

Low personal investment (%) 0.30 0.26 0.34 -0.08** 0.25 0.27 -0.02 0.38 0.23 0.15***

Assets (kEUR) 18.20 18.86 17.57 1.28 21.34 15.73 5.62** 12.19 20.74 -8.55***

Food and accommodation sector (%) 0.13 0.10 0.16 -0.06** 0.08 0.13 -0.04 0.09 0.11 -0.02

Gross margin/Sales 0.75 0.74 0.77 -0.03* 0.74 0.74 0.00 0.71 0.75 -0.03

Other Characteristics

Other demands (%) 0.58 0.62 0.54 0.08** 0.82 0.38 0.44*** 0.51 0.65 -0.15**

Honor loan (%) 0.48 0.47 0.48 -0.01 0.63 0.28 0.36*** 0.43 0.48 -0.05

Sent by a mainstream bank (%) 0.17 0.18 0.15 0.03 0.12 0.26 -0.14*** 0.14 0.20 -0.06

Nb of Observations 782 365 417 202 163 79 286

applicants sent by a mainstream bank are less likely to be assigned to a training program. The intuition behind this gure is two-fold. Borrowers sent by a mainstream bank have either been granted a credit from the bank (these are potentially "high-type" clients) or rejected by a bank (these are potentially "bad" clients). Our model predicts that both high-type and low-type clients are the least likely to be helped. These three variables (other demands, honor loan, sent by a mainstream bank) will be used exclusively in help regression in the empirical model to ease the identication of the model due to the direct link with variable Help.

loan with a subsidized interest-free honor loan and/or help the individual to set other demands. The MFI providing data is aware about this information which is generally available at the moment of entering the data in the information system.

In this paper we are particularly interested in this second stage decision consisting in borrowers' assignment to training programs. While approval process is important, as it will allow us to control for the selection bias (for the sake of a robustness check) we will analyze in the baseline model how the MFI decides to assign a borrower to a training program conditional to loan granting. To do so, we will design a scoring model.

To build a scoring model, we dene as "defaulting" borrowers with 3 or more unpaid installment in their credit history. 22% of all the accepted borrowers had 3 or more delayed payments in their credit history. We will denote these loans as "defaulting" in the following of the paper.

This denition is in line with the MFI's policy. In general, the MFI writes-o all the loans having three or more consecutive delayed payments. Among the clients having received help, 19% are defaulting clients. This proportion amounts to 25% for clients without help. However, this dierence is not signicant according to the t-test. Almost half of the defaulting loans have been assigned to a training program, whereas among performing loans 57% was assigned to a training program. Again the dierence between the two groups is not signicant. To build our measure of risk we will use individual, household and business characteristics. As Table 1 illustrates, there are signicant dierences between defaulting and performing clients. These dierences are usually (with some exceptions) of an opposite sign as those for the approval decision. This presents an indicator of MFI's credit granting process quality. Defaulting clients are more likely to be male, single, long- term unemployed, having lower education and income levels. Concerning business characteristics, defaulting clients are signicantly more likely to have low personal investment and lower level of assets. All these variables will be accounted for in the design of the risk measure presented in the next section.

4 Econometric model

The purpose of this section is to study the relationship between the "type" of the borrowers and their likelihood to be assigned to a training program by the MFI. As shown in the theoretical model help is not necessarily a monotonic function with respect to borrower's type. To dene the type of the borrower we will use a probit equation to model the likelihood of a borrower to default.

Among the explanatory variables we will include individual, household, business characteristics and a dummy indicating if the client was assigned to a training program. We compute the predicted

14Note that the delayed payments need not to be consecutive or unpaid. However, most of delayed payments in the database where consecutive.

probability to be "defaulting", that is the predicted Risk , to proxy borrower's type.

To test for a non-linear relationship between the likelihood to be helped and borrower's type, as suggested by the theoretical framework, we include Risk and Risk

in the Help equation, which is also modeled using a probit equation. Including Risk and Risk

will allow us to test for the simplest form of non-linearity, that is a quadratic relationship between the likelihood to be helped and the predicted risk of a client.

First, in the simplest univariate model we independently estimate two probit equations for help and risk as follows:

y

= x

β

+ λ

Risk + λ

Risk

+

y

=







1 if y

> 0 (Help) 0 if y

≤ 0 (Otherwise)

(4)

y

= w

β

+ α

y

+

y

=







1 if y

> 0 (Def ault) 0 if y

≤ 0 (Otherwise)

(5) where Risk = Φ(w

β ˆ

) is the estimated probability to default of the borrower and β ˆ

vector is estimated using equation (5), Φ(·) is the normal cumulative distribution function, x

is a vector of variables "Other demands", "Honor loan" and "Sent by a mainstream bank", w

is a vector of various controls, y

is a help dummy, and

and

are independent error terms following a normal distribution N (0, 1) . β

and β

are vectors of the loadings of dierent control variables that have to be estimated. λ

and λ

are estimated coecients of our main interest which will determine the form of the relationship between the likelihood to be helped and the type of the borrower. Finally, estimating α

will allow us to identify the impact of help on the probability to default of a borrower.

The results for this univariate model are presented in Table 2, columns (1) and (2) and commented in the next section.

Second, to control for endogeneity between help and risk, as help can impact the risk of the borrower, we jointly model 2 processes, help decision and the probability to default in presence of individual heterogeneity. By estimating simultaneously the two processes, we can avoid to bias the estimator of the variance of the parameters estimates related to the estimated expectation of Risk in the help equation. This model is estimated only for granted loans, as an individual can only be assigned

15The variableRisktherefore corresponds to (1−θ)in our theoretical model. The non-monotonic concave rela- tionship between help and type θ outlined in the theoretical model corresponds by symmetry to a non-monotonic and concave relationship betweenRiskand help, with help increasing in risk for low-risk borrowers and decreasing in risk for high-risk borrowers.

16We use the estimations in the univariate model as starting values for the coecients of the control variables in the bivariate models.

to a training program if he has actually been granted a microcredit. Hence, akin to the univariate case, we do not account for the selection bias in this bivariate probit model. Selection bias is left for the sake of a robustness exercise. In bivariate probit model (Boyes et al., 1989) we allow for some correlation between the error terms of the equations (4) and (5), which now writes as:

y

= x

β

+ λ

Risk + λ

Risk

+

(6) and

y

= w

β

+ α

y

+

(7) For the identication of the model, it is important that the variables in the x

vector are dierent from the variables in w

vector. The three varaibles in the x

vector (honor loan, other demands and sent by a mainstream bank) have a direct link with the help process, which has been carefully justied in the Data section above. Hence, these three variables are perfect canditates to be used exclusively in the Help equation and allow the identication of the model. The presence of correlation between help decision and risk is allowed by imposing the following structure on the error terms:

= ρ

v

+

= ρ

v

+

where the components

,

are independent idiosyncratic parts of the error terms and each one is supposed to follow a normal distribution N (0, 1) . The common latent factor v

entering the compound terms

,

could be considered as an individual unobserved heterogeneity factor. We assume that v

∼ N (0, 1) and that this factor is independent of the idiosyncratic terms. The pa- rameters ρ

and ρ

are free factor loadings which should be estimated. For identication reasons, we impose the constraint ρ

= 1 . Hence, in this model the type of the borrower is proxied by Risk = Φ(w

β ˆ

+ v

) . We maximize the log of the likelihood function which is the sum of the in- dividual contributions to the likelihood (see Appendix A). We present the results of the estimation of the bivariate model in Table 2, columns (3) and (4).

Third, in order to capture the idea that two dierent borrowers observing the same level of help

have dierent inference processes about their type assumed in the theoretical model, we add het-

eroscedasticity to the previous bivariate probit model. The likelihood to be a defaulting borrower,

estimated using realized data, depends on borrowers' behavior, which in turn depends on the in-

ferred type. The inferred type depends on the information received from the MFI (help or not) and

the inference process that can vary across individuals. In other words, the inference process intro-

duces some noise in borrower's behavior (or eort) and consequently some noise on his risk which

implies an increasing and non constant variance and can be naturally represented by a scedastic function attached to the unobservable variable, v

.

The model with heteroscedasticity writes as follows. Help decision is still described by equation (6) with

Risk = Φ(w

β ˆ

+ v

) while the risk equation is modeled as:

P r(y

= 1|w

, v

, y

) = Φ(w

β

+ α

y

+ ρ

v

) (8) where ρ

≡ ρ

exp(α

y

+ δEducation

) , meaning that help impacts directly the probability of default occurrence through α

and indirectly through α

(inference eect). The results of the estimation of the bivariate probit model with heteroscedasticity are presented in Table 2, columns (5) and (6).

5 Regression results

Our results are presented in Table 2.

For benchmarking purposes, in column (1) and (2) we present the results of univariate probit equations for help and risk. They correspond to the equations (4) and (5) estimated separately. In columns (3) and (4) we present the estimations for the bivariate probit model accounting for individual unobserved heterogeneity. We add heteroscedasticity in columns (5) and (6). The non-linear relationship between the likelihood to be helped and the type of the borrower is shaped by the coecients of Risk and Risk

. The Risk loading is positive in all the specications and the loading of the quadratic term is always negative, suggesting that the MFI is more likely not to help borrowers with very low and very high risk, as the probability to be helped is rst increasing with risk and, then, beyond a certain threshold it decreases with risk. Nevertheless, this relationship becomes signicant only in the third specication, in presence of heteroscedasticity.

We can compute using the estimators in column (5) the risk threshold for which the probability to be helped becomes decreasing with risk. To do so we use the derivative:

∂P r(y

= 1|x

, Risk, v

)

∂Risk = (ˆ λ

+ 2ˆ λ

Risk)φ(·)

where φ(·) is a normal density which is always positive. Hence the sign of the previous derivative is given by λ ˆ

+ 2ˆ λ

Risk . It will be positive for Risk smaller than 0.35 and negative otherwise.

17In this paper we are interested in the signs of the loadings and we will not study the sizes of marginal eects.

Hence all the results presented are the estimated coecients rather than marginal eects.

Table 2: Determinants of Help and Risk Processes

Model Univariate probit Bivariate probit without Bivariate probit with heteroscedasticity heteroscedasticity

(1) (2) (3) (4) (5) (6)

Dependent variable: Help Default Help Default Help Default

Explanatory variables:

Risk 1.14 (1.50) 4.06 (3.20) 6.19** (2.65)

Risk² -1.59 (2.50) -5.29 (4.47) -8.97** (3.98)

Other demands 1.06*** (0.17) 1.18*** (0.27) 1.30*** (0.26)

Honor loan 0.51*** (0.16) 0.58*** (0.21) 0.63*** (0.20)

Sent by a mainstream bank -0.56*** (0.19) -0.62*** (0.23) -0.67*** (0.22) ˆ

ρ1 0.19 (0.39) 0.26 (0.23)

Help -0.18 (0.17) -0.25 (0.37) 0.34 (0.29)

Male 0.51*** (0.19) 0.85*** (0.26) 0.65*** (0.23)

Education (# of diplomas) -0.13* (0.07) -0.15 (0.10) -0.23** (0.10)

Single 0.09 (0.19) 0.27 (0.26) 0.15 (0.21)

Unemployed at least 12 months 0.23 (0.18) 0.20 (0.28) 0.14 (0.20)

Household income (kEUR) -0.32*** (0.11) -0.48*** (0.16) -0.49*** (0.14)

Household expenses (kEUR) 0.64*** (0.22) 1.01*** (0.31) 1.00*** (0.29)

Low personal investment 0.31* (0.18) 0.39 (0.27) 0.36* (0.20)

Assets -0.02** (0.01) -0.03*** (0.01) -0.02*** (0.01)

Food and accommodation sector 0.21 (0.30) 0.46 (0.44) 0.35 (0.37)

Gross margin/Sales -0.90** (0.42) -1.07* (0.61) -0.82 (0.54)

ˆ

α2 -2.46 (1.95)

ˆδ 0.33*** (0.11)

Intercept -0.75*** (0.24) 0.04 (0.46) -0.97*** (0.37) -0.23 (0.64) -1.10*** (0.33) -0.37 (0.60)

-2 Log L 372 312 680 676

Observations 340 342 340 340

Standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1

We have estimated the Risk = Φ(w

β ˆ

+ v

) for each client in our data. 86% of the clients have an estimated risk smaller than 0.35 and 14% of the sample represent an estimated risk higher than this threshold. For these 14% of clients the likelihood to be assigned to a training program is decreasing with Risk as the MFI is worried about the negative impact help might have on their inferred type.

Concerning other controls in the help equation we observe a highly signicant positive relation between help and other demands and honor loan, which is in line with the intuition: individuals receiving help are more likely to apply for other demands as they may be encouraged to do so in their training process, and they are more likely to receive honor loans as they are disbursed by the training institutions. Being sent by a mainstream bank is negatively associated with the likelihood to be helped. Individuals sent by a mainstream bank are either rejected by the mainstream bank (and are likely characterized by a very high risk) or are granted a co-nancing credit by the mainstream bank (and are characterized by a very low risk). In both of these situations we expect these individuals to be the least likely to be assigned to a training program, due potential motivation undermining (for high risk individuals) or to the presence of a good performance which does not need help (for low risk individuals). ρ ˆ

is not signicant, suggesting that the endogeneity bias is not very strong between the help and risk equations. Nevertheless, a bivariate model taking into account the individual unobserved heterogeneity is preferred to univariate equations which do not account for individual heterogeneity.

Concerning risk equation, help decreases the likelihood to default in univariate specications and in the bivariate model without heteroscedasticity. However, this coecient is never signicant. In the bivariate model the coecient becomes positive, likely due to the presence of help dummy in the ρ

term as specied in equation 8 with a negative coecient α ˆ

. In spite the sign change, both (direct and indirect) loadings associated to help are not signicant. Male clients are signicantly more likely to default compared to female clients. This coecients is robust in all the specications.

Higher education (the number of achieved diplomas) signicantly decreases the risk of the clients

in specication 1 and 3. However, in column (6) the coecient should be interpreted with care

as it also enters the ρ

term as specied in equation 8 with a positive and signicant loading δ ˆ .

This estimate suggests that higher level of education will signicantly increase the variance of the

unobserved individual heterogeneity term, v

. In other words, there is less certainty about the

inferred type of borrowers with higher education. Household income and expenses are respectively

important negative and positive determinants of the likelihood to default. Borrowers with low

personal investment seem to be riskier in contrast to businesses with larger assets. Finally, the

gross margin to sales ratio is only signicant in the rst two models suggesting that this ratio is associated with lower business risk.

Overall the signs of the loadings are in line with economical intuition. A signicant non-monotonic relationship between the likelihood to be helped and the risk of the borrower emerges in the bivariate probit model accounting for heteroscedasticity. It concerns 14% of our sample.

In the next section we will perform several robustness checks to validate our main results for the looking-glass self eect. We perform three robustness check consisting in the inclusion of the business cycles, controlling for bias selection and dening an alternative measure of risk.

6 Robustness checks

6.1 Controling for business cycles

In this section we control for business cycles in the risk equation in bivariate probit model with and without heteroscedasticity. We do so by adding the lagged growth rate of defaults and new created businesses computed on a quarterly basis. Data used for business cycles

concern businesses grouped according to their economic sector and established exclusively in the region of activity of the MFI providing data. Indeed, the growth of default rates, representing a measure of the sector's economic health, and of new business start-ups, representing a measure of competition on the market can directly impact the risk of the businesses nanced by the MFI. Hence, we introduce 3 lagged growth rates for defaults and newly created businesses in the risk equation. The help process is still characterized by equation (6). Risk equation becomes:

P (y

= 1|w

, v

, y

) = Φ(w

β

+ y

α

+

3

X

q=1

ω

def ault

+

3

X

q=1

η

startup

+ ρ

v

) (9) where, for example, def ault

is the quarterly growth rate of defaults in the sector of the enterprise i which occurred one quarter before the enterprise i has defaulted, or one quarter before data extraction for performing loans, or one quarter before a loan has been fully repaid. Equivalently, startup

is the quarterly growth rate of new businesses created in the sector of the enterprise i which occurred three quarters before the enterprise i has defaulted, or one quarter before data extraction for performing loans, or one quarter before a loan has been fully repaid. The results of the estimation are presented in Table 3.

18Source: Fiben, Banque de France.

19We useρ2ifor the model with heteroscedasticity. Without heteroscedasticityρ2i should be replaced byρ2.

Table 3: Determinants of Help and Risk: Adding Business Cycles

Model Bivariate probit without Bivariate probit with heteroscedasticity heteroscedasticity

(1) (2) (3) (4)

Dependent variable: Help Default Help Default

Explanatory variables:

Risk 9.78 (28.49) 29.23*** (11.90)

Risk² -13.99 (44.19) -35.44*** (14.54)

Other demands 2.63 (5.88) 3.27*** (1.18)

Honor loan 1.42 (3.27) 1.95** (0.90)

Sent by a mainstream bank -1.41 (3.16) -1.43** (0.60) ˆ

ρ1 -2.48 (7.25) 0.39 (0.46)

Help 1.13 (0.71) 0.14 (0.24)

Male 1.38 (1.45) 0.87*** (0.13)

Education (# of diplomas) -0.29* (0.18) -0.17*** (0.05)

Single -0.06 (0.26) -0.02 (0.13)

Unemployed at least 12 months 0.02 (0.26) 0.05 (0.15)

Household income (in K euros) -0.50** (0.20) -0.40*** (0.10) Household expenses (in K euros) 1.26*** (0.39) 0.97*** (0.16)

Low personal investment 0.37 (0.48) 0.27 (0.17)

Assets -0.02 (0.03) -0.004 (0.003)

Food and accommodation sector -0.41 (1.28) -0.03 (0.18)

Gross margin/Sales -0.36 (0.75) -0.46 (0.29)

ˆ

α2 -14.41 (8.01)

δˆ -0.33 (0.37)

ˆ

ω1 0.07*** (0.01) 0.06*** (0.01)

ˆ

ω2 0.05*** (0.01) 0.04*** (0.01)

ˆ

ω3 -0.001 (0.01) 0.00 (0.01)

ˆ

η1 0.01 (0.02) 0.01 (0.02)

ˆ

η2 0.03* (0.02) 0.02** (0.01)

ˆ

η3 0.07*** (0.01) 0.05*** (0.01)

Intercept -2.19 (4.45) -0.70 (1.07) -4.94** (2.11) -0.18 (0.36)

-2 Log L 519 521

Observations 340 340

Standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1