Testing for risk homogeneity in groups: results and discussions

Next, equation (10) is estimated using the heterogeneity measure calculated in section 4.4.2 as the dependent variable. As indicated earlier, this measure proxies how far individual borrowers’ observed risk varies from their partners’. The main interest in this chapter is to investigate whether the observed heterogeneity is entirely explained by matching frictions or whether optimal risk also plays a role, violating the homogenous risk matching hypothesis. Again, because of the censored dependent variable, we estimate a Tobit model of the reduced form equation in (10). To see if the censoring of the heterogeneity variable has an effect on our distribution, the uncensored heterogeneity measure is also estimated using OLS.

A problem that was also noted by Sadoulet and Carpenter (2001) is measurement error in the predicted values for optimal risk and matching friction. If measurement error in these proxy variables is present and substantial, it leads to biased estimates. Since any proxy variable introduces some measurement error, the question is basically how good these proxies are. Since our four indicators for matching frictions all indicate knowledge on (potential) partners we think that a prediction based on these four variables gives a good proxy for matching frictions with minimal measurement error. Also note that the test on the homogeneous risk matching hypothesis is performed on the parameter γ for optimal risk in equation (10). Therefore, in testing for this endogeneity problem using a Durbin-Wu- Hausman test (Verbeek, 2008:144) and potentially solving for it we concentrate on the optimal risk proxy _ˆ*

i

Testing and solving the potential endogeneity problem due to measurement error requires a set of variables that can serve as Instrumental Variables that are both valid and not weak. Validity implies that potential instruments are not correlated with the measurement error or measured with error themselves. Instruments are considered not to be weak when they strongly correlate with the variable to be instrumented, reflected in an F-test value exceeding 10 in the first-stage regression (Murray, 2006). The first requirement cannot easily be assessed and requires careful selection of instruments. Based on these considerations we choose two variables as instruments, i.e. households’ self evaluations of their wealth status compared to people in their neighbourhood and their spread in agricultural plots. The first instrument indicates household’s perceived ability to cope with risk and equals one if the household perceives it has a good wealth status and is zero otherwise. Spread in agricultural plots is also related to risk since one way of diversifying production risk (e.g. due to rainfall, flood, locust) in these areas is by having plots in different geographical locations. This instrumental variable indicates the extent of household’s agricultural plot diversification and is equal to one if less-diversified and zero otherwise. Both variables are easily measured without errors, while at the same time not correlated to potential errors of the heterogeneity (dependent) variable. Regressing the first-best proxy for risk _ˆ*

i

θ on these two variables

indicates that both are significantly related at the 5% level with an overall F-test value of 48.67, indicating that these instruments are not weak and can be used as instruments and to perform the Durbin-Wu-Hausman test. The Durbin-Wu-Hausman test indicated that the null hypothesis of exogeneity of the first best risk proxy _ˆ*

i

θ could not be rejected (p-value 0.88), indicating that measurement error is not a problem for this proxy variable. Results of Tobit, OLS and the (less efficient) IV estimation of equation (10) are given in table 4.3.

Estimates of the Tobit, OLS and IV models all show that the parameters for matching frictions and optimal risk are significantly different from zero, indicating that the observed heterogeneity is explained by both matching frictions and optimal risk choice. In fact, under all estimators, the optimal risk parameter is highly significant.

Table 4.3 Tobit estimates of risk heterogeneity

Variables Tobit OLS IV

Optimal Risk ( *) i θ) 0.738 (0.131)** 0.679 (0.119)** 0.706 (0.232)** Matching Friction (f)) 1.042 (0.469)** 0.981 (0.486)** 0.997 (0.442)** Intercept -0.356 (0.070)** -0.324 (0.078)** -0.338 (0.124)** Tobit, F(2,199); OLS, F(2,198) 16.09** 16.35** 5.56** N 201 201 201

However, matching frictions also matter. This implies, contrary to the commonly held view, that credit groups in group lending are formed among members of different risk types not only because members fall short of finding their perfect match but also because it is to their best interest to do so. Our result does not come as a surprise, given similar previous findings by Sadoulet and Carpenter (2001) and Lensink and Habteab (2003). Using data from a rural area our results supplement these findings and provide more empirical support to the theory posed by Sadoulet (1999) that states that risk heterogeneity might also be an optimal choice instead of being due to matching frictions.

OLS results indicate that the censoring has some effects on parameter estimates but not on their significance. IV estimates are rather similar to the OLS results, as was expected since the Durbin-Wu-Hausman test already showed absence of endogeneity due to measurement error. In view of the theoretical (e.g. Armendáriz De Aghion and Gollier, 2000) and empirical (e.g. Van Tassel, 2000) insights (see section 4.1), and given that our data comes from a rural setting where borrowers are expected to be less mobile with observable economic activities and anonymity is less likely compared to an urban setting, the result presents interesting as well as challenging questions regarding credit group formation. An important question is, apart from matching frictions, why groups are formed risk heterogeneously rather than risk homogeneously. In line with Sadoulet’s (1999) and Guttman’s (2008) theoretical insights, Sadoulet and Carpenter (2001) find some evidence from their (semi-) urban setting that this might be due to missing insurance markets in the area. They suggest that it may be optimal for those looking for insurance due to risk of failure and loss of future borrowing to arrange side-payments (e.g., labor) with those that are able to cover all group debts in case of failure. Therefore, our survey also included questions on such forms of side-payments among group members. However, only four households in the sample reported having such exchanges with group partners. This is small compared to those who had repayment problems, when such an arrangement could have helped to solve it immediately. Thus, based on respondents’ direct reports, there is not enough evidence to conclude the insurance-side- payments claim holds among our borrowers.

Observation from key informants during the survey however reflects group members often engage in some form of traditional networks such as Equb (ROSCA) or other traditional and religious gatherings (e.g., tsebel or mahber)5. The descriptive analysis also shows nearly 40 percent of the respondents who are members of Equb are at the same time members of a credit groups.In fact, suchnetworks are part of the group formation processes and provide the foundation for establishing trust or are in some way linked to borrowing and saving practices of borrowers. In several of the sample sites, particularly those closer to the village towns, borrowers engaged in petty trade activities reported they often synchronize their group credit

5_{Tsebel and mahber are religious gatherings, not necessarily, of the same neighbourhood or socioeconomic} status, that include monthly sainthood-services and festivities common in Tigray; reciprocal in nature, where every participant is duty-bound to serve.

repayments to the allocation of the ‘Equb pot’. Studies (e.g. Besley et al., 1993, 1994) show that the ROSCA pot can be allocated either by random (drawing lots) or by bidding. A different type of the ROSCA in which allocation of the pot is made ‘by consensus’ among members is witnessed in the study area. The explanations for the existence of this type of ROSCA are beyond the scope of this chapter. However, it may be that the ‘consensus’ is explained by cooperative behaviour and trust developed over the years more than the ‘insurance-side-payments’ claimed to be associated with wealth or risk differences observed in credit groups. In the next section, we examine if these elements of social networks can partially explain the probability of individual borrowers’ repayment, which in turn provide insights into the role they play in credit groups.