Econometric strategy

In a linear-in-means model, the identification of peer effects on the total monthly perfor- mance of an individual CKW within the context of social interaction is a nuanced process. Endogeneity in the performance of peers resulting from simultaneity in peer interactions often creates difficulty in the identification of peer effects. This is the reflection problem discussed by Manski (1993).

However, advances in social network analysis such as Moffitt (2001); Cohen-Cole (2006), provide rich methodologies to adjust the linear-in-means model and obtain the identification of peer effects. For instances, Bramoull´e, Djebbari, and Fortin (2009) show that an extension of the linear-in-means model separates peer effects from those of social interaction by sepa- rating the endogenous effects from exogenous effects. The analysis relaxes the assumption of group interactions among peers in a social networks setting (Bramoull´e, Djebbari, and Fortin, 2009). Bramoull´e, Djebbari, and Fortin (2009) empirically use this approach on the US adolescents health (Ad health) data set to identify peer effects in the consumption of recreational services among young adults in 2009.

The method has become popular for studies on peer effects in divers settings including those pertaining to agriculture. For example, Krishnan and Patnam (2014) use it to separate the effects of extension services on the adoption of agricultural technology in Ethiopia, from the peer effects among farmers in the same setting. Similarly, De Giorgi, Pellizzari, and Redaelli (2010) apply the approach to identify peer effects among college students in a University setting in Italy. Further, Fortin and Yazbeck (2011) use the methodology on the add health data set to identify peer effects in weight gain among US adolescents.

3.4.1

Theoretical model

The theoretical model for this analysis carefully follows the theoretical model of Bramoull´e, Djebbari, and Fortin (2009). It consists of a stylized version of the linear-in-means model to disentangle peer effects (i.e endogenous social effects)from exogenous social effects in the context of social network analysis (Bramoull´e, Djebbari, and Fortin, 2009). The approach solves the reflection problem identified by Manski (1993). I posit that each individual ex- tension worker (i.e., CKW) has a peer group whose average performance and characteristics influence his own outcome. I represent vectors by bold, lower case letters, and matrices by capital letters. For a set of CKWs i, (i = 1, ...,n); y_i represents the total monthly perfor- mance (measured by the total number of searches recorded per month). xi = 1 × k vector

of characteristics of i. Peer groups are CKW-specific. Thus, each i, belongs to a particular peer group Pi, with size, ni. Moreover, a peer group contains all CKWs whose monthly

performance or background characteristics may affect the total monthly performance of i. I consider each district as a local network (with constituent of peer groups) in which interactions are structured among CKWs. The network of districts are partially overlapping in that a CKW i in district “A” might interact with any CKW j in district “B”. A CKW i is excluded in the computation of the mean (average) total monthly performance of his/her peers. Specifically, i /∈ Pi. i.e., each CKW is excluded from the peer group averages, Pi.

Three kinds of outcomes are consistent with this model. First, there is endogenous social effect - wherein the total monthly performance (yi) of each CKW is influenced by the average

monthly performance of his peers. This is known as the influence of peers on peers. Second, there is exogenous (contextual) effect - wherein the total monthly performance of each CKW is influenced by the mean (average) characteristics of his peers (i.e., peer characteristics). Third, there is correlated effect - the influence of a common institutional factor on peers. For instance, the effectiveness of the cellphones and the equipment (ready-sets) supplied to CKWs by Grameen APLAB might determine the total monthly performance of a particular

set of CKWs. For instance, if CKWs in district A receive better functional cellphones and equipment than their counterparts in district B, then total performance in district B will lag behind that of district A.

From the theoretical model, there are divers ways by which the effects of peers could be communicated in the context of CKW operations in the this setting. For one, individual CKWs can learn from one another through information exchange on the cellphones they use for their work activities, about how to optimize their performance in order to get the highest monthly remuneration. Moreover, CKWs might benefit from information from peers (or neighbors) about the best approach to reach more farmers, or how to better operate their working equipment (such as during rainy seasons when the ready-set often malfunction due to contact with rain water).

3.4.2

Structural model

The structural model proceed thus;

yi = α + β X j∈Pi yj ni + γxi+ δ X j∈Pi xj ni + i, E[|x] = 0. (3.1)

Where β captures the endogenous effect; δ is the exogenous effect. It is standard to assume that |β| < 1 i reflects unobservable characteristics in the model. The regressors are strictly

exogenous. i.e., E[|x] = 0, where xi is an n × 1 vector of individual CKW characteristics

(such as age, gender and marital status). Hence, I assume no correlated effects in this setting. Moreover, I use the standard assumption that for all j in J, the characteristics of individuals are similar (or common) in each network of neighborhood peers. Thus, all xij

The matrix version of the structural equation gives;

y = αι + βGy + γx + δGx + , E[|x] = 0, (3.2)

Where y is an n×1 vector of the total monthly performance of individual CKWs for the entire network l ; ι is an n × 1 vector of ones; x is an n × k vector of observed own characteristics of individual CKWs; G is an n × n interaction matrix (i.e., weights matrix) representing the relationship between any two CKWs, wherein Gij = 1_{n i} if CKW i is a peer of j, and

0 otherwise. This equation is a spatial auto-regressive (SAR) model with provision for an exogenous social effect term (i.e., δGx). Since (I − βG) is invertible, the restricted reduced form equation follows thus;

y = α(I − βG)−1ι + α(I − βG)−1(γI + δG)x + (I − βG)−1. (3.3)

I assume heteroscedasticity in the variance of the error term, and also that errors are inde- pendently and identically determined (iid).