Estimation Method

I estimate the model in (2.33) using different empirical specifications. The empirical model is inherently dynamic as a result of history dependence. Estimating such model poses a number of challenges. These include selecting the appropriate estimation method, endogeneity, initial conditions problem, interdependence of transfer behavior among senders of different social distances, and censoring of transfer amount due to corner solution. These issues warrant a brief discussion.

The main candidates when dealing with endogeneity due to unobserved individuals ef- fects is the FE approach, which wipes out such bias without imposing restricted distributional assumptions. However, when the model is dynamic with short panel FE estimate is bias and inconsistent. Nickell (1981) derived the analytical expression for the degree of bias and shows that the bias is especially sever when T is small. For this reason, the common approach in the literature is to use dynamic RE models. However, RE method also suffers from biases if the unobserved individual effects are correlated with covariates and misspecification. Besides imposing a restrictive distributional assumption we also need to deal with initial conditions problem. In line with the Mundlak (1978b) and Chamberlain (1982) approach, Wooldridge (2005) proposed a simple method to deal with endogeneity arising from correlation between

lagged dependent variable and the contemporaneous error term as well as initial conditions problem. The method is parametric and estimable using standard software routines such as Stata. In the realm of this framework, the unobserved individual effects term is allowed to be correlated with some of the covariates and the initial dependent variable, which is given by

αj =θ1τj0+θ2xj +uj, (2.34)

where uj ∼ n(0, σu2), τj0 is the initial log of transfer, xj is a vector of over time mean

of selected time varying covariates. Since pre-survey information is not available, I use the log of transfers in the first round as a proxy for initial conditions. Such approach minimizes the initial conditions problem and biases arising from the correlation of unobserved individual heterogeneity with some of the time varying covariates. Therefore, the first I estimate specifications (2.33) with (2.34) using linear dynamic RE method for log of total transfers from informal sources (non-resident family member, relatives, friends, neighbors, and members of informal savings and credit associations (Iqqub and Iddir).

As discussed in the theoretical section since altruism and social norms might play im- portant role, the model should account for different social distances. This could be achieved by estimating separate regressions for transfers from Sender Type 1, Sender Type 2, Sender Type 3 and Sender Type 4. However, transfers from one network type could depend on the other. For instance, a relative may adjust the amount of transfer she makes if a non-resident family member is making a transfer and vice-versa. Or a household seeks help from Sender Type 2 because Sender Type 3 refused to or could not make transfers. For these reasons, the third specification estimates a SUR model which explicitly allows for transfers from different sender types to be correlated. This specification is given by

τmj,t =αmj +β1mτmj,t−1+ X m6=n β2nτnj,t−1+β3myvt+β4myjt+β5mSjt +β6mH˜jt +γmXjt+mjt, (2.35)

where τmj,t is the logarithm of transfer amount made from sender type m = {1,2,3,4} , m = 1 denotes transfer from non-resident family member, m = 2 denotes transfer from a relative, m = 3 denotes transfer from a friend, a neighbor, or informal associations such as Iqqub orIddir and others, andm = 4 denotes transfers from benevolent institutions such as church, mosque, government or non-government aid organizations. The potential correlation between the decisions of different senders can now be handled through the correlation of error terms as follow

jt ∼N4[04×1,σ4]

and

αmj =θm1τmj,0+θm2xmj +umj, (2.36)

where jt is a 4×1 vector of error terms for household j, σ is the covariance matrix and σmn is the covariance between transfer decision made by sender type m and sender type n.

Then this model can be estimated using Stata routine (xtsur) provided by Nguyen (2008). The last estimation issue is that censoring due to corner solutions, which is common in many applications including hours worked, charitable contributions, etc. In our case, there is significant “pile-up” of transfers at zero because for about 80% of the observations transfers are zero. Such kind of censoring results in exaggerated slope estimates commonly referred to as expansion bias (Rigobon and Stoker, 2007). This implies exaggerated estimates of the slope coefficient on the lagged dependent variable, which is also censored. In the spirit of the approach in Wooldridge (2005), Li and Zheng (2008) propose dynamic Tobit using Semiparametric Bayesian approach in a single equation problem. Although, the dynamic Tobit model is a better approach to deal with censoring there are no standard software routines available to estimate the SUR version of it.

Hence, in this paper, for the sake of comparison of the coefficients across single equation estimates and SUR estimates as well as simplicity, the main approach is the linear dynamic RE method. Linear estimation method is also the approach adopted in similar studies such as

De Weerdt and Fafchamps (2011). However, cognizant of such problem I conduct sensitivity analysis by estimating single equation Linear Probability Model using binary dependent variables and panel Tobit model.