Estimation Strategy

The PSM method has been specifically designed to assist researchers in drawing causal inferences in observational studies. The propensity score is a conditional probability that an individual is assigned to the treatment group (Rosenbaum and Rubin, 1983). Generally, it is estimated by using probit (or logit) regression with the covariates collected from the participants as X and participant's status on the treatment variable as Y (Rosenbaum, 1987). The covariates in the probit model are non-treatment variables such as the participant's background characteristics. The estimated propensity score abstracts the information of these covariates. Using such estimated propensity scores, a researcher can match a participant from the treatment group with a participant from the control group to facilitate causal inference.

The use of PSM methods in economics is relatively new. Previous papers include Heckman et al. (1998), Friedlander, et al. (1997), and Dehejia and Wahba (2002). As Dehejia and Wahba (2002) point out, PSM can be invaluable for cross-sectional survey data. In such a setting, resurveying thousands of units at a later date might be costly, making data on the outcome variable for a comparison group difficult to obtain. An important feature of this method is that, after units are matched, the unmatched comparison units are discarded and not directly used in estimating the treatment impact.

Using the propensity score, a researcher can match participants from the treatment group with participants from the control group, so that the treatment group and control group can be balanced. This approach can significantly reduce bias in observational study (Rosenbaum, 1987, 2004; Rosenbaum and Rubin, 1985; Rubin and Thomas, 1992).

Ideally, the households representing one matched pair are identical to each other except for their borrowing from Khushhali Bank. As a consequence, this approach isolates the impact idiosyncratic factors have on outcome variables by reducing observed heterogeneity between KB borrowers and nonborrowers.

Since the true propensity score is unknown, a model-based estimation procedure has been developed (Rosenbaum and Rubin, 1984, 1985). The broadly used probit model for the propensity score is a multi-step approach: (1) selecting the powerful covariates that distinguished the treatment and control groups the most; (2) including the selected covariates and their interaction in a one-equation probit model to estimate the propensity score, using the maximum likelihood method; and (3) using the estimated propensity scores to match treatment and control groups or stratify these two groups into equivalent subclasses. This procedure may include the stepwise model selection, with repeating step (1) to step (3) until the closest treatment and treatment groups are achieved.

After the propensity score is estimated, different algorithms can be employed in order to identify matching partners (Rubin, 1974). The Nearest-Neighbor Algorithm is the most applied algorithm, so we used this algorithm in our estimations.

In this paper, the PSM is based on comparing borrowers to nonborrowers within the same area. A key assumption is that the characteristics of people that enter programs are unchanged over time, and the method should control for the fact that borrowers are not a random group of people.

After identifying the matching partners, the channel effect and the self-selection effect can be determined. As was mentioned earlier, the purpose of the matching approach is to estimate the counterfactual outcome and therefore to correct for the selection biases created by nonrandom sampling of the microfinance program participants (Dehejia and Wahba, 2002). As a consequence, the counterfactual outcome represents the indicators of KB borrowers' wellbeing after accounting for selection biases. This is explained by the fact that matching KB borrowers and nonborrowers based on those variables that influence their participation corrects for the non-random sampling of the borrowers. Thus, the average well-being of KB borrowers before matching still includes self-selection, whereas the average profitability after matching does not.

In this paper we concentrate on estimating the average effect of treatment on the treated (ATT). This parameter estimates the average impact among Khushhali Bank borrowers and is defined as:

Δ^{ˆ ATT} =E[Y¹D=1]−E[Y⁰ | D=1]

where Δ^{ˆ ATT} : Estimated Average Treatment-on-Treated effect,

Y¹: Program participation

Y⁰: Program non-participation

D=1: KB borrower

D=0: Nonborrower

E[Y¹D=1] :Expected outcome after borrowing from KB

E[Y⁰ | D=1] :Hypothetical outcome without borrowing from KB for those who borrowed from KB

Since the counterfactual outcome for those being treated - E[Y⁰ | D=1] - is not observed, a researcher has to choose a proper substitute in order to estimate ATT. If the condition E[Y⁰ | D=1] = E[Y⁰ | D=0] holds, we can use the nonborrowers as a control group. However, due to the self-selection bias, the above condition will not hold; therefore, we use propensity score distribution of participants to estimate the unobservable component.

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