where τ is the average treatment effect for the treated (ATT), R1 denotes
the value of the outcome for household participating in community forestry
and R0 is the value of the same variable for non-participating
households. As noted above, amajor problem is that we do not observe
E(R0|I=1). Although the difference [τe=E(R1|I=1)−E(R0|I=0] can
be estimated, it is potentially a biased estimator.
In the absence of experimental data, the propensity score-matching
model (PSM) can be employed to account for this sample selection bias
(Dehejia andWahba, 2002). The PSMis defined as the conditional probability
that a farmer adopts the new technology, given pre-adoption
characteristics (Rosenbaum and Rubin, 1983). To create the condition
of a randomized experiment, the PSM employs the unconfoundedness
assumption, also known as the conditional independence assumption
(CIA), which implies that once Z is controlled for, participation in community
forestry is random and uncorrelated with the outcome variables.
The PSM can be expressed as: