Propensity Score Matching Model Specification

The major challenge in estimating the impact of microcredit on SME performance is obtaining a reliable estimate of counterfactual outcomes - what would have happened to those who received microcredit if they had not received it. PSM is a common method to estimate causal treatment effects. The use of the propensity score-matching method is to correct for sample selection bias because of observable differences between the treatment and control groups. The fundamental idea of PSM is to match participants and non-participants with identical observable characteristics (

X

). The three pillars of this model are the individual who is SME

i

; treatment which takes the binary treatment

D=1

if the SME received microcredit and 0 otherwise; and the potential outcomes. The impact of a treatment on SME

i

, can be written as:

(4.28)

In the literature, two parameters are most commonly used for estimation (Caliendo & Kopeinig, 2008). First, the average treatment effect (ATE), which can be defined as the difference between the expected outcome of treated and control observations (Caliendo & Kopeinig, 2008). Second, the average treatment effect on the treated (ATT), which is the difference between the outcome of treated and the outcome of the treated if they have not been treated. To illustrate:

(4.29)

16 _{SMEs were asked how many full-time workers they employed; casual or part time workers are not included.}

1 0 i

Y

i

Y

i



=

−

(

1

| ,

1)

(

1

| ,

0)

1

ATT PSM

E Y X D

E

X

E Y X D

D



=

= −

_

=

= _

81 This study focuses on the ATT parameter (Ghalib, Malki, & Imai, 2014; Peprah & Ayayi, 2016; Silva, 2012). The estimation of ATT must satisfy two underlying assumptions:

Conditional independence : This assumption is also known as unconfoundness or

selection of observables; it requires that all variables relevant to the probability of receiving the treatment be observed and included in . This allows the untreated units to be used to construct an unbiased counterfactual for the treatment group.

Common support or Overlap : This implies that, for each value of , there is a

positive probability of being both treated (microcredit borrower) and untreated (non-borrower). This assumption of common support ensures that there is sufficient overlap in the characteristics of treated and untreated units to find adequate matches. SME that fall outside the common support region will be discarded and for these SME the treatment effect will not be evaluated.

The treatment assignment is said to be ‘strongly ignorable’ when both these assumptions are

satisfied (Rosenbaum & Rubin, 1983).

Additionally, using the same survey questionnaire for the treatment and control groups and selecting them from the same locality can make PSM produce low bias estimates (Dehejia & Wahba, 2002). The identical observable characteristics between the treatment and control groups raises the

likelihood of getting matches and hence reduces bias. In addition, potential bias such as non-random placement and self-selection on observed characteristics in participation of microcredit, can be controlled using the PSM method.

In assessing the impact of the microcredit programme on SME performance, this study follows the impact evaluation framework proposed by Oh et al. (2009) whose study evaluated the effect of credit guarantee in the Korean manufacturing sector using propensity score matching. Our estimation strategy is based on comparing the treated and non-treated SMEs. The PSM method includes the following steps.

First, divide the observations into two groups; the SMEs that borrow microcredit are considered the treatment group and SMEs that did not borrow as the control group. Let D= 1 denote the treated observation and D = 0 the control observations. Second, estimate the binary outcome model; this study uses the logit model for the propensity of observations to be assigned into the treated group. The variables such as owner characteristics, SME characteristics and networking may affect the

(Y Y

1

,

0

)

D X|

X

0 < P(D = 1|X) < 1

_X

i

i

82 likelihood of being assigned into the treated group. Third, match the observations from the treated and control groups based on the propensity score. Several matching methods are available such as kernel, nearest neighbour, radius and stratification. This is to find the best possible match for the treated observations. To show the robustness of the estimation, this study applied kernel matching with replacement and radius matching for the comparison to evaluate the impact of microcredit on SME performance using cross sectional data. Kernel matching is used to match all the treated group with a weighted average of all the control group with weights that are inversely proportional to the distance between the propensity score of treated and controls (Arun, Imai, & Sinha, 2006). Radius matching uses the weighted average of all individuals in the control group within the default radius of 0.01. After matching, the unmatched respondents are discarded and not used for further analysis to estimate the impact of the treatment. Fourth, calculate the average treatment effects by

comparing the outcomes y between the treated and control observations after matching:

(4.30)

Where; is the outcome for treatment group (SMEs with microcredit) and is the outcome for control group (SMEs without microcredit)

The coefficient of the average impact of treatment on the treated microcredit scheme 𝛿_𝑃𝑆𝑀𝐴𝑇𝑇 _is

obtained using the propensity score matching method, based on equation (4.29) and rewritten as:

(4.31 Where:

Variables Variable indicators

Outcome of interest (SME performance) –sales growth and employment growth, Log differences between 2012 and 2014, e.g., log (Total Sales 2014)–log (Total Sales 2012)

is microcredit participation;

= 1 if SMEs with microcredit; =0 otherwise.

Covariate of the observed factors including SME owner/manager characteristics (gender, age, marital status, and financial training); number of income earners; SME characteristics (age of enterprise, ownership type and sector).

1 0 1 0 y if D y y if D =  = ₌  1

y

y

₀

(

1

| ,

1)

(

1

| ,

0)

1

ATT PSM

E Y X D

E

X

E Y X D

D



=

= −

_

=

= _

1

Y

D

D

D

D

X

83 The expected value of ATT is defined as the difference between the expected outcome values with and without treatment for those who participated in the treatment (Caliendo & Kopeinig, 2008). To control for selection bias based on observable factors, a set of covariates ( )X was included. The set of controlling covariates should meet the conditions of the matching controlling variables.

The shortcoming of the PSM model is addressing the issue of selection bias by controlling for only observable factors (Dehejia & Wahba 2002). The PSM method fails to account for time invariant unobservable factors when addressing the issue of selection bias. Since panel data are available for the outcome indicators, the Difference-in-Difference (DID) method is used and is discussed in the next section.

In document Accessibility to microcredit and its impact on small and medium sized enterprises' performance in Malaysia (Page 91-94)