A microfinance institution (MFI) operating in rural India is interested in measuring the impact of an individual receiving one of its loans on the future income of the individual. The MFI offers its loans to all qualified borrowers in the region, though not all potential borrowers do in fact take a loan. The MFI observes which individuals in the region takes a loan and then uses gender, age, pre-loan income, occupation, and family size to compute a propensity score for a random sample of individuals in the region, some who have taken a loan and some who have not. A subset of the data collected, including income two years after being offered (and potentially receiving) a loan, is show here:
|
Individual ID
|
Received a Loan?
|
Income (2 years after loan offer)
|
Propensity Score
|
|
1
|
No
|
$2,000
|
0.95
|
|
2
|
No
|
$3,000
|
0.70
|
|
3
|
Yes
|
$2,000
|
0.90
|
|
4
|
Yes
|
$5,000
|
0.85
|
|
5
|
No
|
$3,500
|
0.60
|
a. What is the meaning of these propensity scores? Be precise.
b. Using only these data, use propensity score matching (inexact) with replacement to compute an estimate ofthe average treatment effect on the treated (ATET), wherethe treatment is receiving a loan and the outcome of interest is income after twoyears.
c. Aside from the small sample size, explain one other concern you have with regard tothe validity of thisestimate. Bespecific.