Question

Assume that we are studying a microcredit lending program. We find that before we begin the intervention that household income for the treatment group is $130/month while household income for the control group is $135/month. We also see that one year after the intervention, where everyone in the treatment group took out a loan, that the income for the treatment group is $175/month and for the control group it is $140/month.

a. What would we have estimated the impact of the program to be if we only used a before-after (pre-post) approach to constructing the counterfactual?

b. What would we have estimated the impact of the program to be if we only used a simple-difference approach to constructing the counterfactual?

c. What would we have estimated the impact of the program to be if we used our random assignment to construct the counterfactual? (Assume that the groups are actually balanced at baseline, with both having an income of $120 a month to start)

Answer 1

a) We would have estimated the impact of the program to be simply,

Post_treatment - Pre_treatment = 175-130 = $45 which ignores any sample bias or the time trend associated with the program.

b) A simple difference in difference approach yields the result that the true impact of the program is,

( Post_treatment - Pre_treatment ) - ( Post_control- Precontrol) = (175-130) - (140-135)

= 45 - 5 = $40

c) Had we used random assignment to construct the counterfactual, the true impact of the program would be given by

Post_intervention - Pre_intervention = 175-120 = $55

There is no need to use DiD approach since the people are assigned randomly and they all have same baseline income before intervention.