When we use PSM in a DiD setting, normally, we match the variables before the event (pre-event period). However, is it legitimate to match a covariate that captures the change before and after the event?
For example, we have a DiD model:
Cost of capital = Treated + Post + Treated*Post
Treated and controls are PSM matched. The event under research could cause two effects: an increase in production and an increase in customer satisfaction. We would like to focus on the effect of the increase in customer satisfaction and isolate the effect of the increase in production.
We are considering creating a variable measuring the change in production from before to after the event for each firm and including this variable of production change as an additional covariate in PSM. With this approach, we require the treated and control firms to have a similar change in production around the event, and thereby the effect of the event on the cost of capital can be attributed to the increase in customer satisfaction. Is it legitimate to use the production change as the covariate?
For example, we have a DiD model:
Cost of capital = Treated + Post + Treated*Post
Treated and controls are PSM matched. The event under research could cause two effects: an increase in production and an increase in customer satisfaction. We would like to focus on the effect of the increase in customer satisfaction and isolate the effect of the increase in production.
We are considering creating a variable measuring the change in production from before to after the event for each firm and including this variable of production change as an additional covariate in PSM. With this approach, we require the treated and control firms to have a similar change in production around the event, and thereby the effect of the event on the cost of capital can be attributed to the increase in customer satisfaction. Is it legitimate to use the production change as the covariate?
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