Dropped treatment effect in two-period Difference in Difference Model

[shivansh raman]

Hi, I'm looking at the effect of city budgets on corruption for an assignment. We have two periods 2001 and 2005 so I'm considering the budget in 2001 as the continuous treatment with city and period fixed effects. When I run the following code

gen initial_budget = budget
replace initial_budget = l4.budget if term==2005
areg outcome initial_budget i.term, absorb(city) cluster(city)

The treatment is being dropped due to multicollinearity. Are there alternative ways of coding this or framing the treatment different. Sorry for the basic question!! Thanks in advance!!

[George Ford]

Every city has a budget, so it is not a treatment. For DID, you need 2 periods and 2 groups, both untreated in t0 and one group treated in t1.

[shivansh raman]

Thank you!! Would a dummy for increase in budget over the two periods make sense as a treatment? The budgets are mostly determined according to population categories so we have 7 initial population categories of which some might jump to a higher one due to population growth. Does that creates variation we might plausible exploit via DiD?

[George Ford]

Generally not a good idea to dichotomize a continuous variable. Where would you cut it and why?

And, the question arises whether corruption increases the budget, or does the budget increase corruption? The budget is not exogenous. This is a problem both in a DID or x-sectional analysis.

Tricky problem. Not obvious offhand how to fix it, but there may be a way.

Might start here:

https://www.jstor.org/stable/24027637