# Zero-inflated Poisson regression with unit and time fixed effects (Application in R)

In much need of some assistance.

My question concerns the conceptualization of zero-inflated Poisson regression in a two-way fixed-effects settings. I have crime data and my outcome is 'count' distributed. My cross-sectional unit is the district/precinct and I observe 'counts of crimes' by month in each of those units. I am evaluating a government intervention that is 'in effect' for only a few months throughout the year.

I include "precinct" and "month" fixed effects (i.e., a full set of precinct and month dummies enter the model). I have only one independent variable I am assessing.

Here is the set-up in R:

m1 <- zeroinfl(crime ~ intervention + as.factor(precinct) + as.factor(month_year) | 1, data = DATASET, dist = "poisson")


This was described to me as a model with "simple inflation" as there are no regressors for the zero component. It's computationally intractable to include all the unit and time dummies for both components (approx. 40 for the districts/approx. 50 for the months).

Questions:

1. What does "simple inflation" mean and does it make sense to model the count component in this rather simple way?
2. Do the same regressors "have" to be on both sides of the $$|$$ for this to be worth running?

Any thoughts?