Title: DiD model with staggered adoption and interaction term — sanity check

[Lila Sharma]

Hi all,

I'm working with panel data (U.S. states from 2000–2010) and estimating the effect of Castle Doctrine Laws (CDLs) on burglary rates. The laws were passed in different years across states, so I'm using a staggered adoption DiD design.

I'm also interested in how the effect of CDL varies depending on the unemployment rate in each state-year. Here's what I’ve done:

1. cdl is coded as 1 for a state after it adopts the law, 0 otherwise
2. I generated an interaction: gen cdl_unemp = cdl * unemploy

Model:
xtset state_id year
xtreg burglary cdl unemploy cdl_unemp i.year, fe cluster(state_id)

My interpretation is:

• cdl captures the average effect of the law on burglary when unemployment = 0 (baseline)
• cdl_unemp tells me how that effect changes with higher unemployment
• State and year fixed effects should control for baseline differences and national shocks, so this works like a DiD setup with staggered treatment timing

My question: Does this seem like a reasonable way to estimate a heterogeneous DiD effect based on unemployment? Am I missing anything (e.g., need for region-by-year FEs or event study)?

Thanks in advance — really appreciate any feedback or corrections!

[Jeff Wooldridge]

Kind of looks like a homework assignment ….