Staggered DiD with unbalanced panel data and "cumulative" dependent variable

[Marco Di Luca]

Hi everyone,

I’m conducting an analysis on the impact that receiving a Michelin star has on the opening of new business ventures associated with a restaurant. The database covers the full history of each restaurant, from its opening year (which varies by restaurant) to the present. It includes the number of associated businesses in each year, the year (if any) in which the restaurant received a star, its location, and the type of ownership. There’s also a 1:1 control group consisting of restaurants that were never included in the guide but are otherwise similar to the treated ones.
At the moment, I’m considering a Difference-in-Differences (DiD) approach. I started with a classical 2x2 DiD, using a window of two years before (to account for potential anticipation effects) and five years after the treatment for each restaurant. However, this approach is overly simplistic since the year of treatment (i.e., when the star is awarded) varies across restaurants, which introduces well-known identification issues. I'm therefore considering the Callaway and Sant’Anna ATT estimator, which allows for an event-study-style analysis and better handles the staggered nature of the treatment.
My main concerns revolve around
• the staggered timing
• the unbalanced nature of the panel some restaurants have data covering the full observation period (e.g., one opened in 1960 with treatment in 2009 has data from 2000 to 2024), while others like one opened in 2007 lack earlier years. I can't simply fill in missing pre-opening years with zeros for diversification, as that would bias the analysis.)
• the dependent variable: the number of business ventures is cumulative, meaning it either increases or remains constant. One possible solution is to use the year-over-year difference, but the numbers are very small, and I’m worried about losing meaningful signals.

Any suggestions or references to similar work would be very welcome.

[Jeff Wooldridge]

jwdid works well with unbalanced panels and staggered interventions. I might define the outcome as new entities in the period, and use Poisson regression. Or create a binary variable for any new entity. When I’m at my computer a can send a link to a shared Dropbox that has examples.

[Marco Di Luca]

jwdid works well with unbalanced panels and staggered interventions. I might define the outcome as new entities in the period, and use Poisson regression. Or create a binary variable for any new entity. When I’m at my computer a can send a link to a shared Dropbox that has examples.

Hi Jeff,

Thank you very much for your help, being able to look at the Dropbox examples would be incredibly useful. Could you share the link when you have a moment?

A quick question on jwdid: does it have a built-in option for producing event-study style plots (similar to the ones in the did R package at https://github.com/bcallaway11/did), or is it better to export the ATT estimates and graph them separately?

For context, my dataset is a small, unbalanced panel with the following columns:

• year
• restaurant_id
• treatment_year
• diversification (cumulative count of affiliated ventures)
• delta (difference between diversification of current year and year-1)
• control variables (e.g., indicator for large city, ownership type, etc.)

Given the limited sample size (typical in management studies) do you foresee any power or convergence issues when using jwdid with a Poisson specification?

Reading the help file of jwdid, I thought this command could be right:

DID using not-treated as controls, based on group (rather than individual) fixed effects. Using Poisson regression estimator.

gen emp = exp(delta)
jwdid emp, ivar(restaurant_id) tvar(year) gvar(treatment_year) method(poisson)