Inference

csdid bootstraps by default: 1,000 multiplier-bootstrap iterations with Rademacher multipliers, reported with simultaneous confidence bands (both the number of iterations and the type of band can be changed).

The data

The runs below use the county mortality panel from the JEL-DiD replication package.

import delimited using ///
    "https://raw.githubusercontent.com/pedrohcgs/JEL-DiD/50f4f18/data/county_mortality_data.csv", ///
    clear varnames(1) bindquote(strict) stringcols(_all)
destring deaths population_20_64 year yaca county_code stfips unemp_rate poverty_rate, ///
    replace force
generate double mrate = 100000 * deaths / population_20_64
drop if missing(mrate) | population_20_64 <= 0
generate int gvar = yaca
replace gvar = 0 if missing(gvar) | gvar > 2016
bysort county_code: generate byte nyears = _N
keep if nyears == 11

csdid mrate, ivar(county_code) time(year) gvar(gvar) rseed(20250101)

That single run carries the whole inference apparatus with it (the bootstrap draws, the critical value, the pre-test). Nothing else on this page needs a fresh estimation of the model.

Simultaneous versus pointwise

This matters more than it looks. A pointwise 95% interval is correct for one cell considered alone. Read a table or a plot of fifteen cells, ask whether anything in it is significant, and pointwise intervals will mislead you. Roughly one in twenty cells will exclude zero by chance.

Simultaneous bands cover the whole family at once, so you can scan the table without doing any adjustment in your head. However, they are wider. That extra width is what it costs to look at the whole table when you did not pick one cell in advance.

csdid mrate, ivar(county_code) time(year) gvar(gvar) pointwise    // one at a time

e(cband) and e(pointwise) record which of the two was used. e(crit_val) is the critical value actually applied (a saved run remembers both).

Analytical standard errors

csdid mrate, ivar(county_code) time(year) gvar(gvar) analytical

These are faster, noticeably so on large panels, and pointwise only. We use them while iterating on a specification – the estimates do not change, only the standard errors – and we report the bootstrap.

Reproducibility

An unseeded bootstrap moves by a few percent between otherwise identical runs. The results header warns you. Seed it:

csdid mrate, ivar(county_code) time(year) gvar(gvar) wboot(reps(1000) rseed(20250101))

reps() must exceed 20. A handful of draws cannot support a standard error, and the empirical quantile behind a simultaneous critical value cannot be resolved at all, so csdid refuses the request. We seed every run on this site for that reason, and we would seed the runs behind a published table as well.

Clustering

csdid mrate, ivar(county_code) time(year) gvar(gvar) cluster(stfips)

The influence function is clustered on stfips. That variable must be numeric and nested within units (a county sits inside exactly one state). Treatment here is assigned by state, so clustering at the state level is the defensible choice even though the unit of observation is a county. The clustering applies to analytical and bootstrap inference alike. Note that clustering is a statement about which observations share shocks. The design settles it. We would not pick a cluster variable by looking at the standard errors it produced.

When pre-treatment cells exist, csdid reports a joint Wald test that all of them are zero, automatically, on every run. The test is built from the analytical influence-function covariance, so it does not depend on whether the bootstrap ran.

For what a large p-value is and is not worth, see Pre-testing.