Pre-testing parallel trends

Identification rests on parallel trends. That is an assumption about untreated potential outcomes after treatment starts, a counterfactual quantity, and it is not testable. What is testable is its analogue before treatment: if the cohorts were already diverging beforehand, the assumption is harder to believe.

csdid gives you two ways to look at that: the pre-treatment cells themselves, and a joint test across all of them. We use both, and we would not report one of them without the other.

The data

Let’s build the balanced sample once (the same block used elsewhere on this site) and reuse it for the runs below.

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
save "jel_balanced.dta", replace

The joint pre-test

Every run reports a Wald test of the hypothesis that all pre-treatment ATT(g,t) are zero. The test is stored, whether or not you asked for it:

use "jel_balanced.dta", clear
csdid mrate, ivar(county_code) time(year) gvar(gvar) analytical
display "W       = " e(wald_stat)
display "p-value = " e(wald_pvalue)
display "df      = " e(wald_df)

A small p-value says the pre-treatment cells are jointly distinguishable from zero. A large one does not say that parallel trends holds. It says that this test did not detect a violation, which with modest samples it often cannot do.

Reading the cells

The joint test compresses everything into one number, and the event study is what shows you where a problem actually sits (if there is one):

use "jel_balanced.dta", clear
csdid mrate, ivar(county_code) time(year) gvar(gvar) rseed(20250101)
estat event

Negative event times are pre-treatment (that is the convention here). Look for pattern rather than for stars. A gentle drift toward zero as treatment approaches is more worrying than one isolated period: a drift suggests that the two groups were already converging before anything happened to either of them.

base_period(universal) is the default. Under it the pre-treatment estimates are cumulative and serially correlated, so one bad early period pushes every later point away from zero and can look like a systematic trend. With base_period(varying) each pre-treatment cell is a separate one-period comparison, so a violation appears in the period where it happens. Thus we ask for varying explicitly when pre-testing, and we recommend that you do too. See Base periods.

Power, and what a clean pre-test does not buy you

The pre-test can fail to reject simply because the pre-treatment standard errors are wide. That is low power, and in the output it looks just like clean trends. Report the standard errors, so that a reader can see whether a null result is informative or merely imprecise:

use "jel_balanced.dta", clear
csdid mrate, ivar(county_code) time(year) gvar(gvar) analytical
estat event

Two designs with identical point estimates and very different standard errors tell very different stories about the same “passed” pre-test. Only the one with the tight standard errors is really evidence about the design.

Conditional parallel trends

If parallel trends is only plausible after conditioning on covariates, then condition on them, and say so in the text. The pre-test then applies to the conditional assumption you are actually making:

use "jel_balanced.dta", clear
csdid mrate unemp_rate poverty_rate, ivar(county_code) time(year) gvar(gvar) ///
    method(dr) analytical
display "W       = " e(wald_stat)
display "p-value = " e(wald_pvalue)
estat event

See Covariates and estimators for what each estimator assumes.

If the pre-test fails

A rejection tells you something, and it does not end the analysis. The options worth considering, roughly in order of how much they ask of the data, are these:

Allow anticipation. If the divergence sits immediately before treatment, it may be a response to the announcement and not a violation of parallel trends (see Anticipation).
Change the comparison group. A never-treated group selected differently from the treated cohorts may be the problem, and notyet uses a different one.
Condition on covariates that plausibly drive the differential trend (and that are not themselves affected by the treatment).
Report a sensitivity analysis that asks how large a violation would have to be to overturn the conclusion. This is what we would do whenever the design sits close to the line and the pre-treatment cells are noisy.

What is not defensible is searching over specifications until the pre-test passes and then reporting only that one. We view the pre-test as one piece of evidence on the credibility of a DiD design in a particular application. A piece of evidence that has been selected on no longer carries the information you are asking your readers to take from it.

capture erase "jel_balanced.dta"