Base periods: varying or universal

Every ATT(g,t) is a difference between period t and a base period, the pre-treatment period the comparison is measured from. base_period() chooses which one. It changes the pre-treatment estimates, the shape of an event study, and how many cells you get back. Nothing in this choice moves the headline number: the post-treatment effects are identical under either setting.

universal (the default) compares every period with g-1.
varying compares each pre-treatment period with the one immediately before it, and each post-treatment period with g-1.

Universal is the default because it is the layout an event-study plot assumes, and event studies are how these results are almost always presented. R did and Stata csdid Version 1.82 both default to varying instead, so this is a deliberate departure from both, and base_period(varying) restores their behavior exactly.

The data

Let’s build the balanced sample once. It is the same block used on the other pages (nothing here is specific to base periods), and both specifications run on it.

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

Universal: the default

use "jel_balanced.dta", clear
csdid mrate, ivar(county_code) time(year) gvar(gvar) analytical
display "cells: " e(N_attgt)
estat event

Each pre-treatment number answers a cumulative question: how far this cohort had drifted from the comparison group by period t, measured relative to g-1. This is the layout that most event-study plots assume, with everything measured from a single normalized reference point. We expect most readers of your paper to have it in mind, and that is why we made it the default.

Varying

use "jel_balanced.dta", clear
csdid mrate, ivar(county_code) time(year) gvar(gvar) base_period(varying) analytical
display "cells: " e(N_attgt)
estat event

Each pre-treatment number now answers a local question: whether this cohort’s outcome moved between consecutive periods differently from the comparison group. The pre-treatment cells become a sequence of one-period placebo tests. That is what you want when the question is where a violation happened rather than how far it had accumulated by the time treatment began. See Pre-testing.

What actually differs

Two things change between the two runs. One of them is cosmetic and the other is not, and both are worth seeing.

Cell counts. Universal reports the base period itself, which is zero by construction, so each cohort contributes one extra row. e(N_attgt) therefore shrank when the varying run above dropped those rows. The difference is bookkeeping, and it is still the first thing people notice when they switch between the two specifications.

Which cells agree. Both specifications measure post-treatment periods against g-1, so those cells agree exactly, while the pre-treatment cells differ because they are answering different questions:

use "jel_balanced.dta", clear
quietly csdid mrate, ivar(county_code) time(year) gvar(gvar) base_period(varying) analytical
matrix V = e(attgt)
quietly csdid mrate, ivar(county_code) time(year) gvar(gvar) base_period(universal) analytical
matrix U = e(attgt)

mata {
    v = st_matrix("V"); u = st_matrix("U")
    dpost = 0; dpre = 0
    for (i = 1; i <= rows(v); i++) {
        for (j = 1; j <= rows(u); j++) {
            if (v[i,1] == u[j,1] & v[i,2] == u[j,2]) {
                d = abs(v[i,4] - u[j,4])
                if (v[i,2] >= v[i,1]) dpost = max((dpost, d))
                else                  dpre  = max((dpre, d))
            }
        }
    }
    printf("post-treatment cells, largest difference: %g\n", dpost)
    printf("pre-treatment  cells, largest difference: %g\n", dpre)
}

The post-treatment difference is zero to numerical precision. That is the result we wanted, and it is cheap to verify on your own data. The pre-treatment difference is not zero, and it should not be: the two specifications are asking different questions of the same data!

Note that the comparison is keyed on (cohort, period). The two runs return different numbers of rows, so lining them up by row position would silently compare unrelated cells.

Which to use

Use varying to pre-test parallel trends (this is our main use for it). Each pre-treatment cell is its own one-period test, so a violation shows up in the period where it happens instead of being carried forward into every later cell. See Pre-testing.

Use universal when you want a conventional event-study plot with a single normalized reference period, or when you are presenting cumulative pre-trends. Pre-treatment estimates are then serially correlated by construction. A single early deviation shifts every subsequent point, so a long run of “significant” pre-treatment coefficients may trace back to one bad period.

Whichever you pick, the post-treatment conclusions do not depend on the choice. We would treat this option as a decision about how to display and pre-test the design, and not as a decision about what the design estimates.

capture erase "jel_balanced.dta"