Skip to content

Abstract Search

Primary Submission Category: Difference in Differences

Decomposing Regression Triple-Differences with Staggered Adoption

Authors: Anton Strezhnev,

Presenting Author: Anton Strezhnev*

The triple-differences (TD) design is a popular identification strategy for causal effects
in settings where researchers do not believe the parallel trends assumption of conventional
difference-in-differences (DD) is satisfied. TD designs augment the conventional 2×2 DD
with a “placebo” stratum – observations that are nested in the same units and time peri-
ods as the DD but are known to be entirely unaffected by the treatment. However, many
TD applications go beyond this simple 2x2x2 setting and use observations on many units
across multiple time periods and with many “placebo” strata. A popular estimator is the
“triple-differences” regression (TDR) fixed-effects estimator – an extension of the common
“two-way fixed effects” estimator for DD. This paper decomposes the TDR estimator into
its component two-group/two-period/two-strata triple-differences and shows that interpret-
ing this parameter causally in settings with arbitrary staggered adoption requires strong
assumptions of homogeneity in the treatment effect not only over time but also across strata.
Moreover, under certain forms of treatment staggering, the regression triple-differences esti-
mator no longer consists exclusively of 2x2x2 triple-differences but rather a mixture of triple-
and double-differences, the latter of which are valid only if parallel trends holds. The decom-
position illustrates the importance of being cautious when implementing triple-differences
designs in settings more complex than the 2x2x2