03 · What You Need to Know
What Parallel Trends Requires and How Researchers Should Assess It
The assumption concerns what would have happened without treatment
Difference-in-differences compares changes in outcomes between treated and comparison groups.
For that comparison to identify a causal effect in the conventional setting, the comparison group's observed change must provide a credible estimate of the change the treated group would have experienced without the intervention.
This is the parallel trends assumption.
It concerns untreated potential outcomes, not simply the observed outcomes after treatment.
For example, if student retention at treated universities would have increased by four percentage points without an AI advising system, the comparison group should represent that four-point counterfactual increase under the relevant assumptions.
The observed post-treatment change at the treated universities may differ because the intervention has an effect.
The formal meaning of parallel trends
In a conventional two-group, two-period difference-in-differences design, the assumption can be expressed using potential outcomes.
The expression assumes that the groups and treatment periods are appropriately defined. Additional assumptions, including absence of relevant anticipation and suitable treatment and comparison measurement, are required for the conventional causal interpretation.
In more complex designs, including staggered adoption, the relevant parallel-trends condition may be defined separately for adoption cohorts and comparison populations.
Parallel trends does not require equal baseline levels
One of the most common misunderstandings is that treated and comparison groups must have the same average outcome before intervention.
That is not required by the conventional parallel trends assumption.
Suppose University A has retention of 60%, 65%, and 70% across three pretreatment years. University B has retention of 75%, 80%, and 85%.
The universities differ by 15 percentage points in every year, but both improve by five percentage points annually.
Their observed trajectories are parallel despite different outcome levels.
Such a pattern may support the plausibility of parallel counterfactual trends, although it does not prove that the same relationship would continue after intervention.
Equal baseline levels do not establish parallel trends
Two groups can have identical outcomes immediately before treatment while following very different trajectories.
For example, one university may improve from 70% to 75% to 80%, while another improves from 78% to 79% to 80%.
Both reach 80% immediately before treatment, but the first improves by five percentage points annually while the second improves by one.
If these differences would have continued without intervention, the comparison group's change would not represent the treated group's counterfactual change.
Consequently, selecting comparison groups solely because their latest baseline outcomes match can be misleading.
The broader criteria for a credible comparison group should include treatment assignment, outcome trajectories, and relevant institutional differences.
Why parallel trends cannot be directly tested after treatment
The assumption concerns the treated group's outcome trajectory in a world where treatment did not occur.
Once the intervention is implemented, that counterfactual trajectory is not observed.
Researchers can observe the comparison group's outcomes and the treated group's outcomes under treatment, but they cannot directly observe the treated group's untreated post-treatment outcomes.
Therefore, no statistical test using observed outcomes can definitively establish the post-treatment parallel trends assumption.
Researchers can evaluate evidence consistent or inconsistent with the assumption, but they should distinguish such evidence from proof.
Why pre-intervention trends are useful
Multiple pretreatment observations allow researchers to examine whether treated and comparison groups experienced similar changes before intervention.
For example, retention data across five academic years may reveal whether treated universities were already improving more rapidly than comparison universities.
Substantial differences in observed pre-trends may undermine the credibility of a simple parallel-trends argument.
However, similar pre-trends cannot guarantee that untreated outcomes would have continued changing similarly after treatment.
A new policy, economic shock, institutional reform, or other event may alter one group's trajectory after implementation.
Pre-intervention evidence is therefore informative but not decisive.
Why a nonsignificant pre-trend test does not prove parallel trends
Researchers sometimes estimate an event-study model and test whether pretreatment coefficients differ significantly from zero.
If the test is nonsignificant, they may conclude that parallel trends has been satisfied.
This conclusion is too strong.
Statistical tests can have limited power, particularly when there are few institutions, noisy outcomes, or short pretreatment histories.
Failure to reject a difference does not establish equivalence.
Moreover, selecting or interpreting an analysis conditional on passing a pre-trend test can create additional inferential problems.
Roth's research on pretest-based procedures demonstrates why conventional pre-trend testing can be misleading and why researchers should not treat a passed pretest as a guarantee of unbiased estimation.
Why visual inspection is useful but insufficient
Plotting treated and comparison outcomes across pretreatment periods can reveal important patterns.
Researchers may identify divergent trajectories, abrupt changes, seasonal fluctuations, or differences in outcome variability.
However, visual similarity depends partly on the scale of the graph and the number of available observations.
Two trajectories may appear parallel on a broad vertical scale while differing meaningfully for the research question.
Researchers should examine substantive effect sizes and uncertainty rather than relying on visual impressions alone.
Graphs should support the identification argument, not substitute for it.
Conditional parallel trends may be more plausible
Unconditional parallel trends requires comparable untreated outcome changes without conditioning on additional characteristics.
Conditional parallel trends allows those changes to be comparable after conditioning on specified pretreatment covariates.
For example, universities may have different retention trends because of baseline student composition, institutional type, or regional conditions.
Researchers may be able to defend a conditional comparison among universities with similar relevant pretreatment characteristics.
However, conditioning does not automatically eliminate unmeasured confounding.
The variables used should be justified by substantive knowledge and measured appropriately before treatment.
Overlap is also important because comparisons may require treated and untreated units with sufficiently similar covariate profiles.
Why treatment assignment affects parallel-trends plausibility
The process determining which units receive treatment can provide important evidence about whether parallel trends is plausible.
Suppose universities adopt an AI advising platform because their retention rates have recently declined.
The treated institutions may subsequently experience regression to the mean or other recovery processes even without the intervention.
Comparison universities selected without regard to recent declines may not provide an appropriate counterfactual.
Similarly, institutions chosen because they are improving rapidly may continue following different trajectories.
Researchers should investigate whether treatment assignment responds to past outcomes, expected future outcomes, or institutional characteristics associated with trends.
Concurrent events can violate parallel trends
Parallel trends may be implausible when another event affects treated and comparison groups differently during the evaluation period.
For example, treated universities may introduce an AI advising platform while simultaneously expanding financial assistance.
If the comparison universities do not receive the financial assistance, their retention changes may not represent the treated universities' untreated counterfactual changes.
Even if pre-intervention trends were similar, the concurrent policy can create divergence after implementation.
Researchers should document institutional changes and external events that could differentially influence outcomes.
Anticipation complicates the definition of pretreatment periods
Participants or institutions may respond to an announced intervention before its official implementation date.
For example, universities preparing to adopt an AI advising system may reorganize student support services or train staff in advance.
If these activities affect retention, periods classified as pretreatment may already contain intervention-related effects.
The conventional difference-in-differences interpretation typically requires appropriate handling of anticipation.
Researchers should distinguish announcement, preparation, activation, and meaningful exposure dates.
Where anticipation is plausible, the design may require an explicitly defined anticipation window or alternative treatment timing.
Why staggered adoption complicates the assumption
When institutions adopt an intervention in different periods, there is no single treated-versus-control comparison for the entire study.
Different adoption cohorts may have different counterfactual trajectories and treatment effects.
Modern staggered difference-in-differences approaches commonly define assumptions for particular adoption groups and calendar periods.
For example, not-yet-treated institutions may serve as comparison units for earlier adopters before their own treatment begins.
However, these comparisons remain valid only when the relevant cohort-specific assumptions are credible.
Researchers should not assume that a single overall pre-trend graph establishes parallel trends for every adoption cohort.
The choice of estimator should reflect treatment timing, comparison groups, and possible heterogeneity.
Parallel trends does not mean treatment effects must be constant
The parallel trends assumption concerns untreated potential outcomes.
It does not inherently require the intervention effect to be identical across institutions or constant over time.
However, particular estimators may impose additional restrictions or produce difficult-to-interpret averages when treatment effects are heterogeneous.
For example, conventional two-way fixed-effects estimators in staggered adoption settings can combine comparisons in problematic ways when effects vary across cohorts and exposure durations.
Researchers should distinguish assumptions needed for identification from restrictions introduced by a particular estimator.
How violations of parallel trends affect estimates
Suppose treated universities would have improved retention by eight percentage points without intervention, while comparison universities would have improved by only three.
If researchers assume parallel trends and subtract the comparison group's three-point change, the remaining five points may be incorrectly attributed to the intervention.
In this hypothetical situation, the intervention could have no effect while the difference-in-differences estimate suggests a five-percentage-point benefit.
Alternatively, differential untreated trends could mask a genuine intervention effect or reverse the apparent direction.
The direction and magnitude of bias depend on how the untreated counterfactual trends differ.
Can researchers relax the parallel trends assumption?
Some approaches allow researchers to conduct sensitivity analyses under bounded deviations from parallel trends.
For example, methods developed by Rambachan and Roth permit inference under specified restrictions on how counterfactual trend violations may evolve.
These approaches do not eliminate the need for assumptions. Instead, they make alternative assumptions explicit and examine how conclusions change when departures from exact parallel trends are permitted.
Researchers may also consider alternative comparison groups, covariate adjustment, or different identification strategies when justified.
However, adding flexible trends or more control variables does not automatically repair an invalid counterfactual.
What evidence strengthens a parallel-trends argument?
A credible argument generally combines several forms of evidence.
Relevant information includes the treatment assignment mechanism, historical outcome trajectories, institutional characteristics, policy histories, and plausible sources of differential change.
Multiple pretreatment observations can reveal important divergences, while sensitivity analyses can show how conclusions depend on assumptions about counterfactual trends.
Researchers should also consider whether the intervention itself affects comparison units through spillover.
None of these checks proves parallel trends, but together they can make the assumption more or less defensible.
The aim is a transparent causal argument rather than a declaration that the assumption has been statistically verified.
When parallel trends is too implausible to defend
Difference-in-differences may be unsuitable when treated and comparison units have strongly divergent trajectories that are expected to continue, or when intervention timing is closely linked to anticipated outcome changes.
It may also be inappropriate when major concurrent interventions affect only treated units and cannot be separated from the treatment of interest.
In such circumstances, researchers should reconsider the comparison group or explore another design whose assumptions better match the assignment mechanism.
Regression discontinuity, controlled interrupted time series, or other strategies may be appropriate in particular settings, but none should be selected merely to avoid confronting a weak causal comparison.
The broader question of when difference-in-differences is appropriate ultimately depends on whether the identifying assumptions can be defended.
Watch Out
Parallel trends is an assumption about unobserved untreated outcomes after intervention. A nonsignificant pre-trend test, visually similar historical lines, or identical baseline averages cannot prove that the assumption holds.
