When Does a Policy Begin? Rethinking Anticipation in Difference-in-Differences

A familiar assumption with two meanings

Difference-in-differences, or DiD, compares changes in outcomes between groups that receive a treatment and groups that do not. In the paper’s basic policy example, researchers compare insurance coverage before and after Medicaid expansion in states that expanded the program and states that did not.

The central question is counterfactual: how would coverage have changed in expansion states without implementation? A parallel trends assumption supplies the comparison, asserting that their average change without implementation would have matched that of non-expansion states.

In their preprint, Marco Piccininni, Eric J. Tchetgen Tchetgen and Mats J. Stensrud argue that another familiar condition, “no anticipation,” often carries a mismatch between its mathematical formulation and its practical explanation. Their contribution is a clarification of causal questions and assumptions, rather than a new empirical evaluation of Medicaid.

Information is not backward causation

Read literally, the standard mathematical condition discussed in the paper says that changing a future treatment would not change an earlier outcome. The authors argue that this is already built into conventional causal models that respect temporal order: causes do not act backward in time.

Researchers usually mean something more substantive. People may learn that a policy is coming and change their behavior before implementation. The preprint discusses earlier research reporting evidence consistent with insurers adjusting premiums in anticipation of Medicaid expansion in Pennsylvania, after a waiver application but before federal approval.

These are different causal stories. An application or announcement can precede and influence behavior. That does not require the later implementation itself to affect the past. According to the authors, the standard mathematical formulation does not rule out this response to existing information.

Put the decision into the model

Their proposed remedy is to represent the policy decision separately from implementation. They introduce a variable, P, indicating whether there is a plan to implement the policy. In the setting they examine, this decision occurs before the first outcome measurement, while implementation occurs later.

Their alternative no-anticipation condition says that, among units that planned the policy, the plan has no average effect on that first outcome measurement. This is a substantive restriction: a publicly known decision could change insurance-market behavior before expansion begins and therefore violate it.

The distinction also changes the question being asked. The effect of implementing a policy is not necessarily the same as the effect of deciding to implement it. An intervention on implementation can leave the earlier decision unchanged; an intervention on the decision can change both early responses and subsequent implementation.

Anticipation does not automatically invalidate DiD

A crucial qualification is that early behavioral responses do not, by themselves, invalidate the basic identification argument. The authors show that having treated and untreated units, causal consistency, and their implementation-based parallel trends condition suffice to identify the average implementation effect among treated units. Anticipation can occur while those conditions still hold.

The problem becomes clearer when researchers instead believe that trends would have been parallel had the policy never been planned. That is a different assumption from parallel trends under an intervention preventing implementation alone.

Under a specific set of conditions—including decisions always being executed and decisions affecting the later outcome only through implementation—the authors derive an exact relationship: the usual DiD comparison equals the implementation effect minus the earlier anticipation effect. This is a conditional result, not a universal formula for every study with anticipation.

The same estimate can answer different questions

A hypothetical example involving defective cars illustrates the stakes. Drivers learn that authorities plan to seize dangerous vehicles and switch to replacement cars before seizure occurs. In the authors’ constructed model, actual seizure has no additional effect on accidents among treated regions, whereas the decision reduces expected accidents. The usual DiD comparison correctly identifies the zero implementation effect in that example, despite anticipatory behavior.

The preprint also extends its decision-based framework to staggered adoption across multiple periods. Under a fixed decision-to-implementation lag and specified no-anticipation, consistency, support and parallel trends conditions, familiar DiD comparisons identify effects of the decision.

The practical recommendation is precision, not abandonment of DiD. Researchers should specify whether their intervention concerns a decision or its implementation, then state assumptions about that intervention. The distinction is especially relevant for announced policies; the authors acknowledge that it can be redundant when decision and implementation coincide, or implausible for treatments such as viral outbreaks.