Designing Encouragements to Protect the Exclusion Restriction

Why Encouragement Design Matters

A randomized encouragement can increase treatment uptake without assigning treatment itself. Randomization can make the encouragement independent of participants’ potential outcomes, but it does not ensure that the encouragement affects the outcome only by changing treatment receipt. That additional claim is the exclusion restriction. Whether it is credible depends partly on how the encouragement and its comparison condition are designed.

For example, a text message intended to increase attendance at a counseling program might also prompt people to change their behavior before attending. A payment offered for participation might affect outcomes through income or stress. A transport service might connect participants with care beyond the treatment being studied. In each case, the encouragement may change the outcome even for someone whose treatment receipt would not change.

Designing to protect the exclusion restriction means identifying such pathways in advance and making them less plausible. It does not mean that a favorable first stage, a randomized assignment, or a careful control condition proves exclusion. Those features address other design concerns; the direct pathways still require substantive scrutiny.

Formalizing the Restriction

Let \(Z_i\) denote participant \(i\)'s randomized encouragement assignment, with \(Z_i=1\) for assignment to the encouragement and \(Z_i=0\) for its comparison. Let \(D_i(z)\) be the treatment receipt that would occur under assignment \(z\). Let \(Y_i(d,z)\) be the outcome that would occur if treatment receipt were set to \(d\) and encouragement assignment to \(z\).

This definition is about potential outcomes, not whether participants report noticing the encouragement or whether the research team intends a direct effect. A pathway violates exclusion if changing assignment could change the outcome while holding treatment receipt fixed. The relevant question is therefore not simply “Did the encouragement increase uptake?” but also “What else could assignment change that matters for the outcome?”

For the usual randomized-encouragement interpretation, assignment must also be randomized (or otherwise independent of the relevant potential outcomes), the encouragement must shift treatment receipt, and further assumptions are needed for a complier-effect interpretation, including monotonicity. Exclusion is a separate requirement: randomization cannot substitute for it.

How a Direct Pathway Changes the IV Contrast

A short derivation shows why the design question matters. Suppose \(Z_i\) is randomized and binary, treatment receipt is binary, and monotonicity rules out participants who would take treatment only when assigned to the comparison. Under exclusion, the assignment effect on the outcome is attributable to participants whose treatment receipt changes with assignment. The assignment effect on treatment receipt is the share of such compliers. Their ratio identifies the average treatment effect among compliers.

Now suppose, instead, that the encouragement has a common additive direct effect \(\gamma\), so that \(Y_i(d,z)=Y_i(d)+\gamma z\). For always-takers and never-takers, treatment receipt does not change across assignments; for compliers, it changes from 0 to 1. Writing \(C\) for the complier group, random assignment and monotonicity give:

The corresponding first-stage contrast is \(E[D\mid Z=1]-E[D\mid Z=0]=P(C)\). Thus the Wald ratio becomes:

The derivation is illustrative, not a general correction formula: it assumes a common additive direct effect and the stated binary-treatment and monotonicity setup. It shows that even a modest direct effect can matter when the first stage is small. Without exclusion, the randomized assignment contrast still describes the effect of assignment to the encouragement, but the ratio need not describe the treatment effect among compliers.

Worked Examples: Auditing and Revising an Encouragement

A Practical Design Audit

A useful audit begins before recruitment, with the outcome and treatment stated precisely. “Received care” may be too broad if the target treatment is one named program but the encouragement also changes medication use or access to other services. The team should then trace plausible routes from assignment to outcome, including routes that do not pass through that treatment.

The comparison condition deserves particular attention. “Usual care” may differ from the encouragement group in attention, information, or access, not just in the intended prompt to take treatment. A contact-matched comparison can reduce some of these differences, but matching contact does not ensure that the content or consequences of contact are outcome-neutral.

Common Mistakes and the Limits of Design

• “The encouragement was randomized, so exclusion holds.” Randomization supports independence of assignment; exclusion concerns whether assignment has direct effects on the outcome. They are distinct assumptions.
• “The encouragement was designed only to change uptake.” Intent does not determine causal pathways. A reminder, payment, or ride can have consequences beyond the intended change in treatment receipt.
• “The assignment effect is small, so the direct effect must be small.” The assignment effect combines all routes from assignment to outcome. A small net contrast can reflect cancellation between pathways, not absence of direct effects.
• “A matched control proves the restriction.” Matching contact or logistical support can make selected pathways less plausible, but it cannot verify the counterfactual claim \(Y_i(d,1)=Y_i(d,0)\) for every participant.

The design goal is not to claim that exclusion has been empirically proved. It is to choose an encouragement whose consequences outside treatment receipt are limited and well understood, and to make the comparison as similar as possible in other outcome-relevant respects. The assignment effect remains a meaningful effect of the encouragement itself; a causal treatment-effect interpretation from an instrumental-variable ratio requires the additional exclusion argument.