Why Binary Treatments Can Triple IV Estimates: The Hidden Bias From Coarse Measurement

Insights from the Field

Instrumental variables

Coarsening

Education

Great Britain

Causal inference

Coarsening Bias: How Coarse Treatment Measurement Upwardly Biases Instrumental Variable Estimates was authored by John Marshall. It was published by Cambridge in Pol. An. in 2016.

📊 The Problem: Coarsening Can Warp IV Estimates

Political scientists often convert treatments with multiple intensities (for example, years of schooling) into coarser measures (for example, a binary indicator for completing high school). This common choice can substantially upwardly bias instrumental variable (IV) estimates by subtly violating the exclusion restriction, producing misleading causal inferences.

🔎 How the bias arises and when it matters

Coarsening a multi-intensity treatment can break the exclusion restriction because the instrument may change treatment intensity within a coarse category in ways that affect the outcome beyond the coarse measure.
The magnitude and direction of the bias depend on two features:
the strength and shape of the first stage (how the instrument shifts treatment intensities), and
the underlying causal response function (how outcomes respond to different treatment intensities).
In contrast, IV estimators that use a treatment measure capturing multiple intensities affected by the instrument can recover a consistent causal estimate even when fine-grained measurement at every intensity is unavailable—without requiring a stronger exclusion restriction.

🧾 How the argument is demonstrated

Analytical results show the mechanism by which coarsening introduces upward bias under plausible assumptions.
An empirical illustration examines the long-run effect of high school education on voting Conservative in Great Britain.

📈 Empirical Illustration — Schooling and Conservative Voting

Using the British example, converting years of schooling into a binary indicator for completing high school inflates the IV estimate substantially.
The coarsened measure produces an upward bias of about threefold in the IV estimate relative to an approach that accounts for multiple treatment intensities.

💡 Why this matters for applied researchers

Coarsening is a common practical choice but can seriously distort IV-based causal claims.
Researchers should prefer treatment measures that reflect the range of intensities affected by the instrument or explicitly account for how coarsening interacts with the first stage and response function when interpreting IV estimates.