Spatial Fuzzy Regression Discontinuity Design
Also known as: Spatial Fuzzy RD, Geographic Fuzzy RDD, Spatial Fuzzy RDD, Geo-Fuzzy RD
Spatial Fuzzy Regression Discontinuity Design (Spatial Fuzzy RDD) estimates a local average treatment effect when a geographic boundary determines treatment eligibility but some units on either side of the boundary fail to comply with their assigned status. It combines the spatial running-variable logic of geographic RDD with the instrumental-variable correction for imperfect compliance used in fuzzy RDD.
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When to use it
Use Spatial Fuzzy RDD when (1) treatment assignment is determined by a geographic boundary or administrative line, (2) compliance with that assignment is imperfect — some units cross over or opt out — and (3) you can construct a continuous measure of distance to the boundary. The design is appropriate for observational, geo-coded data where randomisation is infeasible and the boundary is otherwise unrelated to outcomes (exclusion restriction). It is not appropriate when the boundary itself was drawn in response to pre-existing outcome differences, when spatial spillovers between sides are large and uncontrolled, when compliance is too weak at the boundary (first stage F < 10), or when the boundary is too irregular to define a clean running variable.
Strengths & limitations
- Provides a credible causal estimate from observational geo-coded data by exploiting a natural geographic discontinuity.
- Accounts for imperfect compliance through a two-stage IV correction, unlike sharp RDD which assumes full compliance.
- The geographic running variable is typically transparent and verifiable, making the design easy to communicate and audit.
- Local in scope: estimates are for compliers near the boundary, which is often exactly the policy-relevant population.
- Spatial placebo and permutation tests supply unusually rich falsification opportunities compared with non-spatial designs.
- The exclusion restriction — that crossing the boundary affects outcomes only through treatment — can be violated by correlated policies, infrastructure, or sorting along the boundary.
- Estimates are local to compliers near the cutoff and may not generalise to units far from the boundary or non-compliers.
- Thin data near the boundary and irregular geographic shapes make bandwidth selection and inference more complex than in standard RDD.
- Geographic spillovers (commuting, mobility, treatment diffusion) dilute the jump at the boundary and attenuate the estimate.
- Weak first stages — common when compliance varies smoothly rather than jumping sharply — invalidate the IV estimator.
Frequently asked
What makes this 'fuzzy' rather than 'sharp'?
In a sharp RDD every unit above the cutoff is treated and every unit below is not. In a fuzzy design the probability of treatment jumps at the cutoff but does not go from 0 to 1 — some units on the treated side do not comply, and some on the control side obtain treatment anyway. The fuzzy estimator uses the boundary as an instrument to correct for this imperfect compliance.
How do I define the spatial running variable?
Compute the signed perpendicular distance from each unit's geographic location (address, centroid, or GPS coordinate) to the boundary. Positive values denote the nominally treated side; negative values denote the control side. For irregular boundaries, this may require GIS tools to project coordinates and measure distances accurately.
What bandwidth should I use?
The MSE-optimal bandwidth proposed by Calonico, Cattaneo, and Titiunik (2014) — implemented in the rdrobust package in R and Stata — is the standard choice. In spatial designs, inspect the bandwidth geographically to ensure it corresponds to a meaningful physical zone and that observations within it are not severely imbalanced.
How do I handle spatial spillovers?
Define a buffer zone on either side of the boundary and exclude observations within it from the analysis (a 'donut' around the cutoff). This discards units most likely to receive treatment spillovers from the other side, but at the cost of reducing the sample near the cutoff.
When should I choose spatial fuzzy RDD over spatial sharp RDD?
Use fuzzy when first-stage compliance is imperfect — the probability of treatment does not jump from 0 to 1 at the boundary. If all units comply perfectly with which side of the boundary they are on, sharp RDD is sufficient and more efficient. A formal test is to plot and test the discontinuity in treatment take-up at the boundary.
Sources
- Keele, L., & Titiunik, R. (2015). Geographic Boundaries as Regression Discontinuities. Political Analysis, 23(1), 127-155. DOI: 10.1093/pan/mpu014 ↗
- Imbens, G., & Lemieux, T. (2008). Regression Discontinuity Designs: A Guide to Practice. Journal of Econometrics, 142(2), 615-635. DOI: 10.1016/j.jeconom.2007.05.001 ↗
How to cite this page
ScholarGate. (2026, June 3). Spatial Fuzzy Regression Discontinuity Design. ScholarGate. https://scholargate.app/en/causal-inference/spatial-fuzzy-regression-discontinuity
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Fuzzy Regression DiscontinuityCausal inference↔ compare
- Geographic Regression DiscontinuityEconometrics↔ compare
- Instrumental Variables in Health ResearchHealth Economics↔ compare
- Spatial Instrumental VariablesCausal inference↔ compare
- Spatial Regression Discontinuity DesignCausal inference↔ compare