Spatial Unit Root Diagnostic Tests and Transformations • spatialunitroot

Spatial Unit Root Diagnostic Tests and Transformations for R

An R implementation of the spatial unit root methods of Müller & Watson (2024, Econometrica), based on the SPUR Stata package by Becker, Boll & Voth (2025).

R developer & maintainer: Bas Machielsen
Original Stata code due to Sascha O. Becker, P. David Boll, Hans-Joachim Voth

Installation

# install.packages("remotes")
remotes::install_github("basm92/spatialunitroot")

Quick Start

library(spatialunitroot)
library(fixest)

data(chetty)

# Test for a spatial unit root (I(1) null)
spurtest(am ~ 1, data = chetty, coords = ~ s_1 + s_2,
         type = "i1", latlong = TRUE, seed = 42)
#> Spatial I(1) Test Results
#> ---------------------------------------
#> Test Statistic :  5.759
#> P-value        :  0.388

# Test for NO spatial unit root (I(0) null)
spurtest(am ~ 1, data = chetty, coords = ~ s_1 + s_2,
         type = "i0", latlong = TRUE, seed = 42)
#> Spatial I(0) Test Results
#> ---------------------------------------
#> Test Statistic :  3.044
#> P-value        :  0.001

# Half-life confidence interval
spurhalflife(am ~ 1, data = chetty, coords = ~ s_1 + s_2, latlong = TRUE)
#> Lower bound: 463653 m
#> Upper bound: inf

# Remove spatial unit roots via LBM-GLS transformation
transformed <- spurtransform(~ am + fracblack, data = chetty,
                             coords = ~ s_1 + s_2, prefix = "h_",
                             latlong = TRUE)

# Use with fixest
feols(h_am ~ h_fracblack, data = transformed)

The Three Functions

spurtest() — Four spatial unit root tests from Müller & Watson (2024):

`type`	Null hypothesis	Description
`"i1"`	Spatial unit root (I(1))	Tests whether a variable has a spatial unit root
`"i0"`	No spatial unit root (I(0))	Tests whether a variable is spatially stationary
`"i1resid"`	Spatial unit root in residuals	Tests regression residuals for a spatial unit root
`"i0resid"`	No spatial unit root in residuals	Tests regression residuals for spatial stationarity

Also accepts fixest model objects directly: spurtest(feols_model, coords = ~ s_1 + s_2, type = "i1resid")

spurtransform() — Four spatial differencing transformations: - "lbmgls" (default) — LBM-GLS transformation - "nn" — Nearest-neighbor differencing - "iso" — Isotropic differencing (within radius) - "cluster" — Cluster-level demeaning

spurhalflife() — Confidence sets for the spatial half-life (the distance at which spatial correlation drops to 1/2).

Coordinates

Spatial coordinates must be provided as s_* variables (for Stata compatibility) or via a formula:

coords = ~ s_1 + s_2                 # latitude, longitude (with latlong = TRUE)
coords = ~ x + y                     # Euclidean coordinates

References

Becker, S. O., Boll, P. D., & Voth, H. J. (2025). Spatial Unit Roots in Regressions: A Practitioner’s Guide and a Stata Package. Stata Journal.
Müller, U. K. & Watson, M. W. (2024). “Spatial Unit Roots and Spurious Regression.” Econometrica, 92, 1661–1695.
Müller, U. K. & Watson, M. W. (2022). “Spatial Correlation Robust Inference.” Econometrica, 90, 2901–2935.

License

MIT