Panel Spatial Regression
Panel Data Spatial Regression Model · Also known as: spatial panel model, panel spatial econometrics, spatial panel data regression, PSR
Panel Spatial Regression extends standard panel data models by explicitly accounting for spatial dependence among cross-sectional units observed over time. It combines the temporal control of panel fixed or random effects with a spatial weights matrix that encodes geographic or network proximity, yielding unbiased and efficient estimates when observations are spatially correlated across units.
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When to use it
Use Panel Spatial Regression when you have repeated observations on georeferenced or network-linked units (countries, regions, cities, firms) and economic theory or exploratory Moran's I tests indicate spatial dependence in the outcome or the errors. It is the appropriate upgrade from a standard panel model when spillover effects are substantively meaningful — e.g., regional economic growth, disease spread, environmental pollution, or housing markets. Do not use it when spatial dependence is absent (LM tests are insignificant), when the panel has very few time periods (T < 5) and spatial ML may be unreliable, or when the weight matrix is theoretically unjustified or arbitrarily chosen.
Strengths & limitations
- Jointly controls for unobserved unit heterogeneity (fixed/random effects) and spatial spillovers in one coherent framework.
- Produces consistent and efficient estimates of spillover effects (rho) and direct covariate effects (beta) that cross-sectional spatial models or aspatial panel models cannot separately identify.
- LM and robust LM diagnostic tests provide principled model selection between spatial lag, spatial error, and unrestricted specifications.
- Decomposes total effects into direct, indirect (spillover), and total impacts, enabling richer policy interpretation.
- Scales to large spatial panels through GMM estimators, which avoid the computational burden of ML on large weight matrices.
- Results are sensitive to the choice and construction of the spatial weights matrix W; different specifications can yield different rho estimates.
- ML estimation requires a correctly specified error distribution and becomes computationally costly when n is large (>1000 units).
- Fixed effects estimators cannot identify coefficients on time-invariant spatial variables (e.g., geographic area, latitude) unless an IV or correlated random effects approach is used.
- Short panels (small T) combined with large n can produce biased estimates in dynamic spatial panel models if the Nickell bias is not corrected.
- Interpretation of indirect (spillover) effects requires computing the full n x n impact matrix, which is non-trivial to summarise.
Frequently asked
How do I choose between the spatial lag model and the spatial error model for panel data?
Run Lagrange Multiplier (LM) tests on the residuals of a standard panel regression. If LM-lag is significant and LM-error is not, prefer the spatial lag model. If both are significant, use the robust versions (RLM-lag, RLM-error) — whichever remains significant guides the choice. When theory strongly predicts spillovers in the outcome itself (e.g., competitive dynamics), the lag model is preferred on substantive grounds.
What is the difference between direct and indirect (spillover) effects in a spatial panel?
In a spatial lag model the coefficient beta on a regressor x is not the total effect of x on y, because a change in x in one unit feeds back through the spatial lag. The direct effect measures the own-unit impact (including feedback loops), while the indirect effect captures the average impact on all other units. These are computed from the full (I - rho W)^-1 matrix and should be reported instead of bare beta and rho values.
Should I use fixed effects or random effects in a spatial panel?
Apply a Hausman test: if unit effects are correlated with the regressors, fixed effects are consistent (random effects are not). Fixed effects also allow free correlation between unmeasured unit heterogeneity and covariates, which is usually the safer assumption in economic panels. Random effects are more efficient when the correlation is absent and allow identification of time-invariant regressors.
Can I use any distance measure to build the spatial weights matrix W?
Any proximity measure that is theoretically justified and exogenous to the outcome can be used — contiguity, inverse distance, k-nearest neighbours, travel time, or trade intensity. The key requirement is that W is fixed (not data-driven on y) and row-standardised. Sensitivity analysis across two or three plausible W specifications is good practice and strengthens robustness of conclusions.
What software can estimate panel spatial regression?
The splm package in R provides ML and GM estimators for spatial panel models. Python users can use spreg in the PySAL ecosystem. Stata's spxtregress command supports spatial panel estimation from version 15 onward. Elhorst's MATLAB routines are also widely used in applied research.
Sources
- Elhorst, J. P. (2014). Spatial Econometrics: From Cross-Sectional Data to Spatial Panels. Springer. ISBN: 978-3642403408
- Anselin, L., Le Gallo, J., & Jayet, H. (2008). Spatial Panel Econometrics. In: The Econometrics of Panel Data (pp. 625-660). Springer, Berlin, Heidelberg. DOI: 10.1007/978-3-540-75892-1_19 ↗
How to cite this page
ScholarGate. (2026, June 3). Panel Data Spatial Regression Model. ScholarGate. https://scholargate.app/en/spatial-analysis/panel-spatial-regression
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.
- Geographically Weighted RegressionSpatial analysis↔ compare
- Multiscale Geographically Weighted RegressionSpatial analysis↔ compare
- Panel Fixed EffectsEconometrics↔ compare
- Spatial Durbin ModelSpatial analysis↔ compare
- Spatial Error ModelSpatial analysis↔ compare
- Spatial Lag ModelSpatial analysis↔ compare