Spatial Panel Data Model (FE/RE)
Also known as: spatial panel FE/RE, spatial econometric panel, spatial lag/error panel, Uzamsal Panel Modeli (Spatial Panel FE/RE)
The spatial panel model is a family of econometric models that adds spatial dependence to panel data (units observed over time). It combines fixed- or random-effects panel structure with spatial lag, spatial error, or spatial Durbin components, and is developed in the modern spatial-econometrics literature by Elhorst (2014) and Lee & Yu (2010).
Key highlights
- Captures spatial spillovers between neighbouring units that standard panel models ignore.
- Flexible family: spatial lag, spatial error, and spatial Durbin specifications cover different spillover mechanisms.
- Supports both fixed and random effects, so unobserved unit heterogeneity is controlled while modelling neighbourhood dependence.
Intuition
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How it works
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When to use it
Use a spatial panel model when you have panel data (the same units measured over several periods), a continuous outcome, geographic coordinates or a defined neighbourhood structure, and a reasonable sample (at least about 100 observations). It is the right tool when outcomes plausibly spill over between neighbouring units, such as regional economic growth, housing prices, or environmental pollution. The ideal structure is large N with small-to-moderate T (a spatial micropanel). The spatial weight matrix W is usually assumed constant over time; choose between fixed and random effects with a Hausman test, and use LM tests to decide which spatial component (lag, error, or Durbin) is needed.
Strengths & limitations
- Captures spatial spillovers between neighbouring units that standard panel models ignore.
- Flexible family: spatial lag, spatial error, and spatial Durbin specifications cover different spillover mechanisms.
- Supports both fixed and random effects, so unobserved unit heterogeneity is controlled while modelling neighbourhood dependence.
- Cannot be applied without coordinates or a defined neighbourhood structure to build the spatial weight matrix W.
- Results depend on the choice of W and the assumption that it is constant over time.
- Dynamic specifications (with a lagged dependent variable) require bias-corrected LSDV or GMM estimation and are technically demanding (a high-difficulty method).
Common pitfalls
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Applications
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Frequently asked
How do I choose between fixed and random effects?
Use a Hausman test, exactly as in ordinary panel models. If the unit effects are correlated with the regressors, fixed effects are preferred; otherwise random effects are more efficient.
What is the difference between the spatial lag, error, and Durbin specifications?
The spatial lag model lets a unit's outcome depend on its neighbours' outcomes (ρ term); the spatial error model lets unobserved shocks be correlated across neighbours (λ term); the spatial Durbin model also adds spatially lagged predictors. LM tests help decide which component the data require.
What sample size and panel shape do I need?
At least about 100 observations, and the ideal structure is large N with small-to-moderate T — a spatial micropanel. The spatial weight matrix W is usually treated as constant over time.
What if my data has no coordinates?
Without coordinates or a defined neighbourhood structure you cannot build the spatial weight matrix W, so a spatial panel model cannot be applied. Use a standard fixed-effects panel model instead.
Sources
- 1.Elhorst, J. P. (2014). Spatial Econometrics: From Cross-Sectional Data to Spatial Panels. Springer.
- 2.Lee, L. F., & Yu, J. (2010). Estimation of Spatial Autoregressive Panel Data Models with Fixed Effects. Journal of Econometrics, 154(2), 165–185.
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Cite this page
ScholarGate. (2026, June 1). Spatial Panel Model. ScholarGate. https://scholargate.app/spatial-analysis/spatial-panel-model