Testing spatial effects and random effects in a nested panel data model

- We propose a multilevel panel data model to incorporate both spatial effects and nested random effects.
- We construct Lagrange multiplier test statistics for model diagnostic testing purpose.
- We conduct Monte Carlo simulation to show good finite sample performances of these tests.

We propose a multilevel spatial econometric model including spatially correlated error, spatially lagged dependent variable, county-level random effects and nested district-level random effects within a county. We construct joint Lagrange multiplier (LM) test to detect both the spatial effects and the random effects, LM tests to detect the spatial error correlation and/or the spatial lag dependence allowing for both types of random effects, and LM tests to detect the county-level random effects and/or the nested district-level random effects allowing for both types of spatial effects. A Monte Carlo simulation is conducted to show their good finite sample performances.