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This paper suggests a simple test to check if a spatial model’s specifications hold for the entire sample period, that is, to see if the model is stable. Our test is general in that it allows for possible unknown changes, one or more times, in the weighting matrix, in the exogenous variables and/or in the parameters. These changes may occur cross-sectionally or at unknown points in time. The test also allows for additional endogenous regressors, and the error terms are non-parametrically specified. However, if instabilities are detected, our test does not indicate which set of model components is responsible for it. Our Monte Carlo results suggest that the test has extremely high power for almost all the experiments considered. However, the size of the test is low for small sample sizes when additional endogenous regressors are part of the model.

A simple test for stability of a spatial model