The Spatial Hausman Test In A Panel Model

The classic Hausman test is generally used to determine the individual effects in paneldata model. However, the Hausman test would have larger size tortuosity when spatialcorrelation exists in panel data, therefore leading to misunderstanding conclusions much morelikely. It is widely agreed that spatial correlation generally exists in the actual economicoperation. Nevertheless, there are few studies on the method of how to determine theindividual effects in spatial panel data model. As a result, in many empirical researches,researchers ignored the spatial effects and simply adopted the classic Hausman test todetermine the individual effects in spatial panel data model, without understanding that theclassic Hausman test has failed in case that the spatial correlation exists.In this paper, the panel data Spatial Lag (SLAG) model is focused and InstrumentalVariable estimation is applied to estimate both the random and fixed effects specifications ofthe SLAG model. Then follow the idea of the classic Hausman test and propose a spatialHausman test statistics. Finally, prove that this test works well in small panels via a MonteCarlo simulation experiment.The study shows that the size tortuosity of the classic Hausman test increase as thespatial correlation increase, and it is far beyond the range the test can accept when thecorrelation is strong. While the spatial Hausman test is hardly affected by spatial correlationand always maintain an ideal size. As the sample size increases, the size tortuosity of theclassic Hausman test become even larger, while the spatial Hausman test has been furtheramended and the size tortuosity approach0more closely. The impact of the variation ofrandom effects is not significant on either the classic or spatial Hausman test. On the otherhand, the power of both tests decrease as the fixed effects increase. The power of the former isgenerally greater than the latter and both increase to the ideal power as the sample sizeincrease or the correlation between individual effect and independent variables increase.