Spatial bootstrap test, Moran’s I, Monte Carlo, Size distortion, Power, C12, C15, C21, R11,

The spatial weights matrix is usually specified to be time invariant. However, when it are constructed with economic/socioeconomic distance, trade /demographic/climatic characteristics, these characteristics might be changing over time, and then the spatial weights matrix substantially varies over time. This paper focuses on power of Moran’s I test for spatial dependence in panel data models with where spatial weights matrices can be time varying (TV-Moran). Compared with Moran’s I test with time invariant spatial weights matrices (TI-Moran), the empirical power of TV-Moran test for spatial dependence are evaluated. Our extensive Monte Carlo simulation results indicate that Moran’s I test with misspecified time invariant spatial weights matrices is questionable; Instead, TV-Moran test has shown superiority in higher power, especially for cases with negative spatial correlation parameters and the large time dimension.

No abstract

Abstract. Moran's I statistic is the most popular test for spatial dependence. When spatial weights matrices are substantially varying over time, Moran's I test based on a time invariant spatial weights matrix may cause substantial bias. This paper first investigates Moran's I tests for spatial dependence in panel data models where spatial weights matrices can be time varying. Based on time varying and time invariant spatial weights matrices, the empirical size and power of Moran's I tests for spatial dependence are evaluated and compared. Monte Carlo results indicate that size of Moran's I tests based on time varying and misspecification of time invariant spatial weights matrices have not significant difference, especially compared with misspecification time invariant spatial weights matrices, power of Moran's I tests for spatial dependence with time varying spatial weights matrices is much higher. TV-Moran tests are superior to NTV-Moran tests with the misspecification of invariant spatial weights matrix, with larger power.

This paper applies bootstrap methods to LM tests (including LM-lag test and LM-error test) for spatial dependence in panel data models with fixed effects, and removes fixed effects based on orthogonal transformation method proposed by Lee and Yu (2010). The consistencies of LM tests and their bootstrap versions are proved, and then some asymptotic refinements of bootstrap LM tests are obtained. It shows that the convergence rate of bootstrap LM tests is O((NT)−2) and that of fast double bootstrap LM tests is O((NT)−5/2). Extensive Monte Carlo experiments suggest that, compared to aysmptotic LM tests, the size of bootstrap LM tests gets closer to the nominal level of signifiance, and the power of bootstrap LM tests is higher, especially in the cases with small spatial correlation. Moreover, when the error is not normal or with heteroskedastic, asymptotic LM tests suffer from severe size distortion, but the size of bootstrap LM tests is close to the nominal significance level. Bootstrap LM tests are superior to aysmptotic LM tests in terms of size and power.