Small Sample Properties of Tests for Spatial Dependence in Regression Models: Some Further Results

Abstract

It has now been more than two decades since Cliff and Ord (1972) and Hordijk (1974) applied the principle of Moran’s Itest for spatial autocorrelation to the residuals of regression models for cross-sectional data. To date, Moran’sIstatistic is still the most widely applied diagnostic for spatial dependence in regression models [e.g., Johnston (1984), King (1987), Case (1991)]. However, in spite of the well known consequences of ignoring spatial dependence for inference and estimation [for a review, see Anselin (1988a)], testing for this type of misspecification remains rare in applied empirical work, as illustrated in the surveys of Anselin and Griffith (1988) and Anselin and Hudak (1992). In part, this may be due to the rather complex expressions for the moments of Moran’s I, and the difficulties encountered in implementing them in econometric Software [for detailed discussion, see Cliff and Ord (1981), Anselin (1992), Tiefelsdorf and Boots (1994)]. Recently, a number of alternatives to Moran’s Ihave been developed, such as the tests of Burridge (1980) and Anselin (1988b, 1994), which are based on the Lagrange Multiplier (LM) principle, and the robust tests of Bera and Yoon (1992) and Kelejian and Robinson (1992). These tests are all asymptotic and distributed as X ²variates. Since they do not require the computation of specific moments of the statistic, they are easy to implement and straightforward to interpret. However, they are all large sample tests and evidence on their finite sample properties is still limited.