On the <italic>I</italic> -super-2(<italic> <bold>q</bold> </italic>) Test Statistic for Spatial Dependence: Finite Sample Standardization and Properties

<title>Abstract</title> One of the most widely used tests for spatial dependence is Moran's (1950) I test. The power of the test will depend on the extent to which the spatial-weights matrix employed in computing the Moran I test statistic properly specifies existing interaction links between spatial units. Empirical researchers are often unsure about the use of a particular spatial-weights matrix. In light of this Prucha (2011) introduced the I-super- <italic>2</italic> <italic>(</italic>q<italic>)</italic> test statistic. This test statistic combines quadratic forms based on several, say q, spatial-weights matrices, while at the same time allows for a proper controlling of the size of the test. In this paper, we first introduce a finite-sample standardized version of the I-super- <italic>2</italic> <italic>(</italic>q<italic>)</italic> test. We then perform a Monte Carlo study to explore the finite-sample performance of the I-super- <italic>2</italic> <italic>(</italic>q<italic>)</italic> tests. For comparison, the Monte Carlo study also reports on the finite-sample performance of Moran I tests as well as on Moran I tests performed in sequence.