Practical Proposals for Specifying k-Nearest Neighbours Weights Matrices

In this article we introduce and evaluate testing procedures for specifying the number k of nearest neighbours in the weights matrix of spatial econometric models. The spatial J-test is used for specification search. Two testing procedures are suggested: an increasing neighbours testing procedure and a decreasing neighbours testing procedure. Simulations show that the increasing neighbours testing procedures can be used in large samples to determine k. The decreasing neighbours testing procedure is found to have low power, and is not recommended for use in practice. An empirical example involving house price data is provided to show how to use the testing procedures with real data.