A note on testing for spatial error components

The two tests for spatial error components are the Kelejian-Robinson (KR) test and the LM test developed by Anselin (2001). We develop a new form for the LM test which facilitates comparisons to the KR test, and show why the LM test is superior. We develop a second test in the spirit of KR which overcomes this particular shortcoming, but in fact incurs a second shortcoming which renders it inferior even to the original KR test. We discuss this failure as well.