Toward a Unified Approach to Testing for Weak Separability

In this paper we propose a unified framework for testing weak separability. We present a new three-step procedure, which is a joint test of necessary and sufficient conditions that takes account of the possibilities of both measurement error and incomplete adjustment. We illustrate the operational capability of the procedure with an empirical example. At the present time our procedure works well in medium sized samples, but may not be practical for datasets with extremely large sample sizes. As computing technology continues to advance, however, high-powered methods like the one we propose should supplant testing approaches that were originally designed to circumvent computational limitations