  Economic models may exhibit incompleteness depending on whether or not they
admit certain policy-relevant features such as strategic interaction,
self-selection, or state dependence. We develop a novel test of model
incompleteness and analyze its asymptotic properties. A key observation is that
one can identify the least-favorable parametric model that represents the most
challenging scenario for detecting local alternatives without knowledge of the
selection mechanism. We build a robust test of incompleteness on a score
function constructed from such a model. The proposed procedure remains
computationally tractable even with nuisance parameters because it suffices to
estimate them only under the null hypothesis of model completeness. We
illustrate the test by applying it to a market entry model and a triangular
model with a set-valued control function.
