We propose new spanning tests that assess if the initial and additional assets share the
economically meaningful cost and mean representing portfolios. We prove their asymptotic
equivalence to existing tests under local alternatives. We also show that unlike two-step or
iterated procedures, single-step methods such as continuously updated GMM yield numerically
identical overidentifyng restrictions tests, so there is arguably a single spanning test.
To prove these results, we extend optimal GMM inference ...
We propose new spanning tests that assess if the initial and additional assets share the
economically meaningful cost and mean representing portfolios. We prove their asymptotic
equivalence to existing tests under local alternatives. We also show that unlike two-step or
iterated procedures, single-step methods such as continuously updated GMM yield numerically
identical overidentifyng restrictions tests, so there is arguably a single spanning test.
To prove these results, we extend optimal GMM inference to deal with singularities in the
long run second moment matrix of the influence functions. Finally, we test for spanning
using size and book-to-market sorted US stock portfolios.
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