New misspecification tests for multinomial logit models

Misspecification tests for Multinomial Logit [MNL] models are known to have low power or large size distortion. We propose two new misspecification tests. Both use that preferences across binary pairs of alternatives can be described by independent binary logit models when MNL is true. 
\nThe first test compares Composite Likelihood parameter estimates based on choice pairs with standard Maximum Likelihood estimates using a Hausman (1978) test. 
\nThe second tests for overidentification in a GMM framework using more pairs than necessary. 
\nA Monte Carlo study shows that the GMM test is in general superior with respect to power and has correct size