Excerpt from Consistent Estimation of Scaled Coefficients
These estimates may suffice for many applications, such as judging relative marginal utilities in a discrete choice situation. Moreover, because the asymptotic distribution of the instrumental variables estimator is easily established, certain scale free hypotheses can be tested, such as zero restrictions and equality restrictions on the components of B.
More broadly, the ratio estimates provide a consistent benchmark for choosing specific modelling assumptions. Namely, if alternative functional form or stochastic distribution assumptions give rise to substantively different estimates of B, the consistent ratio estimates can guide the choice of the best specification. For example, in a binary discrete choice situation, separate estimates of 8 under logit or probit assumptions could be judged in relation to the consistent instrumental variable ratio estimates.
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