I have a rather general question regarding model identification. Following the discussions in the forum, I learned that NaNs for the standard errors in the output point to problems in model specification/identification. However, most forum posts are devoted to models where NaNs appear in (almost) all parameter estimates. My question now is whether a (very) small number of NaNs in the standard errors (in relation to the total number of parameters to be estimated) is still acceptable, especially if...
- The model is indeed very complex, e.g. ICLV in WTP space, ICLV with a high number of LV, etc.
- Two data sources are used, such as forced choice and free choice data, or stated preferences and revealed preferences data (even though a parameter for differences in scale is estimated).
In my cases, the robust standard errors can still be estimated for the parameters where NaNs appear. However, my Google search indicates that in the case of high robust standard errors the results should be treated with caution, since the standard errors may be unbiased, but not the parameter estimators themselves.
“[...] the probit (Q-) maximum likelihood estimator is not consistent in the presence of any form of heteroscedasticity, unmeasured heterogeneity, omitted variables (even if they are orthogonal to the included ones), nonlinearity of the form of the index, or an error in the distributional assumption [ with some narrow exceptions as described by Ruud (198)]. Thus, in almost any case, the sandwich estimator provides an appropriate asymptotic covariance matrix for an estimator that is biased in an unknown direction.”
Source: Greene, W. H., 2012. Econometric Analysis. Prentice Hall, Upper Saddle River, NJ., pp. 692-693
Unfortunately, I could not find a satisfactory answer in the FAQs, the forum or Google group. Therefore, I would be very happy to hear your expert opinion.
Best
Nico