I believe that the Stata option - i.e. consistency with the ML estimator - should be the default option because (a) it is then clear what is going on, and (b) it is possible to compare the results for the two step estimator with the ML estimator. (I have a general preference for the ML estimator because the two step estimator often seems to generate spuriously low standard errors on the coefficients.) Further, the user should be discouraged from using the two step estimator with non-matching missing data for the reason that you give. But, there is an important secondary consideration. Certain types of survey design can generate systematic patterns of missing data - this would include the answers to questions that are only asked if someone is in the labour force or bought certain goods in the last month. In such cases, exclusion of all observations with missing data can seriously compromise the possibility of estimating a model reliably if the pattern of questions asked/answers is correlated with the selection probability. There is an alternative way of analysing such data. It is straightforward to let a user construct their own two step estimator with different missing data as follows: (a) estimate the probit model for selection and generate the Mills ratio as a new variable; then separately (b) estimate the OLS equation including the Mills ratio as a dependent variable. The corrections are not so difficult and anyone following this route explicitly should know what they are doing and can be warned in the documentation. All that is needed is an option in the probit model to generate the Mills ratio as a post-estimation variable. I haven't checked whether it is there already but it could easily be added. Gordon Hughes