Estimating Equations with Information Loss on at least One Dependent Variable

Efficient, or joint, estimation of a pair of linear equations with the same explanatory variables reduces to separate estimation of each equation. This is no longer the case if information has been lost on at least one dependent variable, for example, if all that is recorded is whether some value is exceeded or not, or if information has been lost completely. This paper considers a class of problems, for which the efficient estimates can be deduced by simple intuitive arguments and which occurs frequently in practice. Some members of the class have already appeared in the literature, but have not been related, while others are new.