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Single equation models with limited dependent variables have received considerable attention in the econometrics literature, but little is known about the specification and estimation of simultaneous-equation models in which some or all endogenous variables are limited. The one relevant published paper by Amemiya 1974 considers a model in which all endogenous variables are truncated at zero, reveals certain necessary restrictions on the model, and suggests a method of estimation. But his model is not applicable to all situations and the merits of his estimation procedure are confined to consistency and tractability. Here we propose an alternative specification which may be more appropriate than Amemiya's for many problems and discuss a relatively simple limited-information estimation procedure.
Nelson et al. (Sun,) studied this question.