ESTIMATION OF CONTINUOUS MODELS ON THE BASIS OF SET-VALUED OBSERVATIONS

In many empirical applications the phenomenon (Y,X) in which we are interested and for which we assume a model Y=f(X;04- e , cannot be observed exactly. Then we can only. say that (Y,X) eA clen+11 where A is a point set. Probit Tobit or discrete choice models are examples. In those cases we say that the observations are set-valued and that the latent phenomenon is observed through a filter . For the model Y=BX-1-e we present a general MIA-method for estimating B and E(eet) which bypasses the well-known problem of the computation of multi-dimensional integrals. Examples.are given for the case where we only observe max(Y1,Y2,Y ) or max (Y1,...,Y6).