Hi - I am looking for a name/title to describe the following
simulatenous-equation model:
This starts with a linear regression model Y = X*b + e, but X is not
observed. However we know X is correlated with an observable variable Z,
with error term independent of e. So at this point, would it be correct
to say this is an instrumental variable model with Z as an instrument
for X?
Furthermore we also observe K = g(X) where g is a step function (for
example, K follows an ordered probit model with X as the latent
variable). So to get the nomenclature straight, can I say that this is a
nonlinear simultaneous equation model (one equation for Y given X, and
one for K given X), with Z as an "instrumental variable for X"?
Of course, how to estimate such a model is another story!
Thanks for whatever suggestions (names or estimation approach) you can
provide.
Al Feiveson
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