posed to consider products of the observables to increase the number of equa- tions in the system and analyzed conditions for identification; Ben-Moshe (2012) provided necessary and sufficient conditions under which this strat- egy leads to identification when there may be some dependence. B. Error correlations with more observables. The extension to non-zero E ( u$_{x}$ | z ) in model 3 is trivial if this expectation is a known function. A more interesting case results if the errors u$_{x}$ and u are related, e.g. With an unknown parameter (or function of observables) ρ if more obser- vations are available more convolution equations can be written to identify all the unknown functions. Suppose that additionally a observation y is available with Without loss of generality consider the univariate case and define w$_{x}$ = E ( xf ( z ) | z ); w$_{y}$ = E ( yf ( z ) | z ) . Then the system of convolution equations ex- pands to y = x ∗ + u$_{y}$ ; u$_{y}$ = ρu$_{x}$ + η$_{1}$ ; η$_{1}$ ⊥ , η, z. u$_{x}$ = ρu + η ; η ⊥ z. 21