Abstract: The identification of parameters in several economic and statistical models hinges on the underlying assumption that some, or all, of the latent signals/errors are independent. Examples include measurement error, linear simultaneous equations and triangular array models.  In the talk we will go over some algebraic techniques that can potentially be used to relax the independence assumption in favor of restrictions on higher order moment or cumulant tensors. Concrete results are discussed for linear simultaneous equations models.