This paper introduces a new method for identifying structural parameters in models with endogenous or mismeasured regressors, particularly in triangular systems and simultaneous equation systems. The method relies on the assumption that the regressors are uncorrelated with the product of heteroskedastic errors, which is a common feature in models with unobserved common factors or measurement errors. The paper provides estimators in the form of two-stage least squares or generalized method of moments (GMM). It also discusses set identification bounds when point identification assumptions fail and applies the methodology to an empirical example estimating Engel curves, where total expenditures may be mismeasured. The results show that the proposed methodology yields estimates similar to those obtained using traditional instruments, demonstrating its reliability in real data settings.This paper introduces a new method for identifying structural parameters in models with endogenous or mismeasured regressors, particularly in triangular systems and simultaneous equation systems. The method relies on the assumption that the regressors are uncorrelated with the product of heteroskedastic errors, which is a common feature in models with unobserved common factors or measurement errors. The paper provides estimators in the form of two-stage least squares or generalized method of moments (GMM). It also discusses set identification bounds when point identification assumptions fail and applies the methodology to an empirical example estimating Engel curves, where total expenditures may be mismeasured. The results show that the proposed methodology yields estimates similar to those obtained using traditional instruments, demonstrating its reliability in real data settings.