Control function approaches and instrumental variables rely on distinct statistical restrictions (such as conditional mean independence versus conditional moment restrictions) and exhibit different performance characteristics, vulnerabilities, and consistency properties depending on model assumptions like linearity and heterogeneity.
The retrieved papers examine both instrumental variable (IV) methods and control function (CF) approaches, directly addressing how these methods differ in assumptions, performance, and applicability under varying model conditions (such as nonlinearity, endogeneity types, and heterogeneity). Papers 3, 4, and 8 explicitly compare or differentiate how IV and CF techniques operate and perform under different assumptions. No papers refute the claim, leading to a verdict of SUPPORTED.