Identification and Estimation in Linear Models with Endogeneity Through Time-Varying Volatility

This paper proposes a novel control function approach to identify and estimate linear models with endogenous variables in the absence of valid instrumental variables. The identification strategy exploits time-varying volatility to address the multicollinearity problem that arises in conventional control function methods when instruments are weak. We establish the identification conditions and show that the proposed method is T-consistent and asymptotically normal. We apply the proposed approach to estimate the elasticity of intertemporal substitution, a key parameter in macroeconomics. Using quarterly data on aggregate stock returns across eleven countries, we find that the data exhibit substantial time variation in volatility, supporting the identifying assumptions. The proposed method yields confidence intervals that are broadly consistent with the general findings in the literature and are substantially narrower than those obtained using weak-instrument robust methods.