Efficient estimation of macroeconomic equations with unobservable states

Macroeconomic equations, such as the consumption Euler equation, New Keynesian Phillips curve, and Taylor rule, are regularly estimated on an individual basis. However, such relations also jointly determine equilibrium, which may contain unobservable states. This paper shows how to utilize such an equilibrium model to improve the efficiency of individual estimators. In comparison with existing related approaches, this simple framework lends itself naturally to modern medium scale dynamic stochastic general equilibrium models. Not only does the derived estimator exhibit smaller asymptotic variance than equation-by-equation GMM, it also tends to be less prone to small sample distortions from weak identification.