VAR-based estimation of Euler equations with an application to New Keynesian pricing

VAR-based estimation of Euler equations exploits cross-equation restrictions that the theory imposes on a vector-autoregressive (VAR) process for market expectations. This paper shows that Sargent's (1979. A note on maximum likelihood estimation of the rational expectations model of the term structure. Journal of Monetary Economics 5, 133-143.) original approach of imposing these restrictions on the endogenous variable of the Euler equation (i.e. computing the rational expectations solution) implies multiple solutions and is therefore impracticable. The paper shows that this identification problem can be circumvented by reverse-engineering the cross-equation restrictions on the forcing variable of the Euler equation. The proposed reverse-engineering approach contrasts with the conventional approach in the literature that avoids the identification problem by constraining the system formed by the Euler equation and the VAR process to yield a unique stable rational expectations equilibrium. This uniqueness condition makes little economic sense because the VAR process is just a reduced-form approximation of true market expectations, and a simulation experiment shows that imposing uniqueness can lead to severe misspecification bias. The severity of this misspecification bias is illustrated in practice with an application to Gali and Gertler's (1999. Inflation dynamics: a structural econometric analysis. Journal of Monetary Economics 44, 195-222.) hybrid New Keynesian Phillips Curve.