Maximum Likelihood Estimation of Dynamic Stochastic Theories with an Application to New Keynesian Pricing

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Abstract
This paper proposes a novel Maximum Likelihood (ML) strategy to estimate Euler equations implied by dynamic stochastic theories. The strategy exploits rational expec- tations cross-equation restrictions, but circumvents the problem of multiple solutions that arises in Sargent's (1979) original work by imposing the restrictions on the forcing variable rather than the endogenous variable of the Euler equation. The paper then contrasts the proposed strategy to an alternative, widely employed method that avoids the multiplicity problem by constraining the ML estimates to yield a unique stable so- lution. I argue that imposing such a uniqueness condition makes little economic sense and can lead to severe misspecification. To illustrate this point, I estimate Gali and Gertler's (1999) hybrid New Keynesian Phillips Curve using labor income share as the measure of real marginal cost. My ML estimates indicate that forward-looking behav- ior is predominant and that the model provides a good approximation of U.S. inflation dynamics. By contrast, if the same estimates are constrained to yield a unique stable solution, forward-looking behavior becomes much less important and the model as a whole is rejected.