Identification Issues in Forward-Looking Models Estimated by GMM, with an Application to the Phillips Curve

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Weak Instrument Robust Tests in GMM and the New Keynesian Phillips Curve (2009, methodology): “The other reduced-form parameter ρ1 is set equal to (1 − ρ2)ρ, so as to keep the first-order autocorrelation coefficient of xt, ρ, fixed at the value estimated from U.S. data on the labor share, as in Mavroeidis (2005).”
Generalized Method of Moments (2005, background): “The problem of weak identification can arise in macroeconomic models: for example, Mavroeidis (2005) demonstrates conditions in which it arises in GMM estimation of versions of the aggregate supply curve, equation (2) above, in which Et[ṗt+1] is replaced by ṗt+1.23 In this section, we briefly…”
Empirical Evidence on Inflation Expectations in the New Keynesian Phillips Curve (2014, background): “3.3.1 Simulation Studies Mavroeidis (2005) illustrates the points mentioned above in the context of GIV estimation of the NKPC, and Kleibergen and Mavroeidis (2009) conduct an extensive set of simulations demonstrating the performance of several alternative GMM methods.”