A Response to Cogley and Sbordone's Comment on "Closed-Form Estimates of the New Keynesian Phillips Curve with Time-Varying Trend Inflation"

In their 2010 comment (which we refer to as CS10), Cogley and Sbordone argue that: (i) our estimates are not entirely closed form, and hence are arbitrary; (ii) we cannot guarantee that our estimates are valid, while their estimates (Cogley and Sbordone 2008, henceforth CS08) always are; and (iii) the estimates in CS08, in terms of goodness of fit, are just as good as other, much different estimates in our paper. We show in this reply that the exact closed-form estimates are virtually the same as the "quasi" closed-form estimates. Our estimates are consistent with the implicit assumptions underlying the first-stage VAR used to form expectations, while the estimates in CS08 are not. As a result, the estimates in CS08 point towards model misspecification. We also rebut the goodness of fit comparisons in CS10, and provide a more credible exercise that illustrates that our estimates outperform CS08's estimates.