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1、Robustness of the Estimates of the Hybrid New Keynesian Phillips CurveJordi Gal, Mark Gertlerand J. David Lpez-SalidoJanuary 2003 (first draft: June 2001)AbstractGal and Gertler (1999) developed a hybrid variation of the New Keynesian Phillipscurve that relates inflation to real marginal cost, expec
2、ted future inflation and laggedinflation. GMM estimates of the model suggest that forward looking behavior is highlyimportant; the coefficient on expected future inflation is large and highly significant. Several authors have argued that our results may be the product of either some formof specifica
3、tion bias or poor estimation methods. Here we show that these claims are incorrect. We show that our results are robust to a variety of estimation procedures, including GMM estimation of the closed form, and nonlinear instrumental variables. Also, as we discuss, others have obtained very similar res
4、ults to ours using maximum likelihood techniques. Hence the conclusions of GG and others regarding the impor- tance of forward looking behavior appear to be robust.CREI and Universitat Pompeu FabraNew York UniversityBank of Spain11Introduction1.1BackgroundGali and Gertler (1999; henceforth, GG) pres
5、ent evidence to suggest that postwar U.S.inflation dynamics are consistent with a simple hybrid variant of the New Keynesian Phillips curve (NKPC). The particular model GG propose is based on Calvos (1983) staggered pricesetting framework. As in Calvo, each firm has a probability of being able to re
6、set its price in any given period, independently of the time elapsed since its most recent price adjustment.In contrast to Calvo, however, of those firms able to adjust prices in a given period, only a fraction 1 set prices optimally, i.e. on the basis of expected future marginal costs. A fraction ,
7、 on the other hand, instead use a simple rule of thumb: they set price equal tothe average of newly adjusted prices last period plus an adjustment for expected inflation,based on lagged inflation t1. The net result is a hybrid Phillips curve that nests the pure forward looking Calvo model as a speci
8、al case. In particular, let mctbe (log) real marginal cost and a subjective discount factor. Then the hybrid Phillips curve (with all variables expressed as a percent deviation from steady state) is given byt= mct+ fEtt+1 + bt1+ t(1)where=(1 )(1 )(1 )1 f=1b=1with = +1(1)1, and where the error term t
9、may arise from either measurement error or shocks to the desired markup. Note that in the limiting case where goes to zero, the equation becomes the pure forward looking NKPC, with b= 0 and f= . Assuming rational expectations and that the error term t is i.i.d., GG estimate equation (1) using Genera
10、lized Method of Moments (GMM) with variables dated t 1 andearlier as instruments. Three principle findings emerge: (1) the coefficient on real marginalcost is positive and statistically significant; (2) the coefficient bis statistically greater than zero, implying that pure forward looking model is
11、rejected by the data; (3) however, forwardlooking behavior is dominant; across a range of estimates, the coefficients fand bgenerallysum to a close neighborhood of unity, with the coefficient on lagged inflation, b, in the interval 0.2 to 0.4. In a subsequent paper, Gali, Gertler and Lpez-Salido (20
12、01, 2001a;1The expression for arises in the case of constant returns to scale. Sbordone (2002) and Gal, Gertler,and Lpez-Salido (2001a) show that with decreasing returns to scale, a given value of is associated with a smaller value of , and hence a smaller degree of price rigidity.2henceforth, GGLS)
13、 broadly confirm these estimates for U.S. data, though they tighten the range of estimates of bto the range of roughly 0.35 to 0.4. A clear message from both papers is that, while the pure forward looking version of the New Keynesian Phillips curve is clearly rejected by the data, the hybrid variant
14、 with a dominant role for forward looking behavior does reasonably well. It is in this respect that the New Keynesian Phillips curveprovides useful insights into the nature of inflation dynamics.A significant corollary result is that the use of real marginal cost as the relevant real sector forcing
15、variable in the hybrid NKPC (as the theory suggests) is critical to the empirical success.2Specifications based instead on ad-hoc “output gap” measures (e.g., detrended logGDP) do not perform well: The coefficient on the output variable is either insignificant orsignificant but with the wrong sign.
16、There has been of course considerable criticism of the output-gap based NKPC (e.g., Mankiw (2001). Our results suggest that a key reason for the lack of success of this formulation is that detrended output is not a good proxy for real marginal cost, in addition to the need to allow for a modest amount of inertial behavior ofinflation.1.2Criticism and Summary of Our ResponseSeveral recent papers (Rudd and W
