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Unformatted text preview: MIT OpenCourseWare http://ocw.mit.edu 14.384 Time Series Analysis Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . GMM Estimation of the NKPC 1 14.384 Time Series Analysis, Fall 2008 Recitation by Paul Schrimpf Supplementary to lectures given by Anna Mikusheva November 7, 2008 Recitation 10 GMM Estimation of the NKPC One popular use of GMM in applied macro has been estimating the NeoKeynesian Phillips Curve. An important example is Gal´ ı and Gertler (1999). This is an interesting paper because it involves a good amount of macroeconomics, validated a model that many macroeconomists like, and (best of all for econometricians) has become a leading example of weak identification in GMM. These notes describe Gal´ ı and Gertler’s paper, then give a quick overview of identification robust inference in GMM, and finally describe the results of identification robust procedures for Gal´ ı and Gertler’s models. Deriving the NKPC You should have seen this in macro, so I’m going to go through it quickly. Suppose there is a continuum of identical firms that sell differentiated products to a representative consumer with DixitStiglitz preferences over the goods. Prices are sticky in the sense of Calvo (1983). More specifically, each period each firm has a probability of 1 − θ of being able to adjust its price each period. If p ∗ is the log price chosen by firms that t adjust at time t , then the evolution of the log price level will be p t = θp t − 1 + (1 − θ ) p ∗ (1) t The first order condition (or maybe a first order approx to the first order condition) for firms that get to adjust their price at time t is ∞ n p ∗ =(1 − βθ ) ( βθ ) k E t [ mc + µ ] (2) t t + k k =0 n where mc t is log nominal marginal cost at time t , and µ is a markup parameter that depends on consumer preferences. This first order condition can be rewritten as: ∞ n n p ∗ t =(1 − βθ ) mc t + (1 − βθ ) ( βθ ) k E t [ mc t + k + µ ] k =1 =(1 − βθ )( µ + mc n ) + (1 − βθ ) βθE t p ∗ t t +1 p t − θp t − 1 Substituing in p ∗ t = 1 − θ gives: n p t − θp t − 1 = 1 − βθ E t [ p t +1 − θp t ] + (1 − βθ )( µ + mc ) 1 − θ 1 − θ t (1 − θ )(1 − θβ ) p t − p t − 1 = βE t [ p t +1 − p t ] + θ ( µ + mc t n − p t ) π t = βE t [ π t +1 ] + λ ( µ + mc n t − p t ) (3) (4) This is the NKPC. Inﬂation depends on expected inﬂation and real marginal costs (or the deviation of log marginal costs from the steady state. In the steady state µ − p = mc .). Estimation 2 Estimation Using the Output Gap Since real marginal costs are diﬃcult to observe, people have noted that in a model without capital, mc n t − p t ≈ κx t where x t is the output gap (the difference between current output and output in a model without price frictions). This suggests estimating: βπ t = π t − 1 − λκx t − λµ + t When estimating this equation,...
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