2.2 A New Keynesian Phillips Curve One of the most important components of the New Keynesian Macro and the current DSGE models is the New Keynesian Phillips Curve (the NKPC). It assumes that the current inflation is determined by the expected inflation and the current economic ac- tivity represented by the output gap. The NKPC can serve to several purposes. First, we can use the NKPC based regressions for inflation forecasting, for testing of anchoring of inflation expectations and also simply for verifying whether the link between inflation and economic activity in the New Keynesian DSGE models can be supported by the data. Your task is to estimate the hybrid version of the NKPC that accounts for inflation persistence as well as for the forward-looking component (note that the equation does not include constant) based on a formulation of the NKPC in a seminal paper by Gal and Gertler (1999): We = Yet- 1+ 7 Entityyi 19up + et The data are for the United States. The expected inflation should be treated as plugging simply the lead of inflation at t+1 (cpiexp) and this endogenous variables should be instrumented using 1st and 4th lag of following instruments: inflation, output gap, unit labour costs, interest rate spread, price of crude oil. GMM should be used for estimation. 1. Derive the GDP gap using the Hodrick-Prescott filter with smoothing parameter A = 1600. The filter shall be applied on log of the real GDP, and the resulting gap shall be multiplied by 100 to obtain gap in % of the real GDP. 2. Show the estimates on a sample starting in 1979. What is the relative importance of lagged and expected inflation? And is the coefficient at output gap significant and positive as predicted by the theory? 3. Reestimate the model on a subsample ending in 2008:3. Did the results changed? Describe how