This is a significant change in the parameterisation of a key macro-economic relationship for the setting of monetary policy. One way of explaining the intuition behind this steepening of the Phillips Curve is that market power reduces the degree of strategic complementarity in price-setting. In a product market closer to perfect competition, firms will be reluctant to raise prices fearful that, with other prices in the economy sticky, demand would fallaway sharply. By reducing the elasticity of demand, market power reduces this risk and thus gives rise to greater flexibility in prices – and hence a lower sacrifice ratio (for example, Ball and Romer (1990)). Let us now put this model into a stochastic setting, by assuming desired mark-ups fluctuate around a trend level according to some stationary stochastic process, log 𝜇𝑡 . These would now appear as cost-push disturbances in the Phillips curve:  𝑢𝑡 =  (1 − 𝜃)(1 − 𝛽𝜃) 1 − 𝛼 log 𝜇𝑡 𝜃 1 − 𝛼 + 𝛼𝜖  (7)  This tells us that, when mark-up shocks strike, a greater degree of market power will mean that a larger fraction of the shock will fall on prices than activity. A rise in market power, through its effect on the slope of the Phillips curve, will cause the Taylor output/inflation variability (policy possibility) frontier to rotate clockwise, with more of the burden following a shock felt by inflation than by output variability. 23  De Loecker and Eeckhout (2018).
Second stage: As mentioned earlier, to get the GMM moment conditions, we need to purge 𝜔𝑖𝑡 from its component observable to the firm. We assume 𝜔𝑖𝑡 follows an AR(1) process so that 𝜔𝑖𝑡 = 𝜌𝜔𝑖,𝑡−1 + 𝜉𝑖𝑡  (𝐴5)  where 𝜉𝑖𝑡 is an idiosyncratic, unobservable (to both the firm and econometrician) shock to technology. This is the part of 𝜔𝑖𝑡 that is assumed to be uncorrelated with optimal input choices and thus forms the basis for the GMM conditions. We know that our 𝑦̂𝑖𝑗𝑡 estimate subsumes both the inputs 𝑣𝑖𝑡 , 𝑘𝑖𝑡 directly and indirectly through 𝜔𝑖𝑡 = ℎ(𝑣𝑖𝑡 , 𝑘𝑖𝑡 ). But since it is consistent, we can express unobserved technology 𝜔𝑖𝑡 as a function of to-be-estimated 𝜷𝑗 : 41  All speeches are available online at www.bankofengland.co.uk/speeches  41  𝜔𝑖𝑡 (𝜷𝑗 ) = 𝑦̂𝑖𝑗𝑡 − 𝑓(𝑣𝑖𝑡 , 𝑘𝑖𝑡 ; 𝜷𝑗 )  (𝐴6)  So, given a 𝜷𝑗 , we can estimate equation (A5) to back out 𝜉𝑖𝑡 (𝜷𝑗 ). In the Cobb-Douglas case, we then have the GMM moment conditions 𝑘 𝐸 (𝜉𝑖𝑡 (𝜷𝑗 ) ( 𝑖𝑡 )) = 0 𝑣𝑖,𝑡−1  (𝐴7)  Note that capital is assumed to be decided one period ahead and therefore should not be correlated with the innovation in productivity. We rely on lagged COGS to identify the coefficients on COGS since current COGS is expected to react to shocks to productivity and hence 𝐸(𝑣𝑖𝑡 𝜉𝑖𝑡 ) is expected to be non-zero.