The Phillips curve under state-dependent pricing

Abstract

This paper is related to a large recent literature studying the Phillips curve in sticky-price equilibrium models. It differs in allowing for the degree of price stickiness to be determined endogenously. A closed-form solution for short-term inflation is derived from the dynamic stochastic general equilibrium (DSGE) model with state-dependent pricing originally developed by Dotsey, King and Wolman. This generalised Phillips curve encompasses the New Keynesian Phillips curve (NKPC) based on Calvo-type price-setting as a special case. It describes current inflation as a function of lagged inflation, expected future inflation, and current and expected future real marginal costs. The paper demonstrates that inflation dynamics generated by the model for a broad class of time and state-dependent price-setting behaviours are well approximated by the popular hybrid NKPC (with one lag of inflation) in a low-inflation environment. This provides an explanation of why the hybrid NKPC performs well in describing inflation dynamics across industrial countries. It implies, however, that the reduced-form coefficients of the hybrid NKPC may not have a structural interpretation. t, a fraction α j,t of vintage-j firms decides to adjust in accordance with (2.4), and a fraction (1 − α j,t ) decides to stick to the old price P j,t . The total fraction of firms adjusting in period t, ω 0,t , is thereforeThe details about the matrices H, A, B and C are given in Appendix B. It is sufficient to note here that e is a unity row vector with [(j + 1)(J − 1) − 1] elements and that the matrices H, A, B and C are square matrices of order [(j + 1)(J − 1) − 1]. The subscript [., j − (i − 1)] then denotes the column of matrix [H(−B) (i−1) A] and [H(−B) (i−1) ] which are premultiplied by e.We refer to (3.5) as the state-dependent Phillips curve (SDPC). According to the SDPC, the deviation of current inflation from the steady state, π t , depends on the deviations from their respective steady-state values of lagged inflation, π t−j , expected future inflation, π t+j , current and expected future real marginal costs, mc t+j , expected future probabilities of non-adjustment, ω j,t+j −ω 0,t , and of the lagged distributions of price vintages,Ω t−j .The number of leads for π t+j , mc t+j , andω j,t+j −ω 0,t are finite, while the number of lags for π t−j andΩ t−j are infinite. The infinite lag structure results from the elimination of the relative prices. However, the coefficients on these lags can be shown to converge to zero since the price adjustment cost and therefore the price-setting behaviour is stochastic implying that ω 0,t > ω j,t , ∀j = 1, 2, . . . , J − 1. How fast this comes about depends again on the assumption made about the adjustment cost distribution and on the state of the economy.The coefficients in the SDPC depend on steady-state inflation, the steady-state distribution of price vintages, the number of price vintages, and the price elasticity of demand. Those on the expected variables also depend on the real discount factor; those on ...

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