THE ECONOMETRICS OF MACROECONOMIC MODELLING
The NPCM defined
Let pt be the log of a price level index. The NPCM states that inflation, defined as Apt = pt — pt_i, is explained by EtApt+i, expected inflation one period ahead conditional upon information available at time t, and excess demand or marginal costs xt (e. g. output gap, the unemployment rate, or the wage share in logs):
Apt = bpi EtApt+i + bp2xt + £pt, (7.1)
where ept is a stochastic error term. Roberts (1995) shows that several New Keynesian models with rational expectations have (7.1) as a common representation—including the models of staggered contracts developed by Taylor (1979b, 1980)[55] and Calvo (1983), and the quadratic price adjustment cost model of Rotemberg (1982). GG gives a formulation of the NPCM in line with Calvo’s
work: they assume that a firm takes account of the expected future path of nominal marginal costs when setting its price, given the likelihood that its price may remain fixed for multiple periods. This leads to a version of the inflation equation (7.1), where the forcing variable xt is the representative firm’s real marginal costs (measured as deviations from its steady-state value). They argue that the wage share (the labour income share) wst is a plausible indicator for the average real marginal costs, which they use in the empirical analysis. The alternative, hybrid version of the NPCM that uses both EtApt+1 and lagged inflation as explanatory variables is also discussed later.
