policymaking is relatively small, and the reason for this is clear. In this model, only when the
Calvo parameter is large, with ξ greater than about 0.90, can discretion be superior. Thus,
analogous to the simple model analyzed in Section 4, there appears to be a threshold value
for ξ below which discretion cannot be superior.
5.2 Adding firm-specific labor and Kimball aggregation
I now make two modifications to the DSGE model. First, following Woodford (2003, 2005),
I introduce firm-specific labor and dispense with the assumption that there is a single aggre-
gate market in which to hire labor. When labor is firm-specific, a firm making its pricing
decision will take into account the effect its price has on its real marginal costs, which are
no longer independent of the pricing decision or identical across firms. Second, drawing on
Eichenbaum and Fisher (2007) and Woodford (2005), to whom interested readers are referred,
I introduce the Kimball (1995) aggregator in place of the Dixit and Stiglitz (1977) aggregator
in the production of the final good. Although some variables, such as wt and mct require
new interpretation, in terms of the aggregate log-linear relationships, these two modifications
manifest themselves in the inflation Phillips curve, which is now given by
πt = β E∕v<.∣ + (l---^ɪ^ɪɪ θι θk mct + vt, (61)
where θι ≡ [1 + ε^∣zp~^j] and θk ≡ [1 + ɪ^rɪj] and where ω ∈ [0, ∞) is the Kimball
curvature parameter, the price elasticity of ε. When ω = 0, the Kimball (1995) aggregator is
equivalent to the Dixit and Stiglitz (1997) aggregator.15
Since {θι,θk} ∈ (0,1), it is clear that the effect of these modifications is to lower the
coefficient on real marginal costs in the Phillips curve, thereby reducing its slope for any given
value of ξ. Of course, it is the very fact that mechanisms like Kimball aggregation and firm-
specific labor markets flatten the Phillips curve that underlies their rising popularity in the
New Keynesian DSGE literature. These mechanisms can rationalize with reasonable estimates
of nominal price rigidity the small coefficient on real marginal costs found in estimated Phillips
curves.
15Although I introduce both firm-specific labor and Kimball aggregation, since both appear to be plausi-
ble, I recognize, indeed exploit, the fact that they have equivalent effects on the slope of the Phillips curve
(Eichenbaum and Fisher, 2007; Levin, Lopez-Salido, and Yun, 2007).
22