Firm-Specific Capital and the New Keynesian Phillips Curve
by Michael Woodford
Columbia University
Abstract
A relation between inflation and the path of average
marginal cost (often measured by unit labor cost) implied by
the Calvo (1983) model of staggered pricing – sometimes referred
to as the "New Keynesian" Phillips curve – has been the
subject of extensive econometric estimation and testing. Standard
theoretical justifications of this form of aggregate-supply
relation, however, either assume (1) the existence of a competitive
rental market for capital services, so that the shadow
cost of capital services is equated across firms and sectors at all
points in time, despite the fact that prices are set at different
times, or (2) that the capital stock of each firm is constant,
or at any rate exogenously given, and so independent of the
firm’s pricing decision. But neither assumption is realistic. The
present paper examines the extent to which existing empirical
specifications and interpretations of parameter estimates are
compromised by reliance on either of these assumptions.
The paper derives an aggregate-supply relation for a model
with monopolistic competition and Calvo pricing in which capital
is firm specific and endogenous, and investment is subject
to convex adjustment costs. The aggregate-supply relation is
shown to again take the standard New Keynesian form, but
with an elasticity of inflation with respect to real marginal cost
that is a different function of underlying parameters than in
the simpler cases studied earlier. Thus the relations estimated
in the empirical literature remain correctly specified under the
assumptions proposed here, but the interpretation of the estimated
elasticity is different; in particular, the implications of
the estimated Phillips-curve slope for the frequency of price
adjustment is changed. Assuming a rental market for capital
results in a substantial exaggeration of the infrequency of
price adjustment; assuming exogenous capital instead results
in a smaller underestimate.
JEL Codes: E30.
Full article (PDF, 46 pages 482 kb)
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