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The Aggregate Implications of Lumpy Investment
in the Presence of Nominal Frictions
First version,
November, 2007; This version, August, 2008
At
the level of the firm or plant, both capital stocks and prices are
typically changed infrequently. We describe a two-dimensional generalized
(S,s) environment which replicates both of these facts, and use it to
examine the implications of firm-specific factors for the dynamics of
output and inflation. Established work on the interaction of real and
nominal rigidities shows that the presence of firm-specific capital
increases the persistence of inflation and the real effects of monetary
shocks, by inducing firms to select smaller price adjustments than they
would if capital was freely adjustable. In the two-dimensional generalized
(S,s) model, installation costs lead to temporarily firm-specific capital,
until the benefits to investment become large enough to warrant payment of
installation costs. Capital depreciation and infrequent replacement
purchases create endogenous fluctuations in marginal cost which increase
firms' willingness to pay menu costs of price adjustment, and the
sensitivity of real aggregates to nominal disturbances falls. While the
literature typically finds the cross-sectional distribution of capital to
be irrelevant for aggregate dynamics, it becomes important in the presence
of small nominal rigidities.
Should Macroeconomists Discount Sales?
June, 2007
We
question the orthodox view that sales are unimportant for understanding
inflation. Through introduction of a new decomposition that analyzes
inflation in terms of both inflation in permanent prices and
cross-sectional changes in sale behavior, we show that at weekly
periodicity changes in permanent prices accounts for as little as 60% of
the variation in inflation. At lower frequencies (semiannual in our sample)
the contributions of sales to inflation are negligible.
Straightforward approximate
stochastic equilibria for nonlinear Rational Expectations models (with Robert G. King and Denny Lie)
August, 2008
Macroeconomists are increasingly
interested in Taylor series approximations to nonlinear rational
expectations models. Using the twin
ideas that an exact rational expectations solution typically makes all
variables depend on an infinite history of shocks and that an approximate
rational expectations solution of a desired order should therefore stretch
shocks at all dates, we develop a practical recipe for a particular Taylor
series approximation approach. The
approach has four highly desirable features. First, it leads to solutions
that are in linear state space form. Second, it permits an extension of the
effects of shocks that accomodates state-dependent responses and
time-varying forecast error volatility. Third, it allows use linear
rational expectations techniques to solve sequentially for the
approximation components ("stochastic differentials") that make
up the Taylor series approximation. Fourth, it allows the simple proof of
results on the nature of Taylor series approximations in Judd [1998] and
Schmitt-Grohe and Uribe [2004], while also resolving some puzzling aspects
of approximations in the literature that are based on alternative Taylor
series approaches.
Recursive optimal policy
design: second order approximation, decision rules, and welfare (with Robert G. King and Denny Lie)
August, 2008
Using
the natural recursive methods approach of Kydland and Prescott [1982] and
Marcet and Marimon [1998], we present a toolkit for studying optimal policy
design and evaluating welfare in a general class of models. Second-order
methods along the lines of Schmitt-Grohe and Uribe [2004] are generalized
in Johnston, King and Lie [2008] so that
new policy environments, including those with time-varying volatility and
state-dependent responses can be solved and evaluated. We present a simple
example using a familiar sticky price model and money demand, which is then
modified to include stochastic volatility of productivity. Second-order
accurate policy responses are shown to depend in quantitatively important
ways on the state vector.
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