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(a ) Explain why, given these assumptions, pi p i (t ) continues to be distributed uniformly over some interval of width S.
(b ) Are there any values of X for which an innitesimal i
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(a ) Show that the expression analogous to (7.81) is a(i) =
(1 e i )
[1 (1 )(1 e i )]
.
(b ) Consider the experiment of a permanent fall in the growth r
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(so mt = mt1 +u t , where u is white noise and has a constant variance). Assume
the prots a rm loses over two periods relative to always having pt = p i
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facts that the models are built up from microeconomic foundations; that
estimated versions of the models match some important features of uctuations reasonably well; that many polic
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responses to current values or past values of variables instead of (or in
addition to) their expected future values, responses to growth rates rather
th
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Modern New Keynesian DSGE Models of Fluctuations
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They assume a costly intermediation technology. The spread between borrowing and lending rates changes because of changes both in the mar
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modeled as exogenous. And there are numerous open-economy extensions.
Examples include Obstfeld and Rogoff (2002); Corsetti and Pesenti (2005);
Benigno
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= 0.1275, = 0.99, = 0.5, and y = 0.125. For each of the disturbances, we will consider both the case of no serial correlation and a serial
correlation
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A large and active literature is engaged in constructing and estimating
more sophisticated quantitative DSGE models that, at their core,
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355
The Canonical New Keynesian Model
As a result, a major goal of extensions and variations of the modelsuch as
those we will discuss in the next sectionis to introduce forces that cause
on
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Chapter 7 DSGE MODELS OF FLUCTUATIONS
The Case of White-Noise Disturbances
The rst step in solving the model is to express output and ination in terms
of their expected future values and the
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The Canonical New Keynesian Model
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useful for analyzing actual macroeconomic uctuations, however, we need
to assume that the central bank follows a rule for the interest rate along the
li
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of an exogenous and unchanging frequency of changes in rms pricing
plans is clearly too strong. The frequency of adjustment is surely the result
of some
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The (1 at )s are falling over time, while gt is rising. Initially the linear
growth of the gt term dominates, and so the output
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an expression of the form
yt =
(1 a i )(E ti m t E t(i+1) m t ).
(7.78)
i=0
To solve the model, we need to nd the a i s. To do t
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Chapter 7 DSGE MODELS OF FLUCTUATIONS
E t m t+i E t 1 m t+i by m for all i 0. Thus pt+i rises by a i m and y t+i rises
by (1 a i ) m.
Equation (7.80) implies that the a i s are increasing in
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reintroduce the idea from the Fischer model that prices are predetermined
but not xed.
Recall that a key result from our analysis in Section 7.2 is that
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anticipated, gradual disination that occurs at a uniform rate: t = 0 for
t 0; t = 0 for t T; and t = [(T t)/T ]0 for 0 < t < T.
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reects the fact that rms do not continually obtain and use all available
information.
Our analysis of the model is similar to th
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and elegance, the new Keynesian Phillips curve is still often used in theoretical models. Following that pattern, we will meet it again in Section 7.8 a
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7.6
Empirical Applications
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The view that high ination has a tendency to continue unless there is
a period of low output is often described as the view that there is ination inertia. That is,
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to labor (see also Sbordone, 2002). Gal and Gertler therefore focus on the
equation:
t = b t1 + f E t t+1 + St + e t ,
(7.65)
where St is labors share.1
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Empirical Applications
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Rudd and Whelans second concern has to do with the information content of current ination. Replacing yt with a generic marginal cost variable,
mct , and then itera
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the process of changing prices at supermarkets, such as the costs of putting
on new price tags or signs on the shelves, of entering the new prices into
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7.5
State-Dependent Pricing
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Density
Mass of probability 1 S s
B A
1
B A
s
K
S
pi pi
FIGURE 7.1
The steady state of the Danziger model
Now consider a one-time monetary shock. Specically, supp
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Empirical Applications
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model. Time-dependent models are grossly contradicted by the data, and
purely state-dependent models fare only slightly better. The timedependent models are contra
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Price
$2.65
$1.14
1
FIGURE 7.3
399
Week
Price of a 9.5 ounce box of Triscuits (from Chevalier, Kashyap, and
Rossi, 2000; used with permission)
does not
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in the expression for rms desired prices to be less than 1) causes the
behavior of the nonadjusters to inuence the rms that change their prices,
and so causes the
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the rms that adjust are disproportionately ones that raise their prices. As a
result, it is not just the number of rms changing their prices that respon