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November 30, 2009
The Global Slack Hypothesis1
Enrique Martínez-García and Mark A. Wynne
Executive Summary: We illustrate the analytical content of the global slack hypothesis
in the context of a variant of the widely-used New Keynesian model of Clarida et al. (2002)
under the assumptions of both producer currency pricing and local currency pricing. The
model predicts that the Phillips Curve for domestic CPI in‡
ation will be ‡
atter, the more
important international trade is to the domestic economy. The model also predicts that
foreign output gaps will matter for in‡
ation dynamics, along with the domestic output gap.
We report some empirical evidence in support of the global slack hypothesis, and document
some of the data challenges associated with estimating foreign output gaps. We also show
that the terms of trade, or a combination of the terms of trade and the real exchange rate,
depending on what one assumes about the choice of currency in which exporters price their
goods, can capture foreign in‡
uences on domestic in‡
ation in an open economy. When the
Phillips Curve includes the terms of trade rather than the foreign output gap, the response
of in‡
ation to the domestic output gap is exactly the same as in the closed economy case.
1
Research Department, Federal Reserve Bank of Dallas. An earlier draft of this paper circulated under the
title “A note on global determinants of in‡
ation.” We thank Todd Clark, Steve Kamin and Jaime Marquez
for comments on an earlier draft, and Janet Koech and Patrick Roy for excellent research assistance. The
views expressed in this paper are those of the authors and do not necessarily re‡ the views of the Federal
ect
Reserve Bank of Dallas or the Federal Reserve System.
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1
Introduction
In recent years, a number of policymakers have addressed the question of whether greater
global economic integration, or globalization, has had a signi…cant impact on in‡
ation in the
U.S. While there appears to be broad agreement on the importance of globalization as a real
phenomenon, there is less agreement on what globalization means for in‡
ation developments
and monetary policy in the U.S. This appears to be due in part to the relative recentness,
in some sense, of globalization, and in part to serious data limitations.
Basic economic theory suggests that globalization, which we will take as being synonymous with the greater openness of the U.S. economy to trade, capital and labor ‡
ows, should
have a¤ected in‡
ation. Speci…cally, if we think of the measured in‡
ation rate as having a
trend and a cyclical component, there are sound reasons for thinking that both have been
a¤ected by the greater openness of the U.S. economy. First, globalization may have lowered
the trend rate of in‡
ation by reducing the in‡
ation bias that arises under discretionary policymaking. This is an argument that is most closely associated with Romer (1993) and Rogo¤
(2003), but it has been made by others as well.2 Second, globalization may have altered the
cyclical behavior of in‡
ation by changing the composition of the basket of goods that is
priced for aggregate price indexes, as suggested by the standard open-economy versions of
the workhorse New Keynesian model of Clarida, Galí and Gertler (2002). Globalization
may also have had a permanent one-time disin‡
ationary e¤ect by increasing the competitive
pressures faced by …rms and workers, although whether and when that one-time e¤ect is
played out seems to be an open question.
The …rst order e¤ects of greater openness, whether to trade, capital ‡
ows or labor, are on
relative prices and real returns. Whether these changes then have implications for in‡
ation,
over the medium to long term, depends very much on how monetary policy responds to
these developments. Globalization does not alter the fact that over the medium to long term
in‡
ation is ultimately determined by the actions of monetary policymakers.
The structure of this paper is as follows. We will employ an extension of the two2
See in particular the contributions of Bohn (1991), Hardouvelis (1992), Fischer (1997), Lane (1997),
Obstfeld (1998) and Evans (2007). All of these papers rely on some variant of the time consistency problem
highlighted by Kydland and Prescott (1977) and elaborated in a model of monetary policy making by Barro
and Gordon (1983). Yet it is not clear how important this problem is in practice. Some central bankers argue
that simply by being aware of the problem has made them less likely to succumb to it. Indeed Blinder (1998)
argues that it is hard to reconcile the argument that central banks have an inherent in‡
ation bias with the
in‡
ation performance in most industrial countries since the 1980s. Second, the Barro-Gordon (1983) analysis
is conducted in a simple partial equilibrium setting. Extensions to a general equilibrium setting by Neiss
(1999), and Albanesi et al. (2003a,b) have found that an increase in a central bank’ incentive to engineer a
s
surprise in‡
ation need not always result in higher in‡
ation due to o¤setting changes in the costs of in‡
ation.
The analyses of Neiss and Albanesi, Chari and Christiano are conducted in a closed economy setting - it
remains to be seen how their results translate to an open economy environment.
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country model of Clarida et al. (2002) to derive a benchmark speci…cation for the open
economy Phillips Curve. We will consider two di¤erent assumptions about how …rms set
prices in export markets: local currency pricing (which is not considered by Clarida et al.
(2002)) and producer currency pricing. We use this model to illustrate two propositions
about the impact of globalization on in‡
ation dynamics. First, foreign slack does matter
for the short-run trade-o¤ between in‡
ation and real variables. Moreover, the coe¢ cient on
domestic slack declines as the economy becomes more open. Second, international relative
prices (speci…cally, the terms of trade) can be su¢ cient to summarize the in‡
uence of foreign
factors on domestic in‡
ation in this class of models. This last result ties in with an older
literature on the Phillips Curve that includes variables like import and commodity prices
on the right hand side of Phillips Curve regressions. When we use the terms of trade to
measure foreign in‡
uences, the theoretical coe¢ cient on domestic slack is exactly the same
as in the closed economy case. These propositions hold regardless of what we assume about
how …rms set their prices internationally, that is, whether they engage in local currency
pricing or producer currency pricing.
We then present some empirical evidence in support of the open economy Phillips Curve
speci…cation. We argue that when it comes to testing open economy speci…cations of the
Phillips Curve, abstracting from changes in trend in‡
ation is important and makes a big
di¤erence to the estimates. We conclude with a brief discussion of the data challenges
associated with estimation of open economy Phillips Curves, and the conceptual di¢ culties
associated with the measurement of output gaps.
2
Globalization and the cyclical component of in‡
ation
- the global slack hypothesis
For the purposes of thinking about in‡
ation dynamics in a multi-country environment, the
basic two-country model of Clarida et al. (2002) has proven to be quite useful. We will work
with a simple extension of that model, which is described in detail in the Appendix.3 Here
we give a quick qualitative review of the main features of the framework.
In the basic setup, there are two countries, designated home (H) and foreign (F ) that
have mass of households n and 1 n respectively but are otherwise symmetric and identical
in all respects. There is a continuum of goods produced by a continuum of monopolistically
competitive …rms with a linear-in-labor technology that is subject to aggregate productivity
shocks. Each …rm supplies the home and foreign markets. All consumption goods are
3
The exposition that follows draws heavily on an extension of Martinez-Garcia (2008).
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perishable - there are no consumer durables or capital. The monopolistically competitive
…rms that are engaged in production set prices to maximize pro…ts subject to a Calvo (1983)
pricing constraint, and supply all that is demanded at a given price.
Household preferences in each country are de…ned over aggregate consumption and labor.
Aggregate consumption in each country is in turn a composite of domestically produced and
foreign produced goods, and the composite domestic and foreign goods are assumed to be
imperfect substitutes. The bundles of domestic and foreign goods that each household consumes are in turn assumed to be composites of an in…nite number of domestically produced
and foreign produced varieties of goods, with these varieties also assumed to be imperfect
substitutes. Furthermore we assume that consumers in each country have a preference for
domestically produced goods (home bias). Households make consumption plans and labor
supply decisions to maximize utility, yielding demand functions for each variety of domestic
and foreign goods, along with standard intratemporal and intertemporal optimality conditions. The labor force is homogenous within a country and immobile across borders, and the
national labor markets are perfectly competitive.4 Hence, wages are equalized within each
country but not necessarily across countries.
International trade is assumed to be costless, and there is no active role for government.
The only nominal friction in the model is the nominal price stickiness in the goods market
which is modelled à la Calvo (1983). Firms may set prices in their local currency (producer
currency pricing), or in the currency of the market into which they are selling (local currency
pricing). When …rms engage in local currency pricing, deviations of the law of one price
occur. Furthermore, …rms engage in third-degree price discrimination across markets and
enjoy monopolistic power in their own product variety. Re-selling is precluded so that the
optimal pricing policy is not reversed by re-sellers exploiting the arbitrage opportunities that
arise in the goods market. The model is described in more mathematical detail in Tables
A1-A4 of the Appendix.
To explore the …rst-order e¤ects of shocks on the dynamics of the economy, we loglinearize the equilibrium conditions around the deterministic zero-in‡
ation steady state. Let
xt
b
ln Xt ln X denote the log deviation of a variable Xt from its steady state value X.
Assuming that Calvo contracts are symmetric across countries, the log-linearized aggregate
supply equation for the domestic …rm in the home market can be written in a familiar form
as,
bH = Et bH + mct pH ;
c
bt
(1)
t
t+1
where
4
(1
)(1
)
. Of course, equation (1) simpli…es to the standard New Keynesian
Clarida et al. (2002) assume that households are monopolostically competetive suppliers of labor.
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Phillips Curve when the consumption basket consists solely of domestically produced goods.
The log-linearized aggregate supply equation for the the foreign …rm selling in the domestic
market can be written analogously as,
bF = Et bF +
t+1
t
p F + st :
bt
b
mct
c
(2)
Substitution of each of these expressions into the log-linearized equation for the CPI in
the home country, i.e.
(3)
)bF ;
bt = bH + (1
t
t
then gives us,
bt = Et (bt+1 ) +
pH + (1
bt
mct
c
) mct
c
p F + st
bt
b
:
(4)
This is a fairly general expression for the open economy New Keynesian Phillips Curve.
It relates domestic CPI in‡
ation to expected future CPI in‡
ation and a weighted average
of domestic and foreign real marginal costs. By invoking additional assumptions on …rms’
pricing behavior and other primitives of the model we will see that it is possible to rewrite
the Phillips Curve in terms of domestic and foreign output gaps.
2.1
Producer currency pricing
We will start with the case of producer currency pricing as in Clarida et al. (2002). Under
producer currency pricing, the law of one price holds and exchange rate pass-through is
ation can
bt b
complete, i.e. pF = pF + st . The expression for the dynamics of domestic CPI in‡
bt
then be rewritten as,
bt = Et (bt+1 ) +
mct
c
pH + (1
bt
) mct
c
pF
bt
;
(5)
which tells us that domestic CPI in‡
ation is a function of expected future domestic CPI
in‡
ation and a weighted average for domestic and foreign real marginal costs. In turn, the
log-linearized real marginal cost functions for domestic and foreign …rms can be written as,
mct
c
mct
c
pH =
bt
pF
bt
=
bt + 'bt + (1
c
y
bt + 'bt
c
y
c
tott
c
) tott
(1 + ') bt ;
a
(1 + ') bt ;
a
(6)
(7)
where we have made use of the labor market clearing conditions as well as the fact that
c
whenever the law of one price holds terms of trade can be expressed as tott = pF st pH =
bt b bt
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c
pH , in which case pt pH = (1
bt
b bt
)tott .
To rewrite the expressions for real marginal costs in terms of gaps (deviations from
the frictionless allocation), we note that the potential or frictionless level of output of the
domestic and foreign countries is de…ned as the output level that prevails whenever the
F
c pH
c
monopolistic …rms price as if prices were fully ‡
exible, i.e. mct bt = 0 and mct bt = 0.5
p
b
We use the notation x to denote the log deviation of a variable Xt from its frictionless
steady-state level X. Thus the pricing equations in the frictionless case can be written in
log-linear terms as,
pF
bt
c
0 = mct
c
0 = mct
bH = bt + 'bt + (1
pt
c
y
bF
pt
= bt + 'bt
c
y
c
)tott
c
tott
(1 + ')bt ;
a
(1 + ')bt :
a
(8)
(9)
We can then use these expressions to rewrite the log-linearized real marginal cost functions
in gap form as,
mct
c
mct
c
pH =
bt
pF
bt
=
(bt
c
(bt
c
bt ) + '(bt
c
y
bt ) + '(bt
c
y
bt ) + (1
y
bt )
y
c
c
) (tott tott );
c
c
(tott tott ):
(10)
(11)
That is, real marginal costs for domestic …rms selling into the domestic economy can
be written in terms of a domestic consumption gap (deviation of consumption from its
frictionless level), (bt bt ), a domestic output gap (deviation of output from its frictionless
c
c
bt ), and a terms of trade gap (deviation of the terms of trade from its frictionless
level), (bt y
y
c
c
level), (tott tott ). Likewise, for foreign producers selling into the domestic market, real
c
marginal costs can be written in terms of a foreign consumption gap, (bt bt ), a foreign
c
c ). Substitution back into equation
c
output gap, (bt bt ), and a terms of trade gap, (tott tott
y y
(5) would then give us an expression relating domestic CPI in‡
ation to expected future CPI
in‡
ation, domestic and foreign output gaps, domestic and foreign consumption gaps and the
terms of trade gap.
However, it is possible to simplify further and derive an expression for the Phillips Curve
in a more familiar form that relates in‡
ation to measures of the output gaps alone by rewriting
the consumption gap and terms of trade gap in each country in terms of the output gaps.
After much algebra (outlined in detail in Martínez-García (2008)) we obtain the following
5
The Dixit-Stiglitz pricing rule for monopolistic competition under ‡
exible prices implies that prices are
equal to a mark-up over marginal costs. The mark-up is a function of the elasticity of substitution across
varieties, , and time-invariant. Therefore, the pricing rule can be log-linearized around the steady state in
terms of prices and marginal costs as stated. The mark-up only a¤ects the steady state allocation, and it is
conventional to add a labor subsidy to eliminate this distortion as well.
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expressions,
mct
c
mct
c
pF =
bt
(
pH = ' +
bt
(1
+
+ '+
1
(
+(
)(1
1
))
1
(
(
)(
+(
)
+(
1
1
)(
)(1
)(
)(1
)+(1
)(
) (1
1
)
(
)(
)
yt
b
)
)(
)(
)
yt
b
)
) +
1
n( 1
bt ;
y
bt +
y
(12)
(13)
bt ;
y
yt
b
)
bt +
y
yt
b
)
)
))+ 1 (
)(1
(
(
)(
(
(1
)+ 1 (
)
n)
. If we impose the assumption of no
n(
)
)+(1 n)( 11 n )
n
home bias in consumption (as do Clarida et al. (2002) and Woodford (2007)), i.e. = ,
then we can write real marginal costs as,
where
mct
c
mct
c
n( n )
+(
n( n )+(1 n)(
pH =
bt
pF
bt
=
and
1
1 n
+ (1
'+
1
)
yt
b
yt
b
bt + (1
y
bt + ' +
y
(1
)
)+
1
yt
b
yt
b
bt :
y
bt (14)
y ;
(15)
If we additionally assume (as also do Clarida et al. (2002) and Woodford (2007)) that the
elasticity of substitution between the home and foreign bundles of varieties is = 1, which
implies that the consumption aggregator is of the Cobb-Douglas type, then the expressions
above for the real marginal costs become,
mct
c
mct
c
pH = [' + ] yt
bt
b
pF
bt
= [' + ] yt
b
bt ;
y
bt :
y
(16)
(17)
Domestic and foreign real marginal costs can be written solely in terms of the domestic and
foreign output gaps.
However, in an open economy the foreign output gap matters not just for the determination of the marginal cost of foreign …rms (and, therefore, to capture the e¤ects on imported
prices) but also for the determination of domestic marginal costs because: (a) domestic …rms
do export their products abroad, so higher foreign demand will force them to pay higher domestic wages; and (b) variations in the terms of trade against foreign competition will a¤ect
their domestic market share and consequently their domestic costs.
We can use the expressions for real marginal costs in (12) and (13) to derive a general
characterization of the domestic Phillips Curve for overall CPI in‡
ation in terms of domestic
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and foreign output gaps alone. The dynamics of domestic CPI in‡
ation can be written as,
bt = Et (bt+1 ) +
where,
;x
;x
h
1
'+ @
' (1
yt
b
;x
0
1
0
)+ @
bt +
y
(1
yt
b
;x
(
) (1
)
(
)(
)
1
)+
1
(
(
i
bt
y
(18)
;
1
A;
(19)
) (1
)(
)
)
1
A:
(20)
If we impose the Clarida et al. (2002) and Woodford (2007) assumption of no home bias in
consumption, = , the coe¢ cients on the output gap terms simplify to,
;x
;x
=
(21)
( + ') > 0
= (1
(22)
) ( + ') > 0:
That is, the foreign output gap will matter for domestic CPI in‡
ation, and there is no
ambiguity about the sign of the e¤ect. Note also that the importance of the foreign output
gap activity is greater, the greater the importance of foreign goods in the consumption
bundle, 1
. Thus, in the context of this simple model at least, two key features of
the global slack hypothesis are apparent. First, the output gap in the foreign country, as
measured by the deviation of output from its frictionless level, matters for domestic CPI
in‡
ation. Second, the Phillips curve will be ‡
atter (relative to the domestic output gap), the
more important are foreign goods in the domestic consumption bundle.
2.2
Local currency pricing
The second case that we need to consider is the assumption of local currency pricing (LCP),
where the law of one price no longer holds. When the general expression for the open
economy Phillips Curve in (4) is rewritten in terms of real marginal costs, we obtain,
b
where dt
goods.
bt = Et (bt+1 ) +
st + p F
b bt
h
mct
c
pH
bt
+ (1
) mct
c
pF
bt
b
+ dt
i
;
(23)
pF is a measure of the deviation from the law of one price for foreign
bt
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The log-linearized expressions for marginal costs under the local currency pricing assumption are,
mct
c
mct
c
pH =
bt
pF
bt
bt + 'bt + (1
c
y
bt + 'bt
c
y
=
c
tott
c
) tott
(1
b
dt
b
) dt
(1 + ') bt ;
a
(24)
(1 + ') bt ;
a
(25)
b
b bt
where dt
pH st pH is a measure of the deviation from the law of one price for
bt
domestic goods. Under local currency pricing, an important distinction needs to be made
between the terms of trade and the relative price of foreign goods. The terms of trade are
c
still de…ned as tott = pF st pH in log-deviations but are no longer equal to pF pH due
bt b bt
bt
bt
to the fact that the law of one price no longer holds in general. As before, the potential or
frictionless level of output of the domestic and foreign economies is de…ned as the output
H
c
level that prevails whenever the monopolistic …rms price according to mct bt = 0 and
p
F
c
mct bt = 0 respectively. This gives us the following pair of equations to characterize the
p
frictionless allocation,
0 =
0 =
bt + 'bt + (1
c
y
bt + 'bt
c
y
c
tott
c
) tott
(1 + ') bt ;
a
(26)
(1 + ') bt ;
a
(27)
which are identical to (8) and (9) since bt = bt = 0 (because, by de…nition, the law of one
d
d
price holds in the frictionless equilibrium).
We can use these relationships to rewrite the expressions for real marginal costs in terms
of gaps as before,
mct
c
mct
c
pH =
bt
pF
bt
bt + ' yt
c
b
bt
c
=
bt + (1
y
bt + ' yt
c
b
bt
c
bt
y
c
) tott
c
tott
c
tott
c
tott
(1
b
dt :
b
) dt ;
(28)
(29)
Note that these equations are identical to equations (10) and (11), except for the presence of
b
b
the terms dt and dt capturing the deviations from the law of one price. Working from these
equations, we can rewrite the Phillips Curve in terms of output gaps, the terms of trade and
the real exchange rate as,
bt = Et (bt+1 ) +
where
;x
and
h
;x
;x
yt
b
bt +
y
;x
yt
b
bt +
y
;rp
(
c
) tott
rst
b
i
; (30)
are de…ned exactly as in (19) and (20), while the new composite
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parameter,
;rp ,
is de…ned as,
1 (
)(
(
)(1+(
;rp
(1
(
) (
)(1+(
)
))
)
))
(1
1
)+(
(
1
)(
)(
)(1
)(
)
)
(31)
:
But this characterization of the Phillips Curve is well-de…ned only if 6= .
Imposing the assumption of no home bias in consumption (as do Clarida et al. (2002)
and Woodford (2007)), i.e. = , we can derive an expression for the Phillips Curve in the
following terms,
bt = Et (bt+1 ) +
h
( + ') yt
b
bt + (1
y
) ( + ') yt
b
bt + (1
y
i
n)rst ;
b
(32)
where (1 n) denotes the foreign population size. In this special case, it su¢ ces to use the
real exchange rate to account for the deviations from the law of one price without having
to subtract the e¤ect of the terms of trade. The coe¢ cients on the domestic and foreign
output gaps can be obtained from the more general composite parameters
;x and
;x
de…ned in (19) and (20) under the assumption of no home bias, but the same is not true of
the composite parameter
;rp .
The two propositions we stated above continue to hold: First, the output gap in the
foreign country, as measured by the deviation of output from its frictionless level, matters for
domestic CPI in‡
ation. Second, the Phillips Curve will be ‡
atter (relative to the domestic
output gap), the more important are foreign goods in the domestic consumption bundle.
The only di¤erence with the Phillips Curve expression we derived under the assumption of
producer current pricing is the presence of a term involving the real exchange rate (net of
terms of trade e¤ects) that captures the contribution of deviations of the law of one price,
whose importance increases with the size of the population of the foreign country (rather
than with its openness to foreign trade).
2.3
Hybrid case
Recall the characterization of CPI in‡
ation under the assumption of producer currency pricing in equation (18) and the characterization of CPI in‡
ation under the assumption of local
currency pricing (whenever 6= ) in equation (30). If we assume that a constant fraction
of …rms 0
1 price according to the local currency pricing rule in each country, CPI
in‡
ation will then be determined as,
bt = (1
) bP CP + bLCP ;
t
t
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with the Phillips Curve then being given by,
bt = Et (bt+1 ) +
h
;x
yt
b
bt +
y
;x
yt
b
bt +
y
;rp
(
c
) tott
rst
b
i
: (34)
On top of the usual assumptions, this result de…nes the in‡
ation dynamics under the assumption that the fraction of local currency pricing …rms is exogenously given, does not
change over time, and is identical in both countries.
While this expression has its conceptual limitations, it is useful in the sense that it
suggests that deviations from the law of one price as re‡
ected in international relative prices
(the real exchange rate net of terms of trade e¤ects) cannot be excluded and ignored in the
Phillips Curve except in the polar case where all …rms in all countries engage in producer
currency pricing (the implicit assumption in Clarida et al. (2002)).
2.4
Discussion
The key parameter determining the quantitative signi…cance of foreign factors for domestic
CPI in‡
ation developments in this and related models is the share parameter for foreign
goods in the consumption basket, 1
. It might be argued that given the composition
of the consumption bundle of the representative U.S. household, and speci…cally the fact
that it seems to be heavily skewed towards goods and services that are either nontraded or
nontradable, this puts a signi…cant limit on how important, in a quantitative sense, foreign
economic activity is likely to be for U.S. in‡
ation developments. As Figure 1 shows, while the
share of imports of goods and services in U.S. GDP has increased from just over 4 percent to
more than 18 percent at the recent peak, international trade in goods and services remains
a lot less important for the U.S. economy than for many other smaller economies.
However, we think such a conclusion would be premature. There are a number of other
channels through which foreign economic activity may matter for domestic in‡
ation dynamics
that are absent from the model outlined above, such as trade in intermediate products and
commodities, and immigration and outsourcing. Leith and Malley (2007) and Rumler (2007)
explore extensions of the basic model sketched out above that allow for trade in intermediate
inputs. The analysis above was conducted in the context of an environment where goods
are mobile across national borders, but labor is not.6 Engler (2009) examines the e¤ect of
labor mobility in the standard New Keynesian model. Engler’ analysis is motivated by
s
the observation that in many cases migration is not a once and for all decision but instead
6
Woodford (2007) also considers a version of the model where there is assumed to be a single global
market for labor, and shows that in such a case the global output gap matters not just for the evolution of
CPI in‡
ation, bt , but for the evolution of domestic product price in‡
ation, bH , as well.
t
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has a signi…cant high frequency component as well. Engler’ analysis is conducted from the
s
perspective of the source country –that is, he looks at how the Phillips Curve relationship
in a small open economy is a¤ected by the possibility that domestic workers can supply
e¤ort to foreign as well as domestic …rms - and he shows that the opening of the labor
market tends to ‡
atten the domestic Phillips Curve. Razin and Binyamini (2008) further
extend Engler’ framework to consider the impact of immigration from the perspective of
s
the receiving country, albeit in the two-country setting of Clarida et al. (2002), and show
that this too leads to a ‡
attening of the Phillips Curve for the domestic economy.7
3
Evidence that foreign activity a¤ects U.S. in‡
ation
There has already been a signi…cant amount of empirical work looking at the impact of
globalization on in‡
ation, and at the impact of foreign economic activity in particular. Orr
(1994) was one of the earliest attempts to evaluate the likely restraining e¤ect of greater slack
overseas on U.S. in‡
ation. Orr focused on imports from the other members of the G7 group
of countries, which at the time he was writing accounted for over half of U.S. imports. Orr
found that despite the restraining e¤ect of excess capacity overseas on producer level in‡
ation
in these trading partners in the early 1990s, it did not translate into signi…cantly lower prices
for U.S. imports from these countries, primarily due to o¤setting movements in exchange
rates. Garner (1994) also investigated the possible impact of the greater openness of the U.S.
economy on simple Phillips Curve relationships between U.S. in‡
ation and domestic capacity
utilization but found no statistically signi…cant e¤ect of the trade share. He also looked at
the e¤ect of foreign capacity utilization, proxying it by capacity utilization in Canada since
it is the U.S.’largest trading partner, but again found no e¤ect.
Tootell (1998) was a more comprehensive assessment of whether resource utilization in
the G7 countries matters for U.S. in‡
ation. Tootell’ point of departure was to ask whether
s
globalization could account for the “missing in‡
ation” in the U.S. in the late 1990s, and he
used a traditional backward looking Phillips Curve speci…cation to address this question.
Tootell found no evidence that foreign slack (as measured by the deviation of unemployment
in the other G7 countries from estimates of the natural rates in those countries) mattered for
U.S. in‡
ation, at least through the middle of 1996, when his sample period ended. Wynne
and Kersting (2007) attempted to replicate Tootell’ …ndings using a similar sample period,
s
and also reported the results of simply extending the sample period to include the past
decade. When they extended the sample period to include the past decade, they found that
the estimated coe¢ cient on the domestic slack variable declined in magnitude and statistical
7
Bentolila et al. (2008) also consider the implications of immigration for in‡
ation dynamics.
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signi…cance (as many other studies have shown), while that on the foreign slack variable
increased. Global slack, at least in the other G7 countries, seems to matter for U.S. in‡
ation
after all.
Much of the recent debate about the implications of globalization for in‡
ation stems
from the widely cited paper of Borio and Filardo (2007) which examined whether global
slack may play a greater role in the determination of domestic in‡
ation than domestic slack.
Rather than employ a labor-market based measure of slack, they use a measure based on
the deviation of aggregate output from potential, and broaden the de…nition of “foreign”
to include not just the other members of the G7, but several of the U.S.’other top trading
partners as well. They found a statistically signi…cant role for the foreign output gap in
explaining in‡
ation in the U.S., and a declining role for the domestic output gap. Subsequent
research by Ihrig et al. (2007) cast doubt on the robustness of Borio and Filardo’ results.
s
Ihrig et al. noted two potential problems with the empirical analysis of Borio and Filardo:
…rst, their de…nition of the dependent variable in their regressions as the di¤erence between
headline consumer price in‡
ation and trend core in‡
ation; and second, their measurement of
in‡
ation as the four-quarter change in the price index rather than the annualized quarterly
change in the price index.
Taking these earlier studies as a point of reference, we decided to investigate whether we
can detect any relationship between in‡
ation in the U.S. and domestic and foreign resource
slack. We consider three very standard measures of resource slack to begin with, namely
capacity utilization in manufacturing, the unemployment rate and the output gap. We start
by looking at the G7 group of countries (for reasons that will become apparent later), de…ning
foreign slack as a simple import-weighted average of the various slack measures. Figures 2-4
plot capacity utilization in U.S. manufacturing, the U.S. unemployment rate and the U.S.
output gap along with the foreign equivalents for the other countries in the G7. Two points
are immediately obvious. First, the short historical coverage of some of the series: our
foreign capacity utilization series only starts in 1985 (the earliest date for which a capacity
utilization measure for U.K. manufacturing is available), while the foreign output gap series
is only available from 1991 (due to German reuni…cation). Second, the U.S. and foreign
measures of resource utilization are highly correlated, suggesting that it may be di¢ cult to
discern a distinct e¤ect on U.S. in‡
ation from resource utilization outside the U.S.8
Table 1 reports the results of a series of simple least squares regressions of headline
and core in‡
ation on the three measures of resource utilization in the U.S. and the other
8
Note that while capacity utilization rates in the U.S. and the rest of the G7 seem to move in tandem most
of the time, there are episodes when the two diverge. The striking discrepancy between capacity utilization
rates in the U.S. and the rest of the G7 in the early 1990s was what motivated Orr’ (1994) analysis.
s
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G7 countries. The simple speci…cations we start with are motivated by the theoretical
analysis above that assumes producer currency pricing, and speci…cally, equation (18). Our
objective here is not to come up with a comprehensive model of U.S. in‡
ation dynamics,
but rather to simply explore whether there are any hints in the data that foreign in‡
uences
may be important. Note that for …ve of the six speci…cations reported, the coe¢ cient on the
foreign resource utilization variable is statistically signi…cant at conventional levels, and of
the right sign. By contrast, the sign on the U.S. resource utilization variable is always of the
wrong sign, and is never statistically signi…cant. The explanatory power of these very simple
2
speci…cations, as measured by the R , is surprisingly high in some cases, and especially where
core in‡
ation is used as the dependent variable. But the results of the Breusch-Godfrey test
for serial correlation in the residuals suggest that all but one of the estimated models are
potentially misspeci…ed.
Recall that the Phillips Curve expressions that we derived above were in terms of deviations from a steady state. The New Keynesian analytical framework provides an account of
in‡
ation dynamics around a (possibly time-varying) steady state, so it seems logical, therefore, when looking for patterns in the data, that we might want to focus on the cyclical
components of di¤erent variables.9 We measure the cyclical components of headline and
core (ex. food and energy) PCE in‡
ation using the Hodrick-Prescott …lter with smoothing
parameter = 1600 and Figures 5 and 6 show the time series for the overall, trend and cyclical components of our two in‡
ation measures. Table 2 reports the results we obtain when we
re-estimate the speci…cations in Table 1 using detrended headline and core in‡
ation as the
dependent variable.10 Again, the estimated coe¢ cients on the foreign resource utilization
variables are always of the right sign, and in many cases are statistically signi…cant. The
coe¢ cient estimates on the U.S. resource utilization variables are also of the correct sign
(except in the speci…cation with core in‡
ation and the output gap), but only statistically
signi…cant in one case. While the explanatory power of these speci…cations is somewhat lower
than for the speci…cations that use the raw in‡
ation measures, there no longer appears to
be a problem with serial correlation in the residuals (as determined by the Breusch-Godfrey
test) for the speci…cations that use core in‡
ation as the dependent variable.
What if we estimate simple speci…cations motivated by the expression we derived for the
open economy Phillips Curve relationship under the assumption of local currency pricing in
9
Carlstrom and Fuerst (2008) also emphasize the importance of controlling for changes in trend in‡
ation
when looking at the relationship between economic slack and in‡
ation. Balakrishnan and Ouliaris (2006)
argue that changes in external trade and global factor markets tend to impact in‡
ation primarily over the
business cycle.
10
In a slight abuse of notation, in our empirical work we use hats “^”to denote the cyclical component of
a series rather than the (log) deviation of the series from a steady state value.
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equation (30) above? These speci…cations include the terms of trade and the real exchange
rate on the right hand side, and as such resemble the speci…cations estimated by Ihrig et
al. (2007).11 Table 3 reports the results. The coe¢ cient on foreign slack as measured by
the unemployment rate is not statistically signi…cant in either the speci…cation for headline
or core in‡
ation. The coe¢ cient on foreign slack as measured by capacity utilization is
signi…cant at the 10% level in the speci…cation for headline in‡
ation, but the strongest
results are obtained when we use the output gap measures. The coe¢ cient on the U.S.
output gap is not signi…cant for either headline or core in‡
ation, but the foreign output gap
is, and is signi…cant at the 1% level in the estimated equation for core in‡
ation. However,
note that all of the estimated equations seem to have serially correlated residuals, although
as in Tables 1 and 2, the problem seems less severe for the speci…cations for core in‡
ation.
To summarize, if we de…ne the world as consisting of just the G7 economies, ordinary
least squares estimates of simple linear Phillips Curve speci…cations motivated by a standard
open economy extension of the New Keynesian model are consistent with the global slack
hypothesis. That is, there seems to be a more signi…cant relationship (in a statistical sense)
between slack in the other economies of the G7 and in‡
ation in the U.S., than between slack
in the U.S. and in‡
ation in the U.S. The evidence is fragile, to be sure, but it does suggest
that there is empirical content to the global slack hypothesis.
So far we have limited ourselves to reporting results where the rest of the world is de…ned
as the other members of the G7. However, while the G7 group still accounts for a signi…cant
share of world GDP and of U.S. imports, these shares are declining, as Figure 7 shows.
A more comprehensive empirical evaluation of the global slack hypothesis would look at a
larger group of countries to measure global slack. However we immediately run into severe
data problems, even if we limit ourselves to the economies of the G20, or our largest trading
partners. For example, estimates of the unemployment rate for China are only available
from 2000, and then only for urban areas. Estimates of capacity utilization in Chinese
manufacturing are only available from 2002, and there are still no o¢ cial estimates of the
level of Chinese real GDP on a quarterly basis that could be used to estimate an output gap
for China.
Figures 8-10 illustrate the data challenge in graphical form. Referring back to the basic
theory, it suggests that the relevant measure of slack in an estimated Phillips Curve is some
sort of trade weighted average of slack in each of our trading partners. Figures 8-10 plot
time series of,
X
impi
t
i
P
(35)
xt ( ) =
t ( );
i2G26
impi
t
i2G26
11
Ihrig et al. (2007) specify in‡
ation as a function of lagged in‡
ation, domestic and foreign slack, and
import, energy and food prices.
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where 2 fcapacity utilization rate in manufacturing, unemployment rate, output gapg,
impi is nominal U.S. imports from country i at date t for the 26 countries (where the euro
t
area is counted as a single country) that are included in the Federal Reserve Board’ broad
s
trade weighted value of the dollar index, and i ( ) = 1 if the slack measure is available
t
for country i as of date t, and i ( ) = 0 otherwise. For example, if we were interested in
t
slack as measured by the unemployment rate and it were possible to obtain a measure of
unemployment for all of our trading partners for the entire sample period, then xt = 1 at all
dates t. If at the beginning of the period we can only obtain estimates of the unemployment
rate for countries that account for half of our imports, then xt = 0:5 initially. As more
countries start reporting unemployment on a regular basis, xt would rise over time. As
our trade shifts towards countries for which we are unable to obtain the necessary data, xt
will fall. In addition to capturing the availability of slack measures for our various trading
partners, this measure also captures the shifting composition of our imports.
Examination of the Figures shows that over the period since 1970, we can at best measure
the degree of capacity utilization in manufacturing in countries that account for about three
quarters of our imports. Prior to 1985, the best we can do is just over 50 percent. For
unemployment we can do better, but only towards the end of the period. For the output
gap, the situation is in between, with coverage of countries accounting for more than 80
percent of our imports towards the end of the sample.
With these caveats about the coverage of various slack measures in mind, we re-estimated
the simple Phillips Curve speci…cations for the broader G26 group of countries that supply
most of the U.S.’imports. We limited ourselves to the output gap as the measure of slack,
and the results are reported in Table 4. Figure 11 shows how this measure compares with the
measure for the U.S. and the other countries of the G7. We addressed the tradeo¤ between
sample size and country coverage by including all countries for which real GDP estimates
are available on a quarterly basis from 1996 on. Note that the coe¢ cient on the foreign
slack measure is statistically signi…cant in three of the four speci…cations we report, while
the coe¢ cient on the domestic slack measure is not signi…cant in any of the speci…cations.
Note that our estimate of the foreign output gap in these regressions does not include China,
due to the idiosyncrasies of China’ national accounts, nor, indeed, measures of the output
s
gap for about 20 to 30 percent (depending on the year) of our trading partners.
So far we have reported simple ordinary least squares estimates of the Phillips Curve
to evaluate the global slack hypothesis, taking lagged in‡
ation as a proxy for expected
future in‡
ation in the various speci…cations. We can also use the fact that under rational
expectations the forecast error bt+1 Et bt+1 will be uncorrelated with information dated t
and earlier to obtain a set of orthogonality conditions that allow us to estimate our most
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general speci…cation of the Phillips Curve (equation (34) above) using the generalized method
of moments (GMM) under the assumption that a fraction (1
) of …rms engage in producer
currency pricing, while the remainder engage in local currency pricing,
Et
n
bt
bt+1
h
+
;x
;rp
yt
b
(
bt +
y
c
)tott
;x
rst
b
yt
b
i
bt
y
(
o
zt = 0;
c
) tott
rst :::
b
(36)
where zt is a vector of variables dated t and earlier. Table 5 reports the results of estimating
the model using GMM, where the vector of instruments zt includes four lags of the headline
PCE in‡
ation rate, four lags of the cyclical component of the labor share in the U.S., four
lags of the import-weighted labor share in the other G7 countries, one lag of the output
gap in the U.S., one lag of the trade weighted output gap in our main trading partners
and four lags of the relative price of oil in the U.S. For six of the eight speci…cations, the
estimated coe¢ cient on the foreign output gap is statistically signi…cant at the 1% level and
of the correct sign, while for only three of the eight speci…cations is the coe¢ cient on the U.S.
output gap statistically signi…cant. Note also that the coe¢ cients on the foreign output gaps
are statistically signi…cant in two of the four speci…cations that include the terms of trade
and the real exchange rate as additional explanatory variables, speci…cally the speci…cations
for core in‡
ation.
3.1
Discussion
The evidence presented here suggests that the global slack hypothesis has some empirical
content, but it is equally clear that the empirical relationship between the cyclical component
of in‡
ation in the U.S. and measures of foreign slack is fragile. There are a number of
possible reasons for this. There is an element of arbitrariness to the measurement of the
cyclical components of statistical series, and well-known end-of-sample problems that may
be particularly important for the short post-1990 sample period that we focus on for most of
our empirical results. Also, measuring resource utilization, slack or output gaps is challenging
at the best of times. For the emerging market economies that are believed to play such an
important role in the pricing decisions of U.S. …rms nowadays, data on aggregate activity
are problematic, and traditional measures of resource utilization such as unemployment
rates or capacity utilization rates in manufacturing are either not available or have very
short histories.
It is also not clear what the relationship is between the conventional statistical measures of
slack we have employed in our empirical analysis and the measures suggested by the modern
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literature. The gap concept in the model outlined above was the deviation of output from its
frictionless level. It is intuitive that the frictionless level of output in such a model will look
a lot di¤erent to the sort of smoothed estimate of trend or potential output generated by the
statistical …ltering or production function approaches to estimating output gaps. Indeed,
Neiss and Nelson (2003, 2005) show that there is a negative relationship between the New
Keynesian concept of the output gap (the deviation of output from its frictionless level) and
the measure commonly used in empirical research (the deviation of output from a smooth,
possibly time varying, trend).
By way of illustration of the potential importance of the di¤erence between the two
concepts of potential output (the statistical one and the model-consistent one), we simulated
the full model as described in Tables A1-A4 of the Appendix under the producer currency
pricing assumption, and then computed the frictionless level of output implied by the model
and the potential output as measured by the application of the Hodrick-Prescott …lter to the
output series generated by the model.12 Figure 12 is an illustrative scatter plot of the two
series of the foreign gap for a sample of 100 periods. For the particular set of parameter values
used to generate these data and a larger sample of 5000 periods, the correlation between the
two series is only 0.05, while the volatility of the model-consistent foreign output gap is merely
0.27 compared with a standard deviation of 0.64 for the Hodrick-Prescott …ltered foreign
output. A fuller evaluation of the global slack hypothesis would complete the speci…cation
of the demand side of the model outlined above, include a speci…cation of a rule for monetary
policy, and then take the full system to the data.
In light of the conceptual and measurement challenges associated with estimating Phillips
Curves in terms of domestic and foreign output gaps, it is worth asking whether we can derive
speci…cations that rely on more easily measured variables such as the terms of trade. Under
the producer currency pricing assumption it is possible to write the terms of trade gap as a
function of domestic and foreign output gaps as follows,
12
c
tott
2
c
tott = 4
1
1
(
)(
)
3
5
h
yt
b
bt
y
yt
b
bt
y
i
:
(37)
We set the structural parameters at = 0:99, = ' = 5, = 1:5, = 0:94, and = 0:75. These
parametric choices are essentially taken from Chari et al. (2002) and very similar to the set-up for the
closed-economy model of Neiss and Nelson (2003, 2005). Countries are of equal size, i.e. n = 1 , and we
2
maintain home bias in consumption, i.e. (1
) = . We assume that the Taylor rule is symmetric in
both countries, inertial, and takes the values estimated for the U.S. by Rudebusch (2006), i.e.
= 0:78,
= 1:33, and x = 1:29. For the AR(1) productivity shock process, we follow Kehoe and Perri (2002)
in setting A = 0:95 and A = 0:7 for the persistence and volatility, while we set the correlation between
domestic and foreign innovations at 0:25 as in Chari et al. (2002). For the AR(1) monetary shock process,
we follow Rudebusch (2006) in setting M = 0 and M = 0:38 for the persistence and volatility, while we set
the correlation between domestic and foreign innovations at 0:5 as in Chari et al. (2002).
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Using this expression to eliminate the foreign output gap term from the Phillips Curve in
equation (18) above, we obtain,
bt =
h
Et (bt+1 ) +
;x
bt :::
y
(' + ) yt
b
1
(
)(
c
tott
c
tott
c
) tott
c
tott
)
(38)
:
That is, the e¤ects of foreign slack on domestic in‡
ation can be fully captured in principle by
movements in the terms of trade gap. Note that the slope of the Phillips Curve with respect
to domestic slack, (' + ), is exactly the same in the open economy and closed economy
speci…cations (i.e., when = = 1 which de…nes the closed economy case) when the open
economy version of the Phillips Curve includes the terms of trade gap instead of the foreign
output gap. The expression for the Phillips Curve can be further simpli…ed to,
bt = Et (bt+1 ) + (' + )
h
bt
y
yt
b
(1
i
(39)
;
if we assume no home bias in consumption, = , as Clarida et al. (2002) and Woodford
(2007) do. Note that the terms of trade gap enters with a negative coe¢ cient whose size
depends on the share of foreign goods in the consumption basket, (1
), and the elasticity
of substitution between home and foreign goods, .
If instead we assume local currency pricing, the relationship between the terms of trade
gap and the output gaps in the domestic and foreign countries includes a term measuring
deviations from the law of one price for foreign goods in the domestic market,
c
tott
2
2
c
tott = 4
+ 41 +
1
1
1
(
1
(
)(
)
)
(
)(
)
3
3
5
h
yt
b
b
5 dt :
bt
y
yt
b
bt
y
i
:::
(40)
b
This relationship depends on dt exclusively because in our framework it can be shown that
b
b
pF pH = pF
bt
bt
bt
pH (see, e.g., Engel (2009)) implying that dt = dt . Moreover, we
bt
can derive from the de…nition of the real exchange rate and the consumption price indexes
the following relationship,
rst = (
b
c
)tott
(1 + (
19 of 50
b
))dt ;
(41)
Authorized for public release by the FOMC Secretariat on 04/29/2016
c
b
along with the fact that in the frictionless equilibrium rst = (
)tott . Hence, whenever
6= , we can rewrite the Phillips Curve in terms of the domestic output gap, the terms of
trade gap and the real exchange rate (net of terms of trade e¤ects) as,
h
bt = Et (bt+1 ) +
;x
+
where the composite parameter
' (1
=
+
' (1
(1
(1
1
(
1
)(
)(
1
1
)(1
)(
i
rst
b
)(
)(
)+(
(
)+(
1
1
(
)+
(
)(
c
tott +
c
tott
)
;
(42)
is de…ned as,
)+(
(1
)+
1
c
) tott
(
bt
y
(' + ) yt
b
)(1
)(
)(
)(
)
)(
)(1
)+ 1 (
)(
1+(
)
)(
(
)
1
)(
)
))
(1
(
)
)
)+ 1 (
)(
1+(
)
1 (
)(
(
)(1+(
)
1
(
)
)
)
) (
)(1+(
)
))
+
;rp
+
;
(43)
and
;rp was de…ned in (31). The composite parameters on the domestic output gap and
the terms of trade gap are the same as under producer currency pricing, as can be observed
in equation (38).
If we make the additional assumption that there is no home bias in consumption (as do
Clarida et al. (2002) and Woodford (2007)), = , we can derive the corresponding Phillips
Curve in terms of the terms of trade gap as,
bt =
Et (bt+1 ) + ( + ')
(1
)
1
n
+'
h
yt
b
rst :
b
bt
y
(1
c
) tott
c
tott :::
(44)
The composite parameters on the domestic output gap and the terms of trade gap are the
same that follow from equation (42) under no home bias and identical to those of the producer
currency pricing speci…cation in (39), but here the real exchange rate su¢ ces to summarize
the contribution of the deviations of the law of one price.
Once again, the responsiveness of CPI in‡
ation to the domestic output gap is exactly
the same as in the closed economy case (i.e., = = 1), and the importance of the terms
of trade gap is directly proportional to the importance of foreign goods in the consumption
basket, (1
), while the importance of real exchange rate movements that account for
deviations of the law of one price depends on the foreign population size, (1 n).
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Thus there is an equivalence between expressing the open economy Phillips Curve in
terms of domestic and foreign output gaps, and expressing it in terms of the domestic output
gap, the terms of trade gap and the real exchange rate (net of terms of trade e¤ects). To
the extent that the traditional Phillips Curve literature has included variables such as oil
and commodity prices (whose movements will be highly correlated with the U.S. terms of
trade) or the real exchange rate as right hand side variables since the 1970s, global slack
has been noted and accounted for implicitly as an important determinant of U.S. in‡
ation
dynamics for a long time. More importantly, it tells us that the validity of the global slack
hypothesis cannot be determined solely on the basis of simple least squares regressions of
the sort reported here and elsewhere in the literature. Ultimately what is needed is a more
structural evaluation of the factors in‡
uencing in‡
ation dynamics in the open economy.
4
Conclusion
Our objective in this paper has been to show that the global slack hypothesis has analytical
content in the context of at least one widely-used framework for thinking about in‡
ation
dynamics in open economies. We have shown that in theory in‡
ation is less responsive to
domestic slack the more exposed a country is to international trade. We have also shown that
foreign slack does matter for domestic in‡
ation when a country is engaged in international
trade, and the importance of foreign slack increases as the share of consumption devoted to
foreign-produced goods increases. We also provided some empirical support for the global
slack hypothesis, and showed that abstracting from ‡
uctuations in trend in‡
ation (as the
theory suggests is appropriate) is important when evaluating the hypothesis. We also noted
the conceptual di¢ culties of measuring the output gaps and suggested that terms of trade
(and other international relative prices) may account for some of the foreign in‡
uences on
domestic in‡
ation and, therefore, allow us to by-pass some of those measurement problems.
There are several avenues for further research. On the theory side, there are many
potential additional channels through which foreign factors might have an impact on domestic
in‡
ation developments which would be worth modelling. Two that spring to mind are
migration, and international trade in raw materials and intermediate inputs. Recent work by
Cortes (2008) and Lach (2007) has shown how the presence of large immigrant populations
can impact domestic prices. And the surge in global commodity prices in 2007 and 2008 was
a reminder of how price dynamics at all stages of the production chain have been impacted
by the shifting distribution of global economic activity.
The model we sketched out is not well suited to address questions of deep structural
change which are arguably at the heart of the debate about the implications of globalization
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for in‡
ation and monetary policy, and therein lies another potentially fruitful avenue for
future research. In our empirical work we argued that it is important to abstract from
‡
uctuations in trend when evaluating the global slack hypothesis, but our theory has little
to say about these changes in trend, or whether they might have implications for short
run dynamics. The literature that addresses the potential impact of globalization on trend
in‡
ation that began with Romer (1993) has largely focused on explaining the role of openness
in accounting for cross-country di¤erences in in‡
ation; an extension to account for di¤erences
over time would be a logical next step.
We used theory to motivate very simple ordinary least squares and GMM estimates of
the Phillips Curve, and there is considerable scope for more sophisticated empirical work.
For example, we did not impose any of the parameter restrictions suggested by the theory,
nor did we employ theory-consistent measures of slack in our estimates. We also limited
ourselves to examining the impact of global slack on in‡
ation dynamics in the United States
- a fuller test of the theory would include an analysis of the determinants of in‡
ation in more
open economies as well.
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Data Appendix
All data were obtained from HAVER Analytics database. Below we use the HAVER
mnemonics to describe the exact series we use.
United States:
Personal Consumption Expenditures Price Index - JCBM@USECON;
Personal Consumption Expenditures less Food and Energy Price Index - JCXFEBM@USECON;
Real GDP - GDPH@USECON;
Unemployment rate - LR@USECON;
Capacity utilization rate in manufacturing - C158BCU@OECDMEI;
Real Exchange rate - FXTWBC@USECON;
Terms of trade - JX@USNA/JM@USNA;
Labor share - YCOMPD@USNA/GDP@USECON;
Relative price of oil - JMMP@USNA/JCBM@USECON.
Japan:
Real GDP - C158GDP@OECDNAQ;
Unemployment rate - C158UR@OECDMEI;
Capacity utilization rate in manufacturing - C158BCU@OECDMEI;
U.S. imports from Japan - M111F158@IMFDOTM;
Share of U.S. imports from Japan - FXWIJAP@USECON.
Germany:
Real GDP- C134GDPC@OECDNAQ;
Unemployment rate - C134UR@OECDMEI;
Capacity utilization rate in manufacturing - C134BCU@OECDMEI;
U.S. imports from Germany - M111F134@IMFDOTM.
France:
Real GDP - C132GDPC@OECDNAQ;
Unemployment rate - C132UR@OECDMEI;
Capacity utilization rate in manufacturing - C132BCU@OECDMEI;
U.S. imports from France - M111F132@IMFDOTM.
United Kingdom:
Real GDP - C112GDPC@OECDNAQ;
Unemployment rate - S112ELRQ@G10;
Capacity utilization rate in manufacturing - C112BCU@OECDMEI;
U.S. imports from th eUnited kingdom - M111F112@IMFDOTM;
Share of U.S. imports from the United Kingdom - FXWIUK@USECON.
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Italy:
Real GDP - C136GDPC@OECDNAQ;
Unemployment rate - C136UR@OECDMEI;
Capacity utilization rate in manufacturing - C136BCU@OECDMEI;
U.S. imports from Italy - M111F136@IMFDOTM
Canada:
Real GDP - C156GDPC@OECDNAQ;
Unemployment rate - C156UR@OECDMEI;
Capacity utilization rate in manufacturing - C156BCUN@OECDMEI;
U.S. imports from Canada - M111F156@IMFDOTM;
Share of U.S. imports from Canada - FXWICAN@USECON.
Euro area:
Real GDP - J025GDPT@EUROSTAT;
Share of U.S. imports from euro area - FXWIEUR@USECON.
Taiwan:
Real GDP - S528NGPC@EMERGEPR:
Share of U.S. imports from Taiwan - FXWITWN@USECON.
Hong Kong:
Real GDP - F532NGPC@EMERGEPR;
Share of U.S. imports from Hong Kong - FXWIHK@USECON.
Malaysia:
Real GDP - F548NGPC@EMERGEPR;
Share of U.S. imports from Malaysia - FXWIMAL@USECON.
Brazil:
Real GDP - S223GPI@EMERGELA;
Share of U.S. imports from Brazil - FXWIBRZ@USECON.
Switzerland:
Real GDP - S146NGPC@G10;
Share of U.S. imports from Switzerland - FXWISW@USECON.
Thailand:
Real GDP - S578NGPC@EMERGEPR;
Share of U.S. imports from Thailand - FXWITHA@USECON.
Philippines:
Real GDP - F566NGPC@EMERGEPR;
Share of U.S. imports from the Philippines - FXWIPHL@USECON.
Australia:
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Real GDP - C193GDPC@OECDNAQ;
Share of U.S. imports from Australia - FXWIAUS@USECON.
Indonesia:
Real GDP - F536NGPC@EMERGEPR;
Share of U.S. imports from Indonesia - FXWIIN@USECON.
India:
Real GDP - H534NGEC@EMERGEPR;
Share of U.S. imports from India - FXWIIND@USECON.
Israel:
Real GDP - S436NGPC@EMERGEMA;
Share of U.S. imports from Israel - FXWIISR@USECON.
Sweden:
Real GDP - C144GDPC@OECDMEI;
Share of U.S. imports from Sweden - FXWISWD@USECON.
Argentina:
Real GDP - S213GPC@EMERGELA;
Share of U.S. imports from Argentina - FXWIARG@USECON.
Chile:
Real GDP - S228GPC@EMERGELA;
Share of U.S. imports from Chile - FXWICHL@USECON.
Colombia:
Real GDP - S233GPC@EMERGELA;
Share of U.S. imports from Colombia - FXWICOL@USECON.
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ation.” Federal Reserve Bank of Dallas Sta¤ Papers Number 2.
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Table 1
Phillips Curve regressions for headline and core in‡
ation
(1)
t
= 0:064
(0:187)
t 1
0:013CUtU S + 0:220 CUtG6
(0:071)
2
(0:036)
Sample period: 1985:I to 2009:II; R = 0:30; N R2 =15.57
(2)
Core
t
= 0:723
(0:064)
0:009CUtU S + 0:043CUtG6
Core
t 1
(0:028)
(0:015)
2
Sample period = 1985:I to 2009:II; R = 0:64; N R2 =15.84
(3)
t
= 0:687
t
(0:076)
U
+ 0:127U Rt S
(0:081)
G6
0:452 U Rt
(0:162)
2
Sample period = 1971:I to 2009:II; R =0.69; N R2 =18.90
(4)
Core
t
= 0:831
(0:061)
Core
t 1
U
+ 0:067U Rt S
G6
0:231 U Rt
(0:074)
(0:117)
2
Sample period = 1971:I to 2009:II; R =0.84; N R2 =9.07
(5)
t
= 0:039
(0:197)
t 1
bG6
0:018yt S + 0:726 yt
bU
(0:398)
(0:159)
2
Sample period = 1991:I to 2009:II; R = 0:20; N R2 =21.80
(6)
Core
t
= 0:539
(0:104)
Core
t 1
bG6
0:126yt S + 0:197 yt
bU
(0:112)
(0:099)
2
Sample period = 1991:I to 2009:II; R = 0:39; N R2 =7.16
Notes to Table 1: All regressions include a constant (not reported). Newey-West HAC standard errors in parentheses. *** denotes signi…cance at the 1% level; ** denotes signi…cance at the 5% level; * denotes signi…cance at the 10%
level. t is measured as the annualized quarterly change in the PCE de‡
ator. Core is measured as the annualized
t
quarterly change in the PCE de‡
ator excluding food and energy. CU U S is measured as the rate of capacity utilization in US manufacturing. CU G6 is measured as an import-weighted average of the rates of capacity utilization in
manufacturing in the other G7 countries. U RU S is measured as the unemployment rate in the US. U RG6 is measured
as an import-weighted average of the unemployment rates in the other G7 countries. yt S is measured as the cyclical
bU
component of US GDP. yt is measured as an import-weighted average of the cyclical component of GDP in the
bG6
other G7 countries. Cyclical components are de…ned using the Hodrick-Prescott …lter with smoothing parameter
= 1600. N R2 is the Breusch-Godfrey Lagrange multiplier test statistic for serial correlation up to order 4 which
has an asymptotic 2 (4) distribution under the null hypothesis of no serial correlation.
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Table 2
Phillips Curve regressions for cyclical components of in‡
ation
(1)
bt =
0:132bt
(0:142)
US
1
d
+ 0:088CU t
(0:068)
G6
d
+ 0:176 CU t
(0:101)
2
Sample period: 1985:I to 2009:II; R =0.17; N R2 =19.36
(2)
dU S
d G6
bCore = 0:049bCore + 0:023CU t + 0:047CU t
t 1
t
(0:035)
(0:107)
(0:034)
2
Sample period: 1985:I to 2009:II; R =0.10; N R2 =6.19
(3)
dU S
0:403 U Rt
bt = 0:307 bt
(0:110)
G6
d
0:525U Rt
(0:161)
(0:368)
2
Sample period: 1971:I to 2009:II; R =0.28; N R2 =12.13
(4)
bCore = 0:473 bCore
t
t 1
(0:146)
US
d G6
0:603 U Rt
d
0:012U Rt
(0:138)
(0:268)
2
Sample period: 1971:I to 2009:II; R =0.38; N R2 =2.23
(5)
bt =
0:205bt
(0:177)
1
+ 0:182yt S + 0:764 yt
bU
bG6
(0:122)
(0:316)
2
Sample period: 1991:I to 2009:II; R =0.29; N R2 =18.57
(6)
bCore =
t
0:202bCore
t 1
(0:106)
0:091yt S + 0:374 yt
bU
bG6
(0:073)
(0:083)
2
Sample period: 1991:I to 2009:II; R =0.28; N R2 =8.09
Notes to Table 2: All regressions include a constant (not reported). Newey-West HAC standard errors in parentheses. *** denotes signi…cance at the 1% level; ** denotes signi…cance at the 5% level; * denotes signi…cance at the
10% level. bt is measured as the cyclical component of the annualized quarterly change in the PCE de‡
ator. bCore
t
US
d
is measured as the cyclical component of the annualized quarterly change in the PCE de‡
ator. CU
is measured
d G6 is measured as the cyclias the cyclical component of the rate of capacity utilization in US manufacturing. CU
cal component of an import-weighted average of the rates of capacity utilization in manufacturing in the other G7
d U S is measured as the cyclical component of the unemployment rate in the US. U RG6 is measured as
d
countries. U R
the cyclical component of an import-weighted average of the unemployment rates in the other G7 countries. yt S
bU
is measured as the cyclical component of US GDP. yt is measured as an import-weighted average of the cyclical
bG6
component of GDP in the other G7 countries. Cyclical components are de…ned using the Hodrick-Prescott …lter with
smoothing parameter = 1600. Breusch-Godfrey N R2 is the Breusch-Godfrey Lagrange multiplier test statistic for
serial correlation up to order 4 which has an asymptotic 2 (4) distribution under the null hypothesis of no serial
correlation.
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Table 3
Phillips Curve regressions including terms of trade and real exchange rate
(1)
(2)
(3)
(4)
bt =
0:332bt
(0:152)
d
+ 0:097CU t
(0:067)
G6
d
+ 0:120 CU t
(0:072)
c
0:330 tott
0:010rert
c
(0:069)
2
(0:043)
Sample period: 1985:I to 2009:II; R =0.31; N R2 =37.98
bCore =
t
bt =
US
1
0:007bCore
t 1
(0:126)
US
d
0:001CU t
(0:032)
d G6
c
+ 0:055CU t + 0:014tott
(0:036)
(0:031)
2
0:035 rert
c
(0:017)
Sample period: 1985:I to 2009:II; R =0.12; N R2 =9.26
0:008bt
(0:112)
dU S
d G6
0:906 U Rt + 0:574U Rt
1
(0:247)
c
0:289 tott
(0:508)
(0:066)
2
0:034rert
c
(0:037)
Sample period: 1973:I to 2009:II; R =0.39; N R2 =23.15
US
d
0:165U Rt
bCore = 0:219bCore
t
t 1
(0:144)
(0:174)
G6
d
0:088U Rt
c
0:167 tott + 0:003rert
c
(0:049)
(0:330)
2
(0:021)
Sample period: 1973:I to 2009:II; R =0.46; N R2 =2.54
(5)
(6)
bt =
0:472 bt
(0:175)
bCore =
t
1
bG6
+ 0:072yt S + 0:639 yt
bU
(0:150
(0:331)
c
0:265015tott
(0:090)
2
0:138 rert
c
(0:063)
Sample period:1991:I to 2009:II; R =0.47; N R2 =27.85
0:221bCore
t 1
(0:107)
c
bG6
0:102yt S + 0:350 yt + 0:011tott
bU
(0:071)
(0:036)
(0:074)
2
0:040 rert
c
(0:014)
Sample period: 1991:I to 2009:II; R =0.31; N R2 =7.96
Notes to Table 3: All regressions include a constant (not reported). Newey-West HAC standard errors in parentheses. *** denotes signi…cance at the 1% level; ** denotes signi…cance at the 5% level; * denotes signi…cance at
the 10% level. bt is measured as the cyclical component of the annualized quarterly change in the PCE de‡
ator.
d U S is
bCore is measured as the cyclical component of the annualized quarterly change in the PCE de‡
ator. CU
t
d G6 is measured as
measured as the cyclical component of the rate of capacity utilization in US manufacturing. CU
the cyclical component of an import-weighted average of the rates of capacity utilization in manufacturing in the
c
other G7 countries. tott is measured as the cyclical component of the US terms of trade (de…ned as the ratio of the
de‡
ator for exports of goods and services to the de‡
ator for imports of goods and services in the national income and
dU S
product accounts). rert is measured as the cyclical component of the real trade weighted value of the dollar. U R
c
d G6
is measured as the cyclical component of the unemployment rate in the US. U R is measured as the cyclical component of an import-weighted average of the unemployment rates in the other G7 countries. yt S is measured as the
bU
G6
cyclical component of US GDP. yt is measured as an import-weighted average of the cyclical component of GDP in
b
the other G7 countries. Cyclical components are de…ned using the Hodrick-Prescott …lter with smoothing parameter
= 1600. Breusch-Godfrey N R2 is the Breusch-Godfrey Lagrange multiplier test statistic for serial correlation up
to order 4 which has an asymptotic 2 (4) distribution under the null hypothesis of no serial correlation.
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Table 4
Phillips Curve regressions including broadest measure of global slack
(1)
(2)
(3)
(4)
bt =
0:217bt
(0:190)
bG26
+ 0:124yt S + 1:236 yt
bU
(0:228)
(0:591)
2
Sample period: 1996:II to 2009:I; R =0.30; N R2 =18.68
bCore =
t
bt =
1
bU
bG26
0:225bCore + 0:020yt S + 0:347 yt
t 1
(0:082)
(0:108)
(0:121)
2
Sample period: 1996:II to 2009:I; R =0.23; N R2 =10.30
0:430bt
(0:178)
1
+ 0:090yt S + 0:782yt
bU
bG26
(0:261)
(0:620)
c
0:260 tott
(0:114)
2
0:143 rert
c
(0:067)
Sample period: 1996:II to 2009:I; R =0.43; N R2 =27.25
bCore =
t
bG26
0:223bCore + 0:005yt S + 0:286 yt
bU
t 1
(0:122)
(0:084)
(0:133)
2
c
0:009tott
(0:036)
0:030 rert
c
(0:017)
Sample period: 1996:II to 2009:I; R =0.23; N R2 =9.86
Notes to Table 4: All regressions include a constant (not reported). Newey-West HAC standard errors in parentheses. *** denotes signi…cance at the 1% level; ** denotes signi…cance at the 5% level; * denotes signi…cance at the
10% level. bt is measured as the cyclical component of the annualized quarterly change in the PCE de‡
ator. bCore is
t
US
measured as the cyclical component of the annualized quarterly change in the PCE de‡
ator. yt is measured as the
b
cyclical component of U.S. GDP. yt
bG26 is measured as an import-weighted average of the cyclical component of GDP
in the U.S.’ main trading partners. We include all trading partners with quarterly real GDP series available from
1996, and allow the weights to change over time to re‡ changing trade patterns. The countries included are the
ect
euro area, Canada, Japan, U.K., Taiwan, Hong Kong, Malaysia, Brazil, Switzerland, Thailand, Philippines, Australia,
c
Indonesia, India, Israel, Sweden, Argentina, Chile and Colombia. tott is measured as the cyclical component of the
U.S. terms of trade (de…ned as the ratio of the de‡
ator for exports of goods and services to the de‡
ator for imports
of goods and services in the national income and product accounts). rert is measured as the cyclical component of
c
the real trade weighted value of the dollar. Cyclical components are de…ned using the Hodrick-Prescott …lter with
smoothing parameter = 1600. Breusch-Godfrey N R2 is the Breusch-Godfrey Lagrange multiplier test statistic for
serial correlation up to order 4 which has an asymptotic 2 (4) distribution under the null hypothesis of no serial
correlation.
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Table 5
GMM estimates of Phillips Curve
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
bt = 0:659 Et bt+1
(0:155)
bG6
0:048yt S + 0:402 yt
bU
(0:127)
(0:389)
bG6
bU
bCore = 0:492 Et bCore + 0:012yt S + 0:231 yt
t+1
t
(0:163)
(0:055)
(0:039)
c
bt = 0:453 Et bt+1 + 0:285 yt S + 0:161yt + 0:052tott
bU
bG6
(0:170)
bCore = 0:246Et bCore
t+1
t
(0:140)
(0:129)
(0:063)
0:127 rert
c
(0:049)
c
0:015yt S + 0:248 yt + 0:105 tott
bU
bG6
(0:054)
(0:215)
(0:053)
(0:034)
0:077 rert
c
(0:023)
bt = 0:765 Et bt+1 + 0:276 yt S + 0:379 yt
bU
bG26
(0:165)
bCore
t
=
(0:143)
0:100Et bCore
t+1
(0:153)
(0:113)
bG26
+ 0:111 yt S + 0:202 yt
bU
(0:046)
(0:037)
c
b
bt = 0:573 Et bt+1 + 0:472 yt S + 0:242y G26 + 0:101tott
bU
(0:183)
bCore =
t
(0:167)
(0:181)
(0:088)
0:121 rert
c
(0:056)
c
bG26
0:363Et bCore + 0:076yt S + 0:400 yt + 0:124 tott
bU
t+1
(0:222)
(0:055)
(0:080)
(0:042)
0:102 rert
c
(0:026)
Notes to Table 5: Sample period for equations (1)-(4) is 1992:1 to 2009:I, for equations (5)-(8) is 1996:III to 2009:I.
*** denotes signi…cance at the 1% level; ** denotes signi…cance at the 5% level; * denotes signi…cance at the 10%
level. bt is measured as the cyclical component of the annualized quarterly change in the PCE de‡
ator. bCore is
t
US
measured as the cyclical component of the annualized quarterly change in the PCE de‡
ator. yt is measured as the
b
cyclical component of U.S. GDP. yt
bG26 is measured as an import-weighted average of the cyclical component of GDP
in the U.S.’ main trading partners. We include all trading partners with quarterly real GDP series available from
1996, and allow the weights to shift over time to re‡ changing trade patterns. The countries included are the euro
ect
area, Canada, Japan, U.K., Taiwan, Hong Kong, Malaysia, Brazil, Switzerland, Thailand, Philippines, Australia,
c
Indonesia, India, Israel, Sweden, Argentina, Chile and Colombia. tott is measured as the cyclical component of the
U.S. terms of trade (de…ned as the ratio of the de‡
ator for exports of goods and services to the de‡
ator for imports
of goods and services in the national income and product accounts). rert is measured as the cyclical component of
c
the real trade weighted value of the dollar. Cyclical components are de…ned using the Hodrick-Prescott …lter with
smoothing parameter = 1600. The instrument set for equations (1)-(4) consists of four lags of the headline PCE
in‡
ation rate, four lags of the cyclical component of the labor share in the US, four lags of the import-weighted labor
share in the other G7 countries, one lag of the output gap in the US, one lag of the output gap in the other G7
countries and four lags of the relative price of oil in the US. We use the same instruments for equations (5)-(8), except
that we replace the lag of output gap in the other G7 countries with one lag of the trade weighted output gap in the
broader group of countries.
33 of 50
Authorized for public release by the FOMC Secretariat on 04/29/2016
Model parameters
Structural parameters
Intertemporal discount factor
0<
Inverse of the intertemporal elasticity of substitution
Inverse of the Frisch elasticity of labor supply
<1
>0
'>0
Elasticity of substitution across varieties within a country
>1
Elasticity of substitution between the home and foreign bundles
>0
Preference of the domestic consumer for home goods
0<
<1
Preference of the foreign consumer for home goods
0<
<1
Domestic population size
0<n<1
Foreign population size
0<1
Calvo price stickiness parameter
n<1
0<
<1
0<
<1
Monetary Policy Parameters
Monetary policy inertia
Sensitivity to deviations from in‡
ation target
Sensitivity to deviations from potential output target
34 of 50
>1
x
>1
35 of 50
0
Rn
1 + it
Short-term (gross) interest rates
Z
! t+1 2
1
Pt
Pt+
Q(! t+1 j! t )
Ct+
Ct
Pt (h) nCt (h) + St Pt (h) (1 n) Ct (h)
(1 + t ) Wt Lt (h)
Rn
nYt
Y (h) dh
R0 t
n
nY t
0 Y t (h) dh
mt;t+
=
RSt
St Pt
Pt
F
Pt
T oTt
H
St Pt
(1
t )Wt
M Ct (h) = M Ct
At
Rn
n t
t (h) dh
0
Intertemporal marginal rate of substitution
Aggregate output
Aggregate potential output
Aggregate pro…ts
Marginal costs (after subsidies)
Terms of trade
Real exchange rate
Total factor productivity
Monetary policy shocks
Price of domestic variety h
Price of foreign variety f
Optimal re-optimzing price of domestic variety h
Optimal re-optimzing price of foreign variety f
Demand of domestic contingent bonds
Demand of foreign contingent bonds
Contingent bond prices
Nominal exchange rate
Pro…ts from domestic variety h
Pro…ts from foreign variety f
Nominal wage of domestic variety h
Nominal wage of foreign variety f
Lump sum taxes
Output of domestic variety h
Output of foreign variety f
Potential output of domestic variety h
Potential output of foreign variety f
Labor demand for domestic variety h
Labor demand for foreign variety f
Aggregate labor supply
Consumption of domestic variety h
Consumption of foreign variety f
Table A1- Notation
Home
Real variables
Yt (h)
Y t (h)
Lt (h)
nLt
Ct (h)
Ct (f )
Nominal variables
Pt (h)
Pt (f )
e
Pt (h)
e
Pt (f )
B H (! t j ! t 1 )
B F (! t j ! t 1 )
Q (! t j ! t 1 )
St
t (h)
Wt (h) = Wt
Tt
Shocks
At
Zt
Useful de…nitions
dh
mt;t+
(1
)W
1 + it
Z
! t+1 2
Ct+
Ct
1
Q
(!t+1 j!t )
Pt
Pt+
t
t
M Ct (f ) = M Ct
At
R1
(1 n) t
(f ) df
n t
"
1
R1
P (f ) nCt (f ) + Pt (f ) (1 n) Ct (f )
St t
= n
(1 + t ) Wt Lt (f )
R1
(1 n) Yt
Y (f ) df
Rn t
1
(1 n) Y t
n Y t (f ) df
1
RSt
1
T oTt
At
Zt
t
(f )
Wt (f ) = Wt
Tt
1
St
(h)
(f )
(h)
t (f )
B H (! t j ! t 1 )
B F (! t j ! t 1 )
Q (! t j ! t 1 )
Pt
Pt
e
Pt
e
P
Yt (f )
Y t (f )
Lt (f )
(1 n) Lt
Ct (h)
Ct (f )
Foreign
#
df
Authorized for public release by the FOMC Secretariat on 04/29/2016
36 of 50
Inte rn a tio n a l p e rfe c t risk -sh a rin g c o n d itio n
Inte rte m p o ra l e ¢ c ie n c y c o n d itio n
Intra te m p o ra l e ¢ c ie n c y c o n d itio n
D e m a n d fo r fo re ig n va rie ty f
D e m a n d fo r d o m e s tic va rie ty h
P ric e s u b -in d e x o f t h e b u n d le o f fo re ig n va rie t ie s
P ric e s u b -in d e x o f th e b u n d le o f d o m e s tic va rie tie s
C o n su m p tio n p ric e le ve l
B u d g e t c o n stra int
C o n s u m p tio n b u n d le o f fo re ig n va rie tie s
C o n s u m p tio n b u n d le o f d o m e s tic va rie tie s
A g g re g a te c o n su m p tio n
L ife tim e u tility
1
H
Ct
=0
"
+1
P
1
=
"
H
Ct
1
1
n
+ (1
)
1 R
n
0 Ct (h)
1
(Ct+ )1
1
1
dh
#
Lt+
F
Ct
1
1+'
1
1
#
1+'
1
Ta b le A 2 - H o u se h o ld s
O p tim iz a tio n
Q ! t+1 j ! t
@
C ! t+1
A
C(! t )
P (! t )
P ! t+1
! t+1 j ! t
;
"
#
1
1 R
1
F
1
1
Ct
d
f
n Ct (f )
1 n
Z
H !
Pt Ct +
Q ! t+1 j ! t B
t+1 j ! t +
! t+1 2
Z
+St
Q
! t+1 j ! t B F ! t+1 j ! t
! t+1 2
F ! j !
1 BH ! j !
Tt
t
t
t 1 +B
t 1 + Wt Lt + t
St
E q u ilib riu m c o n d itio n s
1
H 1
F 1
1
Pt =
Pt
+ (1
) Pt
1
h
i
Rn
1
1
H
H
e
=
Pt 1
+ (1
) Pt (h)
Pt = 1 0 Pt (h)1
dh 1
n
i 1
h
1
1
F
F
1 R 1 P (f )1
e
d 1
f
=
Pt 1
+ (1
) Pt (f )
Pt =
1 n n t
!
!
!
H
Pt
Pt (h)
Pt (h)
H
Ct (h) = 1
Ct
Ct =
H
H
n
n
Pt
Pt
Pt
!
!
!
F
Pt
Pt (f )
Pt (f )
1
F
1
Ct (f ) =
Ct =
Ct
F
F
1 n
1 n
Pt
Pt
Pt
Wt
'
= (Ct ) (Lt )
P
0 t
1
Ct
Et
Hom e
1
RSt =
1
1
1
Ct
Ct
!
F
Pt
H
Pt
h
h
F
Ct
R1
1
n Pt (f )
Pt =
1 R n P (h)1
t
n 0
1
1
H
Ct
=0
Z
1
"
"
H
Ct
1
1
1
1
n
n
1
1
1
d
f
#
#
F
Ct
Lt+
dh
1
1
1+'
1 R
1
n Ct (f )
+ 1
1 R
n
0 Ct (h)
1
1
Fo r e ig n
Ct+
i
dh 1
H
Pt
1
1
=
n
A
1
1
1
n
1
1
F
Pt
+ (1
!
+ (1
1
P
P
(! t )
! t+1
Pt (h)
H
Pt
!
Pt (f )
F
n
Pt
'
Lt
F
Pt 1
H
Pt 1
+ 1
i 1
d 1
f
=
!
Pt (h)
H =
Ct (h) = 1
Ct
H
n
Pt
!
Pt (f )
F =
1
Ct
Ct (f ) =
F
1 n
Pt
Wt
= Ct
P
0 t
C ! t+1
@
Q
! t+1 j ! t =
C (! t )
=
=
"
+1
P
1
1
1
#
1+'
1
! t+1 j ! t
1
e
) Pt (f )
!
H
Pt
Ct
Pt
!
F
Pt
Ct
Pt
1
1
e
) Pt (h)
1
Pt Ct + 1
Q ! t+1 j ! t B H
! t+1 j ! t +
St !
t+1 2
Z
+
Q
! t+1 j ! t B F
! t+1 j ! t
! t+1 2
1 BH
!t j !t 1 + BF
! t j ! t 1 + Wt Lt + t
Tt
St
Ct
Et
1
1
1
1
Authorized for public release by the FOMC Secretariat on 04/29/2016
37 of 50
O p tim a l p ric in g o f …rm f
O p tim a l p ric in g o f …rm h
D e m a n d c o n stra int in fo re ig n m a rke t
D e m a n d c o n stra int in h o m e m a rke t
Te ch n o lo g y
P re s e n t d is c o u n te d va lu e o f p ro …ts fo r f
P re s e n t d is c o u n te d va lu e o f p ro …ts fo r h
O p tim a l p ric in g o f …rm f
O p tim a l p ric in g o f …rm h
A g g re g a te d e m a n d c o n stra int
Te ch n o lo g y
P re s e n t d is c o u n te d va lu e o f p ro …ts fo r re -o p tim iz in g f
P re s e n t d is c o u n te d va lu e o f p ro …ts fo r re -o p tim iz in g h
P o te ntia l o u tp u t fo r …rm h
P o te ntia l o u tp u t fo r …rm f
O p tim a l p ric in g o f …rm f
O p tim a l p ric in g o f …rm h
A g g re g a te d e m a n d c o n stra int
P ro …ts fo r …rm f
Te ch n o lo g y
P ro …ts fo r …rm h
f
Et
=0
+1
P
e
Pt (h) =
0
=0
-
(h) + (1
ed
Ct;t+
ed
Ct;t+
ed
n) Ct;t+
(h)
e
Pt (f ) =
+ (1
-
fd
Et mt;t+ Ct;t+ (h)M Ct+
=0
"
#
+1
P
fd
Et mt;t+ Ct;t+ (h)
=0
+1
P
fd
Et mt;t+ Ct;t+ (f )M Ct+
=0
2
1 +1
P
fd
1
Et 4mt;t+ Ct;t+ (f )
St+
=0
+1
P
5
3
E q u ilib riu m c o n d itio n s (L C P )
Ct+
Ct+
O p tim iz a tio n (L C P )
ed
e
+
nCt;t+ (h) Pt (h)
M Ct+
ed
e
n) Ct;t+ (h) St+ Pt (h)
M Ct+
e
e
Pt (f ) = St Pt (f )
!#
fd
n)Ct;t+ (h)
5
3
1
i
Ct+ A
M Ct+
fd
n)Ct;t+ (h) M Ct+
nCt;t+ (h)+(1
fd
Yt (h) = At Lt (h)
1
0
0
1
f
PH
@ t+ A
@ Pt (h) A
H
n
Pt+
Pt+
1
0
0
1
f
PH
P (h)
@ t
A
@ t+ A
(h) =
H
n
Pt+
Pt+
1
A
1
e
Pt (h)
E q u ilib riu m c o n d itio n s (P C P )
fd
nCt;t+ (h)+(1
Et mt;t+
(h) =
4
2
=0
"
Et mt;t+
=0
+1
P
+1
P
mt;t+
1
ed
nCt;t+
Yt (h) = At Lt (h)
ed
ed
nCt;t+ (h) + (1
n) Ct;t+ (h)
0
1
0
H
Pt+
PH
@n
@
A
@ t+
Ct+ + (1
n)
n
Pt+
n
Pt+
0
h
Pt (h) =
M Ct
1
Pt (f ) = St Pt (f )
d
d
Y t (h) = nCt (h) + (1
n) Ct (h)
O p tim iz a tio n (P C P )
e
Pt (h) =
1
mt;t+
P (h) A
= @ t
H
Pt+
Et
+1
P
=
f
Pt (f )
A
F
Pt+
1
Et
!
ed
n) Ct;t+
(f )
e
Pt (f )
F
Pt
Pt
e
e
Pt (h) = 1 Pt (h)
St
!
A
1
e
Pt (f ) =
e
Pt (h) =
1
1
(f ) =
"
fd
Et mt;t+ Ct;t+ (h)St+
fd
Et mt;t+ Ct;t+ (h)M Ct+
#
Ct+
Ct+
fd
Et mt;t+ Ct;t+ (f )M Ct+
=0
"
#
+1
P
fd
Et mt;t+ Ct;t+ (f )
=0
=0
+1
P
=0
+1
P
+1
P
Yt (f ) = At Lt (f )
1
0
0
1
f
PF
1
@ t+ A
@ Pt (f ) A
F
1 n
Pt+
Pt+
1
0
0
1
f
PF
P (f )
1
@ t
A
@ t+ A
(f ) =
F
1 n
Pt+
Pt+
mt;t+
3
1
e
ed
M Ct+
+ 7
6 nCt;t+ (f ) St+ Pt (f )
4
5
d
e
e
+ (1
n) Ct;t+ (f ) Pt (f )
M Ct+
2
i
1
Ct+ A
M Ct+
1
Ct A
fd
fd
Et mt;t+ nCt;t+ (f )+(1 n)Ct;t+ (f ) M Ct+
=0
"
!#
+1
P
fd
fd
Et mt;t+
nCt;t+ (f )+(1 n)Ct;t+ (f )
=0
+1
P
ed
Ct;t+
1
ed
Ct;t+
=0
(f ) + (1
(f )
n
M Ct
Yt (f ) = At Lt (f )
ed
ed
nCt;t+ (f ) + (1
n) Ct;t+ (f )
0
1
0
F
Pt+
PF
1
1
@n
@
A
@ t+
Ct+ + (1
n)
1 n
Pt+
1 n
Pt+
0
ed
nCt;t+
-
Pt (h) = 1 Pt (h)
St
M Ct
Pt (f ) =
1
d
d
Y t (f ) = nCt (f ) + (1
n) Ct
Fo r e ig n
d
d
nCt (f ) + (1
n) Ct (f )
Pt (f )
Yt (f ) = At Lt (f )
d (f ) + (1
d
nCt
n) Ct (f )
0
!
F
Pt
1
1
@n
Ct + (1
n)
1 n
Pt
1
mt;t+
+1
P
e
Pt (f ) =
0
=0
Pt (f )
F
Pt
+1 h
P
=
Et
= @
Ta b le A 3 - F irm s
O p tim iz a tio n (p o te ntia l, w ith o u t n o m in a l rig id itie s)
Hom e
d
d
nCt (h) + (1
n) Ct (h) (Pt (h)
M Ct )
Yt (h) = At Lt (h)
d
d
nCt (h) + (1
n) Ct (h)
0
1
!
!
!
H
H
Pt
Pt
Pt (h)
@n
Ct + (1
n)
Ct A
H
n
Pt
n
Pt
Pt
E q u ilib riu m c o n d itio n s (p o te ntia l, w ith o u t n o m in a l rig id itie s)
Authorized for public release by the FOMC Secretariat on 04/29/2016
38 of 50
Domestic (contingent) bonds market clearing
Foreign (contingent) bonds market clearing
Market clearing for foreign labor market
Market clearing for domestic labor market
Market clearing for domestic variety h
Market clearing for foreign variety f
Monetary policy (Taylor rule)
Fiscal policy
1 + it =
1
1)
Pt
Pt 1
Yt
Yt
x
nLt =
0
-
n
nB (! t+1 j ! t ) + (1
nB F (! t+1 j ! t ) + (1
H
Lt (h) dh
(1
1
-
Pt
Pt 1
Lt (f ) df
1
1
n
Z
=
n) Lt =
t
Foreign
Zt 1 + it
n) B (! t+1 j ! t ) = 0
n) B F (! t+1 j ! t ) = 0
H
1
n) Ct (h)
n) Ct (f )
1 + it =
Market clearing conditions
Yt (h) = nCt (h) + (1
Yt (f ) = nCt (f ) + (1
Z
Zt (1 + it
1
Table A4 - Policy rules and market clearing conditions
Home
Policy rules
1
t =
Yt
Yt
x
1
Authorized for public release by the FOMC Secretariat on 04/29/2016
Authorized for public release by the FOMC Secretariat on 04/29/2016
Figure 1
US imports as a share of GDP
Percent
20
18
16
14
12
10
8
6
4
2
0
1950
1955
1960
1965
1970
1975
1980
39 of 50
1985
1990
1995
2000
2005
2010
Authorized for public release by the FOMC Secretariat on 04/29/2016
Figure 2
Capacity utilization rates in the US and other G7 countries
Index, 2005Q1=100
115
other G7 countries
110
US
105
100
95
90
85
80
correlation = 0.63
75
1970
1975
1980
1985
1990
40 of 50
1995
2000
2005
2010
Authorized for public release by the FOMC Secretariat on 04/29/2016
Figure 3
Unemployment rates in the US and other G7 countries
Percent
12
US
11
other G7 countries
10
9
8
7
6
5
4
3
correlation=0.20
2
1970
1975
1980
1985
1990
41 of 50
1995
2000
2005
2010
Authorized for public release by the FOMC Secretariat on 04/29/2016
Figure 4
Output gap in the US and other G7 countries
Percent
5
4
US
other G7 countries
3
2
1
0
‐1
‐2
‐3
‐4
‐5
correlation= 0.70
‐6
1970
1975
1980
1985
1990
42 of 50
1995
2000
2005
2010
Authorized for public release by the FOMC Secretariat on 04/29/2016
Figure 5
Declining importance of G7
Percent
70
65
60
55
50
45
40
Imports from other G7 countries as a share of US imports
G7 share of world GDP
35
30
1960
1965
1970
1975
1980
1985
43 of 50
1990
1995
2000
2005
2010
Authorized for public release by the FOMC Secretariat on 04/29/2016
Percent
Figure 6
Headline PCE inflation
15
Headline PCE inflation
10
Cyclical headline PCE
Trend headline PCE
5
0
‐5
‐10
1959
1964
1969
1974
1979
1984
44 of 50
1989
1994
1999
2004
2009
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Figure 7
Core PCE inflation
Percent
12
10
Core PCE inflation
Cyclical core PCE
8
Trend core PCE
6
4
2
0
‐2
‐4
1959
1964
1969
1974
1979
1984
45 of 50
1989
1994
1999
2004
2009
Authorized for public release by the FOMC Secretariat on 04/29/2016
Figure 8
Capacity utilization rate
1.0
China
0.9
Argentina
0.8
Russia
0.7
Sweden
Thailand
0.6
Mexico
0.5
Euro
0.4
UK
Switzerland
0.3
Japan
0.2
Korea
Brazil
0.1
Canada
0.0
1970
1975
1980
1985
1990
46 of 50
1995
2000
2005
Authorized for public release by the FOMC Secretariat on 04/29/2016
Figure 9
Unemployment rate
1.0
Brazil
0.9
Colombia
China
0.8
Korea
Argentina
Thailand
0.7
Malaysia
Israel
0.6
Russia
Euro Area
0.5
Singapore
Phillipines
Mexico
0.4
Hong Kong
Chile
0.3
Australia
Taiwan
0.2
Japan
Sweden
UK
0.1
Switzerland
Canada
0.0
1970
1975
1980
1985
1990
47 of 50
1995
2000
2005
Authorized for public release by the FOMC Secretariat on 04/29/2016
Figure 10
Output gap
1
Mexico
0.9
Russia
Korea
India
0.8
Euro Area
Israel
0.7
Colombia
Thailand
0.6
Argentina
Malaysia
Brazil
0.5
Chile
Indonesia
Indonesia
0.4
Taiwan
Phillipines
Sweden
0.3
Switzerland
Japan
0.2
Singapore
UK
0.1
Australia
Hong Kong
Canada
0
1970
1975
1980
1985
1990
48 of 50
1995
2000
2005
Authorized for public release by the FOMC Secretariat on 04/29/2016
Figure 11
Output gap in the US, G6 and G26
Percent
5
4
US
other G7 countries
G26 countries
3
2
1
0
‐1
‐2
‐3
‐4
‐5
‐6
1970
1975
1980
1985
1990
49 of 50
1995
2000
2005
2010
Authorized for public release by the FOMC Secretariat on 04/29/2016
Figure 12
Relationship between statistical and model‐consistent measures of
foreign slack
2
Foreign output gap compute
ed using Hodrick Prescott filter
1.5
‐2
1
0.5
0
‐1.5
‐1
‐0.5
0
0.5
‐0.5
‐1
‐1.5
‐2
Model‐consistent foreign output gap
50 of 50
1
1.5
2
@FedFRASER