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CESifo-Delphi Conferences on
Global Economic Imbalances:
Prospects and Remedies
CESifo Conference Centre, Munich
11 - 12 November 2005
International Transmission Effects
of Monetary Policy Shocks:
Can Asymmetric Price Setting Explain
the Stylized Facts?
Caroline Schmidt
CESifo
Poschingerstr. 5, 81679 Munich, Germany
Phone: +49 (89) 9224-1410 - Fax: +49 (89) 9224-1409
[email protected]
http://www.cesifo-group.org
International Transmission Eects of Monetary
Policy Shocks:
Can Asymmetric Price Setting Explain the
Stylized Facts?
Caroline Schmidt>
†
August 2005
Abstract
How does an unexpected domestic monetary expansion aect the foreign
economy? Does it induce an increase or a decline in foreign production? In
the traditional two-country Mundell-Fleming model, monetary policy reveals
«beggar-thy-neighbor» eects. Yet, empirical evidence from VARs indicates
that U.S. monetary policy has positive international transmission eects on
both foreign (non-U.S. G-7) output and aggregate demand. In this paper, I
show that a two-country dynamic general equilibrium model with sticky prices
can account for these «stylized facts» if we introduce international asymmetries in the price-setting behavior of firms insofar as home (U.S.) firms set
Mailing address: Konjunkturforschungsstelle der ETH Zürich, Weinbergstasse 35, CH8092 Zürich, Switzerland, Phone: ++41-44-632-6899, Fax: ++41-44-632-1218, E-mail:
[email protected].
†
I am grateful for comments and suggestions from Mick Devereux at an early stage of this work.
Financial support from the Swiss National Science Foundation is gratefully acknowledged. The
paper also benefited substantially from two anonymous referee reports. Remaining errors are my
own.
1
export prices in their own currency only (producer-currency pricing), whereas
producers in the rest of the world price their exports to the U.S. in the local
currency of the export market (local-currency pricing).
Keywords: Asymmetric price setting, Local-currency pricing, New Open
Economy Macroeconomics, International transmission eects of monetary policy, VARs
JEL Classification: F41; E52
2
1
Introduction
In this paper, I show that allowing for international asymmetries in the price-setting
behavior of firms can help to understand the international transmission eects of
monetary policy shocks. How does a domestic monetary expansion aect the foreign
economy? Does it induce an increase or a decline in foreign production? And is it
‘beggar-thy-neighbour’ or does it raise foreign welfare? In the traditional MundellFleming Model, a monetary expansion at home causes a decline in foreign output.
This result is due to the expenditure-switching eect induced by the depreciation
of the home country’s currency. However, empirical evidence obtained from vector
autoregressions assessing the eects of U.S. monetary policy contradicts this implication. Instead, U.S. monetary policy is rather found to have positive spill-over
eects on foreign (non-U.S. G-7) output as well as on foreign aggregate demand. It
will be shown in this paper that these stylized facts can be replicated in a generalized SDGE-model with sticky prices if we introduce international asymmetries in
the price-setting behavior of firms.
With the publication of the Redux model in 1995, Obstfeld and Rogo launched
what is now called the “New Open Economy Macroeconomics” (NOEM), a branch
of research which aims at developing a new workhorse model for open economy
macroeconomics.1 Since 1995 a growing number of extensions to the Redux model
have been developed, also concerning pricing decisions of firms. In one extension of
this literature, Betts and Devereux (2001, 2000, 1996) show that the price-setting
behavior of firms (local-currency pricing compared to producer-currency pricing)
crucially determines the direction of the international transmission eects in response
to a monetary shock. In Betts and Devereux (2001) the positive transmission eect on
foreign output is reproduced for the assumption of complete local-currency pricing in
1
For an excellent survey of the research in this area see Lane (2001a), but also Sarno (2001),
Fendel (2002a) and for a more recent contribution Lane and Ganelli (2003).
3
both countries. Yet, this eect is not transmitted to foreign demand, which remains
unaected, in contrast to the implications of the empirical evidence.
The contribution of this paper is to show that introducing asymmetries in the
price-setting behavior of firms across countries in a generalized standard NOEMmodel helps to overcome this shortcoming. Empirical evidence established by Clark
and Faruqee (1997) and others, suggests that the degree of exchange-rate passthrough to import prices is noticeably lower in the U.S. compared to other G-7
countries and that most of U.S. trade is invoiced in U.S. dollars. For illustrational
purpose, I investigate in this paper the limiting assumption of complete producercurrency pricing in the home country, which represents the U.S., and complete localcurrency pricing in the foreign country representing the rest of the world which is
assumed to consist of the non-U.S. G-7 countries. In this setting, I find that a monetary expansion in the U.S. raises production as well as aggregate demand in the
foreign country. These results indicate that the suggested asymmetric price-setting
behavior provides an explanation to the empirical evidence.
The structure of the paper is as follows. The next section assesses some empirical
evidence on the international transmission eects of monetary policy, focusing on the
results obtained from vector autoregressions. In this context, not only evidence on
the international transmission eects of monetary policy on output, but also on consumption and investment is presented.2 It will be shown that for the flexible exchange
rate period, starting 1974, U.S. monetary policy has had positive spill-over eects on
foreign output for a number of countries as well as for a weighted average of the nonU.S. G-7 countries. This positive international transmission eect is also present for
foreign aggregate consumption and investment. In section 3, a generalized NOEMmodel is derived. It also includes a plausibilisation of the asymmetric price-setting
behavior. Using a first-order approximation around the symmetric steady-state, a
2
The way consumption is aected might be crucial for the resulting welfare implications.
4
one percent permanent increase in home money supply is investigated. The resulting impulse response functions obtained for the three alternative assumptions on
price-setting behavior (complete producer-currency pricing, complete local-currency
pricing and asymmetric price-setting behavior) are presented and discussed in section 4. It will be shown that only for the assumption of asymmetric price setting,
the empirical findings can be replicated. Finally, the corresponding implications on
welfare are presented before section 5 concludes.
2
Empirical evidence
Empirical evidence on international transmission eects of monetary policy has been
provided by a number of authors, albeit mainly for the U.S. Estimating a two-country
VAR, Betts and Devereux (2001) determine the eects of U.S. monetary policy on
foreign output. The foreign country (or the ‘rest of the world’) is proxied by a GDPweighted average of the non-U.S. G-7 countries. For the two expansionary monetary
shocks considered, Betts and Devereux find that foreign output rises significantly.
A positive international transmission eect of U.S. monetary policy on both U.K.
and German output is also found by Faust and Rogers (2003), and Miniane and
Rogers (2003) provide evidence for a positive international transmission eect of
U.S. monetary policy on output even for a large set of countries.
Although there is considerable evidence on the transmission eects on foreign
output, less evidence has been provided for the eects on foreign aggregate demand.
However, if we are interested in the eects on the foreign economy in terms of welfare,
the way foreign consumption is aected is crucial. Holman and Neumann (2002) provide evidence for positive spill-over eects of an expansionary U.S. monetary policy
shock on Canadian consumption and investment besides output. A more extensive
investigation of the international transmission eects of U.S. monetary policy which
likewise includes the eects on foreign demand is undertaken by Kim (2001). As
5
in Betts and Devereux (2001), he constructs a weighted average of non-U.S. G-7
countries to proxy for the rest of the world. Besides an - albeit smaller - positive
transmission eect on foreign output, Kim also finds an increase in foreign aggregate
demand in response to an expansionary U.S. monetary policy shock. However, Kim
does not distinguish between consumption and investment.
To provide more in depth evidence for the eects on foreign consumption and
investment in a two-country-setting, I estimate a two-country VAR similar to the
approaches of Betts and Devereux (2001) and Kim (2001) to determine the eects of
a U.S. monetary policy shock on a weighted average of non-U.S. G-7 countries’ economic aggregates. As Kim (2001) and Holman and Neumann (2002), I use quarterly
data from 1974:1 to 2001:4.3 I consider two alternative monetary policy instruments,
the federal funds rate (FFR) and the ratio of non-borrowed reserves to total reserves (NBR/TR). The variables included in the benchmark model are U.S. GDP,
U.S. consumer prices (CPI), non-U.S. G-7 GDP, FFR, (NBR/TR), a foreign short
term interest rate (IR non-U.S. G-7) and the real exchange rate (REER) for the
shock to the federal funds rate. For the shock to the non-borrowed reserves to total
reserves ratio, the variable included comprise U.S. GDP, U.S. CPI, non-U.S. G-7
GDP, (NBR/TR), the interest rate dierential between the U.S. and the non-U.S.
G-7 and the REER . The real exchange rate is defined such that an increase in REER
corresponds to a depreciation of the U.S. dollar. As in Kim (2001), I add the variables of interest one by one as the last element to the system and then re-estimate
the VAR for each variable. The system is estimated in levels, where all variables
except the interest rates enter the system in logs, and four lags are included. For the
identification I use the Choleski decomposition.4
3
The non-U.S. G-7 data are taken from the IMF-IFS CD-Rom, U.S. data stem from the Bureau
of Economic Analysis or the Federal Reserve Economic Data. All data are seasonally adjusted
except for the interest rates and the exchange rates.
4
For a more detailed description of the analysis and the results, the reader is referred to Schmidt
(2004).
6
Figure 1: Impulse responses to a negative one std. dev. innovation in the U.S. federal
funds rate
1
CPI US
GDP US
1
0.5
0
−0.5
0
5
10
15
FFR US
GDP
non−US G7
0
5
10
15
20
0
5
10
15
20
0
5
10
15
20
0
−0.5
0
5
10
15
−1
20
0.5
IR
non−US G7
1
0.5
NBR/TR
0
0.5
0.5
0
−0.5
0
−0.5
20
1
−0.5
0.5
0
5
10
15
20
0
5
10
15
20
0
−0.5
REER US
vs. non−US G7
10
5
0
−5
For both shocks considered, I find significant spill-over eects not only for foreign
output, but also for non-U.S. G-7 consumption and investment. In the following, only
the resulting impulse responses to a negative one standard deviation innovation of the
U.S. federal funds rate are presented, which are displayed in Figure 1.5 The dotted
and dashed lines represent one and two standard errors respectively.6 In response to
a surprise decrease in the U.S. federal funds rate, both the domestic and the foreign
economy experience an increase in output, where the rise in foreign output is more
delayed. Also, the U.S. real exchange rate depreciates significantly.
Figure 2 displays the eects on foreign consumption and investment. As outlined
5
To facilitate the comparison with the monetary shock in the model, I focus on an expansionary
monetary shock.
6
The standard errors are obtained from 1000 Monte Carlo draws following Doan (1992) and
Uhlig (2001).
7
Figure 2: Impulse Responses of non-U.S. G-7 Consumption and Investment in response to a negative 1 standard deviation Innovation in the U.S. federal funds rate
1.5
1.5
1
1
0.5
0.5
0
0
−0.5
0
5
10
15
−0.5
0
20
non-U.S. G-7 Consumption
5
10
15
non-U.S. G-7 Investment
before, the resulting impulse response functions are obtained by adding the corresponding variables separately as the last element to the benchmark VAR, which is
then re-estimated for each individually included variable. As can be seen from Figure
2, both non-U.S. G-7 consumption and investment increase significantly in response
to an expansionary U.S. monetary policy shock.7 The maximum eect of a negative
one standard deviation innovation of the U.S. FFR on non-U.S. G-7 consumption
amounts to an increase of about 0.25% and is almost similar to the magnitude of the
rise in non-U.S. G-7 GDP. The peak eect on non-U.S. G-7 investment of 0.7% is
about 3 times the size of the increase in GDP. According to these results, an expansionary U.S. monetary impulse not only induces an increase in foreign output, but is
also transmitted to foreign consumption and investment. These eects are found to
be robust to dierent weightings for the construction of the non-U.S. G-7 variables
as well as for dierent identifications of the monetary policy shock, although the
magnitude of the eects can be aected.8
The empirical results seem to question some of the implications of traditional
7
U.S. consumption and investment increase as well.
Robustness checks comprised the inclusion of a commodity price index to reduce the prizepuzzle eect, which induces a more pronounced eect on foreign investment, whereas the eect on
foreign consumption is less important. Ordering the shock first and hence allowing all variables to
respond to the shock immediately has almost no eect on the impulse response functions.
8
8
20
monetary open-economy models. They especially cast doubt on the importance of
the ‘expenditure-switching’ eect, which drives the transmission to foreign output in
most monetary open-economy models such as the Mundell-Fleming and the Dornbusch model, but is also inherent in the Redux model by Obstfeld and Rogo. An effect in the opposite direction on foreign output might occur in response to a monetary
induced worldwide decline in the interest rates, causing overall demand to increase.
If the latter eect is large enough it will compensate for the expenditure-switching
eect and foreign output increases. Kollmann (2001a), who also studies international
transmission eects of monetary policy shocks in a NOEM model, obtains a positive transmission on both foreign output and aggregate demand by making use of
this second eect. However, his results seem to rely on the extremely low calibration
values for interest and consumption elasticities of money demand. Yet, recent estimations of money demand elasticities conducted by Chari, Kehoe and McGrattan
(2002) seem to indicate that these are much higher than the values used by Kollmann. As is shown below, employing the values of Chari, Kehoe and McGrattan, the
positive spill-over eect on foreign output is not reproduced.
A dierent approach to reproduce empirical findings with a theoretical model is
followed by Betts and Devereux (2001). Introducing complete local-currency pricing
in a two-country SDGE-model with sticky prices, they can replicate the positive
transmission eect on foreign output. However, the positive eect is not transmitted
to foreign demand.
In the following sections, I show that if we introduce international dierences in
the price-setting behavior of firms, a dynamic general equilibrium model with sticky
prices can account for the positive international transmission eects of monetary
policy on both foreign output and aggregate demand, independent of the calibration
values for money demand elasticities.
9
3
The Model
In the following, a two-country dynamic general equilibrium model with nominal
price rigidities in the tradition of the Redux model by Obstfeld and Rogo (1995a),
henceforth OR, is derived.9 There are two countries, home and foreign, each inhabited
by a continuum of agents normalized to 1. The home country represents the U.S.,
while the foreign country represents the rest of the world which is assumed to consist
of the non-U.S. G-7 countries. Agents consume consumption goods, supply labor
and accumulate capital which they rent out to firms. A continuum of individual
monopolistic firms resides in the home and the foreign country, which are respectively
indexed by } k 5 [0> 1] and } i 5 [0> 1]. Each firm produces a single dierentiated good,
whereas labor and capital are assumed to be homogenous and can be substituted
across firms without any cost. To distinguish foreign from home agents, the foreign
variables will be identified with an asterisk.
3.1
Consumers
Preferences of the representative agent residing in the home country have the following explicit form.
"
#
µ ¶13
"
13
X
F
"
P
v
v
+
+ ln (1 Kv )
X = Hw v3w
1
1
S
v
v=w
Direct utility is derived from consumption of a basket of dierentiated goods Fw ,
from real money balances
Pw
Sw
, and from leisure (1 Kw ). The parameter denotes the
representative home agent’s subjective discount factor. The intertemporal elasticity
of substitution is given by 1 , while is crucial for money demand elasticities.
9
Since the main features of the model are standard, the derivation is kept rather brief.
10
The home agent faces the following intertemporal budget constraint.
i
k
+ hw Ew+1
+ Sw w = (1 + lw ) Ewk + (1 + lWw ) hw Ewi + w
Sw Fw + Sw Yw + Pw + Ew+1
+Zw Kw + uwN Sw Nw + Pw31
(1)
Nominal expenditures on consumption Sw Fw , investment Sw Yw , money balances
i
k
and hw Ew+1
and the payment of
Pw , two internationally traded riskless bonds Ew+1
nominal lump-sum taxes amounting to Sw w may not exceed the sum of nominal
returns from last period’s bonds in terms of the home currency, i.e. (1 + lw ) Ewk and
(1 + lWw ) hw Ewi , nominal profits w from the shares of home firms, nominal wage income Zw Kw , nominal rental payments received on the capital stock uwN Sw Nw , plus
last period’s money balances Pw31 . I assume that all agents within one country hold
equal shares of all firms residing in this country, and home (foreign) firms profits are
distributed equally among all home (foreign) agents.
The explicit form of the law of motion for capital is
Nw+1
! {Nw+1 Nw }2
= (1 ) Nw + Yw =
2
Nw
(2)
Capital depreciates at the constant rate and increases with investment Yw but at
a decreasing rate because of non-linear capital adjustment costs, which are governed
by !.
The agent maximizes her expected lifetime utility X with respect to Fw > Pw , Kw ,
i
k
and Ew+1
subject to her intertemporal budget constraint and to the law
Nw+1 , Ew+1
of motion for the capital stock. The resulting first order conditions of the domestic
11
representative agent are
5
Fw3
6
¶
µ
9
:
Sw
9
3 :
= Hw 9(1 + lw+1 )
Fw+1 :
7
8
Sw+1
{z
}
|
(3)
(1+uw+1 )
"
## 1
"
Pw
1
= "Fw Hw
Sw
1 1+l1w+1
(4)
1
Zw
= Fw3
(1 Kw )
Sw
(5)
µ
¶
·µ
¶
¸
2
2
Nw+1
Nw+1 Nw
! Nw+2
3
N
3
1+!
Fw = Hw 1 + uw+1 +
Fw+1
2
Nw
2
Nw+1
(6)
(1 + lw+1 ) Hw
·
· 3 µ
¶¸
3 ¸
¡
¢
Fw+1
Fw+1 hw+1
W
= 1 + lw+1 Hw
Sw+1
Sw+1
hw
(7)
The first optimality condition, equation (3), is the Euler equation which determines the optimal intertemporal consumption path. Equation (4) characterizes the
money market equilibrium. The third optimality condition, equation (5), determines
optimal labor supply, while the agent’s optimal investment decision is determined
by equation (6). For the assumption of certainty equivalence used for the linear approximation of the model below, the last optimality condition, equation (7), reduces
to the uncovered interest parity.
The household’s consumption basket is defined as an aggregate of the consumption of home and foreign goods, which takes the explicit form of a CES-function.
¶ 31
µ
³ ´ 31
¢ 31
1
1 ¡
i
k
Fw = Fw + (1 ) Fw
12
(8)
Fwk and Fwi are the home agent’s consumption baskets that consist of domestically produced goods and imported foreign goods respectively.10 The coe!cient determines the degree of home bias in consumption, while the parameter denotes
the elasticity of substitution between domestically produced goods Fwk and imported
foreign goods Fwi .
Both Fwk and Fwi consist of a weighted average of home and foreign dierentiated
goods each of which is produced by an individual monopolistic firm. The composition
of the commodity basket of home goods consumed by agents in the home country is
defined as
31
4 31
Z
¡ ¢ 31
Fwk = C fkw } k g} k D =
0
Consumption of foreign goods is allocated analogously. The parameter denotes
the elasticity of substitution between dierent goods produced within one country, but also governs the magnitude of the markup. For simplicity, I assume that
investment features the same composition as consumption. Then, expenditure minimization of home and foreign agents results in the following total demand for the
representative home good k
|wk
¶3
Swk
[Fw + Yw ]
Sw
¶3 µ kW ¶3
µ kW
Sw
sw (k)
+ (1 )
[FwW + YwW ] =
kW
SwW
Sw
µ
sk (k)
(k) = w k
Sw
¶3 µ
(9)
Total demand for good k consists of the demand of home and foreign agents
weighted with the corresponding expdinture share and depends on relative prices
and substitutabilities besides the aggregate level of expenditures for consumption
and investment in both countries. The individual price of the representative home
10
A notational remark: The superscript k denotes the goods and prices of home producers,
whereas i denotes goods and prices of foreign producers. As goods are traded, we also dierentiate
between prices and goods that are valid for respective markets: Variables marked with an asterisk
identify goods that are sold in the foreign market and prices that are charged in the foreign currency.
13
good k is skw (k). Swk denotes the price level for the basket of domestically produced
goods, which is defined as
1
51
6 13
Z
¡ k ¡ k ¢¢13 k
Swk = 7
g} 8 =
sw }
(10)
0
Correspondingly, Swi , the home price index for imported goods from the foreign
country, is defined as
1
6 13
51
Z ³
´
13
¡ ¢
g} i 8
Swi = 7
siw } i
(11)
0
¡ ¢
where siw } i denotes the home currency price of the foreign good variety } i .
The domestic price level of all goods purchased by home agents is then a weighted
average of Swk and Swi
1
·
³ ´13 ¸ 13
¡ k ¢13
i
Sw = Sw
+ (1 ) Sw
=
(12)
Accordingly, skW
w (k) is the foreign currency price of the representative home good
k, SwkW denotes the foreign currency price level of goods imported from the home
country and SwW is the absolute consumer price level in the foreign country.
As Ricardian equivalence holds in this type of models, assuming a balanced budget has no consequence on the results of the following analysis. For simplicity it is
assumed that all seigniorage revenue accruing to the central bank is redistributed to
agents in form of a lump-sum transfer
Pw Pw31 = Sw w =
This reduces the home economy’s budget constraint to
i
k
+ Ew+1
hw = (1 + lw ) Ewk + (1 + lWw ) Ewi hw + w + Zw Kw + Sw uwN Nw (13)
Sw Fw + Sw Yw + Ew+1
14
3.2
3.2.1
Firms
Pricing
Each firm will set its price so as to maximize expected profits, taking its individual
demand schedule, equation (9), into account. Yet, firms are assumed to set nominal
prices in advance. Following Calvo (1983), each firm faces the same constant probability (1 ) every period to change its price next period and to keep the price
constant, independent of its history of price changes. By the law of large numbers, a
constant fraction (1 ) of firms will actually change their prices each period, while
the remaining fraction cannot adjust their prices.
Following Betts and Devereux (2001, 2000, 1996) and Engel (2000), I also distinguish between two types of firms who dier in their price-setting behavior. One type,
the subset (1 v) of firms, sets one price for its good, independent of the market
where the good is sold. Since the price is set in the currency of the producer, this
pricing behavior is referred to as producer-currency pricing (henceforth PCP). In the
presence of short-run price rigidities import prices of these goods exhibit a complete
exchange-rate pass-through. The second type of firm, represented by the remaining
fraction v, is assumed to set two dierent prices, one for the home market and one
for the foreign market. As both prices are denominated in the respective local currency of the market, this price-setting behavior is referred to as local-currency pricing
(henceforth LCP).11 Contrary to the case of PCP goods, import prices of LCP goods
are not aected by a change in the exchange rate in the presence of sticky prices.
How the two alternative price-setting assumptions aect the international transmission of monetary policy shocks has already been analyzed by Betts and Devereux
(2001). However, Betts and Devereux presume throughout their analyses an identical
fraction of LCP firms in both countries, which is either set to 0 or 1.
11
Firms are assumed to possess su!cient market power, so that international price dierences
for the same good cannot be arbitraged away by agents.
15
Asymmetric Price Setting The contribution of this paper is to consider dierent shares of LCP in both countries, which I refer to as asymmetric price setting.
Empirical evidence provided by the ECU Institute (1995) indicates that about 92%
of U.S. exports and 80% of U.S. imports are invoiced in U.S. dollars, implying a huge
asymmetry in the price-setting behavior between U.S. firms exporting from and foreign firms exporting to the U.S. Further empirical evidence supporting the thesis of
international dierences in LCP between the U.S. and other G-7 countries is also
provided by Clark and Faruqee (1997). They compare the variance of import prices
to the variance of the nominal exchange rate for the G-7 countries and find that
while the relative volatility is basically zero for the U.S., it is much higher for the
remaining G-7 countries.12 Similar results are provided by Knetter (1989) in a comparison of the U.S. and Germany. The results of Gagnon and Knetter (1995), who
assess bilateral automobile export prices from exporters in the U.S., Germany and
Japan, suggest that exports to the U.S. and Canada are invoiced in the importer’s
currency, while exports to the other countries (Japan, U.K., France, Germany, Australia, Switzerland and Sweden) seem to be invoiced in the exporter’s currency. This
asymmetry is also discussed in OR (2000) and Devereux, Engel and Tille (2003), but
has not yet been incorporated into a theoretical model of international transmission
eects of monetary policy. Yet, a recent contribution by Bacchetta and van Wincoop
(2005) addresses the issue of the optimal choice of currency invoicing of exports in a
static framework. In their model, this choice depends on the competition firms face
in the foreign market. Bacchetta and van Wincoop find that a higher market share in
the foreign market provides an incentive for firms to set prices in their own currency
and vice versa, which provides a theoretical argument in favour of the asymmetric
pricing behavior.
In this paper, the asymmetry is implemented in form of the limiting assumption
of complete PCP in the U.S. and complete LCP in the rest of the world. In the
12
The estimates of relative volatility range from 0.25 for the U.K. to 0.94 for Italy.
16
dynamic analysis presented in section 4, the transmission eects for the asymmetric
price-setting assumption will be compared to the outcome for complete PCP and
complete LCP in both countries.
Profit maximization of the representative home PCP firm In the presence of price rigidities à la Calvo, firms set prices so as to maximize their expected
discounted future profits, which are given by
Hw
""
X
()l \w>w+l
l=0
Ã
Sewk>S FS (k) PFw+l
Sw+l
Sw+l
with
\w>w+l =
µ
Fw+l
Fw
¶3
!
#
k>S FS
|w>w+l
(k)
=13
k>S FS
|w>w+l
(k) denotes the expected total demand of the representative home PCP
firm at time w + l provided that the price set at time w is still eective. The optimal
price of the representative home PCP firm at time w, Sewk>S FS (k), is then derived as
a markup over a weighted average of expected future nominal marginal costs.
Sewk>S FS (k) =
1
Hw
hP
"
l
k>S FS
l=0 () \w>w+l Gw>w+l PFw+l
hP
i
"
l
k>S FS
Hw
()
\
G
w>w+l w>w+l
l=0
i
(14)
k>S FS
denotes total expected future real sales revenues of the PCP firm, given
Gw>w+l
that the optimal price chosen at time w is still eective. Since all PCP firms in the
home country face the same constraints, each firm that can adjust its price in period
w will choose the same price Sewk>S FS (k). The home country price index for home PCP
goods S k>S FS is then a weighted average of last period’s price index and the optimal
13
A notational remark: The superscript S FS identifies goods produced and prices charged by
PCP firms, the superscript OFS marks the respective variables for LCP firms.
17
price at time w
Swk>S FS
1
· ³
³
´13 ¸ 13
´13
k>S FS
k>S
FS
= Sw31
+ (1 ) Sew
(k)
=
(15)
Profit maximization of the representative LCP firm The representative LCP
firm faces essentially the same optimization problem as the PCP firm, but maximizes
profits arising from the home and the foreign market, choosing two dierent prices.
Expected profits then are
Hw
""
X
Ã
!
k>OFS
e
S
(k)
PF
w+l
k>OFS
w
|w>w+l
()l \w>w+l
(k)
S
S
w+l
w+l
l=0
Ã
!
#
k>OFS>W
e
(k)
h
PF
S
w+l
w+l
k>OFS>W
w
|w>w+l
+ ()l \w>w+l
(k)
Sw+l
Sw+l
where \w>w+l is defined as above. Sewk>OFS>W (k) denotes the optimal export price of the
representative home LCP firm set in the foreign currency, which is converted to the
k>OFS
k>OFS>W
home currency via the exchange rate hw+l . The quantities |w>w+l
and |w>w+l
denote
home and foreign agents’ demand for the representative home LCP good at w + l
given the prices Sewk>OFS (k) and Sewk>OFS>W (k) set at time w.
In the log-linearized version of the model, the optimal domestic market price of
the home LCP firm is identical to the PCP firm price. Therefore, the home price
index for domestically produced goods, defined in equation (10) above, can simply
be written as
Swk = Swk>S FS =
(16)
The optimal export price Sewk>OFS>W (k) of the representative home LCP firm is
derived as
Sewk>OFS>W (k) =
1
Hw
hP
"
l
kW>OFS PFw+l
l=0 () \w>w+l Gw>w+l
hw+l
hP
i
"
l
kW>OFS
Hw
()
\
G
w>w+l w>w+l
l=0
18
i
(17)
kW>OFS
Correspondingly, Gw>w+l
is defined as expected future real sales revenues of
the LCP firm - albeit only in the export market. As the LCP price for the foreign
market is set in the foreign currency, the optimal newly set price also depends on
the expected future path of the nominal exchange rate, as the LCP firm needs to
consider the increase in markup due to a devaluation of the home currency.
The price index for domestic goods produced by LCP firms evolves analogously
Swk>OFS>W
1
· ³
³
´13 ¸ 13
´13
k>OFS>W
k>OFS>W
e
= Sw31
+ (1 ) Sw
(k)
=
(18)
As prices in the foreign market dier between PCP and LCP firms, the price
index of imported goods is a weighted average of the average prices of foreign LCP
and PCP goods Swi>OFS and Swi>S FS>W targeted at the home market. The respective
weights are determined by the share vi of foreign LCP firms. Therefore, the home
price index of imported foreign goods, defined in equation (11) above, simplifies to
Swi
1
· ³
´13 ¡
´13 ¸ 13
¢³
i>OFS
i>S FS>W
i
i
= v Sw
+ 1v
=
hw Sw
(19)
For analogous reasons, the foreign price index of goods imported from the home
country is defined as
5
SwkW
3.2.2
³
´13 ¡
¢
k>OFS>W
k
7
= v Sw
+ 1 vk
Ã
Swk>S FS
hw
1
!13 6 13
8 =
Production
Firms at home and abroad produce under constant-returns-to-scale, employing the
following Cobb-Douglas production function, displayed for the example of the representative home firm k
|w (k) = Dw Nw (k) Kw (k)13 =
19
Dw represents the common level of technology in the home country, while Nw (k)
and Kw (k) denote the individual capital and labor inputs of the representative home
firm k. Cost minimization implies that firms will demand factor inputs to satisfy
Zw = PFw (1 )
|wk (k)
|k
= PFw (1 ) w
Kw (k)
Kw
(20)
and
Sw uwN = PFw |wk (k)
|k
= PFw w
Nw (k)
Nw
(21)
where PFw denotes the nominal marginal costs of production. Since all firms in
one country have to pay the same wage and face the same rental rate for capital,
marginal costs are the same across all firms residing in one country.
3.3
Market Clearing
In equilibrium, all goods, factor and asset markets need to clear in the home and the
foreign economy. In the home goods market, aggregated demand consists of demand
for LCP and PCP goods
¡
¢
\wk = vk \wk>OFS + 1 vk \wk>S FS
(22)
Total supply in the home country can be written as
\wk =
Z1
0
¡ ¢
¡ ¢
Dw Nw } k Kw13 } k g} k = Dw Nw Kw13
(23)
since all home firms produce with the same capital-labor ratio. The foreign goods
market clears analogously. The home and the foreign money market are in equilibrium
if national money demand corresponds to the respective exogenous supplies of home
and foreign currency provided by the corresponding national central bank. Bond
markets clear in equilibrium if aggregate world assets, i.e. the joint net assets of
20
home and foreign agents, are equal to zero in all periods.
3.4
Equilibrium
Equilibrium is characterized by equations (2), (3), (4), (5), (6), (12), (20), (21), (14),
(15), (17), (18), (22), (23), (16), (19) and their foreign counterparts, demand equation
(9) for both LCP and PCP firms in the home and the foreign economy, as well as
equations (7), (13) and the bonds market equilibrium, which gives 39 equations. This
is a dynamic system in the following thirty-nine variables, given by [w
[w = {Fw > FwW > Kw > KwW > Yw > YwW > Nw > NwW > Zw > ZwW > uwn > uwnW > lw > lWw > PFw > PFwW > hw > Ewk > Ewi
Sw > SwW > Swk > Swi > SwkW > Swi W > Sewk>S FS > Sewk>OFS>W > Sewi>S FS > Sewi>OFS > Swk>S FS >
Swk>OFS > Swi>S FS > Swi>OFS > \wk > \wi > \wk>S FS > \wk>OFS > \wi>S FS > \wi>OFS }
The model is solved by linearizing around the symmetric steady state, where
neither country owns net foreign assets.14 The assumption of an international asymmetric degree of local-currency pricing has no consequences for the determination
of the steady state, since optimal steady-state prices will be equal to the flexible
price solution, which is the same for both LCP and PCP firms. I abstract from real
growth due to technological progress and from growth in the monetary base. Hence,
in equilibrium all nominal and real variables are constant.
3.5
Calibration
The calibrated parameters are presented in table 1. For the baseline calibration,
I choose the following parametrization. In line with the business cycle literature,
the quarterly real interest rate is set to 1% in the steady state. The consumption
elasticity of money demand ( in the model) is commonly estimated to be about
14
For the solution of the model, the MATLAB code provided by Schmitt-Grohé and Uribe (2004)
is employed.
21
unity, see, e.g., Mankiw and Summer (1986), which is the value I adopt. For the
interest elasticity of money demand ( in the model), the estimates vary from
0=39 in Chari et al. (2002) to 0=051 in Mankiw and Summers (1986).15 For the
benchmark calibration, I choose 0=39. The main results are unaected if the value
estimated by Mankiw and Summers (0=051) is employed.16 The benchmark values
for money demand elasticities imply that is about 2=5. The parameter determines
the markup of prices over marginal costs. Consistent with the findings of Basu and
Kimball (1997), which suggest a markup of about 10% in the U.S., I assume = 10.
The capital share is set to 13 . This value is in line with empirical evidence on the
labor share provided by Bentolila and Saint-Paul (2003), which is found to range
from 62% to 68% for the G-7 countries in the 1990s. The rate of depreciation is set
to 0=021, which implies an annual depreciation rate of about 10%, corresponding to
the typical estimates for U.S. data. The steady state share of labour, K 0 , is set to
0=3. For simplicity, the relative preference parameter for real balances, ", is assumed
to be 1. The last two assumptions further determine , the preference parameter for
leisure, to be 2=8. The price adjustment parameter is set such that the average time
between price adjustment for a firm is one year. This implies = 0=75. The import
share in the steady state is assumed to be 15% for both countries. While the U.S.
average import share in the post Bretton Woods era amounts to about 11%, import
shares in the remaining G-7 countries during this time period range from 10% in
Japan to almost 30% in Canada. The value for capital adjustment costs ! is set to 8,
which induces an investment response to an unanticipated increase in home money
supply for the baseline calibration of about 3 times the size of the corresponding
output response in the home country, and thus corresponds to the findings of the
15
Both Chari et al. and Mankiw and Summers use consumption as the relevant quantity variable
for the estimation of money demand elasticities, which corresponds to the setup in the model.
Chari et al. (2002) also implicitly assume a unity consumption elasticity of money demand in their
regression.
16
Yet, this result does not hold for an interest rate elasticity of money demand of 0=01 together
with a consumption elasticity of 0=2, the values chosen in Kollmann (2001a).
22
VAR analysis. Finally, the elasticity of substitution between home and foreign goods
is set equal to 1.5 as found by Hooper and Marquez (1995, Table 4.1) for the
U.S. Finally, dierent degrees of pricing to market in both the home and the foreign
economy are analyzed to determine the eects of dierent price-setting behavior on
the international transmission mechanism of monetary policy shocks.
Table 1: Calibrated parameters
2=5 "
1
10
2=5 0=021 1=5
1
! 8 0=85
1=01
1
2=8 0=75
3
4
Results
In this section, the set of impulse responses obtained for a 1% increase in the home
nominal money supply is presented for three alternative price-setting assumptions:
complete PCP in both countries, complete LCP in both countries and asymmetric
price-setting behavior. The plotted impulse responses are percentage deviations from
respective steady-state values, except for the interest rates, the current account and
net foreign assets. Solid lines show the responses of home variables, dashed lines the
corresponding responses of foreign variables. The horizontal axes depict the number
of quarters.
4.1
PCP vs LCP
Figure 3 displays the impulse responses for complete PCP in both countries, which
is the primal assumption made by OR (1995a), as well as in the Mundell-FlemingDornbusch model. In response to the surprise increase in home money supply in
period 1, home production as well as home aggregate demand increase. Although
foreign consumption and investment experience a temporary — but smaller — increase
23
Figure 3: Impulse responses to a permanent increase in home money supply for the
benchmark calibration and complete PCP
Home & Foreign Output
1
Home & Foreign Consumption
0.4
0.3
0.5
Home & Foreign Investment
4
2
0.2
0
−0.5
0
0.1
0
10
20
0
0
Terms of Trade
10
20
−2
r, r*
0
0
0
−0.2
−0.05
−2
−0.4
−0.1
−4
−0.6
−0.15
−6
−0.8
0
10
20
−0.2
0
Nominal & Real Exch. Rate
10
20
−8
0
−3
x 10
0
P, P*
1.5
1
1
0.5
0.5
0
10
20
ib, ib*
10
20
CA & NFA in % of GDP
0.4
0.3
0.2
0
0
10
time
20
−0.5
0.1
0
10
time
20
0
0
10
time
20
as well, foreign output is basically unaected.
The monetary expansion in the home country causes a decline in the home nominal and real interest rate le and u as depicted in Figure 3. This in turn induces a
boom in home demand as implicit returns on consumption and investment in terms
of utility and the real rental rate on capital outweigh the associated costs in terms
of u. At the same time the home currency depreciates. For complete PCP, import
prices exhibit a complete exchange rate pass-through. Thus, the depreciation leads
to a decline in the average foreign import price, whereas the average price of home
agents’ imports rises. Since the consumer price index which is used to deflate real
money balances comprises respective import prices, the monetary impulse initiated
in the home country is spread to the foreign economy, inducing an increase in foreign
24
consumption and investment as well. Foreign output, however, remains unchanged
since the expenditure-switching due to the change in relative prices redirects the
whole augmentation in world aggregate demand towards goods produced at home.
This result corresponds to the findings of Betts and Devereux (2001). The impact
on the foreign economy depends on the import share, which is presumed to be 15%.
As can be seen from Figure (3), the home country experiences a deterioration of its
terms of trade. At the same time, the home country runs a current account surplus
and accumulates net foreign assets throughout the whole adjustment process.
Compared to the findings in OR (1995), who also assume complete PCP, the main
implications are similar. In response to the monetary expansion at home, the eect on
foreign output is found to be ambiguous in the short run. For a consumption elasticity
of money demand equal to 1, as assumed for the simulations presented here, the eect
turns out to be negative, while the magnitude depends the monopolistic distortion
and on relative country sizes. The eect on foreign consumption is not explicitly
derived. Yet, OR show that as the home country runs a current account surplus in
response to the shock, foreign agents’ consumption exceeds foreign production in the
short run.
Let us now turn to the international transmission eects for complete LCP in
both countries. The corresponding impulse responses are shown in Figure 4. Again,
an unanticipated increase in home money supply raises home production as well as
home consumption and investment in the short run. However, when all producers
set their export prices in the export currency, the increase in money supply also
raises foreign production, whereas foreign aggregate demand even slightly falls. For
complete LCP, there is no exchange rate pass-through to import prices. On the
one hand, this inhibits the foreign consumer price level to fall and thus prevents a
decline in foreign nominal and real interest rates. Therefore, foreign consumption
and investment do not rise. On the other hand, with no exchange rate pass-through
25
Figure 4: Impulse response to a permanent increase in home money supply for the
benchmark calibration and complete LCP
Home & Foreign Output
1
Home & Foreign Consumption
0.3
0.2
0.5
Home & Foreign Investment
4
2
0.1
0
−0.5
0
0
0
10
20
−0.1
0
Terms of Trade
10
20
−2
r, r*
1
0.1
5
0
0.5
0
−3
x 10
10
20
ib, ib*
0
−0.1
0
−0.5
−5
−0.2
0
10
20
−0.3
0
Nominal & Real Exch. Rate
10
20
−10
0
P, P*
1.5
1
1
0.5
0.5
0
10
20
CA & NFA in % of GDP
0.05
0
−0.05
0
0
10
time
20
−0.5
−0.1
0
10
time
20
−0.15
0
10
time
20
to import prices, the expenditure-switching eect is repressed. Hence, the increase
in home agents’ demand is directed to both home and foreign goods according to
the respective expenditure shares of home agents on imports and domestic goods.
Note, however, that although foreign production rises, foreign agents’ income falls.
The devaluation of the home currency deteriorates the foreign country’s terms of
trade. Whereas foreign import prices basically remain unaected, foreign export
prices denoted in the foreign currency fall. Since the deterioration in the terms of
trade more than compensates the increase in foreign production, foreign ‘real income’
falls.
26
4.2
Asymmetric Price Setting
So far, the same degree of LCP was assumed in both countries. Yet, as outlined in
section 3.2.1, empirical evidence indicates asymmetries in the degree of LCP between
the U.S. and the other G-7 countries. For illustrational purposes, I consider a stylized
scenario where all trade in goods is invoiced in the home currency, i.e. in U.S. dollars.
Put dierently, I assume complete PCP in the home country and complete LCP in the
foreign country. As displayed in Figure 5, the unanticipated increase in home (U.S.)
money supply induces a decline in nominal and real interest rates in both countries,
as for the assumption of complete PCP. On this account, foreign consumption and
investment rise. At the same time foreign output increases.
For complete asymmetric price-setting, a devaluation of the U.S. dollar induced
by the U.S. monetary expansion reduces the foreign currency price of foreign country’s imports as in the case of complete PCP. This in turn leads to a decline in the
foreign overall consumer price level S W as shown in Figure 5, inducing an increase in
foreign real balances. The excess supply on the foreign money market allows for a
decline in the foreign nominal and real interest rates, which brings forth an increase
in foreign consumption and investment demand. This propagation mechanism corresponds with the one resulting for complete PCP. On the other hand, import prices
of foreign goods for home agents do not change with the devaluation, as they are set
in the home currency, the U.S. dollar. As there is no exchange rate pass-through to
U.S. import prices, home agents have no incentive to switch from foreign to home
goods, and the expenditure-switching eect is clearly extenuated.17 Thus, the increase in home demand is directed to both home and foreign goods in proportion
to the expenditure shares of U.S. agents. Accordingly, foreign production, which is
demand-determined in the short run, increases. Thus, for the specific assumption
17
In this setting, the home country’s terms of trade still improve initially, albeit by much less.
The reason is that both home country import prices and export prices (in the home currency) are
initially basically fixed, and hence there is not much room for a change in the terms of trade.
27
Figure 5: Impulse responses to a permanent increase in home money supply for the
benchmark calibration and complete asymmetric price-setting behavior
Home & Foreign Output
1
Home & Foreign Consumption
0.4
0.3
0.5
Home & Foreign Investment
4
2
0.2
0
−0.5
0
0.1
0
10
20
0
0
Terms of Trade
0.1
0.1
0
0.05
−0.1
0
−0.2
0
10
20
−2
0
r, r*
0.15
−0.05
10
20
−0.3
−0.005
0
10
20
−0.01
0
P, P*
1
1
0.5
0.5
0
20
0
Nominal & Real Exch. Rate
1.5
10
ib, ib*
10
20
CA & NFA in % of GDP
0.15
0.1
0.05
0
0
10
time
20
−0.5
0
0
10
time
20
−0.05
0
10
time
20
of complete asymmetric price-setting behavior, the home monetary impulse leads
to both, an increase in foreign output and an increase in foreign demand. This result suggests that asymmetric price setting in the export markets might partly be
responsible for the documented positive international transmission eects of U.S.
monetary policy shocks to output and demand in the non-U.S. G7-countries and can
thus contribute to explaining the stylized facts.
4.3
Welfare
The price setting of firms is crucial for welfare results. This has already been demonstrated by a number of authors for closed form solutions. Betts and Devereux (2000)
explicitly derive how the assumption of local-currency pricing aects the interna28
tional welfare implications of a monetary shock. They show that for a high degree of
local-currency pricing, expansionary monetary policy has ‘beggar-thy-neighbour’ effects. Tille (2001) as well as Corsetti and Pesenti (2001) on the other hand find that
for producer-currency pricing, monetary policy has ‘prosper-thy-neighbour’ eects
and can even be ‘beggar-thyself’ for the country raising the nominal money supply.
To provide some further insights into the welfare implications for the three alternative pricing assumptions, the corresponding percentage changes in utility of
home and foreign agents were computed.18 As in OR (1995), only consumption and
leisure eects are considered for utility. As the eects are derived within a firstorder approximation, the results displayed in table 2 should be viewed only as a first
approximation, as the eects of uncertainty are not taken into account.
Table 2: Welfare Eects
PCP
LCP
Asymmetric Price Setting
dU of home agents
0.00065 0.00670
0.00385
dU of foreign agents 0.00212 -0.00392
-0.00065
Similar to the results derived in closed form solutions, a monetary expansion has
‘prosper-thy-neighbour’ eects for the assumption of complete PCP and ‘beggar-thyneighbour’ eects for the assumption of complete LCP using the baseline calibration.
This is due to the reversed eects on foreign output and consumption. As derived
above, for the assumption of complete PCP foreign consumption and investment
rise while foreign labor supply remains unaected in the short run. For LCP, on the
contrary, foreign production (and thus labor input) rises in the short run, without
any expansionary eect on foreign consumption. For the asymmetric price-setting
assumption introduced in this paper, both foreign output and demand rise in response
to the monetary expansion. Hence, the resulting welfare eects are in between the
two extreme cases of PCP and LCP.
18
Welfare eects were derived as the discounted sum of all future utility changes compared to
the steady state path of utility.
29
5
Conclusion
This paper addresses the issue of international transmission eects of monetary policy. In a first step, empirical evidence for positive transmission eects of U.S. monetary policy shocks on non-U.S. G-7 output, consumption and investment was presented. In the remaining part of the paper, I showed that these stylized facts can be
reproduced in a two-country dynamic general equilibrium model with sticky prices,
if we introduce international asymmetries in the price-setting behavior of producers.
Empirical evidence and optimality considerations of firms seem to suggest that most
U.S. firms set their prices in their own currency even for goods designated for export
and hence pursue a producer-currency pricing strategy. At the same time, because
of the size of the U.S. market, producers in Europe and Japan seem more likely to
set the prices for their exports to the U.S. in U.S. dollars and hence pursue a localcurrency pricing strategy. This asymmetric price-setting behavior of firms allows for
positive spill-over eects of a U.S. monetary shock on the non-U.S. G-7 countries,
as the expenditure-switching eect is eliminated in the U.S., while a decline in import prices (and hence the overall price level) in the foreign country remains present,
which induces foreign consumption and investment to rise. Therefore, asymmetries
in the price-setting behavior of firms across countries seem promising for a better understanding of the international transmission of business cycles induced by monetary
policy.
30
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