Financial Globalization and Monetary Transmission�

Simone Meiery

This version: September 2012

Abstract

This paper analyzes how international �nancial integration a¤ects the transmission ofmonetary policy. I extend a standard New Keynesian open economy model to a richerstructure in �nancial markets, allowing for international trading in multiple assets andsubject to �nancial intermediation costs. I analyze two di¤erent forms of �nancial in-tegration, namely an increase in the level of gross foreign asset holdings and a decreasein the costs of international asset trading. The calibrated simulations show that noneof the analyzed forms of �nancial integration undermine monetary policy e¤ectiveness.Under realistic parameterizations, monetary policy is more, rather than less, e¤ective asthe positive impact of strengthened exchange rate and wealth channels more than o¤setthe negative impact of weakened interest rate channels of monetary policy transmission.I also analyze the interaction of �nancial integration with trade integration, varying boththe importance of trade linkages and the degree of exchange rate pass-through. I �nd thatthe positive e¤ects of �nancial integration are ampli�ed by trade integration. Overall,monetary policy is most e¤ective in parameterizations with the highest degree of both�nancial and real integration.

�This paper is based on a chapter of my PhD thesis at the Graduate Institute of International and Devel-opment Studies in Geneva. I would like to thank my supervisor Cédric Tille for his guidance and support andDomenico Giannone, Wouter J. den Haan, Mathias Ho¤mann, as well as conference participants at the 2012Conference on Financial Frictions and Monetary Policy in an Open Economy of the Federal Reserve Bank ofDallas for useful comments. All remaining errors are mine. The views expressed in this paper are those of theauthor and do not necessarily represent those of the Swiss National Bank.

ySwiss National Bank. Email: simone.meier@snb.ch

1 Introduction

This paper analyzes how international �nancial integration a¤ects the impact of monetarypolicy in a standard theoretical open economy framework. Financial integration has been oneof the main developments in the world economy in recent decades and its potential implicationsfor monetary policy transmission have raised several concerns. The basic concern is that�nancial integration has the potential to undermine monetary policy e¤ectiveness, i.e. that inan environment of tightly integrated �nancial markets monetary policy might lose its controlto a¤ect aggregate output and in�ation. There is an active debate on this topic.1 But there arerelatively few formal analyses, especially in the theoretical literature.2 Furthermore, existingcontributions have focused on the implications of real, rather than �nancial integration.3

International �nancial integration can take di¤erent forms and it can have di¤erent e¤ectson monetary policy transmission. While some of these e¤ects are expected to weaken monetarypolicy transmission, others are expected to strengthen it. The combined impact is thus apriori ambiguous and warrants an analysis in a general equilibrium framework. However, theexisting theoretical literature based on general equilibrium models has focused on an analysisof the implications of real, rather than �nancial, integration. Erceg, Gust and López-Salido(2007) use an open economy DSGE model to explore how trade openness a¤ects the economy�sresponses to a monetary, a �scal, and a supply shock. The main result regarding the monetarypolicy shock, de�ned as a reduction in the in�ation target, is that, overall, the responses ofaggregate output and in�ation are quite unresponsive to trade openness. Cwik, Müller andWolters (2010) explore the role of trade integration for monetary policy transmission in amedium-scale new Keynesian model. They �nd that a monetary policy shock has strongeroutput e¤ects in more open economies, as real net exports react more strongly. At the sametime CPI in�ation and domestic in�ation also react more strongly in more open economies,which, in the latter case, is the result of complementarities in price setting. Woodford (2007)o¤ers an analysis of the consequences of global integration of �nancial markets, �nal goodsmarkets, and factor markets for the monetary transmission mechanism in a canonical NewKeynesian open economy model. He �nds that all these forms of integration are unlikely toweaken the ability of national central banks to control the dynamics of in�ation. However, hisanalysis is not suited for an analysis of �nancial markets integration. His model is based on apreference speci�cation with a unit elasticity of substitution between home and foreign goods.This assumption has the property of making asset markets complete, with both countries fullydiversifying their consumption risk.4 Financial integration is thus irrelevant. A �rst crucialextension is therefore an alternative preference speci�cation in which case the nature of assetmarkets matters.

This paper addresses the limitations of existing contributions to capture the e¤ects of

1See e.g. Bernanke (2007), Gonzalez-Paramo (2007), Gudmundsson (2007, 2008), Mishkin (2007), Pa-pademos (2007), Weber (2007), and Yellen (2006), BIS (2006, Chapter IV).

2This issue has also been raised by Romer (2007), Fisher (2006), and Mark Wynne on the occasion of thecreation of the Federal Reserve Bank of Dallas�Globalization and Monetary Policy Institute (Federal ReserveBank of Dallas, Southwest Economy, Issue 1, January /February 2008).

3See Woodford (2007), Erceg, Gust, and López-Salido (2007), and Cwik, Müller, and Wolters (2010).4See Woodford (2007, pp. 4-8) for a proof.

2

�nancial integration. I extend Woodford�s analysis to a model with a richer structure in�nancial markets and analyze two di¤erent forms of �nancial integration. The model I developis an extension of a standard New Keynesian open economy model with sticky prices, modi�edto allow for international trading in multiple assets and subject to �nancial frictions.5 The twocrucial modeling choices, allowing an analysis of two di¤erent forms of �nancial integration,are the inclusion of �nancial intermediation costs for trading assets and the linearization of themodel around an exogenous steady state asset portfolio. The �nancial intermediation costsfor trading assets are de�ned both with respect to deviation from the steady state level andwith respect to changes from last period�s holdings. The costs with respect to deviations fromthe steady state level are just a technical device introduced to ensure stationary responses totemporary shocks.6 However, the costs with respect to changes from last period�s holdingsallow to analyze the impact of a variation in the costs of international asset trading and,in particular, a decrease in the costs for international asset trading which is interpreted asa �rst form of international �nancial integration. The second crucial modeling choice, thelinearization of the model around an exogenous state asset portfolio, means that the steadystate portfolio can be chosen exogenously as a particular solution among the set of feasiblesolutions. An alternative approach would be to solve for the portfolio endogenously in a fullyoptimizing framework.7 However, the exogenous approach allows to choose an internationalportfolio that is in line with the empirical evidence without having to specify all the possibleshocks in the economy and adjust the model in such a way that it delivers that portfolio.8

This approach therefore allows to analyze the impact of a variation in the level of steadystate gross foreign asset positions and, in particular, an increase in steady state gross foreignasset positions which is viewed as a second form of international �nancial integration. Inaddition to these two forms of �nancial integration I also analyze the interaction of �nancialintegration with trade integration, varying both the importance of trade linkages and thedegree of exchange rate pass-through.

The �rst analyzed form of international �nancial integration, a decrease in the costs ofinternational asset trading, could potentially have an impact on the transmission of monetarypolicy through di¤erent demand and supply side e¤ects. On the demand side, a decrease in thecosts of international asset trading could a¤ect both the interest and the exchange rate channelof monetary transmission. The interest rate channel is a priori expected to be weakened bya decrease in the costs of international asset trading. Domestic interest rates might becomeless relevant for domestic spending decisions as in an integrated world consumers� shouldtheoretically be able to engage in more consumption smoothing with the rest of the world. Ifthe costs for trading foreign assets are low agents will save and borrow more in the rest of theworld to cushion the e¤ects of shocks. A monetary policy-induced interest rate shock couldthus have a lower impact on domestic spending decisions and aggregate demand. Furthermore,with globalized �nancial markets and tightened �nancial interdependence domestic interest

5The model is also generalized to include sticky wages, capital as an additional production factor, a non-traded goods and traded goods sector and varying degrees of exchange rate pass-through.

6See Ghironi, Lee, and Rebucci (2007) and Schmitt-Grohé and Uribe (2003).7See e.g. Devereux and Sutherland (2011) and Tille and Van Wincoop (2010).8This approach and motivation is also followed by Tille (2008).

3

rates might increasingly be in�uenced by foreign factors. There is evidence suggesting thatthere are important linkages between US and foreign long-term interest rates and that long-term rates seem to react less to changes in short-term rates than they used to.9

The exchange rate channel is a priori expected to be strengthened by a decrease in thecosts of international asset trading. The tendency for exchange rates to react to monetarypolicy might arguably be more pronounced in tighter integrated markets where the costs fortrading foreign assets are low and capital �ows are more responsive to perceived interest ratedi¤erentials. If the economy is open to trade these reinforced exchange rate movements couldin turn a¤ect aggregate demand and output through their impact on the relative prices ofdomestic to foreign goods, i.e. net exports. Reinforced exchange rate movements can alsohave a direct impact on in�ation through their impact on import prices.10

On the supply side, a decrease in the cost of international asset trading could potentiallylead to a decline in the slope of the Phillips curve, i.e. a decrease in the sensitivity of domesticprices to domestic output gaps. A decline in the slope of the Phillips curve, in turn, couldweaken monetary policy transmission as a control over domestic aggregate spending would notnecessarily imply a control over domestic in�ation as the domestic output gap would cease tobe a signi�cant determinant of domestic in�ation.11 A decrease in the sensitivity of domesticprices to domestic output gaps could arguably be the result of the integration of international�nancial markets as this process has facilitated the access of domestic �rms to a global laborsupply through o¤shoring. The threat of o¤shoring could contribute to a decrease of thesensitivity of real wages to changes in domestic labor market conditions (i.e. a �attening ofthe wage-price Phillips curve) as �rms might become less willing to grant wage increases thatwould impair their cost competitiveness and wages and prices would react less to domesticlabor market and demand conditions.12 Recent empirical research seems to suggest that thesensitivity of in�ation to domestic output gaps has declined in many developed countries inthe last two decades.13 However, there is no consensus on the role of global forces in thatprocess.14 And there are factors other than (�nancial and real) globalization that mightcontribute to a lower sensitivity of prices to domestic output gaps. Flatter Phillips curvescould be the result of better anchored in�ation expectations and the global disin�ation processin the last two decades, namely the fact that price adjustments are less frequent in a lower

9See Kamin (2010) for an overview, Ehrman, Fratzscher and Rigobon (2005), Faust, Rogers, Wang andWright (2007), and Warnock and Warnock (2006). Boivin and Giannoni (2008) �nd that a sizeable fractionof the variance of macroeconomic variables in the US are explained by foreign factors, but little evidence thatthis e¤ect has become more important over time.10See e.g. Yellen (2006), Bernanke (2007), Weber (2007), Mishkin (2007), Papademos (2007), Gudmundsson

(2007), and Gonzalez-Paramo (2007).11See Borio and Filardo (2007), IMF (2006), González-Páramo (2007), and Yellen (2006).12See Yellen (2006) and Gonzalez-Paramo (2007).13See e.g. Loungani, Razin and Yuen (2001), IMF (2006), Kohn (2006), Borio and Filardo (2007), Ihrig,

Kamin, Lindner, and Marquez (2007), Wynne and Kersting (2007), Guilloux and Kharroubi (2008), and Calza(2008).14Rogo¤ (2003, 2006), for example, argues that trade integration should have increased rather than decreased

the sensitivity of prices to domestic demand conditions. Greater competition should lead to lower pro�t marginsand less room for maneuver for �rms which should fasten �rms� responses to changes in cost structures ordemand conditions.

4

in�ationary environment.15

The second analyzed form of international �nancial integration is an increase in grossforeign asset holdings. Between 1970 and 2007 the average gross foreign asset position ofindustrial countries increased from 30 to 300 percent of GDP. Over the same time period,the sum of gross foreign assets and liabilities of industrial countries increased from 60 to600 percent of GDP.16 This form of integration could have an impact on the transmission ofmonetary policy through the demand side. It is expected to strengthen exchange-rate relatedwealth channels and thus a priori expected to strengthen monetary policy transmission. Anincrease in gross foreign assets could strengthen exchange-rate related wealth channels as withan increasing share of domestic savings invested in international �nancial markets households�wealth and �rms�balance sheets become more sensitive to (monetary policy induced) �uctu-ations in exchange rates.17 Exchange rate valuation e¤ects might thus increase the impactof monetary policy on the wealth of domestic agents and thus their spending decisions andaggregate demand.18

The remainder of the paper is organized as follows. Section 2 outlines the model. Section3 discusses the results, and the last section concludes.

2 Theoretical model

The model is a two-country variant of Gali (2008)�s baseline New Keynesian model but ex-tended to allow for international asset trading in both bonds and equities. Asset tradingis subject to transaction costs, following an approach along the lines of Ghironi, Lee andRebucci, 2007. The model also includes investment in capital which is an additional produc-tion factor besides labor. Not only prices, but also wages are assumed to be sticky, and theexchange rate is modelled in �exible manner following the approach of Corsetti and Pesenti(2005). In order to be able to replicate Woodford (2007)�s exercise of analyzing di¤erentdegrees of "trade integration" the consumption basket is divided into traded and nontradedgoods following the approach of Obstfeld and Rogo¤ (2005).

This section outlines the main blocks of the model using the example of the Home coun-try. Analogous equations hold in the Foreign country. To distinguish Home from Foreignvariables, variables for the Foreign country are denoted with a star superscript. A more de-tailed derivation of the model is provided in appendix B. The section is structured into fourdi¤erent subsections describing the behavior of households, �rms, and monetary authorities,as well as the solution method of the model including the calibration.

15See e.g. Gonzalez-Paramo (2007) and Yellen (2006).16See updated and extended version of the External Wealth of Nations Mark II database developed by Lane

and Milesi-Ferretti (2007).17See Gonzalez-Paramo (2007).18Note, however, that if a higher share of domestic wealth is invested in foriegn assets domestic wealth

channels might become less e¤ective.

5

2.1 Households

Each country is populated by a continuum of in�nitely-lived, atomistic households indexedby j (and j� respectively). Home households are assumed to be of a mass � while Foreignhouseholds are assumed to be of a mass (1��). Households consume both Home and Foreigntraded and domestic non-traded goods. In addition to consuming goods households alsosupply labor services.

An in�nitely-lived representative Home household j maximizes the following utility func-tion:

U(j) = Et

1Xt=0

�t�

1

1� � (Ct(j))1�� � �

1 + '(Nt(j))

1+'

�(1)

Following the approach of Obstfeld and Rogo¤ (2005) a fraction 2 [0; 1] of brandsconsumed in a given country are traded goods. Furthermore, a fraction � 2 [0; 1] of thetraded goods are produced in the Home country. therefore denotes the weight of the tradedgoods basket in the overall consumption basket and � denotes the weight of Home tradablesin the traded goods basket. Note that a large value of � means that the Home countrysupplies most of the tradables goods and not that few imported goods are consumed in eithercountry. Such a parametrization is employed in order to be able to replicate Woodford (2007)�sexercise of analyzing di¤erent degrees of "trade integration", namely the small open-economylimit (� = 0), and the case of two countries of equal size (� = 1

2), and the interaction of"trade" with "�nancial market integration". Figure 1 reports the distribution of brands alongthe unit interval in the Home consumption basket.

0 άγ γ 1Home traded goods

(C*HT)

Foreign traded goods(C*

FT)Nontraded goods

(C*N)

Figure 1: Distribution of brands in the Home consumption basket

The Home consumption basket is a standard CES consumption basket over Home andForeign traded goods baskets and the Home non-traded goods basket:

Ct =

� 1!C

!�1!

Tt + (1� )1!C

!�1!

Nt

� !!�1

where CNt is the non-tradables basket and CTt the tradables basket. denotes the weightof the tradables basket and ! is the elasticity of substitution between tradable and non-tradable goods.

6

The tradables basket is de�ned as:

CTt =

��1�C

��1�

HTt + (1� �)1�C

��1�

FTt

� ���1

where CHTt is the consumption sub-basket of individual Home goods and CFTt is theconsumption sub-basket of individual foreign goods. � denotes the weight of Home tradablesin the tradables basket and � is the elasticity of substitution between Home and Foreigntradables.

The consumption sub-baskets CNt, CHTt, and CFTt are de�ned as CES aggregates respec-tively:

CHTt =

"�1

�

� 1�Z �

0(CHTt(i))

��1� di

# ���1

CFTt =

"�1

(1� �)

� 1�Z

� (CFTt(i))

��1� di

# ���1

CNt =

"�1

(1� )

� 1�Z 1

(CNt(i))

��1� di

# ���1

where � is the elasticity of substitution between the di¤erent brands within a sub-basket.The following paragraphs outline the three optimization problems that a household faces:

the allocation of expenditures across the di¤erent sectors and goods, the intertemporal con-sumption and asset allocation, and the wage setting.

2.1.1 Optimal allocation of expenditures

The solution of the optimal allocation of expenditures across di¤erent sectors and goods (seeappendix B for more details) leads to the following aggregate demand equations that a �rmi faces (as explained in more detail below, in addition to the demand from households, �rmsface the demand for an investment input, It, from installment �rms):

YHTt(i) =

POptHTt(i)

PHTt

!�� �PHTtPTt

����PTtPt

��!(Ct + It) (2)

Y �HTt(i) =

POpt�HTt (i)S

��

P �HTt

!�� �P �HTtP �Tt

����P �TtP �t

��!(C�t + I

�t ) (3)

YNt(i) =

POptNt (i)

PNt

!�� �PNtPt

��!(Ct + It) (4)

where YHTt(i) denotes the demand a Home �rm in the traded goods sector producing forthe domestic market faces, Y �HTt(i) denotes the demand a Home �rm in the traded goods

7

sector producing for the foreign market faces, YNt(i) denotes the demand a Home �rm inthe non-traded goods sector faces, St is the nominal exchange rate (de�ned as units of Homecurrency per unit of Foreign currency), and � denotes the degree of pass-through elasticity,which is exogenous and constant within a period and across producers.

2.1.2 Optimal intertemporal allocation

Asset markets comprise four assets: two one-period nominal bonds, denominated in Homeand Foreign currency respectively, and equity shares on Home and Foreign �rms. Bondholdings are denoted BH and BF (B�H and B�F if held by Foreign households) and Homeand Foreign equity shares are denoted by QHt and QFt (Q�Ht and Q

�Ft if held by Foreign

households). Equity shares are assumed to be claims on �rms�pro�ts as explained in moredetail in appendix B. They are assumed to be a balanced portfolio across all �rms in therespective country.

Households pay quadratic �nancial transaction fees to domestic �nancial intermediarieswhen they change their asset holdings. The �nancial intermediation costs are de�ned bothin terms of changes from last period�s holdings and in terms of deviations from steady statelevels. They are de�ned in the currency of the respective country and with respect to ratios tothe respective country�s GDP.19 The de�nition is analogous for all assets (with the subscriptdenoting the respective asset). Using the example of Home equity holdings the �nancialintermediation costs are de�ned as:

QH

2PQt

(QHt+1(j)�QHt(j))2

Ytand

QH2

PQt

�QHt(j)� �QH(j)

�2Yt

As mentioned above the �nancial intermediation costs on changes from last period�s hold-ings (see the �rst term in the above expression) ensure a well-de�ned demand of assets in alog-linearized version of the system and allow to study scenarios di¤ering with respect to theease of �nancial transactions. A decrease in the level of the costs for foreign assets, e.g.

QF,

implies cheaper transaction costs for changing foreign asset holdings which can be seen as oneform of international �nancial integration. The costs with respect to deviations from the levelof steady state asset holding (see the second term in the above expression) are a technicaldevice to ensure stationarity of the equilibrium dynamics.20 As the �nancial intermediationcosts are incurred on changes from last period�s holdings and on deviations from the steadystate level, the steady state of this model can be chosen exogenously as a particular solutionamong the set of feasible solutions. As mentioned above, this fact will be exploited to analyzea second form of international �nancial integration, namely an increase of gross foreign assetholdings.

The �nancial costs are paid to �nancial intermediaries who are assumed to be local, per-fectly competitive �rms owned by domestic households. The �nancial transaction fees are

19This de�nition is used as asset holdings can take negative values (in the case of borrowing). Expressingchanges in holdings (and deviations from the steady state) as ratios to holdings would thus not be a meaningfulde�nition. To ensure measurement in equivalent units assets issued in a given country are expressed in ratiosto that country�s GDP.20See Ghironi, Lee, and Rebucci (2007) and Schmitt-Grohé and Uribe (2003).

8

rebated to households as lump-sum transfers and are therefore not destroyed resources.Given these de�nition the budget constraint of a Home household j is:

PtCt(j) (5)

+PQtQHt+1(j) + QH

2PQt

(QHt+1(j)�QHt(j))2

Yt+ QH2

PQt

�QHt(j)� �QH(j)

�2Yt

+StP�QtQFt+1(j) +

QF

2StP

�Qt

(QFt+1(j)�QFt(j))2

Y �t+ QF2

StP�Qt

�QFt(j)� �QF (j)

�2Y �t

+BHt+1(j) + BH

2

(BHt+1(j)�BHt(j))2

PtYt+ BH2

�BHt(j)� �BH(j)

�2PtYt

+StBFt+1(j) + BF

2St(BFt+1(j)�BFt(j))2

P �t Y�t

+ BF2St

�BFt(j)� �BF (j)

�2P �t Y

�t

= WtNt(j) +

�PQt +

�Vt�Q

��QHt(j) + St

�P �Qt +

�V �t�Q�

��QFt(j)

+(1 + it)BHt(j) + St(1 + i�t )BFt(j) + TIt(j) + T t(j)

where PQt and P �Qt are the nominal prices of Home and Foreign equity shares respectively,

and Vt�Q, and V �t

�Q�the dividend yields in local currency with Vt and V �t denoting the aggregate

pro�ts and �Q and �Q� aggregate equity shares. Aggregate equity shares are �xed and given by�Q = QHt +Q

�Ht and �Q

� = Q�Ft +QFt. Note that equity shares are claims on pro�ts (of pro-duction �rms) not claims on capital. QH , QF , BH , and BF are the �nancial intermediationcosts for Home households which can di¤er across assets, it and i�t are the nominal interestrates, St is the nominal exchange rate (de�ned as units of Home currency per unit of Foreigncurrency), TIt(j) are the lump-sum transfers from installment �rms (the details are explainedin Appendix B), and T t(j) are lump-sum transfers from �nancial intermediaries.

The optimal intertemporal asset and consumption allocation leads to the following Eulerequations in aggregate terms,

for Home equity holdings:

Et

�PQt + QH

PQt(QHt+1 �QHt)

Yt

�(6)

= Et

8><>:Dt;t+1(j)

0B@ QH

(QHt+2�QHt+1)Yt+1

� QHPQt+1

�(QHt+1� �QH)

Yt+1

�+�PQt+1 +

�Vt+1�Q

��1CA9>=>;

for Foreign equity holdings:

9

Et

�StP

�Qt + QFStP

�Qt

(QFt+1 �QFt)Yt

�(7)

= Et

8<:Dt;t+1(j)

0@ QFSt+1P

�Qt+1

(QFt+2�QFt+1)Yt+1

� QHSt+1P�Qt+1

(QFt+1� �QF )Yt+1

+�St+1

�P �Qt+1 +

�V �t+1�Q�

��� 1A9=;for Home bond holdings:

Et

�1 +

BH

(BHt+1 �BHt)Yt

�(8)

= Et

8<:Dt;t+1(j)

0@ BH

(BHt+2�BHt+1)Yt+1

� BH

�(BHt+1� �BH)

Yt+1

�+(1 + it+1)

1A9=;and for Foreign bond holdings:

Et

�St + BF

St(BFt+1 �BFt)

Y �t

�(9)

= Et

(Dt;t+1(j)

BFSt+1

(BFt+2�BFt+1)Y �t

� BFSt+1

(BFt+1� �BF )Y �t

+St+1(1 + i�t )

!)

with Et fDt;t+1g = �Et

��(Ct+1)(Ct)

���PtPt+1

�denoting the discount factor.21

The Euler equations represent the fact that for an intertemporal allocation to be optimalthe cost in terms of foregone utility of acquiring an additional equity share or bond has toequal the discounted marginal utility of the increase in expected consumption derived fromholding that additional asset. To gain a more detailed intuition for the Euler equations onecan rewrite, for example, the Euler equation for Home bond holdings (equation (8)), as:

Et

��Ct+1(j)

Ct(j)

���(10)

= �Et

8>>><>>>:�

PtPt+1

��(1 + it+1) + BH

(BHt+2�BHt+1)Yt+1

� BH

�(BHt+1� �BH)

Yt+1

��+

1

1+ BH

(BHt+1�BHt)Yt

!9>>>=>>>;

Equation (10) states that, all else equal, Home households will be more willing to post-

21An alternative discount factor could be a weighted average of Home and Foreign household�s marginal rateof substitutions.

10

pone consumption to the next period (i.e. increase the ratio�Ct+1(j)Ct(j)

�on the left hand side),

the higher the opportunity costs for consumption today. These opportunity costs are higher:a) the lower expected in�ation (�rst (...) on the right hand side, b) the higher the expectedinterest rate at Home (�rst term in [...] on the right hand side), c) the higher the marginaldecrease in transaction costs for Home bond holdings tomorrow (second term in [...] on theright hand side), due to the fact that an increase in bond holdings today decreases marginaltransaction costs tomorrow, d) the lower the transaction costs for deviations of bond hold-ings from the steady state today (third term in [...] on the right hand side), or e) the lowertransaction costs for increasing Home bond holdings today (last (...) on the right hand side).Furthermore, there is consumption smoothing as, all else equal, an expected increase in con-

sumption tomorrow (numerator of ratio�Ct+1(j)Ct(j)

�on the left hand) increases consumption

today.

2.1.3 Optimal wage setting

In order to model sticky wages the labour market is assumed to be monopolistic.22 Eachhousehold is specialized in a di¤erent type of labor, all of which are used by each �rm. Eachhousehold has some monopoly power in the labor market and posts the (nominal) wage atwhich she or he is willing to supply specialized labor services to �rms that demand them.Wages are sticky where wage setting is modelled as a staggered Calvo-type process where(1� �W ) denotes the probability that a household can reset the wage in any given period.

A household that can reset its wage in period t (whereWOptt (j) denotes the newly set wage)

maximizes the discounted sum of utilities subject to the sequence of �ow budget constraintsand the �rms�labour demand schedules (see appendix B for details). The optimal wage attime t satis�es the following condition:

Et

1Xk=0

(��W )k

"Nt+kjt(j)

�Ct+kjt(j)

��� "WOptt

Pt+k� �W

��Nt+kjt

�'�Ct+kjt

���##= 0 (11)

where�W � �

� � 1i.e. that the optimal real wage is a (constant) markup over all future expected marginal

rates of substitution.Taking account of wage stickiness the aggregate wage index (see also below in the section

on �rms) can be written as

Wt =

��WW

1��t�1 + (1� �W )

�WOptt

�1��� 11��

(12)

i.e. that the wage index is a weighted average of last period�s index and the optimal wageat time t.22See Gali (2008, chapter 6) for details.

11

2.2 Firms

In each country there are two types of �rms."Installment �rms" using the consumption goodto produce capital and "Production �rms" producing the consumption goods with a linearproduction technology using both labor and capital inputs.

The following paragraphs outline the optimal investment decision of installment �rms andthe optimal input demand and price setting decisions of production �rms.

2.2.1 Optimal investment

Installment �rms are competitive, i.e. they take prices as given. They are owned by domestichouseholds who receive any pro�ts in the form of lump-sum transfers and are indexed by I2 [0; �] for the Home country and I� 2 [�; 1] for the Foreign country.

Installment �rms purchase an investment good to produce new capital which they rent outto the production �rms at the (nominal) rental rate Ptrk. It is assumed that the investmentgood features the same composition as the consumption good, i.e. that the investment goodis purchased in the goods market at a price Pt. Capital depreciates at a rate �. Furthermore,the production technology for new capital involves non-linear capital-adjustment cost. Thesecosts are introduced to smooth the investment dynamics. Capital accumulation takes thefollowing form:

Kt+1 = (1� �)Kt + It ��

2

(Kt+1(I)�Kt(I))2

Kt(I)(13)

An installment �rm solves the following optimization problem (subject to 13)

maxKt+1(I)

Et

1Xk=0

Dt;t+k(I)hPt+kr

kt+kKt+k.(I)� Pt+kIt+k.(I)

ii.e. that I assume that an installment �rm I�s discount factor re�ects the intertemporal

marginal rate of substitution of a representative Home household j.23 The pro�ts TI(j) =Ptr

ktKt. � PtIt.of Installment �rms are assumed to be rebated to households as lump-sum

transfers.The optimality condition for investment in aggregate terms can be written as

Et

��1 + �

(Kt+1 �Kt)

Kt

��= �Et

(�(Ct+1)

(Ct)

��� �(1� �) + rkt+1 +

�

2

�K2t+2 �K2

t+1

K2t+1

��)(14)

The optimal investment decision equalizes the cost to increase today�s capital stock by oneunit and tomorrow�s discounted marginal utility derived from this investment. Today�s costof an additional unit of capital consist of the unit itself and the marginal capital adjustmentcost. Tomorrow�s revenues of this investment consist of the increase in the non-depreciated

23An alternative discount factor could be a weighted average of Home and Foreign household�s marginal rateof substitutions.

12

capital stock itself , the expected real interest payment plus the expected decrease in capitaladjustment costs.

2.2.2 Optimal input demand

Production �rms in the traded and non-traded goods are monopolistically competitive �rms,i.e. each production �rm is the sole producer of a di¤erentiated brand. They are indexed by i2 [0; � ; ; 1] where [0; � ] represents the Home traded goods sector and [ ; 1] the non-tradedgoods sector. Foreign �rms are distributed on the interval i� 2 [� + ; ; 1] with [� ; ]representing the Foreign traded goods sector and [ ; 1] the Foreign non-traded goods sector.

A representative Home production �rm i (both in the traded and non-traded goods sector)produces under the following Cobb-Douglas constant-returns-to-scale technology:

Yt(i) = At (Kt(i))1�� (Nt(i))

�

where At is an exogenous technology parameter, Kt(i) is the capital input used by �rm i ,� is the share of labor used in the production process and Nt(i) is an index of the di¤erentiatedlabor inputs used by �rm i:

N(i) ��Z �

0Nt(i; j)

��1� dj

� ���1

where Nt(i; j) denotes the quantity of type-j labor employed by �rm i. � is the elasticityof substitution among the di¤erentiated labor services (� is the mass of Home households).

The solution of the cost minimization problem of a representative Home �rm i with respectto di¤erentiated labor services for a given level of the aggregate labor index is (see appendixB for more details):

Nt(i; j) =

�Wt(j)

Wt

���Nt(i)

The solution of the cost minimization problem of a representative Home �rm i with respectto aggregate factor inputsNt(i) andKt(i) can (in aggregate terms) be written as (see appendixB for more details):

NHTt =�MCtWt

YHTt (15)

NNt =�MCtWt

YNt (16)

KHTt =(1� �)MCt

Pt.rktYHTt (17)

KNt =(1� �)MCt

Pt.rktYNt (18)

13

where

MCt =(Wt)

� �Pt.rkt �1��(1� �)1����At

(19)

2.2.3 Optimal price setting

Prices are sticky where price setting is modelled as a staggered Calvo-type process where(1� �P ) denotes the probability that a �rm can reset its price in any given period.2425 Theprices that Home consumers pay in Home currency for Home traded, Foreign traded and non-traded goods are denoted by PHTt(i); PFTt(i) and PNt(i) , respectively, whereas the prices thatForeign consumers pay in Foreign currency for Home traded, Foreign traded and non-tradedgoods are denoted by a star superscript, namely, by P �HTt(i); P

�FTt(i) and P

�Nt(i), respectively.

The prices that Home producers set are denoted by POptHTt(i) for the Home market; POpt�HTt (i)

for the Foreign market and POptNt (i) , respectively, whereas the prices that Foreign producersset are denoted by POpt�FTt (i) and P

�OptNt (i)for the Foreign market, and POptFTt(i) for the Home

market .To be able to analyze various degrees of exchange rate pass-through a �exible approach

following Corsetti and Pesenti (2005) is adopted. In particular, it is assumed that the degreeof pass-through elasticity, � , is exogenous and constant within a period and across producers.It varies between 0 and 1 such that both the case of complete exchange rate pass-through("producer currency pricing" or PCP), � = 1, and the case of zero exchange rate pass-through("local currency pricing" or LCP), � = 0, can be obtained as particular cases of a uni�edparametrization.

The Foreign-currency price of a Home traded goods brand, P �HT (i), is de�ned as:

P �HTt(i) =POpt�HTt

S�t

Given this de�nition the price received by a Home �rm from an export sales unit to theForeign market is26

StP�HTt(i) =P

Opt�HTt (i)S

1��t

A representative �rm in the Home traded goods sector sets pricesnPOptHTt+k(i); P

Opt�HTt+k(i)

o1k=0

that maximize its expected discounted future pro�ts while

these prices remain e¤ective. Formally, it solves the following problem:

maxPOptHTt(i);P

Opt�HTt (i)

1Xk=0

�kPEt

8>><>>:Dt;t+k(j)0@ �

POptHTt(i)�MCt+kjt

�YHTt+kjt

+�POpt�HTt (i)S

1��t �MCt+kjt

�Y �HTt+kjt

1A9>>=>>;

24This approach has been developed by Calvo (1983).25�P can therefore be interpreted as a measure of price stickiness.26Similarly, the Home-currency price of a Foreign traded goods brand, PFTt(i), is PFTt(i) = P

OptFTt(i)S

�t and

the price received by a Foreign �rm from an export sales unit to the Home market is POptFTt(i)S��1t .

14

subject to the respective demand schedules of Home households and installment �rms,where Dt;t+k(j) denotes the discount factor:

Et fDt;t+k(j)g = �kEt

(�(Ct+k(j))

(Ct(j))

��� PtPt+k

)

i.e. that it is assumed that a representative Home �rm�s discount factor represents theintertemporal marginal rate of substitution of a representative Home household j, and whereMCt denotes the (nominal) marginal cost function (see equation (19) above).27

Optimal prices in the three sectors at time t satisfy the following conditions:

1Xk=0

�kPEt

nDt;t+kYHTt+kjt(i)

�POptHTt � �PMCt+k)

�o= 0 (20)

1Xk=0

�kPEt

nDt;t+kY

�HTt+kjt(i)

�S1��t POpt�HTt � �PMCt+k)

�o= 0 (21)

1Xk=0

�kPEt

nDt;t+kYNt+kjt(i)

�POptNt � �PMCt+k)

�o= 0 (22)

where

�P =�

� � 1i.e. that the prices received by Home �rms are a (constant) markup over expected future

marginal costs.

2.3 Monetary policy

In order to close the model a behavioral rule for the monetary authorities needs to be de�ned.The monetary policy rule of the Home central bank is de�ned as

1 + it = (1 + it�1)�

�PtPt�1

���(Yt)

�y

!(1��)Rt (23)

where � captures the degree of interest-rate smoothing andRt represents a time-varying,exogenousmonetary policy shock that may, for example, represent changes in the in�ation target. In-novations in Rt and their propagation on the other variables in the model are used as ex-periments to analyze the transmission of monetary policy. The monetary policy rule of theForeign central bank is de�ned analogously.

2.4 Solution of the model

The model is de�ned by equations (2) to (23) together with the analogous equations forthe foreign economy and the market clearing conditions in the goods and asset markets (see27A representative �rm in the nontraded goods sector solves an analogous problem.

15

appenidx B for more details). The model is solved by a linearization of these equationsaround a symmetric steady state where the net foreign asset positions of both countries,in�ation and technological progress are zero. As mentioned above, to ensure a stationarysteady state �nancial intermediation costs are imposed on both the changes in asset holdingsas well as deviations from the steady state. Furthermore, as a monetary policy shock wouldlead to non-stationary responses of nominal variables in levels, all Home and Foreign nominalvariables are scaled by the Home and Foreign CPIs, respectively, and the CPIs and the nominalexchange rate are linearized in �rst di¤erences. Appendix B outlines the whole system ofequations as well as a detailed derivation of the steady state and the linearized system. As noanalytical solution of the model can be obtained the linearized model is solved and simulatednumerically.28 The particular interest is in impulse response functions to monetary policyshocks, namely exogenous interest rate shocks on Rt, as de�ned above in the Taylor rule(equation 23). The impact of �nancial market integration is analyzed by comparing impulseresponse functions to such monetary policy shocks in scenarios that di¤er with respect to thedegree of �nancial market integration. The calibration of the baseline and the integrationscenarios is explained in the following paragraphs.

2.4.1 Baseline calibration

The baseline calibration is listed in Table 1. The calibration of the model parameters closelyfollows the standard values assumed in the New Keynesian and Real Business Cycle litera-ture.29 I assume a period length of one quarter and equal model parameters for both countries.

� 0.99 � 0.5 � 0.6 �r 0.6

� 2 � 2 � 0.026�P �Q�QF

�P � �Y �;

�BF�P � �Y �

0.3� 1 � 6 �P 0.66 BH ; QH 1' 1 �W 0.75 � 0.5 BF ; QF 3 0.25 � 21 �� 1.5 ::: 0.005! 2 � 8 �y 0.125

Table 1: Baseline calibration

The calibration of the discount factor � implies a steady state annual return on �nancialassets of about four percent. The assumption on the relative risk aversion coe¢ cient � implies

28The model is solved with Dynare (see Adjemian et al., 2011).29The calibration of the discount factor � and the elasticity of substitution between di¤erent brands within a

sub-basket � is equal to the one in Gali (2008) and Ghironi et al. (2008). The elasticity of substitution betweenHome and Foreign tradables � follows the calibrations of Obstfeld and Rogo¤ (2005), Coeurdacier, Kollman,and Martins (2008), and Ghironi et al. (2008). The parameters related to the modeling of the consumptionbasket, i.e. the weight of the tradables basket in the overall consumption basket , and the elasticity ofsubstitution between tradables and non-tradables ! are calibrated according to Obstfeld and Rogo¤ (2005).The calibration of the relative risk aversion coe¢ cient � is in line with Coeurdacier et al. (2008) and Ghironiet al. (2008). The calibration of the depreciation rate � and the labour share � is in line with Coeurdacieret al. (2008)�s calibrations. The calibration of the labour supply elasticity coe¢ cient ', and the elasticityof substitution among di¤erentiated labour services � follows Tille (2008). The price and wage stickinessparameters �P and �W , as well as and the interest rate rule coe¢ cients �� and �y are calibrated in line withGali (2008).

16

a non-log-utility function. A labour supply elasticity coe¢ cient ' of 1 implies a non-linearcost of e¤ort. The calibration of the elasticity of substitution between di¤erent brands withina sub-basket � implies a steady state markup of prices over marginal costs of 20 percent.Similarly, an elasticity of substitution among di¤erentiated labour services � of 21 implies asteady state markup of wages over the cost of e¤ort of 5 percent. A depreciation rate � of0.026 implies an annual deprecation rate of about 10 percent. Setting the production functionparameter � to 0.6 implies a ratio of wage earnings to GDP of 60 percent. The adjustmentcosts in investment are set such that the volatility of investment amounts to about four timesthe volatility of GDP. A price stickiness parameter �P of 0.66 implies an average price durationof three quarters. The interest rate rule coe¢ cients �� and �y are roughly consistent withobserved variations in the Federal Funds rate over the Greenspan area. A value of �r = 0:6implies a relatively high persistence of the interest rate shock. The steady state technologylevels in both countries are normalized to 1. In the baseline simulations both countries areassumed to be of equal size, i.e. that they have equal shares in the traded goods sector. � istherefore set to 0.5. The exchange rate elasticity is assumed to be 0.5, i.e. that half of thechange in exchange rates are passed on to the local prices of imported goods.

By means of di¤erent calibrations of the remaining two parameter blocks, namely steadystate gross asset holdings and �nancial intermediation costs, di¤erent scenarios of international�nancial integration can be analyzed. In the benchmark scenario (total) steady state grossforeign asset holdings amount to 60 percent of GDP (steady state net foreign asset are assumedto be zero in all scenarios). Such a calibration is roughly in line with the average gross foreignasset positions (in percent of GDP) of industrial economies between 1970 and 1990.30 Thetotal gross foreign asset holdings are split evenly between the two asset categories, i.e. thattotal steady state bond and equity holdings each amount to 30 percent of GDP.31

Financial intermediation costs are calibrated such that the excess returns across di¤erentassets lie in a reasonable range. In a log-linearized version of the system the excess returnfor Home agents of, for example, Foreign with respect to Home bond holdings can be derivedby combining the log-linearized versions of the respective Euler equations (equations 9 and 8above):

Et

n�dxretBF �t

o� Et

nc�st+1 + {�t+1 � {t+1o (24)

� BFEt

(�bFt+1 � bFt

�� �

BF

�bFt+2 � bFt+1

�� BF bFt+1

!)

�Et

(" BH

�bHt+1 � bHt

�� �

BH

�bHt+2 � bHt+1

�� BH bHt+1

!#)30See updated and extended version of the External Wealth of Nations Mark II database developed by Lane

and Milesi-Ferretti (2007).31Note that with the assumption that total net foreign assets are zero, i.e. the condition �S �P �Q �QF � �PQ �Q

�H +

�S �BF � �B�H = 0, together with the four asset market clearing conditions only three cross border holdings have to

be determined. The fourth cross-border holding and all domestic holdings can then be determined residually.As mentioned above bonds are in zero net supply and the total amount of equity holdings are �xed.

17

If the di¤erences across assets in actual and expected changes of holdings (here�bFt+1 � bHt+1

�and

Et

h�bFt+2 � bFt+1

���bHt+2 � bHt+1

�i) are assumed to be about 10 percent then excess

returns of about 15 basispoints would seem reasonable. Given that the costs with respect tothe deviations from the steady state are just a technical device to induce stationarity theyare kept close to zero, namely ::: = 0:005. Equation 24 then implies transaction costs forchanging holdings of

BF=

BH= 1:

[0:0015]| {z }Excess return (LHS of above equations)

� [(1�0:1)� (0:99�((1 � 0:1)� (0:005�0:1)))]| {z }RHS of above equations

In other words, if Home households decide to adjust their Foreign bond holdings by 10 percentof GDP more than their Home bond holdings, they need to get an excess return on Foreignversus Home bond holdings of about 15 basispoints. Thus, in the scenario with low transactioncosts, in line with this reasoning, I set the �nancial intermediation costs at BH = BF = QH = QF = B�H = B�F = Q�H = Q�F = 1. In the "pre-integration" baseline scenario thecosts for foreign assets, i.e. the costs for Home (Foreign) agents of changing Foreign (Home)bonds and equity holdings, are increased threefold to a level of BF = B�H = QF = Q�H = 3.In such a scenario for the decision to adjust Foreign bond holdings by 10 percent more thanHome bond holdings to be optimal, the excess return would need to be about 54 basispoints.32

An alternative way to check the validity of the calibration of transaction costs is to look atthe actual response of excess returns to an interest rate shock. Figure 1 shows the response ofthe excess return of Foreign over Home bonds to a 25 basispoints one-o¤ exogenous positiveshock on the nominal interest rate in the Home country in the Baseline scenario.33 The excessreturns is around 6 basispoints on impact which appears to be reasonable.

32 [0:0054] � [(3�0:2)� (0:99�((3 � 0:2)� (0:005�0:2)))]� [(1�0:1)� (0:99�((1 � 0:1)� (0:005�0:1)))].33Without any further changes induced by the Taylor rule this would correspond to an annualized increase

in the policy rate of 100 basispoints on impact.

18

0 2 4 6 8 10 12 14 16 18­0.06

­0.05

­0.04

­0.03

­0.02

­0.01

0xret bf

Figure 2: Response of excess return to an interest rateshock in the Baseline scenario

The impulse resp onse is shown in p ercentage p oint deviations from the steady

state.

2.4.2 Calibration of �nancial market integration and other scenarios

Moving away from this baseline calibration I study, in a �rst step, two di¤erent scenarioswhich I label "Higher gross foreign asset holdings" and "Lower costs". In the "Higher grossforeign asset holdings" experiment, the level of (total) gross foreign steady state asset hold-ings is increased to 200 percent of GDP which corresponds to about a threefold increase ofthe baseline calibration and is roughly in line with the average gross foreign asset holdings(in percent of GDP) of industrial economies between 1990 and 2007.34 In the second experi-ment, the "Lower costs" scenario, the �nancial intermediation costs of changing foreign assetpositions are reduced to the level of the costs for changing domestic asset holdings (for bothHome and Foreign agents), i.e. BF = B�H = QF = Q�H = 1. The robustness of bothexperiments is checked by additional variations of the parameters and both experiments areanalyzed separately as well as in a combined experiment together.

In addition to analyzing these �nancial market integration experiments I study "trade"integration and a scenario of lower exchange rate pass-through (ERPT) and their interactionwith the two forms of �nancial market integration. I study a scenario with a lower ERPTelasticity as trade integration could arguably lead to a decrease in the ERPT through its e¤ectof increasing competition in export markets. An increased competition in export marketscould lead exporters to limit the �uctuations of the prices paid by consumers in response toexchange rate movements and therefore lead to a lower ERPT. A lower exchange rate pass-through could arguably also be the result of lower average in�ation rates in the past decades,which in turn could be the result of the "discipline e¤ect" of increasing international �nancialintegration. The "discipline e¤ect" is based on the hypothesis that a higher exposure ofcountries to international capital markets, i.e. a higher potential for cross-border capital �ows,

34See updated and extended version of the External Wealth of Nations Mark II database developed by Laneand Milesi-Ferretti (2007).

19

could induce central banks to maintain low in�ation rates.35 In principle, the competition toattract mobile capital could cause local governments to implement "good" policies in orderto attract foreign investors ex ante and to maintain these good policies ex post in order toavoid a capital �ight.36

The calibration of "trade integration" follows Woodford (2007) by lowering the share oftraded goods produced in the Home country, i.e. lowering the size of the Home traded goodsmarket relative to world traded goods markets. In the "integrated", "small open economy",scenario the share of Home traded goods in the overall traded goods basket, i.e. �, is loweredto 0.1. In the scenario with lower ERPT, the exchange rate pass-through elasticity, � , islowered from 0.5 to 0.1, i.e. that only ten percent of the change in exchange rates are passedon to the local prices of imported goods.

3 Results

The simulations of the di¤erent experiments are reported in Figures A1 to A18 in Appendix A.All impulse response functions show the dynamic reaction to a 25 basispoints one-o¤exogenouspositive shock on the nominal interest rate in the Home country.37 Impulse response functionsare shown in percentage point deviations from the steady state. In�ation, and interest ratesare shown in annualized rates (i.e. multiplied by four). To conserve space I do not reportthe dynamics of all variables of the model. In each scenario I report the impulse responses of20 variables including the main macroeconomic variables of the model plus some additionalvariables (derived in detail in Appendix B) such as the dynamics of the current account (CA),its decomposition into the trade balance (TB) and net asset income (NAI), the terms oftrade (TOT), as well as the net foreign asset position (NFA), and the decomposition of thechange in the net foreign assets position (�NFA) into the current account (CA), the change inlocal currency asset prices (�LCAP), and exchange rate valuation (EV).38 In the "Baseline"scenario, for intuitive purposes, an additional Figure reports the reaction of a few furthervariables. Table A1 lists the notation of all reported variables.

The dynamic reaction of the model is as expected and intuitive. Figure A1 and A2 showthe results for the "Baseline" scenario. The contractionary monetary policy shock leads to areduction of Home in�ation of about 0.5% on impact. As a consequence of the increase of theHome interest rate the Home nominal (and real) exchange rate fall on impact (i.e. the Homecurrency appreciates) after depreciating to the new equilibrium. This is in line with some formof an uncovered interest rate parity condition which can be derived from the Euler equations.The increase in the Home nominal (and real) interest rate induces Home households to reduce

35Tytell and Wei (2005) provide some empirical evidence for this hypothesis.36Kroszner (2007) argues that the integration, deregulation and innvoation in �nancial markets has fostered

currency competition which has led to improved central bank performance.37Without any further changes induced by the Taylor rule this would correspond to an annualized increase

in the policy rate of 100 basispoints on impact.38Note that as the model is linearized around stationary variables all variables except in�ation and nominal

exchange and interest rates are real variables, i.e. scaled by the Home and Foreign CPIs, respectively. Forvariables where the steady state is equal to zero, i.e. the trade balance, net foreign income, and net foreignassets the steady state deviations of nominal and real variables are equivalent.

20

their domestic consumption spending, in line with the Euler equations. Home households alsoreduce their import spending. Thus, income-absorption e¤ects (negative (foreign) income andwealth e¤ects which, all else equal, induce Home households to import less) more than o¤setexpenditure-switching e¤ects (an appreciation of the Home currency which, all else equal,induces Home households to import more). Expenditure-switching e¤ects also reduce exports,and as the fall in exports more than o¤sets the fall in imports, net exports fall as well. Thenegative demand shock stemming from the reduction in both consumption and exports leadsto a fall in the return on investment and therefore investment itself. The combined fall inconsumption, net exports, and investment leads to a fall in Home output by around 0.4%.In order to cushion the contractionary monetary policy shock and smooth consumption overtime, Home consumers borrow from Foreign agents in all four asset categories, i.e. sell assetsto Foreigners (as can be seen in the reduction of both Home and Foreign bond and equityholdings reported in the fourth row). As a consequence, the current account and net foreignassets fall. The change in net foreign assets (as can be seen from the decomposition in the�fth row) is not only due to increased borrowing but mainly due to negative exchange ratevaluation e¤ects stemming from the appreciation of the Home currency. Figure A2 reportsthe reaction of some additional variables in the "Baseline" scenario. As a consequence of thenegative demand shock, Home �rms reduce their labor and capital input demand, which leadsto a reduction of both wages and rental rates of capital. The fall in wages and rental rates ofcapital in turn leads to a reduction in marginal costs. As prices are sticky, i.e. some pricescannot be adjusted immediately, Home pro�ts rise. Over time �rms adjust their price settingto the reduction in marginal costs which, as reported in Figure A1, leads to a fall in Homein�ation. Due to the increase in Home interest rates and to restore asset market equilibrium,equity prices fall. Furthermore, as a consequence of the appreciation of the Home currencyand the fall in Home output, the Home terms of trade increase. For completeness, the thirdrow reports the reaction of the main Foreign variables, which is very low, almost insigni�cant,for all variables.

3.1 Lower costs

The �rst international �nancial integration experiment shows that integration in the formof lower �nancial intermediation costs for trading foreign assets indeed weakens part of theinterest rate channel due to an increase in Home consumers�consumption smoothing and a re-duced reaction of consumers�spending and investment. However, in case an economy is opento trade higher consumption smoothing also applies to import spending which, together witha strengthened exchange rate channel, reinforces the decrease of net exports and the overall(contractionary) impact of monetary policy on output and in�ation. Figure A3 reports thedi¤erences in the impulse responses between the "Lower Costs" and the "Baseline" scenarios.There are no qualitative, but only quantitative di¤erences in the reaction of all variables inthe two scenarios. A reduction in �nancial intermediation costs for trading foreign assets leadsto a boost in consumption smoothing by Home households and therefore a higher increasein borrowing from abroad and a lower reduction in consumption and investment spending.Thus, in this respect, �nancial integration reduces the contractionary e¤ect of monetary pol-icy. However, a reduction in �nancial intermediation costs for trading foreign assets not only

21

leads to a lower reduction in consumption and investment spending, but also to a lower reduc-tion in import spending. A lower reduction in import spending increases the contractionarye¤ect of monetary policy (as a reduction in imports has an expansionary e¤ect). Furthermore,a reduction in �nancial intermediation costs for trading foreign assets leads to a higher appre-ciation, arguably due to the fact that in more integrated asset markets exchange rates reactmore to interest rate di¤erentials. This higher exchange rate appreciation further lowers thereduction in imports and increases the fall in exports, i.e. increases the contractionary e¤ectof monetary policy further. Overall, a lower reduction in imports together with a higher fallin exports, and, thus, a higher fall in net exports o¤sets the lower reduction in consumption,and investment and there is a slightly higher contraction in output (about 1% of the initialresponse), as well as in�ation (about 4% of the initial response). Thus, even though mone-tary policy loses some control over consumption and investment due to the fact that Homeconsumers can borrow more easily from the rest of the world, the impact of monetary policyon net exports, output and in�ation are higher in an economy where assets can be tradedmore easily with the rest of the world. It is important to get a sense of how the calibrationof �nancial intermediation costs a¤ects the robustness of this result. Figure A4 reports thesensitivity of the impulse responses to the calibration of �nancial intermediation costs. Theresponse functions are shown for the period of the shock as a function of BF ; QF ; B�H ; Q�H .Thus, as before, the costs for di¤erent categories of foreign assets are the same and symmetricfor the two countries. As found before, the lower the �nancial intermediation costs on foreignassets the more consumers can engage in consumption smoothing with the rest of the worldand therefore the higher the reduction in asset holdings and the lower the reaction of con-sumption, investment and imports. Exports, the trade balance, output, and in�ation reactmore when the costs for trading foreign assets are lower. The sensitivity of the reactions tothe level of costs is not very high. Even if costs are reduced by a factor of 10, the responsesof in�ation and output are a¤ected by only 0.05 and 0.02 percent, respectively, or about 10and 0.5 percent of the initial responses.

3.2 Higher gross foreign asset positions

The second international �nancial integration experiment shows that integration in the formof higher gross foreign asset holdings strengthens wealth channels of monetary transmission.Strengthened wealth channels more than o¤set a weakened interest rate channel and thereforelead to a higher impact on domestic spending. At the same time these strengthened wealthchannels, together with a slightly weakened exchange rate channel lower the impact on netexports. In most of the cases, however, the higher impact on domestic spending outweighsthe lower impact on net exports, and thereby reinforce the overall impact of monetary policyon output. The impact on in�ation is slightly lower initially, but more persistent. Figure A5reports the impulse responses, in particular the di¤erences in the reaction of the main variablesbetween the "Higher gross foreign asset (GFA) holdings" and the "Baseline" scenario. Thereare again no qualitative di¤erences in the responses of any variable, except, as discussedbelow, net exports. The fall in consumption, investment, and output are higher - as is thefall in imports. The higher fall in consumption occurs despite the fact that in an integratedscenario Home agents boost their consumption smoothing, i.e. increase their borrowings from

22

foreigners (as can be seen by the higher reduction in asset holdings in all categories). Thehigher fall in consumption and imports is mainly due to much higher negative shocks ondomestic agents foreign income and wealth, i.e. net foreign income and assets (the responsesare increased by a factor of around three and two, respectively). These dynamics in turn area consequence of higher negative exchange rate valuation e¤ects. Despite a lower appreciationof the Home currency, exchange rate valuation e¤ects are much higher as they a¤ect muchhigher steady state gross positions. Only the contractionary impact of monetary policy onnet exports is reduced. A positive interest rate shock now even leads to a slightly positiveimpact reaction of net exports. The contractionary e¤ect on net exports is reduced as a lowerappreciation of the Home currency lowers the fall in exports and, together with higher negativewealth and income e¤ects, increase the reduction in imports. However, despite a lower impacton net exports, the overall impact on output is increased by 0.01 percent or about 2.5 percentof the initial response. The response of in�ation is slightly moderated on impact (0.025 percentor 5 percent of the initial response), due to a lower impact appreciation of the exchange rate,but it is more persistent. Figure A6 reports the sensitivity of the impulse responses to thecalibration of the level of steady state gross foreign asset positions. The response functions

are shown for the period of the shock as a function of�BF�P � �Y �

;�B�H�P �Y;�P �Q�P �

�QF�Y �;�PQ�P

�Q�H�Y. Thus, as

before, the holdings of di¤erent categories of foreign assets are the same and symmetric forthe two countries. In line with the results above, higher gross foreign asset holdings increasethe negative reaction of consumption, investment and imports, and output. Exports andthe trade balance and in�ation react less with increasing gross foreign asset holdings. Thesensitivity of the reactions to the level of gross foreign assets is a bit higher than before.If holdings are increased to over 700% of GDP, the impact of a monetary policy shock onoutput is increased by 0.1 percent or about 20% of the initial response. The impact of acontractionary monetary policy shock on in�ation is reduced by 0.05 percent or about 15%of the initial response. However, monetary policy always retains its ability to a¤ect in�ation.Note that if total gross foreign asset holdings are more than 700% of GDP, the real exchangerate depreciates on impact which leads not only to a positive reaction of net exports, but alsonet foreign assets.

3.3 Both forms of �nancial integration combined

The experiment interacting both forms of �nancial market integration, i.e. a reduction oftransaction costs for trading foreign assets combined with an increase in the level of grossforeign assets, increases the impact of monetary policy on both output and in�ation as the"positive" e¤ects in the two individual scenarios reinforce each other. Figure A7 reports thedi¤erence in the impulse responses between the two scenarios. A higher impact appreciation ofthe Home currency (arguably due to lower transaction costs, i.e. more integrated internationalasset markets, which make exchange rates more responsive to interest rate di¤erentials) nowhas a higher negative exchange rate valuation e¤ect on Home households�wealth (due to highergross foreign asset positions), which, in turn, increases the negative impact on consumption,investment, imports, output and in�ation. Only the reduction of exports is lower whichleads, together with a higher reduction of imports, to a slightly lower reduction of the tradebalance. However, the former e¤ect outweighs the latter. Overall, this combined form of

23

�nancial integration increases rather than decreases monetary policy e¤ectiveness. Figure A8reports the sensitivity of the results to the calibration of the combination of the two forms of�nancial integration. In particular, it reports the impact reaction of in�ation, output and afew additional variables for further interactions of the calibration of the level of gross foreignasset holdings and of the costs for trading foreign assets. A monetary policy shock has thehighest impact on in�ation and output when gross foreign asset holdings are large and thecosts for trading foreign assets are low. A reduction in the costs for trading foreign assetsalways, i.e. in the combination with any level of gross foreign asset holdings, increases theimpact of monetary policy on both output and in�ation. In contrast, in the combination withcertain levels of the costs for trading foreign assets an increase in foreign asset holdings leadsnot only to a lower e¤ect on in�ation (as seen above), but in certain situations also to a lowere¤ect on output. This is namely the case when the costs for trading foreign assets are verylarge, i.e. there is almost complete �nancial autarky. In such a situation an increase in grossforeign asset holdings leads to marked reduction in the impact of a monetary policy shock onthe exchange rate. A markedly lower exchange rate appreciation in turn markedly lowers thereduction in net exports. As the decreasing impact on net exports outweighs the increasingimpact on domestic spending the overall impact of monetary policy on output and in�ationis reduced.39 Thus, in a situation with high costs for trading foreign assets, an increase ingross foreign asset holdings may weaken monetary policy transmission. However, even withvery high costs for trading foreign assets and very high foreign asset holdings monetary policyretains its impact on both output and in�ation.

3.4 "Trade" integration and its interaction with �nancial integration

The trade market integration experiment (displayed in Figure A9), namely a reduction inthe Home country�s share in the overall traded goods sector, is in line with �ndings in theexisting literature. Monetary policy retains its leverage over output and in�ation even inan environment where the Home traded goods sector is small compared to world markets.The impact on the trade balance and in�ation is reduced, but the impact on consumption,investment, and output is slightly larger. The larger impact on domestic spending and outputis due to larger negative income and wealth e¤ects. Despite a lower exchange rate appreciation,there is a larger fall in net foreign income and assets. The leverage over the trade balance isreduced as a lower impact appreciation of the exchange rate reduces the impact on exports,i.e. lowers the reduction of exports, and, together with higher negative income and wealthshocks, also leads to a higher reduction in import spending. The overall impact on outputis increased by 0.05 percent (or around 0.1 percent of the initial response), while the impacton in�ation is reduced by around 0.02 percent (or around 0.2 percent of the initial response).Figure A10 reports the sensitivity of the results to the calibration of the Home country�sshare in the overall traded goods sector. The sensitivity of the responses of output andin�ation are very low. Overall, increasing trade integration leads to an increasing impacton domestic spending and output, but a decreasing impact on exchange rates, net exports

39 In a scenario with (very) high gross foreign asset holdings in combination with (very) high costs for tradingforeign assets the exchange rate even depreciates rather than appreciates on impact (as seen above in the caseof high gross foreign asset holdings).

24

and in�ation. Figure A11 reports the experiment interacting "trade" integration with bothforms of �nancial integration combined. As the di¤erence in the impulse responses show, aninteraction of all forms of integration leads to the highest "positive" impact on monetary policye¤ectiveness. Furthermore, the combined e¤ect is not just the sum of all individual e¤ects,but the interaction of �nancial and "trade" integration actually leads to an ampli�cation ofthe e¤ects. Strengthened income and wealth e¤ects more than o¤set weakened exchange rateand interest rate channels of monetary transmission. The impact of a monetary policy shockon output and in�ation is reinforced by 0.05 and 0.01 percent (or 15 and 2 percent of theinitial responses), respectively. Figure A12 shows some further scenarios for the interactionof "trade" integration with �nancial integration in the form of lower costs for trading foreignassets, while Figure A13 shows some further scenarios for the interaction of "trade" integrationwith �nancial integration in the form of higher gross foreign asset holdings. The impulseresponses show that for any level of "trade" integration, a reduction in the costs for tradingforeign assets leads to an increase of the impact of monetary policy on output and in�ationdue to strengthened exchange rate and wealth channels which more than o¤set weakenedinterest rate channels. In contrast, for any given level of "trade" integration, an increase ofgross foreign asset holdings leads to an increasing impact of monetary policy on domesticspending and output, but a decreasing impact on exchange rates, net exports and in�ation.These e¤ects are higher the higher the trade integration. However, even with a very lowshare of the Home country�s share in the trade goods sector and very high gross foreign assetpositions, monetary policy still a¤ects in�ation to a non-negligible degree.

3.5 Lower exchange rate pass-through and its interaction with �nancialintegration

Figures 14 to 18 show di¤erent scenarios with a reduction in the ERPT and its interaction withthe two forms of �nancial integration. All experiments show that neither a decrease in theERPT nor its interaction with �nancial integration materially a¤ect the impact of monetarypolicy on output and in�ation. The sensitivity of the responses to the calibration of theexchange rate pass-through elasticity is very low. In general, a lower ERPT lowers monetarypolicy�s impact on in�ation, but increases its impact on output (see Figures A14 and A15).However, the e¤ects are very small. Figure A16 reports the experiment interacting a lowerERPT with both forms of �nancial integration combined. As the di¤erences in the impulseresponses show, this leads to a reinforced impact on output and in�ation of 0.025 and 0.015percent (or 7 percent and 30 percent of the initial responses), respectively. Stronger exchangerate and income and wealth channels, more than o¤set weaker interest rate channels. FiguresA17 and A18 show further calibrations of the interaction of a lower ERPT with the two formsof �nancial integration. Again, for any level of ERPT, a reduction in the costs for tradingforeign assets always increases monetary policy�s impact on output and in�ation. In contrast,for any given level of ERPT, an increase in the level of gross foreign asset holdings, alwaysleads to an increasing impact of monetary policy on output, consumption and investment,but a decreasing impact on exchange rates, net exports and in�ation.

25

4 Conclusions

The simulations of the model show that none of the analyzed forms of international �nancialintegration materially undermines the impact of monetary policy on output and in�ation. Inthe general New Keynesian open economy model presented here, it is di¢ cult to constructscenarios in which �nancial integration or an interaction of �nancial with trade integrationor with a reduction in the ERPT markedly erode monetary policy e¤ectiveness.40 Thus,Woodford (2007)�s results for trade and factor market integration carry over to �nancialintegration.

The simulations show three di¤erent aspects of the impact of �nancial integration on thetransmission of monetary policy. First, the two forms of international �nancial integrationhave opposite e¤ects on the impact of monetary policy on domestic spending decisions. Onthe one hand, integration in the form of lower transaction costs reduces monetary policy�scontrol over domestic spending decisions as it increases the ability of domestic agents tosmooth their consumption over time by borrowing from the rest of the world. This weakensthe interest rate channel of monetary policy transmission. On the other hand, integrationin the form of an increase of gross foreign asset holdings increases monetary policy�s controlover domestic spending as it strengthens the e¤ect of (monetary policy induced) exchangerate valuation e¤ects on domestic agent�s foreign income and wealth. This form of integrationthus strengthens income and wealth channels of monetary policy transmission.

Second, the e¤ects of both forms of integration on the impact of monetary policy ondomestic spending decisions are counteracted by their e¤ects on the impact of monetary policyon the trade balance. Under �nancial integration in the form of a reduction in transactioncosts a weakened interest rate channel reduces the impact not only on domestic spending butalso import spending which, together with a strengthened exchange rate channel increasesmonetary policy�s leverage over net exports. Under �nancial integration in the form of highergross foreign assets strengthened wealth channels increase the impact not only on domesticspending but also on import spending which in turn reduces monetary policy�s leverage overnet exports.

Third, overall, under realistic parameterizations, the "negative" e¤ects of �nancial inte-gration on monetary policy transmission are more than o¤set by the "positive" e¤ects ofintegration. The "negative" e¤ects of a reduction in the costs for trading foreign assets, i.e.a weaker impact on domestic spending (due to a weaker interest rate channel) is more thano¤set by its "positive" e¤ects, i.e. a stronger impact on the trade balance (due to strongerexchange rate channels and the e¤ect of a weaker interest rate channel on import spending) .The "positive" e¤ects of an increase of gross foreign assets, i.e. a stronger impact on domesticspending (due to stronger income and wealth channels) outweighs its "negative" e¤ects, i.e.a weaker impact on the trade balance (due to the e¤ect of stronger income and wealth chan-nels on import spending), especially in combination with reinforced exchange rate channels.Only in a combination of very high gross foreign asset holdings with either very high costsfor trading foreign assets, a very small share of the Home country�s traded goods sector or a

40Also an experiment with an interaction of �nancial integration with a decrease in the exchange rate pass-through, which could arguably be lower in more integrated �nancial and goods markets, does not show anymaterial impact and is therefore not reported.

26

very low ERPT are the "positive" e¤ects of stronger income and wealth channels on domesticspending either more than o¤set by their "negative" e¤ects on the trade balance or by weakerexchange rate channels. However, none of the experiments lead to a material erosion of theimpact of monetary policy on output and in�ation. Monetary policy always retains its abilityto a¤ect output and in�ation. Furthermore, in scenarios with the highest integration (lowcosts, high gross foreign asset holdings and high trade integration) monetary policy is moste¤ective.

This paper is a �rst step in the analysis of the implications of international �nancial inte-gration for the transmission of monetary policy. The focus of this paper is on a standard NewKeynesian framework in which non-neoclassical channels, such as bank- and balance sheet-based channels, cannot be analyzed. The role of non-neoclassical channels in the transmissionof monetary policy remains a very important open question for research.41 Furthermore,the analysis of this paper is based on a calibration exercise. This approach has to be com-plemented not only by an estimation of the model but also by a less structural data-drivenapproach in a vector autoregression framework and a combination of the two along the linesof Boivin and Giannoni (2002). Finally, this paper shows that even if international �nancialintegration does not erode the impact of monetary policy it changes the relative roles of dif-ferent monetary policy transmission channels. The functioning of these di¤erent channels in aglobal environment with integrated �nancial markets warrants a more detailed analysis, boththeoretically and empirically.

41See Boivin, Kiley and Mishkin (2010).

27

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31

Appendix A: Impulse response functions

i interest rate qh real Home equity holdings� in�ation qf real Foreign equity holdings�s change in nominal exchange rate �nfa change in net foreign assetsrer real exchange rate ca real current accounty real gross domestic product �lcap change in local currency asset pricesc real consumption ev real exchange rate valuationinv real investment n labornx real net exports k capitalexp real exports w real wagesimp real imports rk real rental rate of capitalnai real net asset income mc real marginal costsnfa real net foreign assets v real pro�tsbh real holdings of Home bond pq real price of equitiesbf real holdings of Foreign bond tot terms of trade

Table A1: Notation of reported variables

32

0 10 200

0.5

1i

0 10 20­0.5

0

0.5π

0 10 20­0.5

0

0.5∆s

0 10 20­0.2

0

0.2rer

0 10 20­0.4

­0.2

0y

0 10 20­0.2

­0.1

0c

0 10 20­1

0

1inv

0 10 20­0.02

0

0.02nx

0 10 20­0.5

0

0.5exp

0 10 20­0.2

­0.1

0imp

0 10 20­0.04­0.02

0nai

0 10 20­0.15

­0.1nfa

0 10 20­0.03

­0.02

­0.01bh

0 10 20­0.03

­0.02

­0.01bf

0 10 20­0.03

­0.02

­0.01qh

0 10 20­0.03

­0.02

­0.01qf

0 10 20­0.2

­0.1

0∆nfa

0 10 20­0.1

­0.05

0ca

0 10 20­0.1

0

0.1∆lcap

0 10 20­0.2

0

0.2ev

Figure A1: "Baseline"Impulse resp onses are rep orted in p ercentage p oint deviations from the steady state.

33

0 10 20­1

­0.5

0

0.5n

0 10 20­0.05

­0.04

­0.03

­0.02k

0 10 20­0.03

­0.02

­0.01

0w

0 10 20­1

­0.5

0

0.5rk

0 10 20­0.5

0

0.5mc

0 10 20­1

0

1

2v

0 10 20­0.2

­0.1

0pq

0 10 20­0.2

0

0.2tot

0 10 200

0.05

0.1i*

0 10 20­0.2

0

0.2π*

0 10 20­5

0

5

10x 10­3 y*

0 10 20­4

­2

0

2x 10­3 c*

Figure A2: "Baseline"Impulse resp onses are rep orted in p ercentage p oint deviations from the steady state.

34

0 10 20­0.02

­0.01

0i

0 10 20­0.02

0

0.02π

0 10 20­0.05

0

0.05∆s

0 10 20­0.02

0

0.02rer

0 10 20­5

0

5x 10­3 y

0 10 20­2

0

2x 10­3 c

0 10 20­0.01

0

0.01inv

0 10 20­0.01

0

0.01nx

0 10 20­0.05

0

0.05exp

0 10 20­0.05

0

0.05imp

0 10 20­2

0

2x 10­3 nai

0 10 20­0.02

­0.01

0nfa

0 10 20­2

­1.5

­1x 10­3 bh

0 10 20­2

­1.5

­1x 10­3 bf

0 10 20­2

­1.5

­1x 10­3 qh

0 10 20­2

­1.5

­1x 10­3 qf

0 10 20­0.02

0

0.02∆nfa

0 10 20­0.01

0

0.01ca

0 10 200

0.5

1x 10­3∆lcap

0 10 20­0.02

0

0.02ev

Figure A3: Di¤erence "Lower Costs" to "Baseline"Impulse resp onses are rep orted in p ercentage p oint deviations from the steady state. Here the d i¤erences in the

resp onses b etween the "Lower Costs" and the "Baseline" scenarios are rep orted .

35

0 5 100.65

0.7

0.75

γ

i0 5 10

­0.5

­0.4

­0.3

γ

π

0 5 10­0.4

­0.3

­0.2

γ

∆s

0 5 10­0.2

­0.15

­0.1

γ

rer

0 5 10­0.36

­0.34

­0.32

γ

y

0 5 10­0.12

­0.115

­0.11

γc

0 5 10­1

­0.95

­0.9

γ

inv

0 5 10­0.04

­0.02

0

γ

nx

0 5 10­0.4

­0.3

­0.2

γ

exp

0 5 10­0.3

­0.2

­0.1

γ

imp

0 5 10­0.06

­0.05

­0.04

γ

nai

0 5 10­0.15

­0.1

­0.05

γ

nfa

0 5 10­0.015

­0.01

­0.005

γ

bh

0 5 10­0.015

­0.01

­0.005

γ

bf

0 5 10­0.015

­0.01

­0.005

γqh

0 5 10­0.015

­0.01

­0.005

γ

qf

0 5 10­0.15

­0.1

­0.05

γ

∆nf

a

0 5 10­0.08

­0.06

­0.04

γ

ca

0 5 100.09

0.091

0.092

γ

∆lc

ap

0 5 10­0.15

­0.1

­0.05

γ

evFigure A4: Further "Lower Costs" scenarios

Impulse resp onses are rep orted in p ercentage p oint deviations from the steady state. Here the resp ones in the

p eriod of the sho ck are rep orted as functions of the level of costs for trad ing foreign assets.

36

0 10 20­0.02

0

0.02i

0 10 20­0.05

0

0.05π

0 10 20­0.1

0

0.1∆s

0 10 200

0.05rer

0 10 20­0.01

0

0.01y

0 10 20­0.02

­0.01

0c

0 10 20­0.1

­0.05

0inv

0 10 200

0.02

0.04nx

0 10 200

0.1

0.2exp

0 10 20­0.1

­0.05

0imp

0 10 20­0.2

­0.1

0nai

0 10 20­0.2

­0.15

­0.1nfa

0 10 20­0.04

­0.02

0bh

0 10 20­0.04

­0.02

0bf

0 10 20­0.04

­0.02

0qh

0 10 20­0.04

­0.02

0qf

0 10 20­0.2

0

0.2∆nfa

0 10 20­0.1

0

0.1ca

0 10 20­0.2

0

0.2∆lcap

0 10 20­0.5

0

0.5ev

Figure A5: Di¤erence "Higher GFA" to "Baseline"Impulse resp onses are rep orted in p ercentage p oint deviations from the steady state. Here the d i¤erences

b etween the "H igher GFA" and the "Baseline" scenarios are rep orted .

37

0 5 100.65

0.7

0.75

gfa

i0 5 10

­0.5

­0.4

­0.3

gfa

π

0 5 10­0.4

­0.2

0

gfa

∆s

0 5 10­0.2

0

0.2

gfa

rer

0 5 10­0.4

­0.35

­0.3

gfa

y

0 5 10­0.2

­0.15

­0.1

gfac

0 5 10­2

­1

0

gfa

inv

0 5 10­0.2

0

0.2

gfa

nx

0 5 10­0.5

0

0.5

gfa

exp

0 5 10­1

­0.5

0

gfa

imp

0 5 10­1

­0.5

0

gfa

nai

0 5 10­1

0

1

gfa

nfa

0 5 10­0.2

­0.1

0

gfa

bh

0 5 10­0.2

­0.1

0

gfa

bf

0 5 10­0.2

­0.1

0

gfaqh

0 5 10­0.2

­0.1

0

gfa

qf

0 5 10­1

0

1

gfa

∆nf

a

0 5 10­1

­0.5

0

gfa

ca

0 5 100

0.5

1

gfa

∆lc

ap

0 5 10­0.5

0

0.5

gfaev

Figure A6: Further "Higher GFA" scenariosImpulse resp onses are rep orted in p ercentage p oint deviations from the steady state. Here the resp onses in the

p eriod of the sho ck are rep orted as functions of the level of steady state gross foreign assets.

38

0 10 20­0.02

­0.01

0i

0 10 20­0.02

­0.01

0π

0 10 20­0.02

0

0.02∆s

0 10 20­0.01

0

0.01rer

0 10 20­0.05

0

0.05y

0 10 20­0.02

­0.01

0c

0 10 20­0.1

­0.05

0inv

0 10 202

4

6x 10­3 nx

0 10 200.01

0.02

0.03exp

0 10 20­0.03

­0.02

­0.01imp

0 10 20­0.2

­0.1

0nai

0 10 20­0.3

­0.2

­0.1nfa

0 10 20­0.04

­0.02

0bh

0 10 20­0.04

­0.02

0bf

0 10 20­0.04

­0.02

0qh

0 10 20­0.04

­0.02

0qf

0 10 20­0.5

0

0.5∆nfa

0 10 20­0.2

0

0.2ca

0 10 20­0.5

0

0.5∆lcap

0 10 20­0.5

0

0.5ev

Figure A7: Di¤erence "Higher GFA and Lower Costs" to "Baseline"Impulse resp onses are rep orted in p ercentage p oint deviations from the steady state. Here the d i¤erences in the

resp onses b etween the "H igher GFA and Lower Costs" and the "Baseline" sceanrios are rep orted .

39

05

100

5100.5

1

1.5

γ

i

gfa 05

100

510­1

0

1

γ

π

gfa 05

100

510­1

0

1

γ

∆s

gfa 05

100

510­1

0

1

γ

rer

gfa

05

100

510

­0.5

­0.4

­0.3

γ

y

gfa 05

100

510

­0.3

­0.2

­0.1

γ

c

gfa 05

100

510­2

­1

0

γ

inv

gfa 05

100

510

­0.5

0

0.5

γ

nx

gfa

05

100

510­2

0

2

γ

exp

gfa 05

100

510­2

­1

0

γ

imp

gfa 05

100

510­2

­1

0

γ

nai

gfa 05

100

510­5

0

5

γ

nfa

gfa

Figure A8: Further "Higher GFA" and "Lower Costs" scenariosImpulse resp onses are rep orted in p ercentage p oint deviations from the steady state. Here the resp onses in the

p eriod of the sho ck are rep orted as functions of the level of steady state gross foreign assets and of costs for

trad ing foreign assets.

40

0 10 20­0.02

0

0.02i

0 10 20­0.02

0

0.02π

0 10 20­0.05

0

0.05∆s

0 10 200.005

0.01

0.015rer

0 10 20­0.01

0

0.01y

0 10 20­0.01

­0.005

0c

0 10 20­0.1

0

0.1inv

0 10 200

0.01

0.02nx

0 10 200

0.05

0.1exp

0 10 20­0.04­0.02

0imp

0 10 20­0.2

­0.1

0nai

0 10 20­0.21

­0.2

­0.19nfa

0 10 20­0.015

­0.01

­0.005bh

0 10 20­0.015

­0.01

­0.005bf

0 10 20­0.015

­0.01

­0.005qh

0 10 20­0.015

­0.01

­0.005qf

0 10 20­0.5

0

0.5∆nfa

0 10 20­0.2

0

0.2ca

0 10 20­0.05

0

0.05∆lcap

0 10 20­0.2

0

0.2ev

Figure A9: Di¤erence "Higher trade integration" to "Baseline"Impulse resp onses are rep orted in p ercentage p oint deviations from the steady state. Here the d i¤erences in the

resp onses b etween the "H igher goods market integration" and the "Baseline" scenarios are rep orted .

41

0 0.50.65

0.7

α

i0 0.5

­0.44­0.42

­0.4

α

π

0 0.5­0.3

­0.25

­0.2

α

∆s

0 0.5­0.2

­0.15

­0.1

α

rer

0 0.5­0.36

­0.34

­0.32

α

y

0 0.5­0.14

­0.12

­0.1

αc

0 0.5­1.05

­1

­0.95

α

inv

0 0.5­0.02

­0.01

0

α

nx

0 0.5­0.4

­0.3

­0.2

α

exp

0 0.5­0.25

­0.2

­0.15

α

imp

0 0.5­0.2

­0.1

0

α

nai

0 0.5­0.4

­0.2

0

α

nfa

0 0.5­0.03

­0.02

­0.01

α

bh

0 0.5­0.03

­0.02

­0.01

α

bf

0 0.5­0.03

­0.02

­0.01

αqh

0 0.5­0.03

­0.02

­0.01

α

qf

0 0.5­0.4

­0.2

0

α

∆nf

a

0 0.5­0.2

­0.1

0

α

ca

0 0.50

0.1

0.2

α

∆lc

ap

0 0.5­0.3

­0.2

­0.1

α

evFigure A10: Further "Trade integration" scenarios

Impulse resp onses are rep orted in p ercentage p oint deviations from the steady state. Here the resp onses in the

p eriod of the sho ck are rep orted as functions of the level o f "trade integration".

42

0 10 20­0.02

­0.01

0i

0 10 20­0.02

­0.01

0π

0 10 20­0.05

0

0.05∆s

0 10 200.02

0.03

0.04rer

0 10 20­0.05

0

0.05y

0 10 20­0.04

­0.02

0c

0 10 20­0.4

­0.2

0inv

0 10 200.01

0.02

0.03nx

0 10 200

0.1

0.2exp

0 10 20­0.2

­0.1

0imp

0 10 20­1

­0.5

0nai

0 10 20­1

­0.8

­0.6nfa

0 10 20­0.1

­0.05bh

0 10 20­0.1

­0.05bf

0 10 20­0.1

­0.05qh

0 10 20­0.1

­0.05qf

0 10 20­1

0

1∆nfa

0 10 20­0.5

0

0.5ca

0 10 20­0.5

0

0.5∆lcap

0 10 20­1

0

1ev

Figure A11: Di¤erence "Higher trade integration, Higher GFA and LowerCosts" to "Baseline"

Impulse resp onses are rep orted in p ercentage p oint deviations from the steady state. Here the d i¤erences in the

resp onses b etween the "H igher goods market integration , H igher GFA and Lower Costs" and the "Baseline"

scenarios are rep orted .

43

0

0.50

1020

0.7

0.8

α

i

γ 0

0.50

1020

­0.5

­0.4

­0.3

α

π

γ 0

0.50

1020

­0.4

­0.2

0

α

∆s

γ 0

0.50

1020

­0.2

­0.1

0

α

rer

γ

00.5

010

20­0.36

­0.34

­0.32

α

y

γ 00.5

010

20­0.15

­0.1

α

c

γ 00.5

010

20­1.1

­1

­0.9

α

inv

γ 00.5

010

20­0.05

0

0.05

α

nx

γ

0

0.50

1020

­0.4

­0.2

0

α

exp

γ 0

0.50

1020

­0.3

­0.2

­0.1

α

imp

γ 0

0.50

1020

­0.2

­0.1

0

α

nai

γ 0

0.50

1020

­0.4

­0.2

0

α

nfa

γ

Figure A12: Further "Trade integration" and "Lower Costs" scenariosImpulse resp onses are rep orted in p ercentage p oint deviations from the steady state. Here the resp onses in the

p eriod of the sho ck are rep orted as functions of the level of "trade" integration and of the costs for trad ing

foreign assets.

44

0

0.50

510

0.7

0.8

α

i

gfa 0

0.50

510

­0.4

­0.2

0

α

π

gfa 0

0.50

510

­0.5

0

0.5

α

∆s

gfa 0

0.50

510

­0.5

0

0.5

α

rer

gfa

00.5

05

10­0.5

­0.4

­0.3

α

y

gfa 00.5

05

10­0.3

­0.2

­0.1

α

c

gfa 00.5

05

10­4

­2

0

α

inv

gfa 00.5

05

10­0.5

0

0.5

α

nx

gfa

00.5

05

10­2

0

2

α

exp

gfa 00.5

05

10­2

­1

0

α

imp

gfa 00.5

05

10­4

­2

0

α

nai

gfa 00.5

05

10­5

0

5

α

nfa

gfa

Figure A13: Further "Trade integration" and "Higher GFA" scenariosImpulse resp onses are rep orted in p ercentage p oint deviations from the steady state. Here the resp onses in the

p eriod of the sho ck are rep orted as functions of the level of "trade" integration and of the level o f gross foreign

asset hold ings.

45

0 10 200

2

4x 10­3 i

0 10 200

5x 10­3 π

0 10 20­5

0

5x 10­3 ∆s

0 10 20­0.01

­0.005

0rer

0 10 20­2

­1

0x 10­3 y

0 10 20­2

­1

0x 10­3 c

0 10 20­0.01

­0.005

0inv

0 10 20­2

0

2x 10­3 nx

0 10 20­5

0

5x 10­3 exp

0 10 20­0.01

­0.005

0imp

0 10 20­1

­0.5

0x 10­3 nai

0 10 20­5

0

5x 10­3 nfa

0 10 200

0.5

1x 10­3 bh

0 10 200

0.5

1x 10­3 bf

0 10 200

0.5

1x 10­3 qh

0 10 200

0.5

1x 10­3 qf

0 10 20­1

0

1x 10­3∆nfa

0 10 20­1

0

1x 10­3 ca

0 10 20­2

0

2x 10­3∆lcap

0 10 20­5

0

5x 10­3 ev

Figure A14: Di¤erence "Lower ERPT" to "Baseline"Impulse resp onses are rep orted in p ercentage p oint deviations from the steady state. Here the d i¤erences in

the resp onses b etween the "Lower ERPT" and the "Baseline" scenarios are rep orted .

46

0 0.50.67

0.675

τ

i0 0.5

­0.44

­0.43

­0.42

τ

π

0 0.5­0.29

­0.288­0.286­0.284­0.282

­0.28

τ

∆s

0 0.5­0.15

­0.14

­0.13

τ

rer

0 0.5­0.345

­0.34

­0.335

τ

y

0 0.5­0.118

­0.116

­0.114

τc

0 0.5­0.98

­0.97

­0.96

τ

inv

0 0.5­0.019

­0.018

­0.017

τ

nx

0 0.5­0.312

­0.311

­0.31

τ

exp

0 0.5­0.18

­0.17

­0.16

τ

imp

0 0.5­0.05

­0.049

­0.048

τ

nai

0 0.5­0.106

­0.104

­0.102

τ

nfa

0 0.5­0.0127

­0.0127

­0.0127

τ

bh

0 0.5­0.0127

­0.0127

­0.0127

τ

bf

0 0.5­0.0127

­0.0127

­0.0127

τqh

0 0.5­0.0127

­0.0127

­0.0127

τ

qf

0 0.5­0.106

­0.104

­0.102

τ

∆nf

a

0 0.5­0.068

­0.067

­0.066

τ

ca

0 0.50.09

0.092

0.094

τ

∆lc

ap

0 0.5­0.14

­0.13

­0.12

τ

evFigure A15: Further "Lower ERPT" scenarios

Impulse resp onses are rep orted in p ercentage p oint deviations from the steady state. Here the resp onses in the

p eriod of the sho ck are rep orted as functions of the level of "ERPT".

47

0 10 20­0.02

0

0.02i

0 10 20­0.02

0

0.02π

0 10 20­0.02

0

0.02∆s

0 10 20­0.01

0

0.01rer

0 10 20­0.05

0

0.05y

0 10 20­0.02

­0.01

0c

0 10 20­0.1

­0.05

0inv

0 10 200

0.005

0.01nx

0 10 200.01

0.02

0.03exp

0 10 20­0.03

­0.02

­0.01imp

0 10 20­0.2

­0.1

0nai

0 10 20­0.3

­0.2

­0.1nfa

0 10 20­0.04

­0.02

0bh

0 10 20­0.04

­0.02

0bf

0 10 20­0.04

­0.02

0qh

0 10 20­0.04

­0.02

0qf

0 10 20­0.5

0

0.5∆nfa

0 10 20­0.2

0

0.2ca

0 10 20­0.5

0

0.5∆lcap

0 10 20­0.5

0

0.5ev

Figure A16: Di¤erence "Lower ERPT, Higher GFA, and Lower Costs" to"Baseline"

Impulse resp onses are rep orted in p ercentage p oint deviations from the steady state. Here the d i¤erences in the

resp onses b etween the "Lower ERPT , H igher GFA , and Lower Costs" and the"Baseline" scenarios are rep orted .

48

0

0.50

1020

0.65

0.7

0.75

τ

i

γ 0

0.50

1020

­0.5

­0.45

­0.4

τ

π

γ 0

0.50

1020

­0.4

­0.3

­0.2

τ

∆s

γ 0

0.50

1020

­0.2

­0.15

­0.1

τ

rer

γ

00.5

010

20­0.36

­0.34

­0.32

τ

y

γ 00.5

010

20­0.12

­0.115

­0.11

τ

c

γ 00.5

010

20­1

­0.95

­0.9

τ

inv

γ 00.5

010

20­0.04

­0.02

0

τ

nx

γ

0

0.50

1020

­0.4

­0.3

­0.2

τ

exp

γ 0

0.50

1020

­0.3

­0.2

­0.1

τ

imp

γ 0

0.50

1020

­0.06

­0.05

­0.04

τ

nai

γ 0

0.50

1020

­0.15

­0.1

­0.05

τ

nfa

γ

Figure A17: Further "Lower ERPT" and "Lower Costs" scenariosImpulse resp onses are rep orted in p ercentage p oint deviations from the steady state. Here the resp onses in the p eriod of

the sho ck are rep orted as functions of the level o f ERPT and of the costs for trad ing foreign assets.

49

00.5

05

100.65

0.7

0.75

τ

i

gfa 00.5

05

10­0.5

­0.4

­0.3

τ

π

gfa 00.5

05

10­0.4

­0.2

0

τ

∆s

gfa 00.5

05

10­0.2

0

0.2

τ

rer

gfa

00.5

05

10­0.4

­0.35

­0.3

τ

y

gfa 00.5

05

10­0.2

­0.15

­0.1

τ

c

gfa 00.5

05

10­1.5

­1

­0.5

τ

inv

gfa 00.5

05

10­0.2

0

0.2

τ

nx

gfa

00.5

05

10­0.5

0

0.5

τ

exp

gfa 00.5

05

10­1

­0.5

0

τ

imp

gfa 0

0.50

510­1

­0.5

0

τ

nai

gfa 00.5

05

10­0.5

0

0.5

τ

nfa

gfa

Figure A18: Further "Lower ERPT" and "Higher GFA" scenariosImpulse resp onses are rep orted in p ercentage p oint deviations from the steady state. Here the resp onses in the p eriod of

the sho ck are rep orted as functions of the level o f ERPT and of the level o f gross foreign asset hold ings.

50

Appendix B: Technical Appendix of the Model

This technical appendix derives the theoretical model in more detail. Section 1 outlines thederivation of the optimality conditions of households and �rms. Section 2 outlines the aggre-gation of the optimality conditions. Section 3 lists the market clearing conditions. Section 4restates the behavior of the monetary authorities. Section 5 derives the steady state. Section6 log-linearizes the system, and the last section derives some additional variables of interest.

B.1 Optimality Conditions

B.1.1 Optimal allocation of expenditures

The optimization problem with regards to the optimal allocation of consumption involves threestages. The �rst stage is the optimal allocation of consumption across the brands of the threedi¤erent sub-baskets, i.e. the minimization of the costs of purchasing a given aggregate tradedor nontraded goods index. For example, for the Home traded goods basket, a representativeHome household j faces the following optimization problem:

minCHTt(j;i)

Z �

0PHTt(i)CHTt(j; i)di

s:t:

"�1

�

� 1�Z �

0(CHTt(j; i))

��1� di

# ���1

= �CHTt(j)

The FOC with respect to CHTt(j; i) is:

�PHTt(i) = �

24 �

� � 1

"�1

�

� 1�Z �

0(CHTt(j; i))

��1� di

# ���1�1

35�1

�

� 1��� � 1�

�(CHTt(j; i))

��1��1

Multiplying both sides by CHTt(j; i) and integrating overR � 0 :::di:

PHTt = ��

Combining:

PHTt(i) = PHTt

24"� 1

�

� 1�Z �

0(CHTt(j; i))

��1� di

# 1��135� 1

�

� 1�

(CHTt(j; i))� 1�

51

Replacing the Home traded goods consumption basket:

CHTt(j; i) =

�1

�

��PHTt(i)

PHTt

���CHTt(j)

Aggregating over all Home households:Z �

0CHTt(j; i)dj =

Z �

0

�1

�

��PHTt(i)

PHTt

���CHTt(j)dj

CHTt(i) =

�1

�

��PHTt(i)

PHTt

���CHTt

where the aggregate consumption of good i and the aggregate Home traded consumptionbasket are de�ned as:

CHTt(i) �Z �

0CHTt(j; i)dj

CHTt =

Z �

0CHTt(j)dj

The Home traded goods price index can be computed by plugging this aggregate optimalitycondition into the de�nition of the Home traded goods consumption basket:

CHTt =

"�1

�

� 1�Z �

0(CHTt(i))

��1� di

# ���1

yielding:

PHTt =

��1

�

�Z �

0PHTt(i)

1��di

� 11��

By analogous optimization problems one can derive the optimal consumption allocationsand price indices for the Foreign traded goods basket and the Home nontraded goods basket:

CFTt(j; i) =

�1

(1� �)

��PFTt(i)

PFTt

���CFTt(j)

CNt(j; i) =

�1

(1� )

��PNt(i)

PNt

���CNt(j)

and

PFTt ���

1

(1� �)

�Z

� (PFTt(i))

1�� di

� 11��

PNt ���

1

(1� )

�Z 1

(PNt(i))

1�� di

� 11��

52

The second stage is the optimal allocation of consumption between the Home and Foreigntraded goods baskets for a given aggregate traded goods basket, i.e. the minimization of thecosts of purchasing a given traded goods basket. A representative Home household j facesthe following optimization problem:

minCHTt;CFTt

[PHTtCHTt(j) + PFTtCFTt(j)]

s:t:h�1� (CHTt(j))

��1� + (1� �)

1� (CFTt(j))

��1�

i ���1

= �CTt(j)

The FOC with respect to CHTt(j) is:

�PHTt = �

"h�1� (CHTt(j))

��1� + (1� �)

1� (CFTt(j))

��1�

i ���1�1

#h�1� (CHTt(j))

��1��1i

Multiplying by CHTt(j):

PHTtCHTt(j) = ��"h�1� (CHTt(j))

��1� + (1� �)

1� (CFTt(j))

��1�

i ���1�1

#h�1� (CHTt(j))

��1�

iThe FOC with respect to CFTt(j) is:

�PFTt = �

"h�1� (CHTt(j))

��1� + (1� �)

1� (CFTt(j))

��1�

i ���1�1

#h(1� �)

1� (CFTt(j))

��1��1i

Multiplying by CFTt(j):

PFTtCFTt(j) = ��"h�1� (CHTt(j))

��1� + (1� �)

1� (CFTt(j))

��1�

i ���1�1

#h(1� �)

1� (CFTt(j))

��1�

iAdding the two FOCs:

PTt = ��

Combining:

CHTt(j) = �

�PHTtPTt

���CTt(j)

53

and similarly for the foreign traded goods basket:

CFTt(j) = (1� �)�PFTtPTt

���CTt(j)

Aggregating these optimality conditions over all Home households yields for the aggregateHome traded goods consumption in the Home economy:Z �

0CHTt(j)dj =

Z �

0(1� �)

�PHTtPTt

���CTt(j)dj

CHTt = (1� �)�PHTtPTt

���CTt

and similarly for the aggregate Foreign traded goods consumption in the Home economy:

CHTt = (1� �)�PFTtPTt

���CTt

The traded goods price index can be computed by plugging this aggregate optimalityconditions into the de�nition of the traded goods consumption basket:

CTt =

2664� 1�

�

�PHTtPTt

���CTt

!��1�

+ (1� �)1�

(1� �)

�PFTtPTt

���CTt

!��1�

3775�

��1

PTt =h�P 1��HTt + (1� �)P

1��FTt

i 11��

The third stage is the optimal allocation of expenditures between traded and non-tradedgoods for a given overall consumption basket, i.e. the minimization of the costs for purchasinga given overall aggregate consumption basket. A representative Home household j faces thefollowing optimization problem:

minCTt(j);CNt(j)

[PTtCTt(j) + PNtCNt(j)]

s:t:h 1! (CTt(j))

!�1! + (1� )

1! (CNt(j))

!�1!

i !!�1

= �Ct(j)

The FOC with respect to CTt(j) is:

�PTt = �

�h 1! (CTt(j))

!�1! + (1� )

1! (CNt(j))

!�1!

i !!�1�1

�h 1! (CTt(j))

!�1!�1i

54

Multiplying by CTt(j):

PTtCTt(j) = ���h 1! (CTt(j))

!�1! + (1� )

1! (CNt(j))

!�1!

i !!�1�1

� h 1! (CTt(j))

!�1!

iThe FOC with respect to CNt(j) is:

�PNt = �

�h 1! (CTt(j))

!�1! + (1� )

1! (CNt(j))

!�1!

i !!�1�1

� h(1� )

1! (CNt(j))

!�1!�1i

Multiplying by CNt(j):

PNtCNt = ���h 1! (CTt(j))

!�1! + (1� )

1! (CNt(j))

!�1!

i !!�1�1

� h(1� )

1! (CNt(j))

!�1!

iAdding the two FOCs:

Pt = ��

Combining:

CTt(j) =

�PTtPt

��!Ct(j)

An analogous condition holds for the nontraded goods basket:

CNt(j) = (1� )�PNtPt

��!Ct(j)

Aggregating these optimality conditions over all Home consumers:Z �

0CTt(j)dj =

Z �

0

�PTtPt

��!Ct(j)dj

CTt =

�PTtPt

��!Ct

CNt = (1� )�PNtPt

��!Ct

Plugging these aggregate optimality conditions into the de�nition of the overall aggregateconsumption basket:

Ct =

� 1!C

!�1!

Tt + (1� )1!C

!�1!

Nt

� !!�1

yields:

Pt =� P 1�!Tt + (1� )P 1�!Nt

� 11�!

Combining the optimality conditions of these three stages yields:

55

CHTt(j; i) =

�PHTt(i)

PHTt

��� �PHTtPTt

����PTtPt

��!Ct(j)

CFTt(j; i) =

�PFTt(i)

PFTt

��� �PFTtPTt

����PTtPt

��!Ct(j)

CNt(j; i) =

�PNt(i)

PNt

��� �PNtPt

��!Ct(j)

and as derived above the following aggregate price indices:

PHTt =

��1

�

�Z �

0PHTt(i)

1��di

� 11��

(B.1)

PFTt ���

1

(1� �)

�Z

� (PFTt(i))

1�� di

� 11��

(B.2)

PNt ���

1

(1� )

�Z 1

(PNt(i))

1�� di

� 11��

(B.3)

PTt =h�P 1��HTt + (1� �)P

1��FTt

i 11��

(B.4)

Pt =� P 1�!Tt + (1� )P 1�!Nt

� 11�! (B.5)

B.1.2 Optimal intertemporal allocation

Maximizing the utility function subject to the budget constraint with respect to Ct(j),QHt+1(j); QFt+1(j), BHt+1(j), and BFt+1(j) yields the following FOCs:

Ct(j) : (Ct(j))�� � �tPt = 0

QHt+1(j) : ��tEt�PQt + QH

PQt(QHt+1(j)�QHt(j))

Yt

�

��Et

8<:�t+10@

QHPQt+1

(QHt+2(j)�QHt+1(j))Yt+1

(�1) + QHPQt+1(QHt+1(j)� �QH(j))

Yt+1

��PQt+1 +

�Vt+1�Q

�� 1A9=; = 0

56

QFt+1(j) : ��tEt�StP

�Qt + QFStP

�Qt

(QFt+1(j)�QFt(j))Y �t

�

��Et

8<:�t+10@

QFSt+1P

�Qt+1

(QFt+2(j)�QFt+1(j))Y �t+1

(�1) + QFSt+1P�Qt+1

(QFt+1(j)� �QF (j))Y �t+1

��St+1

�P �Qt+1 +

�V �t+1�Q�

���1A9=; = 0

BHt+1(j) : ��tEt�1 +

BH

(BHt+1(j)�BHt(j))PtYt

���Et

(�t+1

BH

(BHt+2(j)�BHt+1(j))Pt+1Yt+1

(�1) + BH(BHt+1(j)� �BH(j))

Pt+1Yt+1

�(1 + it+1)

!)= 0

BFt+1(j) : ��tEt�St + BF

St(BFt+1(j)�BFt(j))

P �t Y�t

���Et

(�t+1

BFSt+1

(BFt+2(j)�BFt+1(j))P �t+1Y

�t+1

(�1) + BFSt+1

(BFt+1(j)� �BF (j))P �t+1Y

�t+1

�St+1(1 + i�t+1)

!)= 0

Combining these equations yields the following Euler equations (for Home equity holdings,Foreign equity hldings, Home bond holdings, and Foreign bond holdings, respectively):

Et

�PQt + QH

PQt(QHt+1(j)�QHt(j))

Yt

�(B.6)

= Et

8<:Dt;t+1(j)

0@ QHPQt+1

(QHt+2(j)�QHt+1(j))Yt+1

� QHPQt+1(QHt+1(j)� �QH(j))

Yt+1

+�PQt+1 +

�Vt+1�Q

�� 1A9=;where

Et fDt;t+1(j)g = �Et

(�(Ct+1(j))

(Ct(j))

��� PtPt+1

)

Et

�StP

�Qt + QFStP

�Qt

(QFt+1(j)�QFt(j))Y �t

�(B.7)

= Et

8<:Dt;t+1(j)

0@ QFSt+1P

�Qt+1

(QFt+2(j)�QFt+1(j))Y �t+1

(�1) + QFSt+1P�Qt+1

(QFt+1(j)� �QF (j))Y �t+1

��St+1

�P �Qt+1 +

�V �t+1�Q�

���1A9=;

57

Et

�1 +

BH

(BHt+1(j)�BHt(j))PtYt

�(B.8)

= Et

(Dt;t+1(j)

BH

(BHt+2(j)�BHt+1(j))Pt+1Yt+1

� BH(BHt+1(j)� �BH(j))

Pt+1Yt+1

+(1 + it+1)

!)

Et

�St + BF

St(BFt+1(j)�BFt(j))

P �t Y�t

�(B.9)

= Et

(Dt;t+1(j)

BFSt+1

(BFt+2(j)�BFt+1(j))P �t+1Y

�t+1

� BFSt+1

(BFt+1(j)� �BF (j))P �t+1Y

�t+1

+St+1(1 + i�t+1)

!)

B.1.3 Optimal wage setting

Maximizing the utility function subject to the budget constraint with respect to WOptt (j)

and taking into account the aggregate wage and employment indices and �rms�labour inputdemand schedules that each household faces (derived below in the section on �rms):

Wt =

�Z �

0Wt(j)

1��dj

� 11��

Nt+k �Z � +(1� )

0N(i)di

Nt+kjt(j) =

WOptt (j)

Wt+k

!��Nt+k

yields:

Et

1Xk=0

(��W )k

2666664UNt+kjt(j)Nt+k

�1

Wt+k

���(��)WOpt

t (j)���1

+�t+k

2664 �

WOptt (j)Wt+k

���Nt+k

!+WOpt

t (j)Nt+k

�1

Wt+k

���(��)WOpt

t (j)���1

3775

3777775 = 0

where UNt+kjt(j) =@U

@Nt+kjt(j)

Plugging this condition into the FOC with respect to Ct+kjt(j) from the intertemporaloptimization problem above yields:

58

Et

1Xk=0

(��W )k

2666664UNt+kjt(j)Nt+k

�1

Wt+k

���(��)WOpt

t (j)���1

+UCt+kjt(j)

Pt+k

2664 �

WOptt (j)Wt+k

���Nt+k

!+WOpt

t (j)Nt+k

�1

Wt+k

���(��)WOpt

t (j)���1

3775

3777775 = 0

where UCt+kjt(j) =@U

@Ct+kjt(j), or

Et

1Xk=0

(��W )k

"Nt+kjt(j)UCt+kjt(j)

"WOptt (j)

Pt+k� �WMRSt+kjt(j)

##= 0

where �W ��

���1

�and MRSt+kjt(j) = �

UNt+kjt(j)

UCt+kjt(j), or

Et

1Xk=0

(��W )k

"Nt+kjt(j)

�Ct+kjt(j)

��� "WOptt (j)

Pt+k� �W

��Nt+kjt(j)

�'�Ct+kjt(j)

���##= 0 (B.10)

where Ct+kjt(j) and Nt+kjt(j) denote consumption and labor supply in period t + k of ahousehold that last reset its wage in period t.

B.1.4 Optimal investment

An installment �rm solves the following optimization problem:

maxKt+1(I)

Et

1Xk=0

Dt;t+k(I)hPt+kr

kt+kKt+k.(I)� Pt+kIt+k.(I)

is:t:

Kt+k+1 = (1� �)Kt+k + It+k ��

2

(Kt+k+1(I)�Kt+k(I))2

Kt+k(I)

i.e. that we assume that an installment �rm I�s discount factor re�ects the intertemporalmarginal rate of substitution of a representative Home household j.

Optimization with respect to Kt+1(I) leads to the following FOC:

�Pt�1 + �

(Kt+1(I)�Kt(I))

Kt(I)

�+Et

(Dt;t+1Pt+1

"rkt+1 + (1� �)

� �2

��2(Kt+2(I)�Kt+1(I))Kt+1�(Kt+2(I)�Kt+1(I))

2

(Kt+1(I))2

� #) = 0Replacing the discount factors and rearranging:

59

1 + �(Kt+1(I)�Kt(I))

Kt(I)(B.11)

= �Et

(�(Ct+1)

(Ct)

��� �(1� �) + rkt+1 +

�

2

�Kt+1(I)

2 �Kt+1(I)2

(Kt+1(I))2

��)

The pro�ts of Installment �rms are assumed to be rebated to households as lump-sumtransfers, TI . The per capita lump-sum transfer T jI is:

T jI =1

�

Z �

0Vt(j)dj =

1

�

Z �

0

�Ptr

ktKt.(j)� PtIt.(j)

�dj =

hPtr

ktKt. � PtIt.

iB.1.5 Cost minimization with respect to di¤erentiated labor

Let Wt(j) denote nominal wage for type-j labor e¤ective in period t for all j 2 [0; n]. Thecost minimization problem of a representative Home �rm i with respect to di¤erentiated laborservices for a given level of the aggregate labor index is:

minNt(i;j)

Z �

0Wt(j)Nt(i; j)dj

s:t:

�Z �

0Nt(i; j)

��1� dj

� ���1

= �Nt(i)

The optimality condition is:

Nt(i; j) =

�Wt(j)

Wt

���Nt(i)

The wage index can be computed by plugging this optimality condition into the de�nitionof the labor index:

Nt(i) =

�Z �

0Nt(i; j)

��1� dj

� ���1

yielding:

Wt =

�Z �

0Wt(j)

1��dj

� 11��

60

B.1.6 Optimal aggregate input demand

A Home �rm i chooses its aggregate factor inputs Nt(i) and Kt(i) in order to solve thefollowing cost minimization problem:

minNt(i);Kt(i)

hWtNt(i) + Pt.r

ktKt(i)

is:t: At (Kt(i))

1�� (Nt(i))� = �Yt(i)

The optimal factor demands can be written as (note that this is just one equation, writtenin two ways):

Nt(i) =�

(1� �)Pt.r

kt

WtKt(i) and Kt(i) =

(1� �)�

Wt

Pt.rktNt(i)

Combining these with the production function, and an expression for marginal costs, twofactor demand equations can be combined in the following way:

Substituting the two optimal factor demands into the production function:

Yt(i) = At (Kt(i))1�� (Nt(i))

�

yields:

Nt(i) =

��

(1� �)Pt.r

kt

Wt

�1��Yt(i)

Atand Kt(i) =

�(1� �)�

Wt

Pt.rkt

�� Yt(i)At

Substituting the rewritten optimal factor demands in the total cost function yields:

TCt(i) = WtNt(i) + Pt.rktKt(i)

= Wt

��

(1� �)Pt.r

kt

Wt

�1��Yt(i)

At+ Pt.r

kt

�(1� �)�

Wt

Pt.rkt

�� Yt(i)At

=

�1

(1� �)1����

�(Wt)

��Pt.r

kt

�1�� Yt(i)At

The marginal costs can then be derived as:

MCt =�TCt(i)

�Yt(i)=(Wt)

� �Pt.rkt �1��(1� �)1����At

(B.12)

Given these marginal costs the optimal factor demands can be written as

Nt(i) = �MCtYt(i)

Wt(B.13)

61

Kt(i) = (1� �)MCtYt(i)

Pt.rkt(B.14)

B.1.7 Optimal price setting

Traded goods sectorA representative �rm in the Home traded goods sector sets prices

nPOptHTt+k(i); P

Opt�HTt+k(i)

o1k=0

that maximize its expected discounted future pro�ts while these prices remain e¤ective. For-mally, it solves the following problem for the domestic market:

maxPOptHTt(i)

1Xk=0

�kPEt

8>><>>:Dt;t+k(j)0@ �

POptHTt(i)�MCt+kjt

�YHTt+kjt

+�POpt�HTt (i)S

1��t+k �MCt+kjt

�Y �HTt+kjt

1A9>>=>>;

where Dt;t+k(j) = �k�(Ct+k(j))(Ct(j))

���PtPt+k

i.e. that it is assumed that a representative Home �rm�s discount factor represents theintertemporal marginal rate of substitution of a representative Home household j,

and where MCt denotes the (nominal) marginal cost function

subject to the respective demand schedules of the Home and Foreign households andinstallment �rms, respectively:

YHTt+kjt(i) =

Z �

0

264�PHTt(i)PHTt+k

��� �PHTt+kPTt+k

��� �PTt+kPt+k

��!(Ct+k(j))

+�PHTt(i)PHTt+k

��� �PHTt+kPTt+k

��� �PTt+kPt+k

��!(I(j))

375 djor aggregated:

YHTt+kjt(i) =

POptHTt(i)

PHTt+k

!�� �PHTt+kPTt+k

����PTt+kPt+k

��!(Ct+k + It+k) (B.15)

and

Y �HTt+kjt(i) =

Z 1

�

264�P �HTt(i)P �HTt+k

��� �P �HTt+kP �Tt+k

��� �P �Tt+kP �t+k

��! �C�t+k(j)

�+�P �HTt(i)P �HTt+k

��� �P �HTt+kP �Tt+k

��� �P �Tt+kP �t+k

��! �I�t+k(j)

�375 dj

or aggregated:

Y �HTt+kjt(i) =

POpt�HTt (i)S

��t+k

P �HTt+k

!�� P �HTt+kP �Tt+k

!�� P �Tt+kP �t+k

!�! �C�t+k + I

�t+k

�(B.16)

62

The FOC with respect to POptHTt(i) is:

1Xk=0

�kPEt

8<:Dt;t+k(j)

0@ POptHTt(i)�YHTt+kjt(i)

�POptHTt(i)+ YHTt+kjt(i)

�MCt+k�YHTt+kjt(i)

�POptHTt(i)

1A9=; = 0

Using the fact that:

�YHTt+kjt(i)

�POptHTt(i)= ��YHTt+kjt(i)

1

POptHTt(i)

!

one can rewrite as:

1Xk=0

�kPEt

8<:Dt;t+k(j)

0@ ��YHTt+kjt(i) + YHTt+kjt(i)

+MCt+k�YHTt+kjt(i)

�1

POptHTt(i)

� 1A9=; = 0

or

1Xk=0

�kPEt

nDt;t+k(j)YHTt+kjt(i)

�POptHTt(i)� �PMCt+k

�o= 0 (B.17)

where �P =���1

Analogously a representative �rm in the Home traded goods sector solves the followingproblem for the other countries:

maxPOpt�HTt (i)

1Xk=0

�kPEt

8>><>>:Dt;t+k(j)0@ �

POptHTt(i)�MCt+kjt

�YHTt+kjt

+�POpt�HTt (i)S

1��t+k �MCt+kjt

�Y �HTt+kjt

1A9>>=>>;

The optimality condition is:

1Xk=0

�kPEt

nDt;t+k(j)Y

�HTt+kjt(i)

�S1��t+k P

Opt�HTt (i)� �PMCt+k

�o= 0 (B.18)

Nontraded goods sectorA representative �rm in the Home nontraded goods sector sets a price PNTt(i) that max-

imizes its expected discounted future pro�ts while that price remains e¤ective. Formally, itsolves the following problem:

maxPOptNt (i)

1Xk=0

�kPEt

nDt;t+k

��POptNt (i)�MCt+k

�YNt+kjt(i)

�o

63

subject to the demand schedules:

YNt+kjt(i) =

Z �

0

264�PNt(i)PNt

��� �PNtPt

��!Ct+k(j)

+�PNt(i)PNt

��� �PNtPt

��!It+k(j)

375 djor aggregated:

YNt+kjt(i) =

POptNt (i)

PNt

!�� �PNtPt

��!(Ct+k + It+k) (B.19)

The optimality condition can be written as:

1Xk=0

�kPEt

nDt;t+kYNt+kjt(i)

�POptNt (i)� �PMCt+k

�o= 0 (B.20)

B.1.8 Monetary policies

The monetary policy rule of the Home central bank is de�ned as:

1 + it = (1 + it�1)�

�PtPt�1

���(Yt)

�y

!(1��)Rt (B.21)

where � captures the degree of interest-rate smoothing, Rt represents a time-varying,exogenousfactor that may, for example, represent changes in the in�ation target.

Analogously, the monetary policy rule of the Foreign central bank is de�ned as:

1 + i�t = (1 + i�t )��

�P �tP �t�1

����(Y �t )

��y

!(1���)(B.22)

B.2 Aggregation

As all households and �rms are symmetric equations (B.4) to (B.20) can be rewritten inaggregate terms by replacing every variable indexed by j, i, or I with the aggregate, e.g. forconsumption:

R �0 Ct(j)dj = �Cjt � Ct.

By taking into account wage stickiness the wage index Wt =�R �0 Wt(j)

1��dj� 11�� can be

aggregated to:

Wt =

��WW

1��t�1 + (1� �W )

�WOptt

�1��� 11��

(B.23)

Similarly, by taking into account price stickiness equations (B.1) to (B.3) can be aggregatedto:

PHTt =

��P (PHTt�1)

1�� + (1� �P )�POptHTt

�1��� 11��

(B.24)

64

PNt ���PP

1��Nt�1 + (1� �P )

�POptNt

�1��� 11��

(B.25)

and

PFTt � StPAV GFTt (B.26)

where

PAV GFTt =��P�PAV GFTt�1

�1��+ (1� �P )

�POPTFTt

�1��� 11��

(B.27)

andPOPTFTt = S��1t POptFTt (B.28)

Total aggregate demand in the Home economy can be written as:

Yt =1

Pt

�� �PHTt � Y Avg

HTt + PAV G�HTt � Y Avg�

HTt

�+ (1� )

�PNt � Y Avg

Nt

��(B.29)

where

Y AvgHTt =

0BBB@��P (PHTt�1)

1�� + (1� �P )�POptHTt

�1��� 11��

PHTt

1CCCA��

�PHTtPTt

����PTtPt

��!(Ct + It)

Y Avg�HTt =

0BB@��

�P�PAV G�HTt�1

�1��+ (1� �P )

�POPT�HTt

�1��� 11���S�1

P �HTt

1CCA��

�P �HTtP �Tt

����P �TtP �t

��!(C�t + I

�t )

=

�PAV G�HTt S�1

P �HTt

��� �P �HTtP �Tt

����P �TtP �t

��!(C�t + I

�t )

65

Y AvgNt =

0BBB@��PP

1��Nt�1 + (1� �P )

�POptNt

�1��� 11��

PNt

1CCCA��

�PNtPt

��!(Ct + It)

Equity shares in a given country are assumed to be claims on pro�ts and represent abalanced portfolio across all �rms of both the traded and nontraded goods sector in thatcountry. The per period pro�ts of a �rm in the traded goods sector which can reset its pricein period t is:

VHTt(i)| {z }for all i=2�P

= POptHTt(i)YHTt(i) + S1��t POpt�HTt (i)Y

�HTt(i)�

hWtNt(i) + Pt.r

ktKt(i)

i

The pro�ts of a �rm in the traded goods sector that cannot reset its price is:

VHTt(i)| {z }for all i��P

= PHTt�1(i)YHTt(i) + PAV G�HTt�1(i)Y

�HTt(i)�

hWtNt(i) + Pt.r

ktKt(i)

i

where

PAV G�HTt =��P�PAV G�HTt�1

�1��+ (1� �P )

�POPT�HTt

�1��� 11��

The total aggregate pro�ts in the Home economy are:

Vt =

Z �

0

264 VHTt(i)| {z }for all i=2�P

+ VHTt(i)| {z }for all i��P

375 di+ Z 1

264 VNt(i)| {z }for all i=2�P

+ VNt(i)| {z }for all i��P

375 diSimilarly, the aggregate pro�ts in the Foreign country are:

V �t =

Z

�

264 V �FTt(i)| {z }for all i=2�P

+ V �FTt(i)| {z }for all i��P

375 di+

Z 1

264V �Nt(i)| {z } difor all i=2�P

+ V �Nt(i)| {z }for all i��P

375 diwhich can be rewritten as:

Vt = � �PHTt � Y Avg

HTt + PAV G�HTt � Y Avg�

HTt

�+ (1� )

�PNt � Y Avg

Nt

�(B.30)

�hWtNt + Pt.r

ktKt

i

66

whereNt = NHTt +NNt (B.31)

Kt = KHTt +KNt (B.32)

The rewritten aggregate pro�ts in the Foreign country are:

V �t = (1� �) �P �FTtY

Avg�FTt + PAV GFTt Y

AvgFTt

�+ (1� )

�P �NtY

Avg�Nt

�(B.33)

��W �t N

�t + P

�t.r

k�t K

�t

�B.3 Market clearing conditions

Bonds are assumed to be in zero net supply, hence:

BHt = �B�Ht (B.34)

andBFt = �B�Ft (B.35)

The aggregate equity supplies are �xed and given by �Q and �Q�:

�Q = QHt +Q�Ht (B.36)

�Q� = Q�Ft +QFt (B.37)

Goods market clearing conditions imply that the aggregate supplies in the di¤erent sectors(taken account of in the derivation of the optimal factor demands above) are equal to thefollowing aggregate demands (in the Home traded goods, the Foreign traded goods, and thetwo nontraded goods sectors, respectively):

YHTt � � �Y AvgHTt + Y

Avg�HTt

�(B.38)

Y �FTt = (1� �) �Y Avg�FTt + Y Avg

FTt

�(B.39)

YNt = (1� )PNtY AvgNt (B.40)

Y �Nt = (1� )P �NtYAvg�Nt (B.41)

B.4 Steady state

The model is de�ned by equations (B.1) to (B.41) together with, where relevant, the analogousequations for the Foreign country. The model is linearized around a steady state where the netforeign asset position of both countries and in�ation are zero. To ensure a stationary steady

67

state all nominal Home and Foreign variables are scaled by the Home and Foreign CPIs,respectively, and the CPIs and the nominal exchange rate are expressed in �rst di¤erences.

The steady state discount factor for the period t,t+k is �Dt;t+k = �k�( �C)( �C)

����P�P= �k.

The steady state interest rates can be derived from the Euler equation on Home bond holdings

�{ =1� ��

(B.42)

The steady state rental rate of capital can be derived from the investment condition

�rk =

�1� ��

�+ � (B.43)

From the optimal goods price equations the following steady state relation can be derived:�POptHT�P=

�POptN�P= �P

MC�P. From the aggregate goods price relations one can derive

�PN�P=

�POptN�P=

�PHT�P=

�POptHT�P= �P

MC�P. Solving for marginal costs yields:

MC�P=

�PHT�P

�P(B.44)

The steady state Home producers PPI in the Foreign country is�PAvg�HT�P

=�POpt�HT�P

= �PMC�P.

The Foreign consumers� price index of the Home traded good is�P �HT�P �

= 1RER

�PMC�P. The

analogous condition in the Home country is therefore:

�PFT�P= RER�P

MC�

�P �(B.45)

The relative traded goods index can be derived from the de�nition of the CPI:42

�PT�P=

2641� (1� )��PHT�P

�1�!

3751

1�!

(B.46)

The relative traded goods price of the imported good can be derived from the de�nition

of the traded goods price index�PFT�P=

"� �PT�P

�1����� �PHT

�P

�1��(1��)

# 11��

. Solving for the price of

42The analogous condition in the Foreign country is�P�T�P� =

24 1�(1� )�

�P�FT�P�

�1�!

35 11�!

.

68

home traded goods yields:

�PHT�P

=

264��PT�P

�1��� (1� �)

��PFT�P

�1���

3751

1��

(B.47)

The de�nition of marginal costs MC�P=

��W�P

��(�rk)

1��

(1��)1���� can be solved for real wages as follows:

�W�P=

MC�P(1� �)1����

(�rk)1��

! 1�

(B.48)

Optimal wage setting�W�P=

�WOpt

�P= �W

� �N'

�C��, where �N = �NHT + �NN , can be solved for

labor demand as follows:

�NN =

�W�P

��C���

��W

! 1'

� �NHT (B.49)

From the capital accumulation equation one can derive:

�I = � �K (B.50)

where �K = �KHT + �KN and �Y = �YHT + �YN .Factor market clearing conditions in the traded goods sector are:

�NHT =�MC

�P�W�P

� ��Y AvgHT + �Y Avg�

HT

�(B.51)

and�KHT =

(1� �)�rk

MC�P� ��Y AvgHT + �Y Avg�

HT

�(B.52)

Similar conditions in the nontraded goods sector, i.e. �YN = (1� ) �Y AvgN , yield

�KN =(1� �)�rk

MC�P(1� ) �Y Avg

N (B.53)

and

�Y AvgN =

�NN�W�P

(1� )�MC�P

(B.54)

where

�Y AvgHT =

� �PHT�P

���� �PT�P

���! ��C + �

��KHT + �KN

��(B.55)

69

�Y AvgFT =

� �PFT�P

���� �PT�P

���! ��C + �

��KHT + �KN

��(B.56)

�C =�Y AvgN�

�PHT�P

��! � � � �KHT + �KN

�(B.57)

The budget constraint:

�P �C + �PQ �QH + �S �P �Q �QF + �BH + �S �BF

� �W �N +

��PQ +

� �V�Q

���QH + �S

��P �Q +

�V �

�Q�

���QF + (1 +�{) �BH + �S(1 +�{�) �BF + �P �rk �K � �P �I

can be solved for the real exchange rate as follows:

RER =

1� �C � �PHT

�P�Y AvgHT � 1

�

�PHT�P(1� ) �Y Avg

N + 1� �

��KHT + �KN

��P �HT�P ��Y Avg�HT

(B.58)

With the interest rate and the rental rate of capital de�ned exogenously (equations B.42and B.43), a system of 27 equations (equations B.44 and B.57 together with the analogousequations for the foreign country and equation B.58) in the following 27 unknowns can bederived:

�PHT�P;�P �FT�P �;�PT�P;�P �T�P �;�PFT�PT;�P �HT�P �T; RER;

�W�P;�W ��P �; MC

�P; MC

�

�P �; �C; �C�;

�NHT ; �N�FT ;

�NN ; �N�N ;�KHT ; �K

�FT ;

�KN ; �K�N ;�Y AvgHT ; �Y Avg�

FT ; �Y Avg�HT ; �Y Avg

FT ; �Y AvgN ; �Y Avg�

N

This system is solved numerically. Given the solution of the system, aggregate factors, �Nand �K, aggregate outputs, �YHT ; �YFT ; �YN ; �Y , and real pro�ts,

�V�Pcan be de�ned recursively.43,44

Note that the calibration of the asset holdings has to satisfy the net foreign asset condition:

�S �P �Q �QF � �PQ �Q�H + �S �BF � �B�H = 0

43The steady state aggregate pro�ts in real terms are�V�P= �

��PAvgHT

�Y AvgHT + PAVG�HT Y AVG�

HT

�+�(1� ) �Y Avg

N �h�W�P�N + �rk �K

i. Steady state Home equity prices in real terms can be derived from the Euler equation on

Home equity holdings:�PQ�P= �

(1��)

��V�P�Q

�. The total stock market capitalization can be written as:

�PQ �Q�P �Y

=

�(1��)

��V�P�Y

�.

44Note that in a symmetric steady state where � = 0:5 all prices in the Home and Foreign country areequal and �S = 1 the following variables (or ratios) can derived analytically: MC

�P= 1

�P(where �P = �

��1 ),

�K�Y= (1��)�

1���

�+�

1�P,�N�Y=

�(1��)�1���

�+�

1�P

���1�

,�W�P=

� 1�P0@ (1��)

( 1��� )+�1�P

1A��1�

,�C�Y= 1� �

�(1��)�1���

�+�

1�P

�

70

which can be reexpressed in real terms as: RER�P �Q�P �

�QF�Y �

�Y ��Y�

�PQ�P

�Q�H�Y+RER

�BF�P � �Y �

�Y ��Y�

�B�H�P �Y= 0,

as well as the market clearing conditions, i.e.�BH�P �Y= �

�B�H�P �Y

and�PQ�P

�QH�Y=

�PQ�P

�Q�Y�

�PQ�P

�Q�H�Y, and

�P �Q�P �

�Q�F�Y �=

�P �Q�Q�

�P � �Y ��

�P �Q�P �

�QF�Y �. Thus, if

�PQ �QF�P �Y

;�PQ �Q

�H

�P �Yand

�BF�P � �Y �

are calibrated the following assetholdings are residually determined as

�B�H�P �Y

= RER�P �Q�P �

�QF�Y �

�Y �

�Y��PQ�P

�Q�H�Y+RER

�BF�P � �Y �

�Y �

�Y

�BH�P �Y

= ��B�H�P �Y

�B�F�P � �Y �

= ��BF�P � �Y �

�PQ�P

�QH�Y=�PQ�P

�Q�Y��PQ�P

�Q�H�Y

�P �Q�P �

�Q�F�Y �

=�P �Q�Q�

�P � �Y ���P �Q�P �

�QF�Y �

B.5 Linearized model

The model is solved by linearizing the stationary versions of equations (B.1) to (B.41) togetherwith, where relevant, the analogous equations for the Foreign country around the symmetricsteady state outlined above. The variables of the linearized system are expressed in percentage(or log-) deviations from the steady state.45

Stationarizing and linearizing equations (B.1) to (B.41) and the relevant Foreign equationsyields a system of 52 equations (equations B.59 to B.110 below) in 52 unknown variables: pQt, p�Qt ,qFt , q

�Ht; ct , c

�t ; bFt , b

�Ht; crert; wt , w�t ; It , I�t ; kt; , k�t ; pHTt , p�FTt; �t , ��; p�HTt ,

pFTt; pTt , p�Tt; c�st; cmct , cmc�t ; nNt , n�Nt; nHTt , n�FTt; rkt , rk�t ; kHTt , k�FTt; vt , v�t ; nt , n�t ; kNt, k�Nt; yt , y

�t ; bHt , b

�Ft; qHt , q

�Ft; yHTt , y

�FTt; yNt , y

�Nt;bit , bi�t . The following paragraphs list

the whole system with all non-linearized and linearized equations.

45Thus, for a variable x: x � X� �X�X

� dX�X� lnX � ln �X. All prices and wages are expressed in relation to

the CPI, e.g. pQt �PQtPt

��PQ�P

�PQ�P

�dPQtPt�PQ�P

� ln�PQtPt

�� ln

��PQ�P

�. Asset holdings are expressed in relation to real

GDP, e.g. QHt � QHt� �QH�Y

� dQHt�Y. In�ation is de�ned as �t � Pt

Pt�1and �t � ln

�PtPt�1

�.

71

Aggregate Euler equationsThe linearized version of:

PQtPt

+ QH

�PQ�Y Pt

(QHt+1 �QHt)!

= �

�(Ct+1)

(Ct)

��� PtPt+1

0BB@ QH

�PQ

�Y Pt(QHt+2 �QHt+1)�

QH

�PQ

�Y Pt

�QHt+1 � �QH

�+

PQt+1Pt+1

Pt+1Pt

+

Vt+1Pt+1

Pt+1Pt

�Q

!!1CCA

is:

QH

�QHt+1 � QHt

�(B.59)

= � (ct � Et fct+1g) + � QH

�Et

nQHt+2

o� QHt+1

�� QH QHt+1 + Et fpQt+1g

!+(1� �)Et fvt+1g � pQt

The linearized version of:

P �QtP �t

+ QF�S �P �Q

�Y �P �t St(QFt+1 �QFt)

!

= �

�(Ct+1)

(Ct)

��� PtPt+1

0BBB@ QF

�S �P �Q�Y �P �t St

(QFt+2 �QFt+1)� QH

�S �P �Q�Y �P �t St

�QFt+1 � �QF

�+

0@St+1St

0@P �Qt+1P �t+1

P �t+1P �t

+

0@ V �t+1P�t+1

P�t+1P�t

�Q�

1A1A1A1CCCA

is:

QF

�QFt+1 � QFt

�(B.60)

= � (ct � Et fct+1g)� Et f�t+1g

+�� QF

�Et

nQFt+2

o� QFt+1

�� QH

�QFt+1

�+ Et

�p�Qt+1

�+Et

���t+1

+ Et

nc�st+1o+ (1� �)Et �v�t+1� p�QtThe linearized version of:

72

1 +

BH

�P

�Y

�BHt+1Pt

� BHtPt

�1

Pt

!

= Et

8<:��(Ct+1)

(Ct)

��� PtPt+1

0@ BH

�P

�Y

�BHt+2Pt+1

� BHt+1Pt+1

��1

Pt+1

�� BH

�P�Y

�BHt+1Pt+1

� �BH�P

�1

Pt+1

+(1 + it+1)

1A9=;is:

BH

�Et

nbHt+1

o� bHt

�(B.61)

= � (ct � Et fct+1g)� Et f�t+1g+ �

0@ BHEt

nbHt+2 � bHt+1

o� BHEt

nbHt+1

o 1A+Et f{t+1g

The linearized version of:

1 +

BF

�P � �S

�Y �St

�BFt+1P �t

� BFtPt

�1

P �t

!

= Et

8>>><>>>:��(Ct+1)

(Ct)

��� PtPt+1

0BBB@ BF

�P � �S

�Y �St

�BFt+2P �t+1

� BFt+1P �t+1

��1

P �t+1

�� BF

�P � �S

�Y �St

�BFt+1P �t+1

� �BF�P �

�1

P �t+1

+St+1St(1 + i�t )

1CCCA9>>>=>>>;

is:

BF

�Et

nbFt+1

o� bFt

�(B.62)

= � (ct � Et fct+1g)� Et f�t+1g+ �

0@ BFEt

nbFt+2 � bFt+1

o� BFEt

nbFt+1

o 1A+Et

nc�st+1o+ Et �{�t+1The analogous Foreign Euler equations in linearized terms are:

�QH

�Q�Ht+1 � Q�Ht

�(B.63)

= ��c�t � Et

�c�t+1

�� Et

���t+1

+�� �QH

�Et

nQ�Ht+2

o� Q�Ht+1

�� Q�H

�Q�Ht+1

�+ Et fpQt+1g

�+Et f�t+1g � Et

nc�st+1o+ (1� �)Et fvt+1g � pQt73

�QF

�Q�Ft+1 � Q�Ft

�(B.64)

= ��c�t � Et

�c�t+1

�+ �

0@ �QF

�Et

nQ�Ft+2

o� Q�Ft+1

�� �QF Q

�Ft+1 + Et

np�Qt+1

o 1A+(1� �)Et

�v�t+1

� p�Qt

�BH

�Et

nb�Ht+1

o� b�Ht

�(B.65)

= ��c�t � Et

�c�t+1

�� Et

���t+1

+ �

0@ �BHEt

nb�Ht+2 � b�Ht+1

o� B�HEt

nb�Ht+1

o 1A�Et

nc�st+1o+ Et f{t+1g �BF

�Et

nb�Ft+1

o� b�Ft

�(B.66)

= ��c�t � Et

�c�t+1

�� Et

���t+1

+ �

0@ �BFEt

nb�Ft+2 � b�Ft+1

o� �BFEt

nb�Ft+1

o 1A+Et

�{�t+1

Aggregate Home consumer�s budget constraintThe linearized version of:

74

Ct

+PQtPt

QHt+1 + QH

2

�PQ (QHt+1 �QHt)2

Pt �Y+ QH2

�PQ�QHt � �QH

�2Pt �Y

+StP

�t

Pt

P �QtP �t

QFt+1 + QF

2

�S �P �Q (QFt+1 �QFt)2

Pt �Y+ QF2

�S �P �Q�QFt � �QF

�2Pt �Y

+BHt+1Pt

+ BH

2

�P�BHt+1Pt

� BHtPt

�2Pt �Y

+ BH2

�P�BHtPt� �BH

�P

�2Pt �Y

+StP

�t

Pt

BFt+1P �t

+ BF

2

�S �P ��BFt+1P �t

� BFtP �t

�2Pt �Y

+ BF2

�S �P ��BFtP �t

� �BF�P �

�2Pt �Y

=Wt

PtNt +

PQtPt

+

VtPt�Q

!!QHt +

StP�t

Pt

0@P �QtP �t

+

0@ V �tP �t�Q�

1A1AQFt

+(1 + it)BHtPt

+StP

�t

Pt(1 + i�t )

BFtP �t

+hrktKt. � It.

i+ T t

is:

�Cct (B.67)

+�PQ�P

�QH�Y�Y pQt +

�PQ�P�Y qHt+1

+SP �

P

�P �Q�P �

�QF�Y ��Y �crert + SP �

P

�P �Q�P �

�QF�Y ��Y �p�Qt +

SP �

P

�P �Q�P ��Y �QFt+1

+�Y bHt+1 +�BF�P � �Y �

�Y �SP �

Pcrert + SP �

P�Y �bFt+1

=�W�P�Nwt +

�W�P�Nnt +

�PQ�P

�QH�Y�Y pQt +

�(1� �)�

� �PQ�P

�QH�Y�Y vt +

1

�

�PQ�P�Y QHt

+1

�

SP �

P

�P �Q�P �

�QF�Y ��Y �crert + SP �

P

�P �Q�P �

�QF�Y ��Y �p�Qt

+

�(1� �)�

�SP �

P

�P �Q�P �

�QF�Y ��Y �v�t +

1

�

SP �

P

�P �Q�P ��Y �QFt

+1

�

�BH�P �Y

�Y {t +1

��Y bHt +

1

�

SP �

P

�BF�P � �Y �

�Y �crert + 1

�

SP �

P

�BF�P � �Y �

�Y �{�t +1

�

SP �

P�Y �bFt

+�rk �Krkt + �rk �Kkt � �IIt.

75

Wage dynamicsEquations:

Et

1Xk=0

(��W )k

"Nt+kjt(j)

�Ct+kjt(j)

��� "WOptt

Pt+k� �W

��Nt+kjt(j)

�'�Ct+kjt(j)

���##= 0

and: �Wt

Pt

�1��=

0@�W Wt�1Pt�1

1PtPt�1

!1��+ (1� �W )

WOptt

Pt

!1��1Acan be linearized and combined to:

wt ��

�W

1 + � (�W )2

�wt�1 �

��W

1 + � (�W )2

��t (B.68)

+

���W

1 + � (�W )2

�Et fwt+1 + �t+1g+

(1� �W ) (1� ��W )1 + � (�W )

2 f'nt + �ctg

w�t ��

�W

1 + � (�W )2

�w�t�1 �

��W

1 + � (�W )2

���t (B.69)

+

���W

1 + � (�W )2

�Et�w�t+1 + �

�t+1

+(1� �W ) (1� ��W )

1 + � (�W )2 f'n�t + �c�t g

Capital accumulationThe linearized version of:

Kt+1 = (1� �)Kt + It ��

2

(Kt+1 �Kt)2

Kt

is:kt+1 � (1� �) kt + �It (B.70)

and, analogously:k�t+1 � (1� �) k�t + �I�t (B.71)

Optimal investmentThe linearized version of: �

1 + �(Kt+1 �Kt)

Kt

�= �Et

(�(Ct+1)

(Ct)

��� �(1� �) + rkt+1 +

�

2

�K2t+2 �K2

t+1

K2t+1

��)

76

is:��kt+1 � kt

�� Et

n� (ct � ct+1) + ��rkrkt+1 + ��

�kt+2 � kt+1

�o(B.72)

and, analogously:

��k�t+1 � k�t

�� Et

n��c�t � c�t+1

�+ ��rkrk�t+1 + ��

�k�t+2 � k�t+1

�o(B.73)

Price dynamicsCombining the linearized version of:

1Xk=0

�kPEt

(�k�(Ct+k)

(Ct)

��� PtPt+k

YHTt+kjt

POptHTt

Pt� �P

MCt+kPt+k

Pt+kPt

!)= 0

1Xk=0

�kPEt

8><>:�k�(Ct+k)(Ct)

���PtPt+k

Y �HTt+kjt��St�1St

�1�� �S1��t POpt�HTtPt

�� �P

�St+kSt�1

���1 MCt+kPt+k

Pt+kPt)

�9>=>; = 0

1Xk=0

�kPEt

(�k�(Ct+k)

(Ct)

��� PtPt+k

YNt+kjt

POptNt

Pt� �P

MCt+kPt+k

Pt+kPt

)

!)= 0

�PHTtPt

�1��=

0@�P PHTt�1Pt�1

1PtPt�1

!1��+ (1� �P )

POptHTt

Pt

!1��1A�PAV G�HTt

Pt

�1��=

0@�P PAV G�HTt

Pt�1

1PtPt�1

!1��+ (1� �P )

S1��t POpt�HTt

Pt

!1��1AP �HTtP �t

=

1

StP �tPt

!PAV G�HTt

Pt�PNtPt

�1��=

0@�P PNt�1Pt�1

1PtPt�1

!1��+ (1� �P )

POptNt

Pt

!1��1A�PTtPt

�1��=

"�

�PHTtPt

�1��+ (1� �)

�PFTtPt

�1��#

1 =

"

�PTtPt

�1�!+ (1� )

�PNtPt

�1�!#and the analogous Foreign equations yields a system of the following eight price equations:46

46Note that the domestic traded goods price and the nontraded goods price are equivalent. Thus, thenontraded goods price will bedropped in the �nal system

77

Domestic traded goods price index

pHTt ��

�P

1 + � (�P )2

�pHTt�1 �

��P

1 + � (�P )2

��t (B.74)

+�

��P

1 + � (�P )2

�Et fpHTt+1 + �t+1g+

(1� �P ) (1� �P�)�1 + � (�P )

2� cmct

p�FTt ��

�P

1 + � (�P )2

�p�FTt�1 �

��P

1 + � (�P )2

���t (B.75)

+�

��P

1 + � (�P )2

�Et�p�FTt+1 + �

�t+1

+(1� �P ) (1� �P�)�

1 + � (�P )2� cmc�t

Domestic traded goods price index in the other countryThe domestic traded goods price index in the other country can be solved for in�ation:

�t � dp�HTt�1 + crert�1 � 1 + � (�P )2�P

!�dp�HTt + crert� (B.76)

+�Et

n dp�HTt+1 + crert+1 � (1� �P ) (1� �) c�st+1 + �t+1o+(1� �P ) (1� �P�)

�Pcmct

��t � dpFTt�1 � crert�1 � 1 + � (�P )2�P

!(dpFTt � crert) (B.77)

+�Et

n dpFTt+1 � crert+1 + (1� �P ) (1� �) c�st+1 + ��t+1o+(1� �P ) (1� �P�)

�Pcmc�t

Traded goods price indexThe traded goods price index can be solved for the other country�s traded goods price index:

pFTt �1

(1� �) �PFT�P

1� �PT�P

�!1�� pTt �

�

�PHT�P

1� �PT�P

�!1��

(1� �) �PFT�P

1� �PT�P

�!1�� pHTt (B.78)

78

p�HTt �1

�

0@ �P �HT�P �

1��P�T�P�

�1A1��

p�Tt �

(1� �)

0@ �P �FT�P �

1��P�T�P�

�1A1��

�

0@ �P �HT�P �

1��P�T�P�

�1A1��

p�FTt (B.79)

Consumer price indexThe consumer price index can be solved for the traded goods price index:

pTt �( � 1)

�PHT�P�PT�P

!1�!pHTt (B.80)

p�Tt �( � 1)

0@ �P �FT�P ��P �T�P �

1A1�! p�FTt (B.81)

Change in nominal exchange rateThe linearized version of a rewritten de�nition of the change in the nominal exchange rate:

StSt�1

=

�StP

�t

Pt

��Pt�1

St�1P �t�1

��PtPt�1

��P �t�1P �t

�yields:

c�st � crert � crert�1 + �t � ��t (B.82)

Marginal costsThe linearized version of:

MCtPt

=

�WtPt

�� �rkt�1��

(1� �)1����Atis:

cmct = �wt + (1� �) rkt � at (B.83)

and, analogously:

cmc�t = �w�t + (1� �) rk�t � a�t (B.84)

79

Labor market clearingThe linearized version of:

NHTt =�MCt

PtWtPt

YHTt

NNt =�MCt

PtWtPt

YNt

is:

nNt � (cmct + yNt � wt) (B.85)

and, analogously:n�Nt � (cmc�t + y�Nt � w�t ) (B.86)

as well as:

nHTt � (cmct + yHTt � wt) (B.87)

andn�FTt � (cmc�t + y�FTt � w�t ) (B.88)

Capital market clearingThe linearized version of:

KHTt =(1� �)rkt

MCtPt

YHTt

KNt =(1� �)rkt

MCtPt

YNt

is:kNt �

�cmct + yNt � rkt � (B.89)

and, analogously:

k�Nt ��cmc�t + y�Nt � rk�t � (B.90)

as well as:

kHTt ��cmct + yHTt � rkt � (B.91)

and:k�FTt �

�cmc�t + y�FTt � rk�t � (B.92)

Aggregate laborThe linearized version of:

Nt = NHTt +NNt

is:

80

nt ��NHT

�NnHTt +

�NN

�NnNt (B.93)

and, analogously:

n�t ��N�HT�N� n

�FTt +

�N�N�N� n

�Nt (B.94)

Aggregate capitalThe linearized version of:

Kt = KHTt +KNt

is:

kt ��KHT

�KkHTt +

�KN

�KkNt (B.95)

and, analogously:

k�t ��K�FT�K� k

�FTt +

�K�N�K� k

�Nt (B.96)

Aggregate outputThe linearized version of:

Yt = �

0B@�PHTtPt

�1�� �PTtPt

���!(Ct + It)

+�StP �tPt

��P �HTtP �t

�1�� �P �TtP �t

���!(C�t + I

�t )

1CA+(1� )

�PNtPt

�1�!(Ct + It)

!

is:

yt �

0BBBBBBBBBBBB@�

0BBBBBBBBBBBB@

� �PHT�P

�1��� �PT�P

���!( �C+�I)

�Y (1� �)pHTt + (�� !) pTt+

�C

( �C+�I)ct +

�I

( �C+�I)It

!

+

�SP�P

�� �P�HT�P�

�1��� �P�T�P�

���!( �C�+�I�)

�Y crert + (1� �)p�HTt + (�� !) p�Tt+

�C�

( �C�+�I�)c�t +

�I�

( �C�+�I�)I�t

!

1CCCCCCCCCCCCA

1CCCCCCCCCCCCA(B.97)

+

0B@0B@(1� )

��PHT�P

�1�! ��C + �I

��Y

1CA (1� !) pHTt + �C��C + �I

� ct + �I��C + �I

� It!1CA

81

and, analogously:

y�t �

0BBBBBBBBBBBB@(1� �)

0BBBBBBBBBBBB@

��P�FT�P�

�1��� �P�T�P�

���!( �C�+�I�)

�Y � (1� �) p�FTt + (�� !) p�Tt+

�C�

( �C�+�I�)c�t +

�I�

( �C�+�I�)I�t

!

+

�SP�P

��1� �PFT�P

�1��� �PT�P

���!( �C+�I)

�Y � �crert + (1� �) pFTt + (�� !) pTt

+�C

( �C+�I)ct +

�I

( �C+�I)It

!

1CCCCCCCCCCCCA

1CCCCCCCCCCCCA(B.98)

+

0B@0B@(1� )

��P �FT�P �

�1�! ��C� + �I�

��Y �

1CA (1� !) p�FTt + �C���C� + �I�

� c�t + �I���C� + �I�

� I�t!1CA

Aggregate pro�tsThe linearized version of:

VtPt

= �

0B@�PHTtPt

�1�� �PTtPt

���!(Ct + It)

+StP �tPt

�P �HTtP �t

�1�� �P �TtP �t

���!(C�t + I

�t )

1CA+(1� )

�PNtPt

�1�!(Ct + It)

!��Wt

PtNt + r

ktKt

�is:

vt = �

0BBBBBBBBB@

� �PHT�P

�1��� �PT�P

���!( �C+�I)

�V�P

(1� �) pHTt + (�� !) pTt+

�C

( �C+�I)ct +

�I

( �C+�I)It

!

+

�SP�P

�� �P�HT�P�

�1��� �P�T�P�

���!( �C�+�I�)

�V�P crert + (1� �) p�HTt + (�� !) p�Tt

+�C�

( �C�+�I�)c�t +

�I�

( �C�+�I�)I�t

!

1CCCCCCCCCA(B.99)

+(1� )

��PHT�P

�1�! ��C + �I

��V�P

(1� !) pHTt

+�C

( �C+�I)ct +

�I

( �C+�I)It

!

��W�P�N

�V�P

(wt + nt)��rk �K�V�P

�rkt + kt

�

82

and, analogously:

v�t = (1� �)

0BBBBBBBBB@

��P�FT�P�

�1��� �P�T�P�

���!( �C�+�I�)

�V ��P�

(1� �) p�FTt + (�� !) p�Tt+

�C�

( �C�+�I�)c�t +

�I�

( �C�+�I�)I�t

!

+

1

SP�P

!� �PFT�P

�1��� �PT�P

���!( �C+�I)

�V ��P��

�crert + (1� �) pFTt + (�� !) pTt + �C

( �C+�I)ct +

�I

( �C+�I)It

�

1CCCCCCCCCA(B.100)

+(1� )

��P �FT�P �

�1�! ��C� + �I�

��V ��P �

(1� !) p�FTt +

�C���C� + �I�

� c�t + �I���C� + �I�

� I�t!

��W ��P ��N�

�V ��P �

(w�t + n�t )�

�rk� �K�

�V ��P �

�rk�t + k�t

�Asset market clearingsThe linearized versions of:

BHtPt �Y

= �B�Ht

Pt �Y

BFt = �B�Ft

�Q = QHt +Q�Ht

�Q� = Q�Ft +QFt

are:bHt = �b�Ht (B.101)

bFt = �b�Ft (B.102)

qHt � �q�Ht (B.103)

qFt � �q�Ft (B.104)

Goods market clearingsThe linearized versions of:

YHTt = �

0B@�PHTtPt

��� �PTtPt

���!(Ct + It)

+�P �HTtP �t

��� �P �TtP �t

���!(C�t + I

�t )

1CA

83

Y �FT = (1� �)

0B@�PFTtPt

��� �PTtPt

���!(Ct + It)

+�P �FTtP �t

��� �P �TtP �t

���!(C�t + I

�t )

1CAYNt = �(1� )

1

�

�PNtPt

��!(Ct + It)

!are:

yHTt (B.105)

= �

0BBBBB@� �PHT

�P

���� �PT�P

���!( �C+�I)

�YHT

(��) pHTt + (�� !) pTt+

�C

( �C+�I)ct +

�I

( �C+�I)It

!

+

��P�HT�P�

���� �P�T�P�

���!( �C�+�I�)

�YHT

(��) p�HTt + (�� !) p�Tt+

�C�

( �C�+�I�)c�t +

�I�

( �C�+�I�)I�t

!1CCCCCA

y�FTt (B.106)

= (1� �)

0BBBBB@�

�P�FT�P�

���� �P�T�P�

���!( �C�+�I�)

�Y �FT

(��) p�FTt + (�� !) p�Tt+

�C�

( �C�+�I�)c�t +

�I�

( �C�+�I�)I�t

!

+

� �PFT�P

���� �PT�P

���!( �C+�I)

�Y �FT

(��) pFTt + (�� !) pTt+

�C

( �C+�I)ct +

�I

( �C+�I)It

!1CCCCCA

yNt � (�!) pHTt +�C�

�C + �I� ct + �I�

�C + �I� It (B.107)

and, analogously:

y�Nt � (�!) p�FTt +�C��

�C� + �I�� c�t + �I��

�C� + �I�� I�t (B.108)

Taylor rulesThe linearized versions of:

1 + it = (1 + it�1)�

�PtPt�1

���(Yt)

�y

!(1��)Rt

1 + i�t = (1 + i�t )��

�P �tP �t�1

����(Y �t )

��y

!(1���)are:

{t � �{t�1 + (1� �)����t + �yyt

�+ rt (B.109)

84

{�t � ��{�t�1 + (1� ��)�����t + ��yy�t (B.110)

B.6 Additional variables

The current account is de�ned as:

CAt = BHt+1 �BHt + St (BFt+1 �BFt)+PQt (QHt+1 �QHt) + StP �Qt (QFt+1 �QFt)

Using the asset market clearing conditions the current account can also be written as thesum of the trade balance and net asset income:

CAt = Sti�tBFt � itB�Ht + St

�V �t�Q�

�QFt �

�Vt�Q

�Q�Ht| {z }

Net asset income

+Vt +WtNt + PtrktKt.| {z }

PtYt

� PtIt. � PtCt

| {z }Trade balance

The net foreign asset position of the Home country (at the end of period t) is:

NFAt+1 = StBFt+1 �B�Ht+1 + StP �QtQFt+1 � PQtQ�Ht+1

The dynamics in the net foreign asset position are:

NFAt+1 �NFAt = StBFt+1 �B�Ht+1 + StP �QtQFt+1 � PQtQ�Ht+1��St�1BFt �B�Ht + St�1P �Qt�1QFt � PQt�1Q�Ht

�Using the asset market clearing conditions this can also be written as the sum of the

current account, changes in local currency asset prices, and exchange rate valuation e¤ects(note that the asset position that Home consumers accumulate today (until the end of theperiod), depends on today�s current account and the valuation changes to last period (andtherefore price changes with respect to last period):

NFAt+1 �NFAt = CAt

�(PQt � PQt�1)Q�Ht +�P �Qt � P �Qt�1

�St�1QFt| {z }

Changes in local currency asset prices

+(St � St�1)BFt + (St � St�1)P �QtQFt| {z }Exchange rate valuation

If the linearized version of the current account, the net foreign asset positions and their

subcomponents are de�ned in terms of a stationary variable such as output, i.e. bcat � dCAtPt�Y,

85

dnait � dNAItPt�Y, btbt � d

TBtPt�Y, dnfat+1 � d

�NFAt+1

Pt

��Y

, d�nfat+1 � d�NFAt+1

Pt�NFAt�1

Pt�1

��Y

, dclcapt �dCLCAPt

Pt�Y

, and bevt � dEVtPt�Y, then they can be derived as:

bcat � bHt+1 � bHt +RER�Y �

�Y

�bFt+1 � bFt

�+�PQ�P

�QHt+1 � QHt

�+�P �Q�P �RER

�Y �

�Y

�QFt+1 � QFt

�and dnait � bcat � btbtwhere47

btbt = �

0BBB@�SP�P

�� �P�HT�P�

�1��� �P�T�P�

���!( �C�+�I�)

�Y crert + (1� �)p�HTt + (�� !) p�Tt+

�C�

( �C�+�I�)c�t +

�I�

( �C�+�I�)I�t

!1CCCA

�(1� �)

0BBB@�SP�P

��1� �PFT�P

�1��� �PT�P

���!( �C+�I)

�Y �crert + (1� �) pFTt + (�� !) pTt

+�C

( �C+�I)ct +

�I

( �C+�I)It

!1CCCA

and

dnfat+1 ��BF�P � �Y �

RER�Y �

�Ycrert +RER �Y ��Y bFt+1 � b�Ht+1

+�P �Q�P �

�QF�Y �RER

�Y �

�Ycrert + �P �Q

�P �

�QF�Y �RER

�Y �

�Yp�Qt +

�P �Q�P �RER

�Y �

�YQFt+1

��PQ�P

�Q�H�YpQt �

�PQ�PQ�Ht+1

and d�nfat+1 � dnfat+1 �dnfat47Note that the log-linearized version of real exports in terms of Home currency isdexpt = crert+(1� �) p�HTt+

(�� !) p�Tt+�C�

( �C�+�I�)c�t +

�I�

( �C�+�I�)I�t ; while the log-linearized version of real imports in terms of Home currency

is dimpt = (1� �) pFTt + (�� !) pTt + �C

( �C+�I)ct +

�I

( �C+�I)I.

86

or

d�nfat+1 � RER�Y �

�YbFt+1 �RER

�Y �

�YbFt + bHt+1 � bHt| {z }

CA...

+�P �Q�P �RER

�Y �

�YQFt+1 �

�P �Q�P �RER

�Y �

�YQFt �

�PQ�PQ�Ht+1 +

�PQ�PQ�Ht| {z }

...CA

+RER�Y �

�Y

�BF�P � �Y �

�c�st � b�t + b��t�+RER �Y ��Y �P �Q�P �

�QF�Y �c�st| {z }

EV

+RER�Y �

�Y

�P �Q�P �

�QF�Y �crert �RER �Y ��Y �P �Q

�P �

�QF�Y �crert�1 �RER �Y ��Y �P �Q

�P �

�QF�Y �c�st| {z }

�LCAP...

+RER�Y �

�Y

�P �Q�P �

�QF�Y �p�Qt �RER

�Y �

�Y

�P �Q�P �

�QF�Y �p�Qt�1 �

�PQ�P

�Q�H�YpQt +

�PQ�P

�Q�H�YpQt�1| {z }

...�LCAP

where

dclcapt � ��PQ�P

�Q�H�YpQt +

�PQ�P

�Q�H�YpQt�1

+�P �Q�P �

�QF�Y �RER

�Y �

�Ycp�Qt � �P �Q

�P �

�QF�Y �RER

�Y �

�Yc�st + �P �Q

�P �

�QF�Y �RER

�Y �

�Ycrert

��P �Q�P �

�QF�Y �RER

�Y �

�Ycrert�1 � �P �Q

�P �

�QF�Y �RER

�Y �

�Ycp�Qt�1

and

bevt � �BF�P � �Y �

RER�Y �

�Yc�st � �BF

�P � �Y �RER

�Y �

�Yb�t + �BF

�P � �Y �RER

�Y �

�Yb��t + �P �Q

�P �

�QF�Y �RER

�Y �

�Yc�st

87