the global economy model (gem): theoretical framework€¦ · the global economy model (gem):...
TRANSCRIPT
The Global Economy Model (GEM):Theoretical Framework�
Paolo PesentiFederal Reserve Bank of New York, NBER and CEPR
This draft: January 2008
�The views expressed here are those of the author, and do not necessarily re�ect the positionof the International Monetary Fund, the Federal Reserve Bank of New York, the Federal ReserveSystem, or any other institution with which the author is a¢ liated.
Contents
1 Introduction 2
2 Peeking inside the box: model structure and basic notation 2
3 General considerations 33.1 Country size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3.1.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33.2 Growth trend . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.2.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43.3 Prices and in�ation rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.3.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43.4 Notational conventions and other formal aspects . . . . . . . . . . . . . . . . 5
4 The domestic macroeconomy in partial equilibrium 54.1 Final goods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
4.1.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64.2 Demand for intermediate goods . . . . . . . . . . . . . . . . . . . . . . . . . . 7
4.2.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84.3 Supply of intermediate goods . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
4.3.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94.4 Price setting in the nontradables sector . . . . . . . . . . . . . . . . . . . . . 11
4.4.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124.5 Price setting in the tradables sector . . . . . . . . . . . . . . . . . . . . . . . 134.6 Consumer preferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.6.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154.7 Budget constraint (forward-looking households) . . . . . . . . . . . . . . . . 15
4.7.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174.8 Consumer optimization (forward-looking households) . . . . . . . . . . . . . . 17
4.8.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194.9 Consumer optimization (liquidity-constrained households) . . . . . . . . . . . 20
4.9.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204.10 Fiscal policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.10.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.11 Monetary policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.11.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234.12 Market clearing in the domestic economy . . . . . . . . . . . . . . . . . . . . 23
5 World interdependencies in general equilibrium 245.1 Demand for imports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
5.1.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265.2 Price setting in the tradables sector and exchange rate pass-through . . . . . 26
5.2.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275.3 Market clearing in the world economy . . . . . . . . . . . . . . . . . . . . . . 285.4 Measuring output and trade balance . . . . . . . . . . . . . . . . . . . . . . . 29
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1 Introduction
This paper has two purposes. First, it provides a thorough exposition of the theoreticalframework underlying the Global Economy Model (GEM), as the model stands aroundearly 2008. Second, it discusses a number of variants and alternative features considered inthe GEM-related literature since Laxton and Pesenti (2003). For an updated survey of GEMand other DSGE applications at the IMF the reader is referred to Botman et al (2007).In what follows, each section starts with a formal description of the relevant equations,
and is followed by a presentation of modeling variants and options. When appropriate, thesection provides a more detailed discussion of how the building blocks of GEM relate to theliterature. It is worth emphasizing from the very beginning that the paper is meant to beused as a technical reference on GEM and related models, with apologies for the somewhatpedantic attention to details and formulas that stems directly from this premise.The paper is organized as follows. Section 2 provides an intuitive presentation of the
structure of the model and introduces the reader to its basic notation. Section 3 discussesgeneral elements and formal aspects of GEM. Section 4 describes the country-speci�c build-ing blocks of GEM, treating as exogenous the variables related to international trade in prod-ucts and assets (a partial-equilibrium approach suitable to modeling small open economies).Section 5 introduces international interdependencies and considers the full-�edged general-equilibrium version of the model. Consistent with the open nature of GEM as well as thepurpose of this contribution, there is no conclusion.
2 Peeking inside the box: model structure and basicnotation
Building on recent theoretical developments in international �nance and monetary eco-nomics, especially the �New Open-Economy Macroeconomics� literature since the seminalcontributions of Maurice Obstfeld and Kenneth Rogo¤ (1995, 2000, 2002), GEM aims toprovide an optimizing intertemporal framework capable of addressing basic policy questionsinvolving international transmission of policy and structural shocks, while reproducing keyelements of macroeconomic interdependence among countries and regional blocs.Like other recent dynamic, stochastic, general-equilibrium (DSGE) models, the design
of GEM combines the long-run properties of real business cycle models with short-run�Keynesian�dynamics stemming from nominal rigidities and inertia in the in�ation process.While obviously indebted to the classic Mundell-Fleming-Dornbusch tradition, GEM buildson explicit microfoundations allowing for a tightly integrated treatment of positive elementsand welfare considerations.A useful way to approaching GEM is by familiarizing with its broad characteristics and
notation with the help of a visual representation. Figure 1 illustrates the key macroeconomicvariables in a representative country.Consider �rst the households sector. Each household consumes a �nal good (C in Figure
1), and supplies labor (`) to all domestic �rms. Some households do not have access to capitalmarkets. They �nance their consumption exclusively through disposable labor incomes. Theremaining households own the portfolio of domestic �rms and the domestic capital stock(K), which they rent to domestic �rms. They also buy and sell two bonds: a domestic bonddenominated in domestic currency, and an international bond issued in zero net supplyworldwide. When households sell or purchase the international bond they pay a premium
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to �nancial intermediaries, whose size is a function of the aggregate net asset position of thecountry. Labor and physical capital are immobile internationally. The market for capital iscompetitive, and capital accumulation is subject to adjustment costs. In the labor marketwage contracts are subject to nominal rigidities.On the production side, �rms produce the �nal goods, an array of di¤erentiated inter-
mediate goods, and provide intermediation services.In each country there are two �nal goods � a consumption good (A) and an investment
good (E) � produced by perfectly competitive �rms. The consumption good is consumedeither by domestic households or by the government (GC). Similarly, demand for the in-vestment good is split between private agents (I) and the public sector (GI). Final goodsare produced by using all available intermediate goods as inputs.There are many varieties of intermediate goods, each produced by a single �rm under
conditions of monopolistic competition. Each intermediate good is produced by using do-mestic labor inputs and domestic capital. Intermediate goods are either nontraded (N) ortraded internationally (T ). The nontraded intermediate goods can be purchased by thegovernment (GN ) or used in the production of the �nal goods (NN ). Domestic tradablesused by domestic �rms are denoted Q, imports from all other country blocs are denoted M .Imports are subject to short-term adjustment costs that temporarily lower the response ofdemand to changes in relative prices. Prices of intermediate goods are subject to adjustmentcosts (nominal price rigidities).Finally, the government purchases the two national �nal goods, as well as nontradable
services. As treasury, the government �nances its expenditures with net taxes on the do-mestic private sector. As central bank, the government manages the national short-termnominal interest rate. Monetary policy is speci�ed in terms of a credible commitment toguarantee price stability by managing the domestic nominal short-term interest rate.
3 General considerations
3.1 Country size
The world economy consists of a set N of regional blocs (�countries�). The size of the worldeconomy is normalized to one. The size of each country H is denoted sH , with 0 < sH < 1
andPH s
H = 1 for H 2 N . The country size measures the world share of private agentswho are resident in the country: both households and �rms in country H are de�ned overa continuum of mass sH .
3.1.1 Discussion
For applications focused on short- and medium-term analysis, the country size sH can betreated as a constant parameter. This speci�cation is problematic in simulation exercisesin which one or more countries grow for a prolonged period of time below (or above) thecommon trend (the latter is de�ned in Section 3.2 below). In these cases, maintainingthe country size constant over time leads to an upward (downward) bias of the long-termeconomic relevance of these countries in a global context. Also, since the number of productvarieties and labor inputs in each country is normalized to sH , constant country sizes implythat the sectoral extensive margins (the number of �rms and varieties in any given sector)remain constant over time as well, and there is no labor immigration. For the time being,the current version of GEM does not encompass endogenous �rms�entry and exit across
3
sectors and countries. A possible way to deal with these issues is to let sH be time-varyingand equal (for instance) to the size of GDP (or alternative measures of a country�s economy)in country H relative to the world GDP . The model-based notion of GDP is discussed laterin Section 5.4.
3.2 Growth trend
There is a common stochastic trend for the world economy (the variable TREND), whosegross rate of growth between time t and time � is denoted gt;� � TREND�=TRENDt.All quantity variables in each country are expressed in detrended terms, that is as ratios ofTREND. The exception is labor e¤ort `, bounded by endowment. In the long run gt;t+1converges to gSS and gt;� converges to g
��tSS , where gSS is a constant.
3.2.1 Discussion
Each (detrended) real variable is stationary, that is converges to a well-de�ned steady-statelevel. This applies to all relative prices, including terms of trade and real exchange rates.In the long term there is balanced growth (at the rate g) across countries and sectors. Theassumption is less restrictive than it appears, as it is always possible to engineer persistent(albeit not permanent) deviations from balanced growth for an arbitrarily long period oftime. Variants of the model could be considered to account for unit roots in relative prices,but they are not discussed here.
3.3 Prices and in�ation rates
As a convention throughout the model, nominal prices expressed in domestic currency aredenoted with uppercase variables, while relative prices are denoted with lowercase variables.Without loss of generality, in each country the consumption good A is the numeraire of theeconomy and all national relative prices are expressed in terms of domestic consumptionunits, that is relative to the Consumer Price Index (CPI). For instance, if PA denotes thenominal CPI and PE the nominal price of one unit of the E good, pE � PE=PA denotes theprice of one unit of E in terms of A. Of course, by de�nition we have pA = 1.Also we denote the (gross) CPI in�ation rate between time t and time � with �t;� �
PA;�=PA;t. The in�ation rate in sector E is therefore equal to:
�Et;� �pE;�pE;t
�t;� (1)
In steady state the in�ation rate �t;t+1 converges to �SS and �t;� converges to ���tSS , where
�SS is a constant equal to the in�ation target of the government.
3.3.1 Discussion
GEM is coded up after transforming all prices in relative terms, so that nominal prices donot appear in the model. Precisely for the same reason why all quantities are de�ned indetrended terms, by normalizing all prices relative to the domestic nominal trend PA weavoid dealing with unit roots, either nominal or real, in quantitative simulations of the modelover very long time horizons. Since the in�ation rate �t;� is part of the model solution, onecan always reconstruct the nominal path for the CPI level by arbitrarily setting the value ofPA at some initial time t = 0 and computing PA;t = PA;0�0;t. In the main text we typically
4
adopt the notation with relative (lowercase) prices. We only switch to the notation withnominal (uppercase) variables when appropriate in order to simplify the exposition.As observed above, all relative prices p converge to well-de�ned steady-state levels. If two
countries have di¤erent steady-state in�ation rates, re�ecting di¤erent policy preferences forthe domestic nominal anchor, in steady state the nominal exchange rate between the twocountries depreciates at a rate equal to the di¤erence between the two in�ation rates whilethe CPI-based real exchange rate remains constant. We return on this point in Section 4.8.Usually in�ation variables carry a double time index. In most applications time t is
measured in quarters, so that �t�1;t measures the quarterly in�ation rate at time t, (�t�1;t)4
measures the annualized quarterly in�ation rate at time t, and �t�4;t measures the year-on-year in�ation rate at time t. When there is no risk of confusion, we adopt the notation �tas shorthand for quarterly in�ation �t�1;t.
3.4 Notational conventions and other formal aspects
The convention throughout the model is that variables which are not explicitly indexed(to �rms or households) are expressed in domestic per-capita terms. For instance, At �(1=s)
R s0At(x)dx and `t � (1=s)
�R s0`t(n)dn+
R s0`t(h)dh
�. Variables without time indexes
as well as variables with subscript SS are used interchangeably to denote steady-state levels.For instance, gSS = g.GEM allows for a rich menu of stochastic processes. As a general convention throughout
the model, when we state that variable X follows an autoregressive process, we mean thatthe process for X is coded as:
Xt = (1� �X)XSS + �XXt�1 + eX;t (2)
where 0 < �X < 1, XSS is the steady-state value of Xt, and eX;t is an i.i.d. shock. Ifvariable X is strictly positive, a logarithmic transformation is considered:
lnXt = (1� �X) lnXSS + �X lnXt�1 + eX;t (3)
Alternative speci�cations can be introduced depending on the speci�c nature of the simu-lation exercise.It is worth emphasizing that GEM has been developed and coded up in non-linear
terms. This choice not only enhances the transparency of the model code relative to thetheoretical apparatus, but also allows for seamless higher-order extensions of the analysisbeyond the traditional �rst-order approximations around the non-stochastic steady state.This �exibility is particularly relevant for welfare analyses involving at least second-orderexpansions around the steady-state equilibrium. In one case below, however, we �nd ituseful to focus the presentation on the linear approximations of the GEM equations, inorder to facilitate the comparison between our framework and similar analytical models.
4 The domestic macroeconomy in partial equilibrium
This section is devoted to the country-speci�c elements of the model that do not involveinternational interactions. Thus, in what follows we consider a representative country underthe working assumption that trade-related variables are exogenous and determined outsidethe equilibrium. For this reason, country-speci�c indexes play no role in this section. Generalequilibrium considerations and a fuller notation involving country indexes are introduced inSection 5.
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4.1 Final goods
In each country there is a continuum of symmetric �rms producing two �nal goods, A (theconsumption good) and E (the investment good). Both goods are produced under perfectcompetition.Consider �rst the consumption sector. Each �rm is indexed by x 2 [0; s]. Firm x�s
output at time t is denoted At(x). The consumption good is produced with the followingnested constant elasticity of substitution (CES) technology:
At(x) = f(1� A)1"A NA;t(x)
1� 1"A +
1"A
A [�1�A
A QA;t(x)1� 1
�A
+(1� �A)1�A MA;t(x)
1� 1�A ]
�A�A�1
�1� 1
"A
�g
"A"A�1 (4)
Three intermediate inputs are used in the production of the consumption good A: a basketNA of nontradable goods, a basket QA of domestic tradable (import-competing) goods,and a basket MA of imported goods. The elasticity of substitution between tradables andnontradables is "A > 0, and the elasticity of substitution between domestic and importedtradables is �A > 0. The weights of the three inputs are, respectively, 1 � A, A�A and A (1� �A) with 0 < A; �A < 1.Firm x takes as given the prices of the three inputs and minimizes its costs pNNA(x) +
pQQA(x) + pMAMA;t(x) subject to the technological constraint (4). Cost minimizationimplies that �rm x�s demands for intermediate inputs are:
NA;t(x) = (1� A) p�"AN;t At(x) (5)
QA;t(x) = A�Ap��AQ;t p
�A�"AXA;t At(x) (6)
MA;t(x) = A (1� �A) p��AMA;tp
�A�"AXA;t At(x) (7)
where pN , pQ and pMA are the relative prices of the inputs in terms of �nal consumptionbaskets, and pXA is the cost-minimizing price of the composite basket of domestic andforeign tradables, or:
pXA;t �h�Ap
1��AQ;t + (1� �A) p1��AMA;t
i 11��A (8)
The production technologies in the consumption and investment sectors can be quanti-tatively di¤erent but their formal characterization is similar, with self-explanatory changesin notation. For instance, a �rm e 2 [0; s], that produces the investment good, demandsnontradable goods according to:
NE;t(e) = (1� E) (pN;t=pE;t)�"E Et (9)
4.1.1 Discussion
Note that pMA and pME are sector-speci�c as they re�ect the di¤erent composition ofimports in the two sectors, while pN and pQ are identical across sectors. In Section 5.1below we discuss the role of import adjustment costs and their e¤ects on relative prices.The weights A, �A, E and �E can be modeled as constant parameters or as autoregres-
sive processes. In the latter case, they can be interpreted as preference shifters, re�ectingshifts in households�consumption demand from tradables to nontradables, or from import-competing goods to foreign imports.
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The CES speci�cation is notationally cumbersome but widely adopted in DSGE modelsto allow for a �exible parametrization of elasticities. Of course, when the elasticities areequal to one the equations collapse to the traditional Cobb-Douglas speci�cation. In mostapplications the elasticities of substitution between import-competing goods and imports,�A and �E , are likely to be larger than the elasticities of substitution between nontradablesand tradables, "A and "E . Note however that there are no theoretical restrictions on thesize of these elasticities.
4.2 Demand for intermediate goods
Intermediate inputs come in di¤erent varieties (brands) and are produced under conditionsof monopolistic competition. In each country there are two kinds of intermediate goods,tradables and nontradables. Each kind is de�ned over a continuum of mass s. Without lossof generality, we assume that each nontradable good is produced by a single domestic �rmindexed by n 2 [0; s], and each tradable good is produced by a �rm h 2 [0; s].Focusing �rst on the basket NA, this is a CES index of all domestic varieties of nontrad-
ables. Denoting as NA (n; x) the demand by �rm x of an intermediate good produced by�rm n, the basket NA(x) is:
NA;t(x) =
"�1
s
� 1�NZ s
0
NA;t (n; x)1� 1
�N dn
# �N�N�1
(10)
where �N > 1 denotes the elasticity of substitution among intermediate non-tradables.Firm x takes as given the prices of the nontradable goods p(n) and minimizes its costsR s
0p(n)NA;t(n; x)dn subject to (10), obtaining:
NA;t(n; x) =1
s
�pt(n)
pN;t
���NNA;t(x) (11)
where pN (the Lagrange multiplier) is the cost-minimizing price of one unit of the non-tradable basket, or:
pN;t =
��1
s
�Z s
0
pt (n)1��N dn
� 11��N
(12)
The basket NE is similarly characterized. Aggregating across �rms, and accounting forpublic demand of nontradables � here assumed to have the same composition as privatedemand � we obtain the total demand for good n as:Z s
0
NA;t(n; x)dx+
Z s
0
NE;t(n; e)de+GN;t(n)
=
�pt(n)
pN;t
���N(NA;t +NE;t +GN;t) =
�pt(n)
pN;t
���NNt (13)
where NA;t = (1=s)R s0NA;t(x)dx (and similar).
Following similar steps we can derive the domestic demand schedules for the intermediategoods h: Z s
0
QA;t(h; x)dx+
Z s
0
QE;t(h; e)de =
�pt(h)
pQ;t
���TQt: (14)
Demand for imported intermediate goods will be characterized in Section 5.1 below.
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4.2.1 Discussion
The elasticity of substitution �, either in the nontradables or the tradables sector, can bemodeled as a constant parameter or as a time-varying stationary process.In Section 5.2.1 we discuss how (13) changes when distribution services are considered.
4.3 Supply of intermediate goods
Each nontradable good n is produced with the following CES technology:
Nt(n) = ZN;t
�(1� �N )
1�N `t(n)
1� 1�N + �
1�N
N Kt(n)1� 1
�N
� �N�N�1
(15)
Firm n uses labor `(n) and capital K(n) to produce N(n) units of its variety. �N > 0 is theelasticity of input substitution, and ZN is a stochastic process for productivity, common toall producers of nontradables.Following the notational convention regarding prices, we let mct, wt and rt denote
marginal costs, wages and rental rates in consumption units. Firm n minimizes its costswt`t(n) + rtKt(n) subject to (15). Cost minimization yields the marginal cost in nontrad-ables production as:
mct(n) =1
ZN;t
n(1� �N )w1��Nt + �Nr
1��Nt
o 11��N (16)
and the capital-labor ratio is:
Kt(n)
`t(n)=
�N1� �N
�rtwt
���N(17)
In each country, labor inputs are di¤erentiated and come in di¤erent varieties (skills).Each input is associated to one household, de�ned over a continuum of mass equal to thecountry size and indexed by j 2 [0; s]. Each �rm n uses a CES combination of all availablelabor inputs:
`t(n) =
"�1
s
� 1 LZ s
0
`(n; j)1� 1
L dj
# L L�1
(18)
where `(n; j) is the demand of labor input of type j by the producer of good n and L > 1is the elasticity of substitution among varieties of labor inputs.Cost minimization implies that `(n; j) is a function of the relative wage:
`t(n; j) =1
s
�wt(j)
wt
�� L`t(n) (19)
where w(j) is the wage paid to labor input j and the wage index w is de�ned as:
wt =
��1
s
�Z s
0
wt(j)1� Ldj
� 11� L
(20)
Similar considerations hold for the production of tradables. We denote by T (h) thesupply of each intermediate tradable h. Using self-explanatory notation, we have:
Tt (h) = ZT;t
�(1� �T )
1�T `t(h)
1� 1�T + �
1�T
T Kt(h)1� 1
�T
� �T�T�1
(21)
8
where ZT is total factor productivity. Aggregating across �rms, we obtain the total demandfor labor input j as:Z s
0
`t(n; j)dn+
Z s
0
`t(h; j)dh
=
�wt(j)
wt
�� L 1s
�Z s
0
`t(n)dn+
Z s
0
`t(h)dh
�=
�wt(j)
wt
�� L`t (22)
where ` is per-capita total labor in the economy.
4.3.1 Discussion
Recall that all variables are de�ned in detrended terms. The implicit assumption is thatin each country the e¤ectiveness of labor e¤ort ` grows at the same rate as TREND, sothat a shock Z (either in the tradables or in the nontradables sector) is de�ned as a totalfactor productivity deviation from the common world trend. The model allows for country-speci�c changes in Z that do not a¤ect the long-run balanced-growth properties of themodel. Therefore, one can consider a scenario in which the level of Z changes permanently,or one in which Z grows or falls for some time, but not a scenario in which Z grows or fallspermanently in steady state. Variants of the model allow for the possibility of transitoryshocks to the e¤ectiveness of labor or capital in addition to total factor productivity.A variant of the model considered in Julliard et al (2006) introduces adjustment frictions
in the labor market. The adjustment terms re�ect the fact that it takes time for labor inputsto be fully productive in production, so that from the viewpoint of national producers theire¤ective costs are higher in the short term than in steady state. Rewrite equation (15) as:
Nt(n) = ZN;t
�(1� �N )
1�N `�t (n)
1� 1�N + �
1�N
N Kt(n)1� 1
�N
� �N�N�1
(23)
where `�(n) is �e¤ective�labor, de�ned as the product of two components:
`�t (n) = `t(n) (1� �N [`t(n)]) (24)
In the expression above, `(n) is the same CES basket of di¤erentiated labor inputs asde�ned in (18). However, now we assume that changes in labor are subject to �rm-speci�cadjustment costs. These costs are speci�ed relative to the past observed level of labore¤ort in the sector and are zero in steady state. Speci�cally, �N [`(n)] can be modeled as aquadratic term:
�N [`t(n)] =�L2
�`t(n)
`N;t�1� 1�2
(25)
where as usual `N;t�1 = (1=s)R s0`t�1(n)dn. In this case, expression (17) is replaced by
Kt(n)
`�t (n)=
�N1� �N
rt
wt=(1� �N;t(n)� `t(n)�0N;t(n))
!��Nand the marginal cost mc(n) is given by:
mct(n) =1
ZN;t
0@(1� �N ) wt1� �N;t(n)� `t(n)�0N;t(n)
!1��N+ �Nr
1��Nt
1A 11��N
(26)
9
The adjustment terms in the previous equation re�ect the fact that, if `t(n) di¤ers from`N;t�1, producers�costs are temporarily higher to account for the losses of e¢ ciency associ-ated with the change in labor inputs.Another variant of GEM allows for heterogeneity in labor skills, to model situations in
which di¤erences between high- and low-skills workers may be relevant. As we discuss be-low, there are two types of households, LC-type households and FL-type households (theseindexes will be explained in Section 4.6 ). FL-type households represents a share (1� sLC)of domestic households and are indexed by j 2 [0; s (1� sLC)]. LC-type households repre-sent a share sLC of domestic households and are indexed by j 2 (s (1� sLC) ; s]. Supposeeach type of household supplies a di¤erent type of labor input, and each type comes in manydi¤erentiated varieties. In this case, (18) is replaced with:
`t(n) =
�s
1 L
LC `LC;t(n)1� 1
L + (1� sLC)1 L `FL;t(n)
1� 1 L
� L L�1
(27)
where `LC(n) is a basket of LC-type labor inputs, `FL(n) a basket of FL-type inputs, and L the elasticity of substitution between the two types. The two baskets are de�ned as:
`FL;t(n) =
"�1
s (1� sLC)
� 1 FL
Z s(1�sLC)
0
`(n; j)1� 1
FL dj
# FL FL�1
(28)
`LC;t(n) =
"�1
s � sLC
� 1 LC
Z s
s(1�sLC)`(n; j)
1� 1 LC dj
# LC LC�1
(29)
where `(n; j) is the demand of labor input j by the producer of good n and FL; LC > 1
are the elasticities of substitution among skills. Cost minimization implies that `(n; j) is afunction of the relative wages:
`t(n; j) =
8>>><>>>:1
s
�wt(j)
wFL;t
�� FL �wFL;twt
�� L`t(n) for FL inputs
1
s
�wt(j)
wLC;t
�� LC �wLC;twt
�� L`t(n) for LC inputs
(30)
where the wage indexes wLC , wFL and w are de�ned as:
wFL;t =
"�1
s (1� sLC)
�Z s(1�sLC)
0
wt(j)1� FLdj
# 11� FL
(31)
wLC;t =
"�1
s � sLC
�Z s
s(1�sLC)wt(j)
1� LCdj
# 11� LC
(32)
wt =hsLC w
1� LLC;t + (1� sLC)w
1� LFL;t
i 11� L (33)
Similar considerations hold for the tradables sector. Aggregating across �rms, we obtainthe total demand for FL-type labor input j as:Z s(1�sLC)
0
`t(n; j)dn+
Z s(1�sLC)
0
`t(h; j)dh =
�wt(j)
wFL;t
�� FL �wFL;twt
�� L(1� sLC) `t
(34)
10
where once again ` is per-capita total labor in the economy. Similarly, total demand forLC-type labor input j is:Z s
s(1�sLC)`t(n; j)dn+
Z s
s(1�sLC)`t(h; j)dh =
�wt(j)
wLC;t
�� LC �wLC;twt
�� LsLC `t (35)
The elasticities L, FL and LC can be modeled as constants or as time-varying autore-gressive processes.
4.4 Price setting in the nontradables sector
Consider now pro�t maximization in the intermediate nontradables sector. The key elementhere is the presence of nominal rigidities. They are modeled as costs to nominal priceadjustment measured in terms of total pro�ts foregone, building on Rotemberg (1982) andIreland (2001). To illustrate as clearly as possible the role of nominal inertias, we �nd ituseful to cast the analysis �rst in terms of nominal prices, and later move back to our usualnotation involving relative prices.Each �rm n takes into account the demand (13) for its product and sets its nominal price
Pt(n) to maximize the present discounted value of pro�ts. The adjustment cost is denotedGPN;t [Pt(n); Pt�1(n)] and is a function of both current and lagged prices. The benchmarkparameterization we adopt allows the model to reproduce realistic nominal dynamics:
GPN;t(n) ��PN2
�Pt(n)=Pt�1(n)
�N;t�1� 1�2
(36)
The adjustment cost is related to changes of the nominal price of nontradable n relative tothe lagged in�ation rate in the nontradables sector �N;t�1. Underlying this speci�cation isthe notion that �rms should not be penalized when their price hikes are indexed to some(publicly observable) measures of aggregate or sectoral in�ation.The price-setting problem is then characterized as:
maxPt(n)
TRENDtPA;t
Et
1X�=t
Dt;�gt;� [P� (n)�MC� (n)]
�P� (n)
PN;�
���NN� (1�GPN;� (n)) (37)
where Dt;� (with Dt;t = 1) is the appropriate nominal discount rate, to be de�ned below ineq. (66). As real variables are detrended, eq. (37) includes the rate of growth of the globaltrend between t and � .The �rst order condition is:
0 =
�1� �N
�Pt(n)�MCt(n)
Pt(n)
���Pt(n)
PN;t
���N(1�GPN;t(n))
� [Pt(n)�MCt(n)]
�Pt(n)
PN;t
���N @GPN;t@Pt(n)
� EtDt;t+1gt;t+1 [Pt+1(n)�MCt+1(n)]
�Pt+1(n)
PN;t+1
���N Nt+1Nt
@GPN;t+1@Pt(n)
(38)
where:
@GPN;t@Pt(n)
= �PN
�Pt(n)=Pt�1(n)
�N;t�1� 1�
1
�N;t�1
1
Pt�1(n)(39)
@GPN;t+1@Pt(n)
= ��PN�Pt+1(n)=Pt(n)
�N;t� 1�Pt+1(n)=Pt(n)
�N;t
1
Pt(n)(40)
11
Since marginal costs are symmetric across nontradables producers, sayMCt(n) =MCNt,�rms n charge the same equilibrium price P (n) = PN . The �rst order condition can thereforebe simpli�ed as:
0 = f[PNt (1� �N ) + �NMCNt] (1�GPN;t(n))g � f[PNt �MCNt]@GPN;t@Pt(n)
PNtg
� fEtDt;t+1gt;t+1 [PNt+1 �MCNt+1]Nt+1Nt
@GPN;t+1@Pt(n)
PNtg (41)
There right hand side of the previous equation consists of three expressions in curly brack-ets. When prices are fully �exible (GPN = 0), only the �rst expression matters and theoptimization problem collapses to the standard markup rule:
PNt =�N
�N � 1MCNt (42)
where the gross markup is a negative function of the elasticity of input substitution. De-viations from markup pricing occur if �rms are penalized for modifying their prices in theshort term. The speed of adjustment in response to shocks depends on the trade-o¤ be-tween current costs (second expression in curly brackets) and future expected costs (thirdexpression), making the price-setting process forward-looking.We can now return to the standard notation in terms of relative prices: the optimization
problem can be written as:
maxpt(n)
TRENDtEt
1X�=t
Dt;�gt;��t;� [p� (n)�mc� (n)]�p� (n)
pN;�
���NN� (1� �PN;� (n)) (43)
where the adjustment costs � are now expressed as a function of relative prices:
�PN;t(n) ��PN2
��tpt(n)=pt�1(n)
�N;t�1� 1�2
(44)
Note that �PN;t = GPN;t, pt(n)@�PN;t=@pt(n) = Pt(n)@GPN;t=@Pt(n) and pt(n)@�PN;t+1=@pt(n)= Pt(n)@GPN;t+1=@Pt(n). The �rst order condition is then:
0 = (1� �PN;t(n)) [pt(n) (1� �N ) + �Nmct(n)]� [pt(n)�mct(n)]@�PN;t@pt(n)
pt(n)
� EtDt;t+1�t;t+1gt;t+1 [pt+1(n)�mct+1(n)]Nt+1Nt
@�PN;t+1@pt(n)
pt(n) (45)
4.4.1 Discussion
Note that when � is very large, the �rst order condition is approximately solved by pt(n) �mct(n) regardless of how sizable �PN is. This implies that in a competitive economy (large�N ) prices must move in tandem with the shocks a¤ecting marginal costs, even though such�exibility entails large adjustment costs. Instead, if price setters have strong monopolypower (�N is close to one, its minimum value), they can charge a high average markup overmarginal costs. In this case, when marginal costs increase due to cyclical conditions, �rms�nd it optimal to maintain relatively stable prices and absorb the change in productioncosts through a markup squeeze. In other words, when �N is small, �rms are able to keeptheir prices well above marginal costs and accommodate changes in demand through supplyadjustments, without corresponding changes in prices. Other things being equal, an increasein �N reduces �rms�ability to use markup �uctuations as a shock absorber.
12
It can be useful to express the pricing equation above as a �rst-order approximationaround the steady state where �PN;t = @�PN;t=@pt(n) = @�PN;t+1=@pt(n) = 0, �Nt =�Nt�1 = �Nt+1 = �, Dt;t+1�Nt+1gt;t+1 � 1=(1 + r) and p(n) = �N= (�N � 1)mc(n). Alsofor simplicity consider the case in which there is zero growth in steady state or g = 1, sothat 1=(1 + r) = �. De�ning yNt � mct(n)=pt(n), we can rewrite (45) as:
0 = f(1� �N + �NyNt) (1� �PN;t(n))g � f(1� yNt)@�PN;t@pt(n)
pt(n)g
� fEtDt;t+1gt;t+1�t;t+1 (1� yNt+1)Nt+1Nt
@�PN;t+1@pt(n)
pt(n)g (46)
Now linearize in the neighborhood of the steady state:
0 = �NdyNt �1
�N�PN
�d�Nt � d�Nt�1
�
�+ Et�
1
�N�PN
�d�Nt+1 � d�Nt
�
�(47)
De�ne c�Nt = d�Nt=� and cyNt = dyNt=yN . Obtain:
(�N � 1) byt = 1
�N�PN (c�Nt � c�Nt�1)� 1
�N�PNEt� (c�Nt+1 � c�Nt) (48)
which can be rewritten as a log-linear Phillips curve with full indexation, an expression thatrelates changes in in�ation to expected changes in in�ation and real marginal costs:
�c�Nt = cyNt + �Et�c�Nt+1 � (�N � 1) �N�PN
(49)
Similar considerations apply to the tradables sector.Notice that markup/monopoly power in our setup (�) a¤ects directly the slope of the
Phillips curve . The important implication is that a reduction of monopoly power in GEM(higher �) makes the Phillips curve steeper and reduces the sacri�ce ratio faced by theeconomy. Similar considerations apply to an increase in price �exibility (lower �PN ).Variants of the model can exploit alternative assumptions about the degree of indexation
and in�ation inertia in the model, simply by modifying the denominator of the term inbrackets in (36) or (44). For instance, a model in which:
�PN;t(n) ��PN2
�tpt(n)=pt�1(n)
��N;t�1�1��t
� 1!2
(50)
implies weighted indexation with respect to past sectoral in�ation and current economy-widein�ation, and the resulting Phillips curve is characterized by asymmetries between forward-and backward-looking components of the in�ation process:
c�Nt = �c�Nt�1+(1� �) b�t+ cyNt+�Et (c�Nt+1 � �c�Nt � (1� �) b�t+1) � (�N � 1) �N�PN
(51)
4.5 Price setting in the tradables sector
In this section we only consider optimal price setting for domestic �rms selling in the domes-tic market, and we abstract from the role of the distribution sector. Later we consider theprice-setting problem faced by exporters and consider a variant of the model encompassingdistribution services.
13
The analysis is similar to the nontradables sector above. Adopting a self-explanatorynotation, the price-setting problem of �rm h at time t can be characterized as follows:
maxpt(h)
TRENDtEt
1X�=t
Dt;��t;�gt;� [p� (h)�mc� (h)]�p� (h)
pQ;�
���TQ� (1� �PQ;� (h)) (52)
and the �rst-order condition in a symmetric equilibrium with p(h) = pQ is:
0 = (1� �PQ;t(h)) [pt(h) (1� �T ) + �Tmct(h)]� [pt(h)�mct(h)]@�PQ;t@pt(h)
pt(h)
� EtDt;t+1�t;t+1gt;t+1 [pt+1(h)�mct+1(h)]Qt+1Qt
@�PQ;t+1@pt(h)
pt(h) (53)
4.6 Consumer preferences
In each country there is a continuum of households indexed by j 2 [0; s], the same indexof labor inputs. Some households have access to capital markets, some do not. The latter�nance their consumption by relying exclusively on their labor incomes. We refer to the �rsttype as �Ricardian�or �forward-looking�(FL). We refer to the second type as �non-Ricardian�or �liquidity-constrained�(LC). The two types of households can also be heterogeneous inthe labor market, as discussed above.For each household j, we denote with Wt(j) the lifetime expected utility and specify its
preferences as:
Wt(j) � TRENDtEt
1X�=t
�t;�g1��t;� u� ( C� (j); `� (j) ) (54)
where the instantaneous felicity is a function of (detrended) consumption C and labor e¤ort`:
ut ( Ct(j); `t(j) ) =ZU1� � [Ct(j)� bc
Cj;t�1gt�1;t
� ZV1 + �
(`t(j)� b``j;t�1)1+�
(1� b`)�]1�� (55)
In the expressions above �t;� is the discount rate between time t and time � , possiblytime-varying and di¤erent across countries. In steady state �t;� converges to �
��tSS where
�SS is a constant.The term g1��t;� in (54) implies that the disutility of labor e¤ort increases with the
common trend, an assumption required to guarantee balanced growth. The implicit as-sumption is that technological progress associated with home production activities followsthe same trend as the e¤ectiveness of labor in manufacturing production. The restrictionlim�!1�t;�g
1��t;� < 1 is imposed to ensure that utility is bounded.
The parameter � in (55), which a¤ects the curvature of consumption utility, is thereciprocal of the elasticity of intertemporal substitution. The parameter �, which a¤ects thecurvature of labor disutility, is the reciprocal of the Frisch elasticity of labor supply.There is habit persistence in consumption with coe¢ cient 0 < bc < 1. The term Cj;t�1
in (55) is past per-capita consumption of household j�s peers, (i.e., either forward-looking orliquidity-constrained agents). Similarly, there is habit persistence in leisure with coe¢ cient0 < b` < 1. Households�preferences are therefore symmetric within their respective cate-gories but, because of di¤erent reference groups in habit formation, they are not symmetricacross categories.
14
The marginal utilities of consumption and leisure are:
@ut(j)
@Ct(j)= ZU [Ct(j)� bc
Cj;t�1gt�1;t
� ZV1 + �
(`t(j)� b``j;t�1)1+�
(1� b`)�]�� (56)
�@ut(j)@`t(j)
= ZU [Ct(j)� bcCj;t�1gt�1;t
� ZV1 + �
(`t(j)� b``j;t�1)1+�
(1� b`)�]��ZV (
`t(j)� b``j;t�11� b`
)�
(57)
and the marginal rate of substitution is:
MRSt(j) = �@ut(j)=@`t(j)
@ut(j)=@Ct(j)= ZV (
`t(j)� b``j;t�11� b`
)� (58)
4.6.1 Discussion
The speci�cation of the utility function builds on Greenwood, Hu¤man and Hercowitz(1988). The main reason underlying the choice of this parameterization relatively to alterna-tive options (such as additive separability or Cobb-Douglas aggregators) is that it generatesrelatively high volatility in consumption and counter-cyclical trade balances, consistent withempirical stylized facts. This is because hours worked are determined exclusively by the realwage (see (71) below after accounting for (58)), leading to a direct link between �uctuationsin labor e¤ort and consumption growth.The terms ZU and ZV can be modeled as positive parameters or autoregressive processes.
Note that ZV is normalized so that in a steady state with `t(j) = `j;t�1 the marginal rateof substitution is independent of habit persistence
4.7 Budget constraint (forward-looking households)
The individual �ow budget constraint for Ricardian agent j 2 [0; (1� sLC) s] is:
Bt(j) + "tB�t (j) � (1 + it�1)
Bt�1(j)
�t�1;tgt�1;t+ (1 + i�t�1) [1� �B;t�1]
"tB�t�1(j)
��t�1;tgt�1;t
+ (1� �K) rtKt(j) + (1� �L)wt(j)`t(j) ( 1� �W;t(j) )� Ct(j)� pE;tIt(j) + �t(j)� TTt(j) (59)
Households hold two nominal bonds, one denominated in domestic currency and onedenominated in an international currency. We will refer to the country issuing the interna-tional currency as the �center�. In terms of our notation, Bt(j) is holdings of the domesticbond by household j, expressed in terms of domestic consumption units, B�t (j) is holdingsof the international bond, expressed in terms of center consumption units, and "t is theCPI-based real exchange rate, expressed as the price of one center consumption basket interms of domestic consumption. If the domestic currency is also the international currency" is equal to 1. Below, when we introduce explicit country indexes, "H;J is the price ofone consumption basket in country J in terms of country H�s consumption baskets, andsimilarly "H;� is the bilateral real exchange rate of country H relative to the center.The short-term nominal rates it and i�t are paid at the beginning of period t + 1 and
are known at time t. The two rates are directly controlled by their respective nationalgovernments, so that i� is the onshore rate in the center country. The spread betweenonshore rate paid in the center country and the o¤shore rate received by domestic investorsis denoted �B . Only the center-currency bond is traded internationally and is in zero net
15
supply worldwide. The domestic bond is in zero net supply at the domestic level (althoughlater we consider a model variant encompassing public debt).Agents who take a position in the international bond market must deal with �nancial
intermediaries who charge a transaction fee �B on sales/purchases of the international bond.The presence of the �nancial friction �B guarantees that international net asset positionsfollow a stationary process and the economies converge asymptotically to a well-de�nedsteady state. This transaction cost is a function of the average net asset position of thewhole economy. Speci�cally, we adopt the following functional form:
1� �B;t = (1� �B1exp (�B2 ["tB
�t =GDPt � b�FDES ])� 1
exp (�B2 ["tB�t =GDPt � b�FDES ]) + 1
� ZB;t)��t�1;t�t�1;t
(60)
where 0 � �B1 � 1, �B2 > 0, and "tB� � (1=s) "tR s(1�sLC)0
B�(j)dj represents the per-capita net asset position of the country in consumption units. The term b�FDES is the�desired�net asset position of the country expressed as a ratio of GDP . This variable mea-sures the degree of international exposure that �nancial intermediaries consider appropriatefor the economy, based on their assessment of the global economic outlook.To understand the role played by �B , suppose �rst that b�FDES = ZB = 0 and �
� = �.In this case, when the net asset position of the country is equal to its �desired� level ofzero, it must be the case that �B = 0 and the return on the international bond is equalto 1 + i�. If the country is a net creditor worldwide �B rises above zero, implying thatthe country�s households lose an increasing fraction of their international bond returns to�nancial intermediaries. When holdings of the international bond go to in�nity, the returnon the international bond approaches (1 + i�) (1� �B1). By the same token, if the countryis a net debtor worldwide �B falls from zero to ��B1, implying that households pay anincreasing intermediation premium on their international debt. When net borrowing goesto in�nity, the cost of borrowing approaches (1 + i�) (1 + �B1). In nonlinear applications ofGEM the parameter �B2 controls the �atness of the �B function: if �B2 = 0 then �B = 0regardless of the net asset position; if �B2 tends to in�nity then 1��B = (1� �B1) for anyarbitrarily small net lending position, and 1� �B = (1 + �B1) for any arbitrarily small netborrowing position. An appropriate parameterization allows the model to generate realisticdynamics for net asset positions and current account.Consider now the other components of (60). The term b�FDES can be positive or negative.
The above considerations are still valid after reinterpreting the concepts of �net creditor�or�net borrower�in terms of deviations from the desired levels.The variable ZB;t can be modeled as a stochastic process with zero mean in steady state,
provided that �uctuations in ZB are not large enough to push �B above 1. In our framework,uncertainty in international �nancial intermediation plays the same role that �uncoveredinterest parity shocks�or risk-premium �uctuations play in similar open-economy models.Finally, when rates of time preference diverge across countries and �� 6= �, the transac-
tion cost is appropriately modi�ed to account for asymmetries in real interest rates acrosscountries, as in Faruqee et al. (2007)..Let�s consider now the remaining components in the budget constraint. Households ac-
cumulate physical capital which they rent to domestic �rms at the after-tax rate r (1� �K).Gross investment before depreciation is denoted I. The law of motion of capital is:
Kt+1(j)gt;t+1 = (1� �)Kt(j) + �I;t(j)Kt(j) 0 < � � 1 (61)
where � is the country-speci�c depreciation rate of capital. Capital accumulation is subjectto adjustment costs: �I(:) is an increasing, concave, and twice-continuously di¤erentiable
16
function of the investment/capital ratio It(j)=Kt(j) with two properties entailing no adjust-ment costs in steady state: �I(� + g � 1) = � + g � 1 and �0I(� + g � 1) = 1. The speci�cfunctional form we adopt is quadratic and encompasses inertia in investment:
�I;t(j) �It(j)
Kt(j)(1 + ZI;t)�
�I12
�It(j)
Kt(j)� (� + g � 1)
�2� �I2
2
�It(j)
Kt(j)� It�1Kt�1
�2(62)
where �I1, �I2 � 0, ZI;t is a transitory shock (modeled as a negative adjustment cost) andg is the steady-state growth rate.Labor incomes w` are taxed at the rate �L. Each FL-type household is the monopolistic
supplier of a speci�c labor input and sets the nominal wage for its labor input j accountingfor its demand `(j) = (w(j)=w)
� L `. There is sluggish wage adjustment due to resourcecosts that are measured in terms of the total wage bill. The adjustment cost is denoted�WFL (for Wage Forward-Looking) and its speci�cation is the analog of (44) above:
�WFL;t(j) ��WFL
2
��twt(j)=wt�1(j)
�W;t�1� 1�2
(63)
where �W is the wage in�ation rate.Ricardian households own all domestic �rms and there is no international trade in claims
on �rms�pro�ts. The variable � includes all dividends accruing to shareholders, plus allrevenue from nominal and real adjustment rebated in a lump-sum way to all Ricardianhouseholds, plus revenue from �nancial intermediation which is assumed to be provided bydomestic �rms exclusively. A formal de�nition of � is given below in equation (119).Finally, agents pay lump-sum (non-distortionary) net taxes TT denominated in con-
sumption units.
4.7.1 Discussion
In GEM it is assumed that all intermediation �rms are owned by the country�s residents, andthat their revenue is rebated to domestic households in a lump-sum fashion. A simple variantof the model in which intermediation �rms are owned by foreign residents leaves the basicresults virtually unchanged. There are no intermediation costs for center residents enteringthe international bond market, that is, there is no di¤erence between onshore and o¤shorecenter interest rates. Note that the choice of currency denomination of the internationalbond is arbitrary, and any available country currency is viable.Both desired (b�FDES) and actual ("B
�=GDP ) net asset positions converge over the longterm to their steady-state value b�F;SS .
4.8 Consumer optimization (forward-looking households)
The representative Ricardian household chooses bond holdings, capital and consumptionpaths, and sets wages to maximize its expected lifetime utility (54) subject to (59) and (61),taking into account (22) (or (34) if there are di¤erent types of labor).For expositional convenience, it is worthwhile to write explicitly the maximization prob-
17
lem of agent j 2 [0; (1� sLC) s] in terms of the following Lagrangian:
maxCt(j);It(j);Bt(j);B�
t (j);Kt+1(j);wt(j)TRENDtEt
1X�=t
�t;�g1��t;� f u
�C� (j) ; w� (j)
� Lw L� `��
+ �� (j) ( �B� (j)� "�B�� (j) +(1 + i��1)B��1(j)
���1;�g��1;�+(1 + i���1)(1� �B;��1)"�B���1(j)
����1;�g��1;�
+ (1� �L)w� (j)1� Lw L� `� (1� �W;� [w� (j); w��1(j)])+ (1� �K) r�K� (j)� C� (j)� pE;�I� (j) + �� (j)� TT� (j) )+ �� (j) ( �K�+1(j)g�;�+1 + (1� �)K� (j) + �I;� [I� (j)=K� (j)]K� (j) ) g (64)
where � and � are the multipliers associated with, respectively, the budget constraint andthe capital accumulation process.The �rst order conditions with respect to Ct(j) and It(j) yield:
�t(j) = @ut(j)=@Ct(j) = �t(j)�0I;t(j)=pE;t (65)
In a symmetric setup, @ut(j)=@Ct(j) is the same across Ricardian agents j. Their stochasticdiscount rate and pricing kernel is therefore the variable Dt;� , which is de�ned as:
Dt;� � �t;�g1��t;�
���t
1
�t;�
1
gt;�(66)
Accounting for the above expressions, the �rst order conditions with respect to Bt(j) andB�t (j) are, respectively:
1 = (1 + it)EtDt;t+1 (67)
1 = (1 + i�t ) (1� �B;t)Et (Dt;t+1�t;t+1) (68)
where � denotes the rate of nominal exchange rate depreciation against the US, or:
�t;� ="�"t
�t;���t;t
(69)
The �rst order condition with respect to Kt+1(j) is:pE;t�0I;t(j)
Etgt;t+1 = Etf Dt;t+1�t;t+1gt;t+1( (1� �K) rt+1
+pE;t+1�0I;t+1(j)
[1� � + �I;t+1(j)� �0I;t+1(j)It+1(j)
Kt+1(j)] ) g (70)
Expression (70) links capital accumulation to the behavior of the after-tax price of capital(1� �K) r. In a non-stochastic steady state 1 + (1� �K) r=pE is equal to the sum of thenatural real rate g�=� and the rate of capital depreciation �.Finally, taking the �rst order condition with respect to w(j), the Ricardian household�
wage rate is set according to:
LMRSt(j)1
wt(j)= ( L � 1) [1� �WFL;t(j)] (1� �L) +
@�WFL;t(j)
@wt(j)wt(j) (1� �L)
+ EtDt;t+1�t;t+1gt;t+1wt+1(j)
wt(j)
(wt+1(j)=wt+1)� L
(wt(j)=wt)� L
`t+1`t
@�WFL;t+1(j)
@wt(j)wt(j) (1� �L) (71)
where MRS has been de�ned in (58) above. The interpretation of (71) is similar to (112)above. In a non-stochastic steady state the real wage w(j) is equal to the marginal rate ofsubstitution between consumption and leisure, MRS = �u`=uc, augmented by the markup L= ( L � 1) which re�ects monopoly power in the labor market. For an analysis of wagerigidities in open-economy general equilibrium models see e.g. Corsetti and Pesenti (2001).
18
4.8.1 Discussion
In a non-stochastic steady state (67) implies (1 + iSS) =�SS = g�SS=�SS : recall that �SSis the (gross steady-state quarterly) in�ation rate, (1 + iSS) =�SS is the equilibrium realinterest rate, gSS is the (gross steady-state quarterly) rate of growth of the world economy,1=�SS is the rate of time preference, and g
�SS=�SS is the steady-state �natural�real interest
rate of the economy. International di¤erences in natural rates can arise from asymmetricrates of time preference. The �nancial friction �B in (60) is appropriately adjusted to takeinto account these asymmetries.Expressions (67) and (68) yield the risk-adjusted uncovered interest parity, recalling that
the return on international bond holdings is modi�ed to account for the costs of intermedi-ation �B . In steady state the interest di¤erential (1 + iSS) =[(1 + i�SS) (1� �B;SS)] is equalto the steady-state nominal depreciation rate of the currency vis-a-vis the US, and relativepurchasing power parity holds.Note that the expectation operator on the left hand side of (70) is needed as shocks to
the trend gt;t+1 are not part of the information set at time t. This is because variables areexpressed as deviations from the current trend. An alternative speci�cation which expressesvariables as deviations from the lagged trend would make little di¤erence.When the two types of households also represent di¤erent types of labor inputs with
di¤erent elasticities, the �rst order condition (71) is replaced by:
FLMRSt(j)1
wt(j)= ( FL � 1) [1� �WFL;t(j)] (1� �L) +
@�WFL;t(j)
@wt(j)wt(j) (1� �L)
+ EtDt;t+1�t;t+1gt;t+1wt+1(j)
wt(j)
(wFL;t+1=wt+1)� L
(wFL;t=wt)� L
`FL;t+1`FL;t
@�WFL;t+1(j)
@wt(j)wt(j) (1� �L)
(72)
A variant of the model considers the role of money. De�ne asM the stock of real moneybalances held by household j. The budget constraint (59) becomes:
Mt(j) +Bt(j) + "tB�t (j) �Mt�1(j) + (1 + it�1)
Bt�1(j)
�t�1;tgt�1;t
+ (1 + i�t�1) [1� �B;t�1]"tB
�t�1(j)
��t�1;tgt�1;t+ (1� �K) rtKt(j) + (1� �L)wt(j)`t(j) ( 1� �W;t(j) )
� Ct(j) [1 + �S;t(j)]� pE;tIt(j) + �t(j)� TTt(j) (73)
Consumption spending is subject to a proportional transaction cost �S that depends onthe household�s money velocity v, where:
vt(j) �Ct(j)
Mt(j)(74)
A suggested functional form for the transaction cost (implying a satiation point for thedemand of real balances) is:
�S (vt) = �S1vt +�S2vt
� 2 (�S1�S2)1=2 (75)
Agents optimally choose their stock of real money holdings M so that at the marginshopping costs measured in terms of foregone consumption are equal to the bene�ts frominvesting in yield-bearing assets. The �rst order condition with respect toMt(j) is:
1� �0S;t(j)v2t (j) = EtDt;t+1 (76)
19
which de�nes real money balancesM as a positive function of consumption and a negativefunction of the nominal interest rate. Other equations of the model need to be modi�edappropriately to account for the presence of money. For instance, the asset pricing kernel isnow equal to:
Dt;� � �t;�g1��t;�
���t
1
�t;�
1
gt;�
1 + �S;t(j) + �0S;t(j)vt(j)
1 + �S;� (j) + �0S;� (j)v� (j)(77)
and the government budget constraint is modi�ed so that seigniorage revenue is rebated ina lump-sum fashion through net transfers.
4.9 Consumer optimization (liquidity-constrained households)
As liquidity-constrained households have no access to capital markets, their optimal choicesare con�ned to labor supply. Similar to the Ricardian households, they can optimally settheir wages to exploit their market power. Also similar to the Ricardian households, theyface adjustment costs for their wages. These costs are denoted �WLC;t (for Wage LiquidityConstrained) and are similar to (63). Di¤erent from the Ricardian households, however,their optimal choices are purely static and do not entail forward-looking components.The maximization problem of agent j 2 ((1� sLC) s; s] can be written in terms of the
following static Lagrangian:
maxCt(j);wt(j)
u ( Ct(j); w� Lt (j)w
Lt `t ) + �t(j) [ �Ct(j)� TTt(j)
+ (1� �L)wt(j)1� Lw Lt `t(1� �WLC;t(j) ] (78)
It is assumed that redistributive policies TT rebate to LC-type households the income lossesassociated with wage adjustment, so that their consumption level is:
Ct(j) = (1� �L)wt(j)`t(j) (79)
The �rst order conditions with respect to C(j) and w(j) determines partial adjustment ofwages:
LMRSt(j)1
wt(j)= (1� �L) [( L � 1) ( 1� �WLC;t(j) ) +
@�WLC;t(j)
@wt(j)wt(j) ] (80)
Denoting wFL the wage rate w(j) that solves (71), and wLC the wage rate w(j) thatsolves (80), equation (20) determines the wage rate for the whole economy as:
w1� Lt = sLCw
1� LLC;t + (1� sLC)w
1� LFL;t (81)
4.9.1 Discussion
When two types of labor inputs are considered, equation (80) is replaced by:
LCMRSt(j)1
wt(j)= (1� �L) [( LC � 1) ( 1� �WLC;t(j) ) +
@�WLC;t(j)
@wt(j)wt(j) ] (82)
4.10 Fiscal policy
Public spending falls on nontradable goods, both �nal and intermediate. In per-capita terms,GC is government consumption, GI is government investment, and GN denotes public pur-chases of intermediate nontradables. There are four sources of (net) tax revenue: taxes on
20
capital income �K , taxes on labor income �L, import tari¤s tar, and lump-sum taxes netof transfers to households TT . In the benchmark version of GEM the government follows abalanced budget rule:
0 = Gt �GREV;t (83)
where:Gt � GC;t + pE;tGI;t + pN;tGN;t (84)
and GREV is aggregate government revenue, to be de�ned below in Section 5.3.
4.10.1 Discussion
Although GEM has not been designed to analyze �scal policy issues in detail, variants ofthe model can be designed to provide a satisfactory quantitative assessment of budgetarydynamics. In what follows we consider a possible extension in this direction, followingFaruqee et al (2007,2008).The government �nances the excess of public expenditure over net taxes by issuing debt
denominated in nominal currency, denoted B in per-capita terms. All national debt is heldexclusively by domestic (Ricardian) agents. The budget constraint of the government is:
Bt � (1 + it�1)Bt�1
�t�1;tgt�1;t+Gt �GREV;t (85)
De�ne now the average tax rate for the economy � as:
� t � GREV;t=GDPt (86)
Similarly, de�ne the de�cit-to-GDP ratio as:
DEFtGDPt
=
�Bt �
Bt�1�t�1;tgt�1;t
�=GDPt (87)
From (85), in steady state we have:
BSSGDPSS
=�SSgSS
�SSgSS � (1 + iSS)
�GSS
GDPSS� �SS
�=
�SSgSS�SSgSS � 1
DEFSSGDPSS
(88)
The previous equations de�ne the relations between debt-to-GDP, average tax rate, andde�cit-to-GDP ratio which are sustainable in the long term. In what follows we treat thelong-run debt-to-GDP ratio as a policy parameter set by the government, and let �SS andDEFSS=GDPSS be determined by (88).The government is assumed to control lump-sum taxes, trade policy parameters, � and
�K directly, while �L is endogenously determined. A possible speci�cation for the �scal rulefor � is:
� t = (� t�1 + � t + Et� t+1) =3 + �TAX1(Bt
GDPt� �TAX2bTAR;t � (1� �TAX2)
Bt�1GDPt�1
)
+�TAX3
�DEFtGDPt
� DEFSSGDPSS
�+ �TAX4
�Gt
GDPt� GSSGDPSS
�(89)
where bTAR is the targeted debt-to-GDP ratio, a variable that converges to BSS=GDPSS insteady state. The tax rate is a smoothed function of past and expected future rates, adjustedupward when the current debt-to-GDP ratio is above the average of its current target and its
21
past observed level, when the current de�cit-to-GDP ratio is above its sustainable steady-state level, and when current government spending as a share of GDP is above its long-runlevel.By construction, public debt is exclusively held by domestic agents, and the net asset
position of the country is independent of the extent of public borrowing. This feature ofthe model is of course highly unrealistic. A way to enhance the realism of the simulationsis by introducing a link between the desired net asset position of country H and the debtto GDP ratios in the world economy as follows:
b�HFDES;t = b�HFNEUT � �HF1BHt
GDPHt+XJ 6=H
�J;HF2BJt
GDP Jt(90)
According to the previous expression, b�HFDES is equal to a country-speci�c constant, b�HFNEUT ,
adjusted to account for changes in the debt-to-GDP ratios in either the domestic economy(BH=GDPH) or in the other countries in the world (BJ=GDP J).This speci�cation provides a plausible (albeit judgmental) link between debt imbalances
and net asset positions. When the national debt-to-GDP ratio increases, domestic agentsreduce the share of foreign securities in their portfolios by selling the international bondto foreigners. By the same token, if the debt-to-GDP ratio increases in the center country,international investors would require a higher return on center securities, leading to a highershare of center assets in their portfolios or a reduction of net borrowing from the center.Of course, our approach should be viewed only as a crude approximation to the actual de-
terminants of cross-country spreads and interest rate premia in response to macroeconomicimbalances, whose endogenization should be eventually incorporated in a self-containedmodel. It remains unclear, however, whether the �nal bene�ts of such a framework signi�-cantly outstrip the costs of incorporating the large amount of complications from which weabstract here.Quantitatively, one could take b�FDES as a free variable and estimate the �F1 and �F2
parameters on the basis of empirical evidence on the link between net asset positions anddebt levels. Alternatively, one could rely on cross-fertilization with respect to alternativetheoretical models able to shed light on the structural determinants of these parameters.In Faruqee et al (2007), for instance, the calibration of (90) has relied on results based onthe Global Fiscal Model, an overlapping-generation multi-country model developed at theInternational Monetary Fund.
4.11 Monetary policy
The government controls the short-term rate it. Monetary policy is speci�ed in terms ofannualized interest rate rules. The speci�cation of the interest rule is likely to changeaccording to the nature of the simulation exercise. A benchmark speci�cation is:
(1 + it)4= !i (1 + it�1)
4+ (1� !i)
�1 + ineutt
�4+ !1Et (�t�1;t+3 ��t�1;t+3) (91)
The current interest rate it is an average of the lagged rate it�1 and the current �neutral�rate ineutt , de�ned as:
1 + ineutt ��0:25t�4;t (gt�1;t)
�
�t�1;t(92)
where �t��;t��+4 is the year-on-year gross CPI in�ation target (either explicit or implicit)prevailing at time t for the four-quarter period between t� � and t� � +4. This average is
22
adjusted to account for the expected in�ation gap three quarters in the future. In a steadystate when all constant targets are reached it must be the case that the nominal interest rateis equal to the neutral level, equal to the product of the equilibrium �natural�real interestrate g�=� times the in�ation target:
1 + iSS = 1 + ineutSS =
�0:25SS g�SS�SS
=�SSg
�SS
�SS: (93)
4.11.1 Discussion
The rule (91) could be modi�ed to include policy responses to a set of other variables (suchas measures of the output gap level or growth, the exchange rate, the current account etc.)expressed as deviations from their targets. For an extension to price-level path targeting,the reader is referred to Laxton, N�Diaye and Pesenti (2006). For an introduction to optimalmonetary policy in open economies see e.g. Corsetti and Pesenti (2005).
4.12 Market clearing in the domestic economy
Maintaining international variables exogenous for the time being, the model is closed byimposing the following resource constraints and market clearing conditions.In each country, the domestic resource constraints for capital and labor are, respectively:Z s(1�sLC)
0
Kt(j)dj �Z s
0
Kt(n)dn+
Z s
0
Kt(h)dh (94)
and:
`t(j) �Z s
0
`t(n; j)dn+
Z s
0
`t(h; j)dh (95)
The resource constraint for the nontradable good nH is:
Nt(n) �Z s
0
NA;t(n; x)dx+
Z s
0
NE;t(n; e)de+GN;t(n) (96)
while the tradable h can be used by domestic �rms or imported by foreign �rms (see below).The �nal good A can be used for private or public consumption:Z s
0
At(x)dx �Z s
0
Ct(j)dj + sGC;t (97)
and similarly for the investment good E:Z s
0
Et(e)de �Z (1�sLC)s
0
It(j)dj + sGI;t (98)
Market clearing in the domestic bond market requires:Z s(1�sLC)
0
Bt(j)dj = sBt (99)
where Bt = 0 in the benchmark model (see discussion above for the treatment of publicdebt Bt > 0).
23
5 World interdependencies in general equilibrium
So far all trade-related variables have been taken as exogenous. Now we close the modelby considering a multi-country general-equilibrium setting. The notation becomes slightlymore complicated, as explicit country indexes must be introduced. We will refer to H as the�home�country and to J 6= H as one of the remaining �foreign�countries. When a doublecountry index is considered in the case of bilateral trade variables, the �rst index refers tothe importing (destination) country and the second index to the exporting (source) country.Multi-country applications of GEM can be found e.g. in Faruqee et al (2007, 2008).
5.1 Demand for imports
The derivation of the foreign demand schedule for good h is analytically more complex but,as we show in (108) at the end of this section, it shares the same functional form as (13) and(14) above, thus can be written as a function of the relative price of good h (with elasticity�T ) and total foreign demand for imports.We focus �rst on import demand in the consumption good sector of country H. Denote
the representative �rm in the consumption sector as xH 2 [0; sH ]. Its imports MHA (x
H) area CES function of baskets of goods imported from the other countries, or:
MHA;t(x
H)1� 1
�HA =
XJ 6=H
�bH;JA
� 1
�HA
�MH;JA;t
�xH� �
1� �H;JMA;t
�xH� � �1� 1
�HA (100)
where:0 � bH;J � 1;
XJ 6=H
bH;J = 1 (101)
In (100) above �HA is country H�s elasticity of substitution across exporters: the higher is�HA , the easier it is for �rm xH to replace imports from one country with imports from an-other. The parameters bH;JA determine the composition of the import basket across countries.MH;JA (xH) denotes imports from country J by �rm xH located in country H.The response of import volumes to changes in demand as well as their price elasticities are
typically estimated to be smaller in the short term than in the long run. To model realisticimports dynamics, such as the delayed and sluggish adjustment to changes in relative pricestypically referred to as the �J curve�, we assume that bilateral imports are subject to bilateraladjustment costs �H;JMA. These costs are speci�ed in terms of import shares relative to �rmxH�s output. They are zero in steady state. Speci�cally, GEM adopts the parameterization:
�H;JMA;t[MH;JA;t (x
H)
AHt (xH)
=MH;JA;t�1
AHt�1] =
�H;JMA
2
h�MH;JA;t (x
H)=AHt (xH)�=�MH;JA;t�1=A
Ht�1
�� 1i2
�1 +
h�MH;JA;t (x
H)=AHt (xH)�=�MH;JA;t�1=A
Ht�1
�� 1i2�(102)
with �H;JMA � 0. The speci�cation is such that �H;JMA[1] = 0, �H;JMA[1] = �H;JMA=2, and�H;JMA[0] = �
H;JMA[2] = �H;JMA=4. Alternative parameterizations (for instance, quadratic) could
be considered, although the suggested one has proven to be useful in non-linear simulationexercises with relatively large shocks.Denoting pH;JM the price in country H of a basket of intermediate inputs imported from
J , �rm xH minimizes its costsPJ 6=H p
H;JM MH;J
A (xH) subject to (100). Cost minimization
24
implies:
MH;JA;t (x
H)�1� �H;JMA;t(x
H)�
�1� �H;JMA;t(x
H)�MH;JA;t (x
H)�0H;JMA;t(xH)��HA = bH;JA
pH;JM;t
pHMA;t(xH)
!��HAMHA;t(x
H) (103)
where �0H;JMA (xH) is the �rst derivative of �H;JMA(x
H) with respect to MH;JA (xH) and the
cost-minimizing import price index pHMA(xH) is the Lagrangian multiplier:
pHMA;t(xH) =
24XJ 6=H
bH;J
pH;JM;t
1� �H;JMA;t(xH)�MH;J
A;t (xH)�0H;JMA;t(x
H)
!1��HA351
1��HA
(104)
In principle, the import price pHMA(xH) is �rm-speci�c, as it depends on �rm xH�s import
shares. To the extent that all �rms xH are symmetric within the consumption sector, how-ever, there will be a unique import price pHMA. It follows that p
HMAM
HA =
PJ 6=H p
H;JM MH;J
A (1��H;JMA)=(1� �
H;JMA �M
H;JA �0H;JMA ).
Consider now the basket MH;JA (xH) in some detail. In analogy with (10) above, it is a
CES index of all varieties of tradable intermediate goods produced by �rms hJ operating incountry J and exported to country H. Denoting as MH;J
A
�hJ ; xH
�the demand by �rm xH
of an intermediate good produced by �rm hJ , the basket MH;JA
�xH�is:
MH;JA;t (x
H) =
"�1
sJ
� 1
�JT
Z sJ
0
MH;JA;t
�hJ ; xH
�1� 1
�JT dhJ
# �JT�JT�1
(105)
where �JT > 1 is the elasticity of substitution among intermediate tradables, the sameelasticity entering (14) in country J .The cost-minimizing �rm xH takes as given the prices of the imported goods pH(hJ)
and determines its demand of good hJ according to:
MH;JA;t (h
J ; xH) =1
sJ
pHt (h
J)
pH;JM;t
!��JTMH;JA;t (x
H) (106)
where MH;JA;t (x
H) has been de�ned in (103) and pH;JM is:
pH;JM;t =
"�1
sJ
�Z sJ
0
pHt�hJ�1��JT dhJ# 1
1��JT
(107)
The import demand schedules in the investment good sector can be derived in perfectanalogy with the analysis above. As a last step, we can derive country J�s demand schedulefor country H�s intermediate good hH , that is, the analog of (14). Aggregating across �rms(and paying attention to the order of the country indexes) we obtain:Z sJ
0
MJ;HA;t (h
H ; xJ)dxJ +
Z sJ
0
MJ;HE;t (h
H ; eJ)deJ
=sJ
sH
pJt (h
H)
pJ;HM;t
!��HT �MJ;HA;t +M
J;HE;t
�(108)
25
5.1.1 Discussion
Import adjustment costs �H;JMA and �H;JME are treated in GEM as expenditures associatedwith intermediation activities (transportation, distribution, training, etc.) Thus, they showup somewhere else in the economy as revenue for the �rms that provide these services,and as dividend incomes for the households who own these �rms. Below, we include thesecomponents in the de�nition of �.Variants of the model can include trade in commodities, parts, raw materials and other
�upstream�intermediate goods. The reader is referred to Laxton and Pesenti (2003) for adetailed algebraic treatment.
5.2 Price setting in the tradables sector and exchange rate pass-through
In Section 4.5 above we characterized the optimal price set by a �rm producing tradableintermediate goods for the local market. We now reconsider the price-setting problem in thetradables sector from the vantage point of the �rm hH located in country H and exportingto all other countries J 6= H. We also introduce the distinction between import prices atthe national level and at the border level. National import prices pJ(hH) are paid by �rmslocated in country J to purchase one unit of the variety hH . These are the prices that enterequations such as (103) above. Border import prices are indexed with a bar (e.g. pJ(hH)).These are the prices set by the exporting �rm hH . The di¤erence between the two pricesstems from trade barriers such as tari¤s. Below we consider a more general speci�cationof the model in which the gap between the two prices re�ects distribution costs and retailmargins. In terms of our notation, we have:
pJt (hH) =
�1 + tarJ;H
�pJt (h
H) (109)
where tarJ;H is a proportional tari¤ duty imposed by country J over its imports fromcountry H.To the extent that di¤erent country blocs represent segmented markets in the global
economy, each �rm hH in country H has to set di¤erent prices for the domestic market andall other export markets. Since the �rm faces the same marginal costs regardless of the scaleof production in each market, the di¤erent price-setting problems are independent of eachother.Exports are invoiced (and prices are set) in the currency of the destination market.
Accounting for (108), the price-setting problems of �rm h in country H at time t can thenbe characterized as follows:
maxpJt (h
H)TRENDtEt
1X�=t
DHt;��
Ht;�gt;� ["
H;J� pJ� (h
H)�mcH� (hH)]
� sJ
sH
�1 + tarJ;H
�pJ� (h
H)
pJ;HM;�
!��HT �MJ;HA;� +M
J;HE;�
��1� �J;HPM;� (h)
�(110)
where pJ;HM is the price of the basket of country J�s imports from country H, and MJ;HA +
MJ;HE is country J�s aggregate imports from country H. The term "H;J is the bilateral
real exchange rate between country H and country J (an increase in "H;J represents areal depreciation of country H�s currency against country J). The term �H;JPM (h
H) denotes
26
adjustment costs related to changes of the price of good hH in country J . These costs arethe analogs of (44) above:
�J;HPM;t(hH) � �J;HPM
2
�JtpJt (h
H)=pJt�1(hH)
�J;HM;t�1� 1!2
(111)
where �M is the in�ation rate for bilateral imports prices. Despite its fastidiousness, thenotation above is straightforward and the equations are self-explanatory.
Accounting for �rms� symmetry (pJ(hH) = pJ;HM and�1 + tarJ;Ht
�pJ(hH) = pJ;HM in
equilibrium), pro�t maximization yields:
0 =�1� �J;HPM;t(h
H)� h"H;Jt pJt (h
H)�1� �HT
�+ �HT mc
Ht (h
H)i
�h"H;Jt pJt (h
H)�mcHt (hH)i @�J;HPM;t
@pJt (hH)pJt (h
H)� EtfDHt;t+1�
Ht;t+1gt;t+1
�h"H;Jt+1p
Jt+1(h
H)�mcHt+1(hH)i MJ;H
A;t+1 +MJ;HE;t+1
MJ;HA;t +M
J;HE;t
!@�J;HPM;t+1
@pJt (hH)
pJt (hH)g (112)
If adjustment costs in the export market are relatively large, the prices of country H�sgoods in the foreign markets are characterized by signi�cant stickiness in local currency.In this case, the degree to which short-term exchange rate movements (and other shocksto marginal costs in country H) a¤ect import prices in country J is rather small � as inChari, Kehoe and McGrattan (2002). If instead the �J;HPM coe¢ cients are small, expression(112) collapses to a markup rule, and exchange rate pass-through is full:
"H;Jt pJt (hH) = "H;Jt pJ;HM;t =
�HT�HT � 1
mcHt (113)
If �rm hH faces small adjustment costs in all sales markets, both domestic and foreign, thelaw of one price holds at the border level:
pHQ;t = "H;Jt pJ;HM;t =�HT
�HT � 1mcHt (114)
5.2.1 Discussion
In the previous paragraph, low exchange rate pass-through is the result of nominal pricestickiness in export prices. There is no need, however, to limit our analysis of the deter-minants of pass-through to the role of nominal rigidities. As an example of an alternativeapproach, the variant of GEM studied in Laxton and Pesenti (2003) and based on work byCorsetti and Dedola (2005) considers the role of the distribution sector. In this section webrie�y summarize this extension and its implications for export prices.Suppose that �rms producing the �nal goods A and E in country J do not import
intermediate tradables directly from the foreign producers. Instead, �rms in the distributionsector purchase tradables abroad and distribute them to the �rms producing the �nal good.The distribution technology is Leontief: to make one unit of an intermediate good availableto downstream producers, �rms in the distribution sector require � � 0 units of the non-tradables basket N . Thus, total demand for nontradables (13) in country J is appropriately
modi�ed as�pJt (n
J)=pJN;t���JN �NJ
A;t +NJE;t +G
JN;t + �
JPH 6=J(M
J;HA;t +M
J;HE;t
�.
27
Firms in the distribution sector are perfectly competitive. Because of distribution costs,there is a wedge between producer (border) and consumer (retail) prices even in the absenceof tari¤s and trade barriers. It follows that:
pJt (hH) =
�1 + tarJ;H
�pJt (h
H) + �JpJN;t (115)
From the vantage point of �rm hH exporting to country J , the price-setting equation (112)then becomes:
0 =�1� �J;HPM;t(h
H)�"
"H;Jt pJ� (hH)(1� �HT ) +
"H;Jt �JpJN;t1 + tarJ;H
+ �HT mcHt (h
H)
#
�h"H;Jt pJt (h
H)�mcHt (hH)i @�J;HPM;t
@pJt (hH)(pJ� (h
H) +�JpJN;t
1 + tarJ;H)� EtfDH
t;t+1�Ht;t+1gt;t+1
�h"H;Jt+1p
Jt+1(h
H)�mcHt+1(hH)i MJ;H
A;t+1 +MJ;HE;t+1
MJ;HA;t +M
J;HE;t
!@�J;HPM;t+1
@pJt (hH)(pJ� (h
H) +�JpJN;t
1 + tarJ;H)g
(116)
The key implication of the presence of a distribution sector is that, even in the absenceof adjustment costs, pass-through is no longer full. In fact, when he �J;HPM coe¢ cients aresmall, the above expression collapses to a double-markup rule:
"H;Jt pJt (hH) = "H;Jt pJ;HM;t =
�HT�HT � 1
mcHt +�J
�HT � 1"H;Jt pJN;t1 + tarJ;H
(117)
"H;Jt pJt (hH) = "H;Jt pJ;HM;t =
�HT�HT � 1
mcHt�1 + tarJ;H
�+
�J
�HT � 1"H;Jt pJN;t (118)
5.3 Market clearing in the world economy
All pro�ts and intermediation revenue accrue to Ricardian households:Z sH(1�sHLC)
0
�Ht (jH)djH =
Z sH(1�sHLC)
0
(1 + i�t�1)�HB;t�1
"H;�t B�Ht�1(jH)
��t�1;tgt�1;tdjH
+
Z sH(1�sHLC)
0
�HWFL;t(jH)�1� �HL;t
�wHt (j
H)djH +
Z sH
sH(1�sHLC)�HWLC;t(j
H)�1� �HL;t
�wHt (j
H)djH
+
Z sH
0
�pHt (n
H)�mcHt (nH)�(
Z sH
0
NHA;t(n
H ; xH)dxH +
Z sH
0
NHE;t(n
H ; eH)deH +GHN;t(nH))dnH
+
Z sH
0
�pHt (h
H)�mcHt (hH)�(
Z sH
0
QHA;t(hH ; xH)dxH +
Z sH
0
QHE;t(hH ; eH)deH)dhH
+XJ 6=H
Z sH
0
["H;Jt pJt (hH)�mcHt (hH)](
Z sJ
0
MJ;HA;t (h
H ; xJ)dxJ +
Z sJ
0
MJ;HE;t (h
H ; eJ)deJ)dhH
+XJ 6=H
Z sH
0
MH;JA (xH)�0H;JMA;t(x
H)
1� �H;JMA;t(xH)�MH;J
A �0H;JMA;t(xH)
!pH;JM MH;J
A (xH)dxH
+XJ 6=H
Z sH
0
MH;JE �0H;JME;t(e
H)
1� �H;JME;t(eH)�MH;J
E �0H;JME;t(eH)
!pH;JM MH;J
E (eH)deH (119)
where "H;� is the bilateral real exchange rate between country H and the center country.
28
It may be helpful to go through the single elements on the right hand side. The �rstexpression (integral) is revenue associated with �nancial intermediation in the bond market.The second and third expressions are revenue associated with wage adjustment by eitherforward-looking or liquidity-constrained agents. Note that revenue associated with priceadjustment is not included here, as it is a cost for some �rms and a revenue for others.The fourth expression is monopoly pro�ts in the nontradables sector (if �entry costs�wereconsidered, they would appear here as negative items o¤setting these pro�ts). The �fthexpression is domestic monopoly pro�ts in the tradables sector. The sixth expression isexport pro�ts.The last two expressions in (119) are revenue associated with import adjustment, both
in the consumption sector and in the investment sector. The sum of these last componentsis referred to as IMPADJ (for import adjustment) in what follows.The tradable good hH can be used by domestic �rms or imported by foreign �rms:
Tt�hH��Z sH
0
QA;t(hH ; xH)dxH +
Z sH
0
QE;t(hH ; eH)deH
+XJ 6=H
Z sJ
0
MJ;HA;t (h
H ; xJ)dxJ +
Z sJ
0
MJ;HE;t (h
H ; eJ)deJ
!(120)
Market clearing in the international bond market requires:XJ
Z sJ (1�sJLC)
0
B�Jt (jJ)djJ = 0: (121)
Finally, government revenue is given by:
GHREV;t �1
sH
Z sH
0
TTHt (j)dj + �HKr
Ht
Z sH(1�sHLC)
0
KHt (j)dj + �
HL
Z sH
0
wHt (j)`Ht (j)dj
!
+1
sH
XJ 6=H
tarH;Jt
Z sJ
0
pHt (hJ)�MH;JA;t (h
J) +MH;JE;t (h
J�)dhJ (122)
Together with the appropriate transversality conditions, this concludes the description ofthe equilibrium.
5.4 Measuring output and trade balance
GEM codes all quantity variables in per-capita terms. For the vast majority of the equationsabove the aggregation is straightforward. In this section we focus on the two most importantmacrovariables in the model, gross domestic product and the current account.De�ne �rst per-capita net �nancial wealth in country H as:
FHt � 1
sH(1 + i�t�1) [1� �B;t�1]
Z sH(1�sHLC )
0
"H;�t B�Ht�1(jH)
��t�1;tgt�1;tdjH (123)
Aggregating the budget constraints across private and public agents after imposing theappropriate transversality conditions, the law of motion for �nancial wealth is:
EtDHt;t+1�
Ht;t+1gt;t+1F
Ht+1 = FHt + �HB;t�1
�1 + i�t�1
�"H;�t B�Ht�1
��t�1;tgt�1;t+ pHN;tN
Ht + pHT;tT
Ht
+XJ 6=H
�pHM;t � p
H;JM;t
��MH;JA;t +M
H;JE;t
�+ IMPADJHt � CHt � pHE;tIHt �GHt (124)
29
where the total value of tradables is de�ned as:
pHT;tTHt � pHQ;t
�QHA;t +Q
HE;t
�+XJ 6=H
sJ
sH"H;Jt pJ;HM;t
�MJ;HA;t +M
J;HE;t
�(125)
Recall that the variable IMPADJ is the sum of the last two terms in (119).Expression (125) can be written as:
CURBALHt = "H;�t
B�Ht �
B�Ht�1��t�1;tgt�1;t
!= NFPHt + TBALHt (126)
The left hand side of (126) is country H�s current account in domestic consumption units.The �rst term on the right hand side is net factor payments from the rest of the world tocountry H:
NFPHt =i�t�1"
H;�t B�Ht�1
��t�1;tgt�1;t(127)
TBAL is the trade balance or net exports:
TBALHt = EXHt � IMH
t (128)
where total exports EX are evaluated at border prices:
EXHt = pHT;tT
Ht � pHQ;t
�QHA;t +Q
HE;t
�(129)
and, similarly, total imports IM are evaluated at border prices:
IMHt =
XJ 6=H
pH;JM;t
�MH;JA;t +M
H;JE;t
�(130)
Using the de�nition above, the model-based Gross Domestic Product (in consumptionunits) is:
GDPHt = AHt + pHE;tE
Ht + p
HN;tG
HN;t + TBAL
Ht
= pHN;tNHt + pHT;tT
Ht +
XJ 6=H
�pHM;t � p
H;JM;t
��MH;JA;t +M
H;JE;t
�+ IMPADJHt (131)
Note that there is a discrepancy between GDP measured according to national accountingstandards (goods output), and GDP measured as manufacturing output. This discrepancyre�ects the portion of the revenue from sales of goods associated with making importsavailable to downstream users, such as costs incurred with imports adjustment and wedgesbetween border- and market-prices of imported goods.
30
References
[1] Botman D., P. Karam, D. Laxton and D. Rose, 2007, �DSGE Modeling at the Fund:Applications and Further Developments�, IMF Working Paper, April.
[2] Chari V.V., P. Kehoe, and E. McGrattan, 2002, �Can Sticky Prices Generate Volatileand Persistent Real Exchange Rates?�, Review of Economic Studies 69 (3), pp.533-63.
[3] Corsetti G., and L. Dedola, 2005, �Macroeconomics of International Price Discrimina-tion�, Journal of International Economics 67, pp. 129-156.
[4] Corsetti G., and P. Pesenti, 2001, �Welfare and Macroeconomic Interdependence�, ,Quarterly Journal of Economics 116 (2), pp.421-446.
[5] Corsetti G., and P. Pesenti, 2005, �International Dimensions of Optimal MonetaryPolicy�, Journal of Monetary Economics 52 (2), pp. 281-305.
[6] Faruqee H., D. Laxton, D. Muir and P. Pesenti, 2007, �Smooth Landing or Crash?Model-Based Scenarios of Global Current Account Rebalancing�, in R. Clarida (ed.),G7 Current Account Imbalances: Sustainability and Adjustment, Chicago, IL: Univer-sity of Chicago Press, forthcoming.
[7] Faruqee H., D. Laxton, D. Muir and P. Pesenti, 2008, �Would Protectionism DefuseGlobal Imbalances and Spur Economic Activity? A Scenario Analysis�, Journal ofEconomic Dynamics and Control, forthcoming.
[8] Greenwood, J., Z. Herkowitz, and G. Hu¤man, 1988, � Investment, Capacity Utilizationand the Business Cycle.�American Economic Review 78,.pp. 402-17.
[9] Ireland, P., 2001. �Sticky-price models of the business cycle: speci�cation and stability.�Journal of Monetary Economics 47 (1), 3-18.
[10] Juillard M., P. Karam, D. Laxton and P. Pesenti, 2006, �Welfare-Based MonetaryPolicy Rules in an Estimated DSGE Model of the U.S. Economy�, European CentralBank Working Paper No.613, April.
[11] Laxton D., P. N�Diaye, and P. Pesenti, 2006, �De�ationary Shocks and MonetaryRules: An Open-Economy Scenario Analysis�, Journal of the Japanese and Interna-tional Economies 20 (4), International Finance, pp.665-698.
[12] Laxton D., and P. Pesenti, 2003, �Monetary Rules for Small, Open, EmergingEconomies�, Journal of Monetary Economics 50 (5), pp. 1109-1146.
[13] Obstfeld M., and K. Rogo¤, 1995, �Exchange Rate Dynamics Redux�, Journal of Po-litical Economy 103, pp. 624-660.
[14] Obstfeld M., and K. Rogo¤, 2000, �New Directions for Stochastic Open EconomyModels�, Journal of International Economics 50 (1), pp. 117-153.
[15] Obstfeld M., and K. Rogo¤, 2002, �Global Implications of Self-Oriented National Mon-etary Rules�, Quarterly Journal of Economics 117, pp. 503-36.
[16] Rotemberg, J., 1982. �Sticky prices in the United States�. Journal of Political Economy90, 1187-1211.
31
Figure 1: The Structure of the Model
I
E
GI
GN
K
C Gc
A
N
T
Q M Abroad
L
32