The US Dollar and Trade Deficit: WhatAccounts for the Late 1990s?∗

Benjamin Hunt and Alessandro Rebucci†

First Draft: February 2003(Preliminary and Incomplete)

Abstract

This paper asks to which extent productivity shocks may account forreal exchange rate and trade balance developments in the US in the sec-ond half of the 1990s. The analysis is based on a version GEM calibratedto analyze macroeconomic interdependence between the US and the restof the world. The paper concludes that the Balassa-Samuelson effect of apermanent productivity shock in the tradable sector of the economy mayexplain about half of the US dollar real appreciation in the late 1990s, buta broadly defined “risk premium” and some uncertainty about the persis-tence of these shocks are needed to match the data more satisfactorily.

Keywords: Balassa-Samuelson Effect; Distribution Costs, Productiv-ity Shocks; Real Exchange Rate; Risk Premium Shocks, Trade Balance,Non-Traded Goods; US Economy.

∗This paper builds upon the work of Paolo Pesenti and Doug Laxton, who developed GEM(Global Economy Model ), the new multi-country simulation model of the IMF Research De-partment, and made it operational. The authors wish to thank also Chris Erceg, Chris Guast,and Luca Guerrieri at the Federal Reserve Board and Tam Bayoumi for countless discussionsand comments, and Ken Rogoff for encouraging this research project. In addition, the authorsacknowledge the invaluable input of Michel Juillard and Susanna Mursula in developing someof the numerical procedures used in the quantitative analysis of the model, and thank JaewooLee, Matthew Canzonieri and seminar participants at Georgetown University for thier usefulcomments. Remaining errors are of the authors.

†The views expressed here are those of the authors and do not necessarily reflect theposition of the International Monetary Fund. E-mail addresses: bhunt@imf.org and arebuc-ci@imf.org.

1

I Introduction

The late 1990s saw a coincidence of events in the U.S. striking enough to require

an explanation. After a long period of modest growth, productivity accelerated

markedly. The acceleration in productivity was accompanied by an investment

boom, a gradual appreciation in the real exchange rate and a marked deteri-

oration in the external balance (Figure 1). Optimists saw the U.S. economy

entering a new era of prosperity driven by technology, while pessimists pointed

to growing financial imbalances characteristic of an unsustainable boom.

The subsequent recession has tempered the wings of both camps. It has

taken some of the shine off the optimists’ “new-economy” paradigm. At the

same time, the slowdown has been less steep and less U.S. specific, and the

rate of increase in productivity has remained more buoyant, than the pessimists

had predicted. Indeed, to some extent, the jury remains out on the underlying

causes, and hence consequences, of the acceleration of growth in the late 1990s.

This paper uses the IMF Research Department’s new Global Economy Model

(GEM), a multi-country simulation model for macroeconomic analysis and pol-

icy evaluationthe, to examine what may account for the real exchange rate

appreciation and external balance deterioration and broader business cycle de-

velopments in the U.S. in the second half of the 1990s.

GEM is a New-Open-Economy-Macroeconomics model.1 While not unique

in its class, GEM’s structure is of sufficient complexity to potentially provide

a satisfactory representation of trade and financial interdependence between

advanced and/or emerging market economies. Specifically, GEM is rich both

in terms of potential sources of disturbance to the economies considered as well

as in terms of complexity of the endogenous propagation mechanism of these

1See Lane (2001) and Sarno (2000) for surveys of the literature. Following the seminal

contribution of Obstfeld and Rogoff (1995, 1996), the New-Open-Economy-Macroeconomics

literature, has extended to open economies the new-Keynesian stochastic dynamic general

equilibrium framework with nominal rigidities and monopolistic competition that had previ-

ously proven successful in modeling the business cycle of closed-economies. Despite the wealth

of theoretical contributions already available, the new framework has not yet supplanted the

time-honored Mundell-Fleming-Dornbusch paradigm as the workhorse for international macro-

economic analysis and policy formulation. However, efforts are now underway at some policy

institutions (including the US Federal Reserve, the European Central Bank and the IMF) at

exploring the potential for the use of the new framework.

2

shocks. In addition, it is a multisector model; import and export equations are

derived from assumptions on trade specialization, tastes and technologies, and

short-run demand determination of output is explicitly micro funded with cost

of price adjustment and some market power.

The paper first examines the degree to which a permanent, country-specific

productivity shock associated with the IT revolution can explain the behavior of

the U.S. economy in the late 1990s. As we shall see, the Balassa-Samuelson effect

of such a productivity shock in the tradable sector allow us to explain about half

of the dollar appreciation in the late 1990s. According to our results, however, a

productivity shock is not the end of the story. To match the exchange rate data

and the broader business cycle picture more satisfactorily, we need to add two

features: a learning mechanism with regard to the persistence of the productivity

acceleration and another shock–a reduction in the perceived riskiness of US

assets.2 These results suggest that both sides of the “new economy” debate had

a point. The behavior of the U.S. economy in the late 1990s likely reflected both

a genuine productivity shock as well as financial market factors.

The rest of the paper is organized as follows. Section two describes the

main theoretical features of the model. Section three discusses the model base-

line calibration and its numerical solution. Section four reports on the model’s

main dynamic and static properties. Section five concludes. First order condi-

tions of the optimization problems and other theoretical details are reported in

appendix.

II The model

The basic structure of the model is outlined in this section and illustrated in

Figure 2.3 The world economy consists of two countries, Home (identified with

the US in this application) and Foreign (identified with the rest of the world).

Foreign variables are indexed with a star. In each country there are households,

2This point is also made by Erceg, Guerrieri, and Gust (2002) (henceforth EGG) and Hunt

(2002), among others.3For a detailed presentation of GEM see Pesenti (2002). For an application of GEM to the

analysis of interest rate rules in advanced transition economies see Laxton and Pesenti (2003).

The reader familiar with the GEM’s theoretical framework may skip this section and move on

to section three, in which we describe the model calibration.

3

firms, and a government.

Each household is infinitely lived, consumes a single non-tradable final good

(A), and is the monopolistic supplier of a differentiated labor input (`) to all

domestic firms. Wage contracts are subject to adjustment costs, which give rise

to nominal wage rigidities.

Each household owns all domestic firms and the domestic capital stock (K),

which it rents to domestic firms. The market for capital is competitive, but

capital accumulation is subject to adjustment costs. Labor and capital are

immobile internationally. Households trade short-term nominal bonds, denom-

inated in Foreign currency, and issued in zero net supply worldwide. There

are intermediation costs for Home households entering the international bond

market. No other asset is traded internationally.

Firms produce a continuum of non-tradable final goods, a continuum of dif-

ferentiated non-tradable intermediate goods (N), a continuum of differentiated

tradable intermediate goods (T ), and provide distribution and financial inter-

mediation services.

The final good is produced by perfectly competitive firms that use all inter-

mediate goods: non-tradable goods (NN), domestic tradables (Q) or imported

tradables (M) as inputs. The final good can be consumed by domestic house-

holds (C) or the government (GA), or used for investment (I).

Each intermediate good is produced by a single firm under conditions of

monopolistic competition by using labor and capital. Prices of intermediate

goods are subject to adjustment costs, which give rise to nominal price rigidities.

Each non-tradable intermediate good is either used directly in the production

of the non-tradable final good or used indirectly in the distribution sector to

make tradable intermediate goods available to firms producing the final good.

Each tradable intermediate good is used either in the production of the domestic

non-tradable final good or in the production of the foreign final good (Q and

M∗, respectively).

Firms in the distribution sector operate under perfect competition. They

purchase tradable intermediate goods worldwide (at the producer price) and

distribute them to firms producing the final good (at the consumer price). Local

non-tradables are the only input in the provision of distribution services.

Government spending (GA) falls exclusively on the final non-tradable good.

4

Government spending is financed through tax and seigniorage revenues. The

government controls the national short-term nominal interest rate. Monetary

policy is specified in terms of interest rate rules.

A Final goods production

There is a continuum of symmetric Home firms producing the Home final good,

indexed by x ∈ [0, s], where 0 < s < 1 is a measure of country size. World

size is normalized to 1, and Foreign firms producing the Foreign final good are

indexed by x∗ ∈ (s, 1].Home firm x’s output at time (quarter) t is denoted At(x).4 The final good

is produced with the following CES technology:

At(x) ≡"γ1ε

³ν

1εQM Qt(x)

1− 1εQM + (1− ν)

1εQM [Mt(x) (1− ΓM,t(x))]1−

1εQM

´ εQMεQM−1(1−

1ε)

(1)

+(1− γ)1ε NN,t(x)

1− 1ε

i εε−1

Three intermediate inputs are used in the production of the final good: a basket

Q of Home tradable goods, a basket M of imported Foreign tradable goods,

and a basket NN of Home non-tradable goods. The elasticity of substitution

between tradables and nontradables is ε, while the elasticity of substitution

between domestic and imported tradable inputs is εQM . The parameters γ and

ν determine the degree of openness of the economy and the extent to which

Home preferences are skewed toward home goods (i.e., home bias).5 In the

spirit of Erceg, Guerrieri and Gust (2002), we also assume that it is costly to

change the share of the imported goods in total production. Imports are subject

to adjustment costs ΓM , where:6

ΓM,t(x) ≡ φM2

µMt(x)

At(x)/Mt−1At−1

− 1¶2.(2)

4The convention throughout the model is that variables which are not explicitly indexed

(to firms or households) are expressed in per-capita (average) terms. For instance, At ≡(1/s)

R s0 At(x)dx.

5The model can be easily re-interpreted as if households consumed directly a basket A of

domestic and imported final goods. In this case γ and ν would be interpreted as preference

parameters.6Different from EGG, it is assumed that for the firm it is costly to adjust its current

imports/output ratio relatively to the past aggregate imports/output ratio.

5

Home firm x takes the prices of the intermediate baskets PQ, PM and PN

as given, and solves the following minimization problem:

{Qt(x),Mt(x), NN,t(x)} = argmin {PQ,tQt(x) + PM,tMt(x) + PN,tNN,t(x)

(3)

+ Pt

At(x)−γ 1

ε

³ν

1εQM Qt(x)

1− 1εQM + (1− ν)

1εQM [Mt(x) (1− ΓM,t(x))]1−

1εQM

´ εQMεQM−1(1−

1ε)

+ (1− γ)1ε NN,t(x)

1− 1ε

i εε−1¶¾

,

where Pt is the consumption price of the final good, equal to its marginal cost.7

Foreign variables are similarly defined and Foreign firms solve an analogous

maximization problem.8

B The distribution sector

Firms producing the final good cannot purchase the intermediate tradables di-

rectly from the producers. Instead, firms in the distribution sector purchase

tradables both domestically and abroad and distribute them to the firms pro-

ducing the final good. The distribution technology is Leontief: to make one

unit of an intermediate good available to downstream producers, firms in the

distribution sector require η ≥ 0 units of the non-tradable basket N . There areno distribution costs for non-tradables.9

Firms in the distribution sector are perfectly competitive. Because of dis-

tribution costs, there is a wedge between producer and consumer prices (that

is, between wholesale and retail prices). We denote with p the consumer price

(that is, the price paid by Home firms producing the final good) and with p̄

the Home-currency producer price (that is, the price paid by Home firms in

the distribution sector) of an intermediate good. For each good n, h, and f ,

respectively, it follows that :

pt(n) = p̄t(n), pt(h)− p̄t(h) = pt(f)− p̄t(f) = ηPN,t(4)

7First order conditions and other technical derivations can be found in Appendix.8This is the case throughout the rest of this section unless explicitly noted.9The specification of the distribution sector builds on Corsetti and Dedola (2002).

6

C Price setting in the intermediate goods sector

Demand and supply for tradable and non-tradable intermediate goods are de-

rived in Appendix. Here we focus on firms’ pricing behavior, which is a key

aspect of the model.

Consider profit maximization in the Home country’s intermediate non-tradable

sector. Each firm n takes into account its demand for its product (equation 26

in Appendix) and sets the nominal price p(n) by maximizing the present dis-

counted value of real profits, in the presence of sluggish price adjustment due

to resource costs measured in terms of total profits.

The adjustment cost is denoted ΓPN,t:

ΓPN,t(n) ≡ φN12

µpt(n)

πpt−1(n)− 1¶2+

φN22

µpt(n)/pt−1(n)PN,t−1/PN,t−2

− 1¶2

(5)

where φN1,φN2 ≥ 0 and π > 0, with π denoting the gross steady-state rate of

inflation. This specification generalizes Rotemberg’s (1982) quadratic cost of

price adjustment. Drawing from Ireland (2001), the adjustment cost has two

components. The first component is related to changes in the nominal price

relative to steady-state inflation. The second component is related to changes

in firm n’s price inflation relative to the past observed inflation rate in the

whole non-tradables sector. As costs apply to both changes in the nominal

price level and the inflation rate, they allow the model to reproduce realistic

inflation dynamics encompassing nominal inertias and staggering.

Thus, the price setting problem is:

{pτ(n)}∞τ=t = argmaxEt∞Xτ=t

©Dt,τ [pτ(n)−MCτ(n)]ND

t (n) [1− ΓPN,τ (n)]ª,

(6)

where the discount rate Dt,τ is the intertemporal marginal rate of substitution

in consumption of the representative household, to be defined below. The first

7

order condition for this problem is:

0 = [1− ΓPN,t(n)] [pt(n) (1− θ) + θMCt(n)]

− [pt(n)−MCt(n)] φN1pt(n)πpt−1(n)

µpt(n)

πpt−1(n)− 1¶

− [pt(n)−MCt(n)] φN2pt(n)/pt−1(n)PN,t−1/PN,t−2

µpt(n)/pt−1(n)PN,t−1/PN,t−2

− 1¶

+EtDt,t+1 [pt+1(n)−MCt+1(n)] Nt+1(n)Nt(n)

∗·φN1pt+1(n)

πpt(n)

µpt+1(n)

πpt(n)− 1¶

(7)

+φN2pt+1(n)/pt(n)

PN,t/PN,t−1

µpt+1(n)/pt(n)

PN,t/PN,t−1− 1¶¸,(8)

which, in the absence of price stickiness or when prices are fully flexible (φN1 =

φN2 = 0), comes down to the simple markup rule:

pt(n) =θ

θ − 1MCt(n).(9)

Consider now the Home firm producing tradables. The price setting problem

in the tradable sector is similar to that in the non-tradable sector (see Appen-

dix), although the presence of the distribution sector intensive in non-tradables

implies that the simple mark up rule above, in the absence of price rigidities,

becomes:

p̄t(h) =θ

θ − 1MCt(h) +η

θ − 1PN,t(10)

and:

Etp̄∗t (h) =θ

θ − 1MCt(h) +η∗

θ − 1EtP∗N,t.(11)

As stressed by Corsetti and Dedola (2002), in the presence of distribution

costs, exchange rate pass-through is less than perfect (i.e., ∂ log p̄∗t (h)/∂ log Et ≤1) and the law of one price does not hold in the presence of distribution costs

(i.e., p̄t(h) 6= Etp̄∗t (h)) even if the prices of the tradable goods are flexible.In this context, asymmetry in relative productivity, relative wages, or relative

costs of capital drive a wedge between Home and Foreign prices of good h.

Markups in both markets are state-contingent and vary as functions of the

shocks. Similar considerations apply to the retail (consumer) market (thus,

∂ log p∗t (h)/∂ log Et ≤ 1 and pt(h) 6= Etp∗t (h)).

8

D Labor market

Each household is the monopolistic supplier of a labor input j. Using equal on

31 in Appendix and its analogs, total demand for type j input is:

`t(j) =

µWt(j)

Wt

¶−φ`t(12)

where `t is per-capita total labor in the Home economy. Each household sets

the nominal wage for input type j accounting for (12).

Following Kim (2000), there is sluggish wage adjustment due to resource

costs that are measured in terms of the total wage bill. The adjustment cost is

denoted ΓW,t, with:

ΓW,t(j) ≡ φW1

2

µWt(j)

πWt−1 (j)− 1¶2+

φW2

2

µWt(j)/Wt−1 (j)Wt−1/Wt−2

− 1¶2

(13)

where φW1,φW2 ≥ 0. As was the case for prices above, wage adjustment costshave two components. The first one is related to changes of the nominal wage

relative to its gross steady-state rate of inflation. The second component is

related to changes in wage inflation relative to the past observed rate for the

whole economy.

E Consumer preferences and optimization

Households’ preferences are additively separable in consumption and labor ef-

fort. Denoting with Wt(j) the lifetime expected utility of Home agent j, we

have:

Wt(j) ≡ Et∞Xτ=t

βτ−t [U (Cτ (j))− V (`τ(j))] ,(14)

where β is the discount rate, identical across countries.

There is habit persistence in consumption according to the specification:

Ut(j) = ZU,t log (Ct(j)− bCt−1)(15)

where Ct−1 is past per-capita Home consumption and 0 < b < 1. The term ZU,tis a preference shock common to all Home residents.

The parametric specification of V is:

Vt(j) = ZV,t`(j)1+ζ

1 + ζ(16)

9

where ζ > 0 and ZV,t is a shock to labor disutility. Foreign agent j∗’s preferences

are similarly specified.

The representative Home household chooses bond and money holdings, cap-

ital and consumption paths, and sets wages to maximize its expected lifetime

utility (14) subject to the budget constraints (42) and (46), in Appendix and

taking into account (12).

The model is then closed by imposing the resource constraints and mar-

ket clearing conditions described in Appendix. The model calibration and the

solution techniques used are described in the next section.

III Model calibration and solution

A Calibration

The quarterly, two-country model presented in the previous section is calibrated

to simulate interdependence between the US, and the rest of the world. The

strategy to develop a baseline calibration is to rely on parameter values sup-

ported by available empirical evidence whenever possible or values that have

already been used in the literature.

We work with a standard, simple specification for preferences and technolo-

gies by assuming that the production functions for both traded and non-traded

goods have a Cobb-Douglass functional form and that the period utility func-

tion is additive-separable in consumption and labor effort and logarithmic in

consumption (i.e., unitary intertemporal elasticity of substitution). These as-

sumptions guarantee that the model converges to a steady state consistent with

balanced growth following persistent shocks to the rate of growth of total factor

productivity (TFP)–that imply a permanent change in the level of TFP.10

In general, we retain as much symmetry as possible between the Foreign and

the Home economy, except for those parameters that need to be set asymmet-

rically to characterize the US economy. These include country size and home

bias in consumption.

10Work is underway to generalize GEM to allow for labor-augmenting technical progress

and multiplicative, separable period utility function so that a CES production function and

an intertemporal elasticity of substitution different from one could also be used in analyzing

shocks with permanent level effects, while maintaining balanced growth.

10

Home country size (s) relative to the rest of the world is measured in terms of

(relative) GDP. We set s at 0.25 percent. For the home bias, we adopt parameter

values that yield realistic import and export ratios. In particular, the choice of

the relative weight of the non-tradable sector (γ) and the Home bias parameter

(ν) and their foreign equivalents determines the degree of openness of the two

economies assumed. In the baseline, we set γ = γ∗ = 0.67, ν = 0.98 and

ν∗ = 0.75 . This implies that there is no home bias in the Foreign economy and

some home bias in the Home economy compared to country size.

We assume that the weight of capital in the production of traded goods is

about a third (αT = α∗T = 0.36). In the non-traded good sector, we assume

that the capital share is slightly smaller–i.e., αN = α∗N = 0.30. Together, these

result in an investment-to-GDP ratio of about 20 percent a capital-to-GDP ratio

of about 2.11

The habit persistence parameter (b) is set to 0.931. The marginal disutility

of labor effort is V 0 = `ζ. Estimates of ζ based on micro-data consider anything

between 3 and 20 as a reasonable range. For instance, Gali, Gertler and Lopez-

Salido (2002) take ζ = 5 as their baseline, but Kollmann (2001) chooses ζ = 1

(linear disutility of labor) following the real business cycle literature. We assume

ζ = ζ∗ = 3. The discount rate, β, is the same in the two countries. The steady-

state real interest rate is 1/β = (1 + i) /π. A typical yearly calibration for the

real interest rate is 3-4 percent. We follow Christiano, Eichenbaum and Evans

(1999) and set β = 1.03−0.25.

The elasticity of substitution between traded and non-traded in goods in

final consumption, ε, is set at a relatively low level, 0.44 in both countries,

following Stockamn and Tsar (1995). The elasticity of substitution between

home and foreign tradable goods, instead, is assumed to be much higher–i.e.,

εQM = ε∗QM = 3. This is higher than in other studies, although the range

of plausible options is large and our sensitivity analysis suggests that all we

need to generate an appreciation in response to a permanent, country specific

productivity shock is a value larger than one.12

11Because GEM’s steady state has no growth, this ratios are lower than it would normally

be in the presence of growth.12Empirical studies of the price elasticity of import demand such as Hooper and Marquez

(1995) report a median value of 0.6 for Japan, Germany and UK. Gali and Monacelli (2002)

choose a unitary value as their baseline. Others, including Chari, Kehoe and McGrattan

11

Aggregate data suggest an annual depreciation rate for capital of about

10 percent, so δ = δ∗ = 0.025. The adjustment cost parameters for capital

accumulation, φI1 and φI2, are set at 50 and 4 respectively.

Burstein, Neves and Rebelo (2000) highlight the link between the distribu-

tion cost coefficient, η, and the wholesale/retail margin and set the parameters

η and η∗ equal to unity. However, in our model the wholesale/retail margin is a

function of other structural parameters such as the demand elasticities, and the

choice of the distribution parameter η also affects the degree of exchange rate

pass-through. Our baseline is η = η∗ = .33 in both the Home and the Foreign

economy, implying a moderate degree of pass-through consistent with empirical

evidence (See Campa and Goldberg (2001).

The elasticities of substitution among differentiated intermediate goods, θ

and θ∗, are evaluated by considering the steady-state price markups. For in-

stance, the markup is θ/ (θ − 1) in the tradeable sector, if there are no distribu-tion costs. Martins, Scarpetta and Pilat (1996) estimate the average markup for

manufacturing sectors at around 1.2 in most OECD countries over the period

1980-92. However, some authors rely on lower estimates: for instance, Chari,

Kehoe and McGrattan (2001) choose 1.1, while Morrison (1990), Domowitz,

Hubbard and Petersen (1988) suggest that a range between 1.2 and 1.7 may be

plausible. Benigno and Thoenissen (2001) estimate a parameter value yielding

a mark up of 1.16 for non-traded and 1.18 for traded in the United Kingdom.

We set θ/ (θ − 1) = 1.2 or θ = 6 in both countries.The elasticities of substitution among differentiated labor inputs, φ and φ∗,

are related to the wage markup. According to Gali, Gertler and Lopez-Salido

(2002), values between 1.15 and 1.4 for the sum of the steady-state wage and

price markups can be thought of as “falling within a plausible range”. For

instance, Benigno and Thoenissen (2001) estimate φ to imply a mark up of 1.24

for the UK, and 1.33 for the Euro area. Our parameterization takes φ = φ∗ = 6

to yield a mark up of 1.2.

The transaction cost parameters in the bond market are φB1 = 0.01 and

φB2 = 0.01, leading to a very slow reversion of the net asset position between

Home and Foreign to its steady-state value. This feature guarantees that in

(2001) and Smets and Wouters (2002a), set the elasticity of substitution between Home and

Foreign goods at 1.5.

12

the short-to-medium term the properties of the model–especially the degree

of persistence of bond holdings and the dynamics of the current account–are

largely unaffected by the asymptotic convergence condition.

Money demand plays a residual role in our model. We follow Schmitt-Grohe

and Uribe (2001) and set φS1 = 0.011 and φS2 = 0.075 in both countries,

consistent with their estimates of money demand in the US.

The baseline calibration of the model assumes a significant degree of struc-

tural inflation persistence in wages and prices in the tradable sector (controlled

by φT2 and φW2), but it does not assume any adjustment costs for changes in

the level of prices (φT1 = φW1 = 0). The adjustment cost parameters that

determine the degree of structural inflation persistence were calibrated to be

consistent with a sacrifice ratio of 1.2 in the Home and Foreign economy.13 This

assumption implies values for φN2, φT2, and φW2 equal to 400.

The baseline calibration of the model assumes that the prices of imported

goods that are purchased by wholesalers respond instantaneously to changes in

exchange rates (φM1 = φM2 = φ∗M1 = φ∗M2 = 0).

B Solution

The steady-state and dynamic simulations are solved with Portable Troll. The

steady state of the model is solved numerically by using a Newton-based algo-

rithm that has been designed to solve large models with significant nonlineari-

ties.14 We also rely upon a version of this algorithm to compute forward-looking

solutions of the model under the assumption of perfect foresight or kalman-filter-

based learning.

IV What accounts for the late 1990s?

How well can the model match the stylized facts of the US business cycle in the

late 1990s briefly presented in the introduction? We consider first the effect of

13The sacrifice ratio is defined to be the cumulative annual output gap that is required to

permanently reduce inflation by one percentage point. A sacrifice ratio of 1.2 is consistent

with the that implied by the FRB/US model under rational expectations.14 See Juillard and Laxton (2003) for a discussion of the robustness properties of this nu-

merical procedure. For a discussion Newton-based algorithms see Armstrong et al. (1998)

and Julliard et al. (1998).

13

a fully anticipated, country specific shock to productivity. The acceleration in

productivity occurs only in the tradable goods sector and thus leads to a Balassa-

Samuelson effect through the change in the price of tradable goods relative to

the price of non-tradable goods. We then add a learning process about the

expected persistence of this shock that is more in line with that observed in

forecasts of real growth in the U.S. over the period. Finally we add a broadly

defined risk premium shock to improve the match between the model and the

data. As we shall see, the Balassa-Samuelson effect is crucial to predict correctly

the sign of the exchange rate response. Adding uncertainty and a second shock,

however, results in a more accurate fit of the broader picture in the U.S. in the

late 1990s.

A Increased Productivity

The shock we consider is a long-lived, one percentage point acceleration in

the rate of growth of total factor productivity (TFP) in the Home tradable

sector. This acceleration lasts for five years, subsequently decaying slowly with

a quarterly auto-regressive coefficient of 0.975, implying a half life of ten years

once it starts to decay. This implies a permanent increase in the TFP level of

about 15 percentage points in steady state. A shock of this magnitude is broadly

consistent with the available evidence on the acceleration in productivity growth

in the United States in the second half of the 1990s.15

Figure [3] shows a first set of results. The solid line reports the key styl-

ized facts presented in the introduction for ease of reference. The dashed line

represents the impulse response of the model calibrated as in the baseline case

described in the previous section, assuming that the shock started in the first

15Estimates of the acceleration in labor productivity growth during the second half of the

1990s vary, but generally point to an increase somewhat in excess of one percent per year, on

average, broken down between capital deepening, TFP, and other factors (e.g., IMF WEO,

October 2001 issue, Table 3.4). Most of these estimates attribute about a third of the increase

to capital deepening and only two thirds to TFP and other factors. The evidence also suggests

that the acceleration in productivity growth was primarily in the tradable sector (Figure 4),

including IT but possibly also the broader manufacturing sector. We ignore the possibility

that the shock originated partly from autonomous capital deepening or innovation in the

semi-finished-good sector. To break down the productivity shock analyzed in intermediate

and semi-finished good components and investigate its diffusion to the whole economy is a

natural extension of this work in GEM.

14

quarter of 1996. The dotted line represents the response to the same shock in a

version of the model calibrated without non-tradable goods.16 This highlights

clearly the role of the Balassa-Samuelson effect of the productivity shock in

explaining the exchange rate response.

The baseline model presented in the previous section predicts the sign of the

exchange rate movement correctly, both on impact and in the long run, and, to

a lesser extent, also its magnitude: the exchange rate appreciates by roughly 7

percent on impact and then gradually appreciates further over the following five

years, reaching a level roughly 10 percent above its initial steady state. In the

long run, it appreciates by about 15 percent compared with an appreciation of

the US dollar by about [25] percent, cumulatively, between 1996 Q1 and 2001

Q3.

The different exchange rate response in the case in which there is no Balassa-

Samuelson effect in the model is striking. In the same model without non-

tradables, the real exchange rate exhibits only a very mild appreciation on

impact and then depreciates gradually. In this case, it depreciates by roughly 4

percent in steady state.

The Balassa-Samuelson effect stems from the presence of the non-tradable

sector combined with perfect labor mobility between the two sectors which

equalizes their nominal wages. With higher productivity in the tradable sector,

the marginal product of labor is higher and so must be the real wage. To achieve

a higher real wage, the price of the tradable good relative to the non-tradable

good declines. Because the foreign sector’s elasticity of substitution between

the foreign and home tradable good is relatively high (recall that εQM = 3), the

decline in the home country relative price of tradables necessitates that the real

exchange rate appreciate to moderate foreign demand and maintain a balanced

trade in the long run.

Figure [4] illustrates this point further by tracing out this comparative static

16 Some minor changes to the baseline calibration are required to eliminate non-tradable

goods from the model. Specifically, γ is increased to unity and η is set to zero in both the

Home and the Foreign economy. The home bias parameter, ν, is set to 0.958 to maintain a

import-to-GDP ratio of 13 percent. The Home country’s capital share αT is set to 0.33 to

maintain an investment-to-GDP ratio of 20 percent. The shock is also calibrated appropriately

so that it has the same long run effect on the level of output, even though the tradable sector

now represents about 40 percent of the total economy.

15

property of the model. The figure graphs the relation between the steady-

state change in the real exchange rate and different values of the elasticity of

substitution between the foreign and home tradable good, when the model is

subjected to a positive tradable sector productivity shock.17 As the elasticity

of substitution increases above unity, the productivity shocks leads to a steady-

state appreciation of the real exchange rate. Conversely, as the elasticity of

substitution falls below unity the steady-state real exchange rate depreciates in

the face of the productivity shock.

In the model calibrated without non-tradable goods, and thus without a

Balassa-Samuelson effect, the real exchange rate must depreciate to create the

demand needed to sell the additional tradable goods. With no fall in the Home

price of the tradeable good after the increase in tradable productivity, the Home

economy now has an excess supply of tradable goods. To increase demand for the

goods in both the Foreign country and the Home country, the real exchange rate

must depreciate; thereby lowering the relative price of the Home tradable good

in terms of the Foreign tradable good in both the Foreign and Home economies.

A closely related point is that without non-tradables the model does not track

the historical path of the trade balance nearly as well.

However, as is often the case with rational expectations, the model exhibits

too rapid a response to the shock and does not track well the other variables

considered . In particular, consumption immediately responds strongly as ra-

tional consumers understand fully how the acceleration in productivity growth

will affect their wealth. This drives demand above supply leading to a pickup

in inflation and a tightening of monetary policy, which dampens the response

of investment, further constraining supply. Moreover, even the exchange rate

jumps too much in the baseline model compared to historical data.

To improve upon this first set of results, we now consider how expectations

of the persistence in the productivity shock might have affected the dynamics.

In the last subsection, we then consider the value added of a second shock.

17For this comparative statics experiment, the model is calibrated so that the steady-state

effect of a productivity shock on the real exchange rate is zero when the elasticity of sub-

stitution between the foreign and home tradable good is unity. To achieve this the model

calibrated with no distribution sector and no home bias.

16

B Uncertainty over the shock’s persistence

To represent uncertainty on the shock’s persistence, we augment the model with

a signal extraction process, similar to that employed by EGG (2002), whereby

agents learn gradually about the persistence of the shock. This gradual learning

is consistent with the historical evolution of the five-year-ahead forecasts of the

acceleration in real growth in the United States plotted in Figure 5. These

forecasts (from the Congressional Budget Office and the consensus of Blue Chip

Forecasters) suggest that over the first three years of acceleration in productivity

growth, expectations about its persistence were quite low. In the fourth and fifth

years expectations about the persistence of this acceleration increased sharply.

This uncertainty is incorporated by integrating the following signal extrac-

tion problem into the simulation analysis:

∆Zt = Pt + Tt,

Pt = ρ · Pt−1 + εt,

Tt = 0 · Tt−1 + νt,

where ∆Zt is the observed growth in productivity, Pt is the unobserved persis-

tent component, Tt is the unobserved temporary component, ρ is the autore-

gressive coefficient on the persistent component (set to 0.975), εt ∼ N(0,σ2ε),and νt ∼ N(0,σ2ν).Given the model of productivity growth and the period t observed growth in

productivity, the Kalman filter is used to generate optimal estimates of period

t’s persistent and temporary components. These estimates are then used along

with the model to generate forecasts of productivity growth beyond period t. At

period t+1, a new observation on productivity growth is received and estimates

of period t+1’s persistent and temporary components are generated. These in

turn are used to generate new forecasts of future productivity growth and so

on. Using this model, the speed with which agents learn the truth about the

persistent component of the shock we are considering depends on the relative

variances of the persistent and temporary components. If agents use a model in

which they expect the variance of the persistent component to be high relative

to the temporary component, then they will learn quickly. If, on the other hand,

this relative variance is expected to be low, they will learn rather slowly.

17

In addition to the five-year-ahead forecasts of the acceleration in U.S. real

growth, Figure 5 also contains three alternative paths for the expectations of

the five-year-ahead acceleration in real growth. These paths are generated by

using the Kalman filter to solve the signal extraction problem based on the

above model when it is subjected to the productivity shock considered in the

simulation analysis. The path labeled “high-variance” represents expectations

of the five-year-ahead growth rate based on a very high expected variance of the

persistent component. Using this relative variance, the Kalman filter is able to

perfectly forecast the persistent component. The path labeled “low variance”

reflects expectations of the five-year-ahead growth rate based on a low expected

variance of the persistent component as done by EGG (2002). While the “low-

variance” path results in slower learning about the persistent component than

under certainty, it still does not capture the trend in the forecasts data that

suggests that very little learning occurred in the early years with very rapid

learning in the last two.

To capture this aspect we extend the signal extraction model and allow for

expectations of the variance of the persistent component to be time varying.

Now εt ∼ N(0,σ2εt), and νt ∼ N(0,σ2νt) This time-varying relative variance iscalibrated to yield the path for the five-year-ahead expectation of real growth

given by the path labeled “time-varying variance". Although this path still

incorporates more learning in the early years than is suggested by the evolution

of the forecasts of real growth, it captures the basic non-linear trend better.

As Figure [6] shows, when agents learn about the persistence of the pro-

ductivity shock slowly, there is a much milder initial increase in consumption.

Given the increase in productivity, this slower response of consumption implies

more spare capacity that puts downward pressure on inflation and allows nomi-

nal interest rates to fall. A lower cost of capital results in a more rapid increase

in investment than under certainty about the persistence of the shock. Further,

the resulting increase in real GDP growth is also much closer to the histori-

cal acceleration. In addition, the real exchange rate does not jump on impact

following the shock and appreciates gradually in a manner which is more con-

sistent with the historical data. Nonetheless, the slower appreciation of the real

exchange rate results in a notably smaller deterioration in the trade balance.

Clearly something else is needed to explain the external performance of the U.S.

18

economy.

Integrating a model of learning into the simulation of the productivity shock

goes some way toward allowing the baseline model to match not only the sign

of the exchange rate response but also its shape. In addition, it helps match the

broader picture in the key stylized facts. Yet, the magnitude of the real exchange

rate appreciation, the trade balance deterioration, the inflation decline, and

consumption and investment responses remain smaller than those observed in

the data. It is thus natural to consider additional shocks, which is what we now

turn to.

C Decreased risk premium

The reduction in the perceived riskiness of investments in U.S. assets is a factor

often mentioned as a possible explanation of the business cycle developments of

the late 1990s, in addition to faster productivity growth. In particular it is an

obvious way of explaining the large appreciation of the dollar over that period

and the significant deterioration in the trade balance.

While the assertion that productivity growth accelerated during the sec-

ond half of the 1990s is well supported by the evidence, the proposition that

investors’ subjective evaluation of the riskiness of US assets changed in the sec-

ond part of 1990s is more tentative because estimates of the unobserved risk

premium are difficult to generate. Wadhwani (1999) provides some evidence

that the equity risk premium declined in the United States in the latter half of

the 1990s although Jagannathan and others (2001) provide estimates that sug-

gests that the decline in the risk premium is evident over the last three decades.

Nonetheless, economic developments in south east Asia, Latin America, Japan

and Europe in the latter half of the 1990s provide some support for considering

the possibility of shift in investor sentiment toward US assets. In fact, the Asian

currency crisis and its spillover effects to Latin America, the stagnant economic

performance of Japan, and uncertainties and frictions related to the introduc-

tion of Euro could all have contributed to investors viewing US assets as being

less risky in the latter half of the 1990s.

In light of this evidence, we add to our simulation analysis a shock to the

risk premium demanded on US assets. This shock consists of a 100 basis point

decline in the Home country risk premium that lasts for five years and then

19

subsequently decays with an autoregressive parameter of 0.95. As in the case

of the productivity shock, we assume that agents learn over time about its

persistence.We achieve this by adding a second signal extraction problem to the

model. Further, we assume that the two shocks are correlated and thus the

learning process about the persistence of the risk premium shock evolves in a

(non-linear) fashion similar to that incorporated for the productivity shock.18

Incorporating both a productivity and risk premium shock into the analysis

yields very good results, which are reported in Figure 7. The combination

of these two shocks enables the model to closely reproduce the key stylized

facts discussed thus far. The initial response of the real exchange rate is less

well characterized, it jumps slightly. However, even in this case its subsequent

path tracks the evolution of actual data very closely. The deterioration in the

trade balance is also virtually identical to that in the data, while the paths for

investment, consumption, real growth, and the decline in inflation are matched

in a satisfactory manner.

A key to this last result is not only the mere addition of an additional

source of disturbance to the model, but also its intrinsic propagation mechanism.

Specifically, the presence of the distribution sector intensive in the non-tradable

good plays a pivotal role in tracking the historical data well. The distribution

sector combines non-tradable and tradable goods resulting in incomplete pass-

through of changes in the exchange rate to final goods prices. With incomplete

pass-through, the net export position in the Home country remains stronger

than it otherwise would, maintaining domestic demand and not allowing too

much deterioration in the trade balance. Without the distribution sector, im-

ports would rise too much, exports decline too much, and demand for home

output would need to be supported by a decline in nominal interest rates. This

decline in nominal interest rates, in turn, would lead to a weaker real exchange

rate than in the data, a worse trade balance, lower inflation and slower growth.

18One justification for assuming that the two shocks are correlated can be found in the

fact that the model does not include international trade in equities. Consequently, the return

parity condition appearing in the model of the exchange rate does not include the return to

capital. If we interpret the shock to the risk premium as attempting to capture the capital

flows that would have obtained in the face of the productivity shock if the model incorporated

international trade in equities, then agents’ expectations of the persistence in the two shocks

should also be correlated.

20

V Conclusions

The evolution of the U.S. economy in the late 1990s presents economists with

an interesting puzzle. Unlike the (monetary) business cycles in the previous

two decades, the period of accelerating growth of the late 1990s was not quickly

followed by a significant increase in inflation, tightening of monetary policy and

reversal in real activity. Instead, inflation remained subdued, and interest rates

remained stable, the U.S. exchange rate appreciated and capital flowed into the

U.S. financing a significant deterioration in the trade balance. Moreover, there

is now growing evidence that the acceleration in real activity was driven largely

by an acceleration in productivity growth broadly related to innovation in the

IT sector.

In this paper we have used GEM to investigate how much of these develop-

ments may be explained by a temporary but persistent acceleration in tradables

sector productivity growth. We find that a model with both tradable and non-

tradable goods, through the Balassa-Samuelson effect explains about half of the

appreciation in the Dollar and the deterioration in the trade balance. Allowing

agents to learn only slowly about the shock’s persistence does not only improve

the matching of the shape of the exchange rate response but improves also the

fit of real growth, investment, consumption and inflation responses to the shock.

However, even after integrating learning into the model, a productivity shock

alone does not appear sufficient to explain the data fully. Adding a temporary

but persistent decline in the perceived riskiness of U.S. assets to the productivity

shock enables the model to closely track the historical evolution of the real

exchange rate, the trade balance, real growth, investment, consumption and

inflation. As in the case of the productivity shock, the presence of non-tradable

goods is key, through their role in the distribution sector, for the model’s ability

to match historical data.

This analysis provides the basis for a retrospective assessment of business

cycle developments in the U.S. in the second half of the 1990s and goes some

way toward reconciling existing interpretations.

21

A Appendix: The model’s details

A Final goods production

Cost minimization in Home final good production (problem 1 in the main text)

yields the following demands by firm x:

Qt(x) = γν

µPQ,t

Pt

¶−εQM µPX,t

Pt

¶εQM−εAt(x)(17)

NN,t(x) = (1− γ)

µPN,t

Pt

¶−εAt(x)(18)

Mt(x) = γ (1− ν)

µPM,t

Pt

¶−εQM µPX,t

Pt

¶εQM−εAt(x) ∗·

1− ΓM,t(x)− φM

µMt(x)

At(x)/Mt−1At−1

− 1¶µ

Mt(x)

At(x)/Mt−1At−1

¶¸εQM1− ΓM,t(x)(19)

where the shadow price of the basket of tradables is:

PX,t

Pt=

"ν

µPQ,tPt

¶1−εQM+ (1− ν)

µPM,tPt

¶1−εQM∗

∗·1− ΓM,t − φM

µMt

At/Mt−1At−1

− 1¶µ

Mt

At/Mt−1At−1

¶¸εQM−1# 11−εQM

.

B Intermediate goods

B.1 Demand

Consider the basket of Home intermediate non-tradable goods NN . This is a

CES index of differentiated goods defined over a continuum of mass s. Each of

these goods is produced by a single Home firm indexed by n ∈ [0, s]. Similarly,the baskets Q and M are CES indexes of differentiated intermediate tradables

produced in the Home country and imported from the Foreign country, respec-

tively. Home firms in the tradable sector are indexed by h ∈ [0, s], while Foreignfirms in the tradable sector are indexed by f ∈ (s, 1].Now, defining NN (n, x) as the demand of the intermediate good n by firm

x, the basket of intermediate non-tradable goods demanded by firm x, NN(x),

22

is defined as:

NN,t(x) ≡"µ1

s

¶ 1θZ s

0

NN,t (n, x)1− 1

θ dn

# θθ−1

,(20)

where θ > 1 denotes the elasticity of substitution among intermediate non-

tradables. Thus:

Qt(x) ≡"µ1

s

¶ 1θZ s

0

Qt (h, x)1− 1

θ dh

# θθ−1

,(21)

Mt(x) ≡"µ

1

1− s¶ 1

θ∗ Z 1

s

Mt (f, x)1− 1

θ∗ df

# θ∗θ∗−1

,(22)

where θ∗ > 1. Hence, the cost-minimizing prices of the baskets of intermediate

goods PN , PQ and PM are given by:

PN,t =

·µ1

s

¶Z s

0

pt (n)1−θ

dn

¸ 11−θ

(23)

PQ,t =

·µ1

s

¶Z s

0

pt (h)1−θ

dh

¸ 11−θ

(24)

PM,t =

·µ1

1− s¶Z 1

s

pt (f)1−θ∗

df

¸ 11−θ∗

.(25)

The nontradable good n is used directly in the production of the final good

and by firms in the distribution sector. Hence, aggregating across x, it can be

shown that total demand for n is:

NDt (n) =

µpt(n)

PN,t

¶−θ[NN,t + η (Qt +Mt)] .(26)

Similarly, Home demands for the tradable intermediate goods h and f are given

by:

Qt(h) =

µpt(h)

PQ,t

¶−θQt,(27)

Mt(f) =s

1− sµpt(f)

PM,t

¶−θ∗Mt.(28)

Foreign variables are similarly characterized.

23

B.2 Supply

Home nontradables are produced by symmetric firms using labor `(n) and cap-

ital K(n). The technology for production of good n is Cobb-Douglas:

NSt (n) ≡ ZN,t

h`t(n)

(1−αN )Kt(n)(αN)i,(29)

where ZN is a common total factor productivity (TFP) shock.

Differentiated labor inputs in the Home country are indexed by j ∈ [0, s].We define:

`t(n) ≡"µ1

s

¶ 1φZ s

0

`(n, j)1−1φ dj

# φφ−1

,(30)

where `(n, j) is the demand of labor input of type j by the producer of good n

and φ > 1 is the elasticity of substitution among labor inputs.

Firms producing intermediate goods take the prices of labor inputs and

capital as given. Cost minimization implies that the demand for labor input j

by firm n is a function of the relative wage:

`t(n, j) =

µ1

s

¶µWt(j)

Wt

¶−φ`t(n)(31)

whereW(j) is the nominal wage paid to Home labor input j and the wage index

W is defined as:

Wt =

·µ1

s

¶Z s

0

Wt(j)1−φdj

¸ 11−φ

.(32)

Denoting R the Home nominal rental price of capital, firms solve the follow-

ing cost-minimization problem:

{`t(n),Kt(n)} = argmin{Wt`t(n) +RtKt(n) +

MCt(n)³NSt (n)− ZN,t`t(n)(1−αN )Kt(n)(αN)

´},

where the MC(n) is the nominal marginal cost. Cost minimization yields:

`t(n) = (1− αN)

µWt

MCN,t(n)ZN,t

¶NSt (n)

ZN,t(33)

Kt(n) = αN

µRt

MCN,t(n)ZN,t

¶NSt (n)

ZN,t.(34)

The production of Home tradables, TS(h), Foreign nontradables NSt (n

∗)

and Foreign tradables TS(f) is similarly characterized.

24

B.3 Price setting in the Home tradable intermediate goods sector

Denoting the nominal exchange rate with E , firm h’s price setting problem in

the Home tradable intermediate sector is:

{p̄τ(h), p̄τ∗(h)}∞τ=t = argmaxEt∞Xτ=t

Dt,τ {[p̄τ(h)−MCτ(h)] ∗(35)

∗µp̄τ(h) + ηPN,τ

PQ,τ

¶−θQτ [1− ΓPQ,τ (h)] + [Eτ p̄τ∗(h)−MCτ(h)] ∗

∗Ãp̄τ∗(h) + η∗P ∗N,τ

P∗M,τ

!−θMτ∗

1− ss

£1− Γ∗PM,τ (h)

¤where the costs ΓPQ,t(h) and Γ∗PM,t(h) are the analogs of (5):

ΓPQ,t(h) ≡ φQ12

µp̄t(h)

πp̄t−1(h)− 1¶2+

φQ22

µp̄t(h)/p̄t−1(h)P̄N,t−1/P̄N,t−2

− 1¶2

(36)

Γ∗PM,t(h) ≡φ∗M1

2

µp̄∗t (h)

π∗p̄∗t−1(h)− 1¶2+

φ∗M2

2

Ãp̄∗t (h)/p̄∗t−1(h)P̄ ∗M,t−1/P̄

∗M,t−2

− 1!2

(37)

Profit maximization yields:

0 = [1− ΓPQ,t(h)] p̄t(h)

p̄t(h) + ηPN,t[p̄t(h) (1− θ) + ηPN,t + θMCt(h)]

− [p̄t(h)−MCt(h)] φQ1p̄t(h)πp̄t−1(h)

µp̄t(h)

πp̄t−1(h)− 1¶

− [p̄t(h)−MCt(h)] φQ2p̄t(h)/p̄t−1(h)P̄N,t−1/P̄N,t−2

µp̄t(h)/p̄t−1(h)P̄N,t−1/P̄N,t−2

− 1¶

+EtDt,t+1 [p̄t+1(h)−MCt+1(h)] Qt+1(h)Qt(h)

∗·φQ1p̄t+1(h)

πp̄t(h)∗

∗µp̄t+1(h)

πp̄t(h)− 1¶+

φQ2p̄t+1(h)/p̄t(h)

P̄N,t/P̄N,t−1

µp̄t+1(h)/p̄t(h)

P̄N,t/P̄N,t−1− 1¶¸

(38)

25

and

0 =£1− Γ∗PM,t(h)

¤ p̄∗t (h)p̄∗t (h) + η∗P ∗N,t

£Etp̄∗t (h) (1− θ) + η∗EtP ∗N,t + θMCt(h)¤

− [Etp̄∗t (h)−MCt(h)]φ∗M1p̄

∗t (h)

π∗p̄∗t−1(h)

µp̄∗t (h)

π∗p̄∗t−1(h)− 1¶

− [Etp̄∗t (h)−MCt(h)]φ∗M2p̄

∗t (h)/p̄

∗t−1(h)

P̄∗M,t−1/P̄∗M,t−2

Ãp̄∗t (h)/p̄∗t−1(h)P̄ ∗M,t−1/P̄

∗M,t−2

− 1!

+EtDt,t+1£Et+1p̄∗t+1(h)−MCt+1(h)¤M∗t+1(h)M∗t (h)

·φ∗M1p̄

∗t+1(h)

π∗p̄∗t (h)∗

∗µp̄∗t+1(h)π∗p̄∗t (h)

− 1¶+

φ∗M2p̄∗t+1(h)/p̄

∗t (h)

P̄ ∗M,t/P̄∗M,t−1

Ãp̄∗t+1(h)/p̄∗t (h)P̄ ∗M,t/P̄

∗M,t−1

− 1!#(39)

which, in the absence of price stickiness, become:

p̄t(h) =θ

θ − 1MCt(h) +η

θ − 1PN,t(40)

and:

Etp̄∗t (h) =θ

θ − 1MCt(h) +η∗

θ − 1EtP∗N,t.(41)

C Households budget constraint and asset menu

The individual flow budget constraint for agent j in the Home country is:

Mt(j) +Bt+1(j) + EtB∗t+1(j) ≤(42)

Mt−1(j) + (1 + it)Bt(j) + (1 + i∗t ) [1− ΓB,t]EtB∗t (j) +RtKt(j)+ PL,tLt(j) +Wt(j)`t(j) [1− ΓW,t(j)]− PtCt(j) [1 + ΓS,t(j)]− PtIt(j) +Πt −NETTt(j).

Home agents hold domestic moneyM and two bonds, B and B∗, denominated

in Home and Foreign currency, respectively. The short-term nominal rates it+1and i∗t+1 are paid at the beginning of period t + 1 and are known at time t.19

The two short-term rates are directly controlled by the national governments.

Only the Foreign-currency bond is traded internationally: the Foreign bond is19We adopt the notation of Obstfeld and Rogoff (1996, ch.10). Specifically, our timing

convention has Bt(j) and B∗t (j) as agent j’s nominal bonds accumulated during period t− 1and carried over into period t.

26

in zero net supply worldwide, while the Home bond is in zero net supply at the

domestic level.

A financial friction ΓB is introduced to guarantee that net asset positions

follow a stationary process and the economies converge asymptotically to a

steady state.20 Drawing on Benigno (2001), Home agents face a transaction cost,

ΓB, when they take a position in the Foreign bond market. This cost depends on

the average net asset position of the whole economy and is zero only when Home

agents do not hold any Foreign-currency assets. This implies that in a non-

stochastic steady state Home agents have no incentive to hold Foreign bonds and

net asset positions are zero worldwide. An appropriate parameterization allows

the model to generate realistic dynamics for net asset positions and current

account.

Specifically, we adopt the following functional form for ΓB :

ΓB,t+1 = φB1

exp

µφB2

EtB∗H,t+1Pt

¶− 1

exp

µφB2

EtB∗H,t+1Pt

¶+ 1

+ ZB,t(43)

with 0 < φB1 < 1, φB2 > 0 and B∗H,t ≡ (1/s)R s0 B∗t (j)dj and where ZB,t is a

shock term.21

Ignoring ZB, when average Home holdings of the Foreign bond are zero,

ΓB = 0. When Home is a net lender and holdings of the Foreign bond go to

infinity, ΓB raises from zero to φB1, implying that Home households lose an

increasing fraction of their Foreign bond returns to financial intermediaries.22

Similarly when Home is a net borrower and holdings of the Foreign bond go

to minus infinity, ΓB falls from zero to −φB1 implying that Home householdspay an increasing intermediation premium on their debt. The parameter φB2controls the flatness of the ΓB function, hence the speed of convergence to the

steady state with zero net asset positions worldwide.

As for ZB , we note that uncertainty in international financial intermediation

plays in the GEM the same role that “uncovered interest parity shocks” or risk-20Alternative approaches to guarantee stationarity rely on parametric assumptions as in

Corsetti and Pesenti (2001a,b), time-varying discount rates or demographic dynamics as in

Ghironi (2003).21Fluctuations in ZB cannot be too large to push ΓB above 1.22 It is assumed that all intermediation firms are owned by Home residents, and that their

revenue is rebated to Home households in a lump-sum fashion.

27

premium fluctuations play in other open-economy models such as McCallum

and Nelson (1999) or Kollmann (2001).

Money transaction services enter GEM through a shopping technology. Specif-

ically, consumption spending is subject to a proportional transaction cost ΓSthat depends on the household’s money velocity v, where:

vt(j) ≡ PtCt(j)Mt(j).(44)

Following Schmitt-Grohe and Uribe (2001), the particular functional form for

the transaction cost is:

ΓS (vt) = φS1vt +φS2vt− 2pφS1φS2(45)

Agents optimally choose their stock of real money holdingsM/P so that at the

margin shopping costs measured in terms of foregone consumption are equal to

the benefits from investing in yield-bearing assets.

Home agents also accumulate physical capital which they rent to Home firms

at the nominal rate R. The law of motion of capital is:

Kt+1(j) = (1− δ)Kt(j) +ΨtKt(j) 0 < δ ≤ 1(46)

where δ is the depreciation rate.

To simulate realistic investment flows, capital accumulation is subject to

adjustment costs. Capital accumulation is denoted ΨtKt(j), where Ψ(.) is an

increasing, concave, and twice-continuously differentiable function of the invest-

ment/capital ratio, It(j)/Kt(j), suchg that Ψ(δ) = δ and Ψ0(δ) = 1, which

entails no adjustment costs in steady state. The specific functional form we

adopt is quadratic:

Ψt ≡ It(j)

Kt(j)− φI1

2

µIt(j)

Kt(j)− δ (1 + ZI,t)

¶2− φI2

2

µIt(j)

Kt(j)− It−1Kt−1

¶2(47)

where φI1,φI2 ≥ 0 and ZI,t is a shock.23Home agents own all Home firms and there is no international trade in claims

on firms’ profits. The variable Π includes all profits accruing to Home house-

holds, plus all Home-currency revenue from nominal and real adjustment costs

23An unexpected increase in ZI,t is equivalent to an increase in the rate of capital depreci-

ation that raises investment relative to baseline.

28

rebated in a lump-sum way to all Home households, plus revenue from financial

intermediation which is assumed to be provided by Home firms exclusively.

Finally, Home agents pay lump-sum (non-distortionary) net taxes NETTt(j)

denominated in Home currency. Similar relations hold in the Foreign country,

with the exception of the intermediation frictions in the financial market.

D Consumer optimization

The maximization problem of Home agent j can be written in terms of the

following Lagrangian:©Cτ (j), Iτ (j),Mτ (j), Bτ+1(j), B

∗τ+1(j),Kτ+1(j),Wτ (j)

ª∞τ=t

=

argmaxEt

∞Xτ=t

βτ−t©U [Cτ (j)]− V

£W−φτ (j)Wφ

τ `τ¤

+ (1/µτ (j))£−Mτ (j)−Bτ+1(j)− EτB∗τ+1(j) +Mτ−1(j) + (1 + iτ )Bτ (j)

+ (1 + i∗τ ) [1− ΓB,τ ] EτB∗τ (j) +RτKτ (j) +

+ PL,τLτ (j) +Wτ (j)1−φWφ

τ `τ [1− ΓW,τ {Wτ (j),Wτ−1(j)}]−PτCτ (j) [1 + ΓS,τ {Mτ (j), Cτ (j)}]− PτIτ (j) +Πτ −NETTτ (j)]

+λτ [−Kτ+1(j) + (1− δ)Kτ (j) +Ψτ {Iτ (j)/Kτ (j)}Kτ (j)]}(48)

where 1/µ and λ are the multipliers associated with, respectively, the budget

constraint and the law of motion for capital.

With complete domestic markets,24 in a symmetric equilibrium, U 0(Ct(j)) =

U 0(Ct) for all agents j, where C is per-capita Home consumption. Now define:

Dt,τ ≡ βPtU

0(Cτ )£1 + ΓS,t + Γ

0S,tvt

¤PτU 0(Ct)

h1 + ΓS,τ + Γ0S,τvτ

i ,(49)

which is Home agents’ stochastic discount rate and the Home pricing kernel.

Then the first order conditions with respect to Bt+1(j) and B∗t+1(j) imply:

1 = (1 + it+1)EtDt,t+1 =¡1 + i∗t+1

¢(1− ΓB,t+1)Et

µDt,t+1

Et+1Et

¶,(50)

24While markets are internally complete, guaranteeing equalization of the marginal utility

across each country’s residents, markets are not complete internationally and the marginal

utilities of Home and Foreign agents need not be equal.

29

which is a risk-adjusted uncovered interest parity condition–recalling that the

return on lending to Foreign is reduced (and the cost of borrowing from Foreign

is increased) by the costs of intermediation ΓB. In a non-stochastic steady state

1+ i = π/β, where π is the gross steady-state inflation rate and 1/β is the gross

rate of time preference, and the interest differential (1 + i) / (1 + i∗) is equal to

the steady-state nominal depreciation rate of the Home currency.

The first order conditions with respect to Mt(j), Kt+1(j) and Wt(j) are,

respectively:

1− Γ0S,tv2t = EtDt,t+1(51)

1

Ψ0t= Et

½Dt,t+1

Pt+1Pt

µRt+1Pt+1

+1

Ψ0t+1∗

∗·1− δ +Ψt+1

µ1− Ψ

0t+1

Ψt+1

It+1(j)

Kt+1(j)

¶¸¶¾(52)

φV 0t (j)U 0t(j)

PtWt(j)

= (φ− 1) [1− ΓW,t(j)]

+Wt(j)

·φW1

πWt−1 (j)

µWt(j)

πWt−1 (j)− 1¶+

φW2Wt−2Wt−1(j)Wt−1

µWt(j)/Wt−1(j)Wt−1/Wt−2

− 1¶¸

−Et½Dt,t+1Wt+1(j)

`t+1(j)

`t(j)

φW1Wt+1(j)

πW 2t (j)

µWt+1(j)

πWt (j)− 1¶¾

−Et½Dt,t+1

Wt+1(j)

Wt(j)

`t+1(j)

`t(j)

φW2Wt+1(j)/Wt (j)

Wt/Wt−1

µWt+1(j)/Wt (j)

Wt/Wt−1− 1¶¾

(53)

Expression (51) defines real money balances M/P as a positive function of con-

sumption and a negative function of the nominal interest rate. Expression (52)

links capital accumulation to the behavior of the real price of capital R/P .

In a non-stochastic steady state 1 + R/P is equal to the sum of the rate of

time preference 1/β and the rate of capital depreciation δ.25 Finally, expression

(53) describes the dynamics of real wages. In a non-stochastic steady state the

real wage W/P is equal to the marginal rate of substitution between consump-

tion and leisure, V 0/U 0, augmented by the markup φ/ (φ− 1) which reflectsmonopoly power in the labor market.

Optimization also implies that households exhaust their intertemporal bud-

get constraint: the flow budget constraint (42) holds as equality and the follow-

25 If the shocks ZI , Z∗I are permanent, 1 +R/P = 1/β + δ (1 + ZI) in steady state.

30

ing transversality condition:

limτ→∞EtDt,τ [Mτ−1(j) + (1 + iτ)Bτ(j) + (1 + iτ∗) (1− ΓB,τ ) EτBτ∗(j)] = 0(54)

must be satisfied.

Similar results characterize the optimization problem of Foreign agent j∗.

E Government

Public spending falls entirely on the non-tradable final good, GA. Governments

finance public expenditure through net lump-sum taxes and seigniorage revenue.

Thus, the budget constraint of the Home government is (in per capita terms):

sPtGA,t ≤Z s

0

NETTt(j)dj +

Z s

0

[Mt(j)−Mt−1(j)] dj.(55)

The government controls the short-term rate it+1. Monetary policy is spec-

ified in terms of generalized interest-rate rules of the form:

(1 + it+1)4 − 1 = ωi

h(1 + it)

4 − 1i

(56)

+(1− ωi)h¡1 + it+1

¢4 − 1i+ ω1Et

·Pt+τPt−4+τ

−Πt+τ¸+Θ (zt)

where the left hand side is the annualized interest rate, it is the lagged interest

rate, 0 < ωi < 1, and it+1 is the desired interest rate, defined as:26¡1 + it+1

¢4=1

β4Pt+τPt−4+τ

.(57)

In this expression, Pt+τ/Pt−4+τ is the year-on-year gross CPI inflation rate τ

quarters into the future, and Πt+τ is the year-on-year gross inflation target τ

quarters into the future. The term Θ is a function of a set, zt, of observablevariables (including the output gap, the exchange rate, etc.) expressed in devi-

ation from their targets and determining feedback rules for the nominal interest

rate. In a steady state in which all targets are reached, including a constant

inflation target Π, it must be the case that:

1 + it+1 = 1 + it+1 =1

β

µPtPt−4

¶0.25=Π0.25

β=

π

β.(58)

26Our specification facilitates the comparison with Taylor-style rules in log-linearized

models.

31

Foreign variables are similarly characterized. Any steady-state discrepancy

between i and i∗ (thus, between π and π∗) determines the steady-state rate of

exchange rate depreciation (for π > π∗) or appreciation (for π < π∗).

F Market clearing

The Home non-tradable final good can be used for private consumption C,

government consumption GA and investment I:Z s

0

At(x)dx ≥Z s

0

Ct(j)[1 + ΓS,t(j)]dj + sGA,t +

Z s

0

It(j)dj(59)

The resource constraint for good n is NS(n) ≥ ND(n). In equilibrium this

constraint holds as an equality and implies p(n) = PN . Similar considerations

hold for the other price indexes.

The Home tradable h can be used by Home firms or imported by Foreign

firms, so that T (h) ≥ Q(h)+M∗(h) and, in aggregate, sT ≥ sQ+(1− s)M∗(h).The resource constraint for factor markets are:Z s

0

`t(j)dj =

Z s

0

`t(n)dn+

Z s

0

`t(h)dh+

Z s

0

`t(o)do(60) Z s

0

Kt(j)dj =

Z s

0

Kt(n)dn+

Z s

0

Kt(h)dh+

Z s

0

Kt(o)do.(61)

Finally, similar expressions hold abroad, while market clearing in the asset

market requires:Z s

0

Bt(j)dj = 0,Z s

0

B∗t (j)dj +Z 1

s

B∗t (j∗)dj∗ = 0.(62)

B Appendix: Learning

[To be completed and revised]

32

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37

Figure 1: United States: Stylized Facts (1994q1-2000q4)

1994 1995 1996 1997 1998 1999 200090

95

100

105

110

115

120

125

90

95

100

105

110

115

120

125

Real Effective Exchange Rate(Index; 1990=100)

1994 1995 1996 1997 1998 1999 2000-4.5

-4.0

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

-4.5

-4.0

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

Trade Balance(Expressed as a percent of GDP)

1994 1995 1996 1997 1998 1999 2000-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

Difference in GDP Growth From 1980-95 Average (Year-on-year; In percent)

1994 1995 1996 1997 1998 1999 2000-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

Difference in Inflation From 1992-95 Average(CPI all items less energy; Year-on-year; In percent)

1994 1995 1996 1997 1998 1999 200022.0

22.5

23.0

23.5

24.0

24.5

25.0

25.5

22.0

22.5

23.0

23.5

24.0

24.5

25.0

25.5

Investment(Expressed as a percent of GDP)

1994 1995 1996 1997 1998 1999 200059.0

59.5

60.0

60.5

61.0

61.5

59.0

59.5

60.0

60.5

61.0

61.5

Consumption(Expressed as a percent of GDP)

K

L

L*

K

*

TN

INTE

RM

ED

IATE

GO

OD

ST*

N*

QN

NM

M*

Q*

NN

*

AA

*FI

NAL

GO

OD

S

IG

AC

GA

*C

*I*

HO

ME

FOR

EIG

N

Fig.

2. G

EM’s

Bas

ic S

truc

ture

Figure 3: United States: Stylized Facts and Model Simulation Paths (1994q1-2000q4)Productivity Shock

(Solid - Actual data, Dashed - Tradable good only version, Dotted - Tradable plus nontradable good version)

1994 1995 1996 1997 1998 1999 200090

95

100

105

110

115

120

125

90

95

100

105

110

115

120

125

Real Effective Exchange Rate(Index; 1990=100)

1994 1995 1996 1997 1998 1999 2000-4.5

-4.0

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

-4.5

-4.0

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

Trade Balance(Expressed as a percent of GDP)

1994 1995 1996 1997 1998 1999 2000-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

Difference in GDP Growth From 1980-95 Average (Year-on-year; In percent)

1994 1995 1996 1997 1998 1999 2000-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

Difference in Inflation From 1992-95 Average(CPI all items less energy; Year-on-year; In percent)

1994 1995 1996 1997 1998 1999 200022.0

22.5

23.0

23.5

24.0

24.5

25.0

25.5

22.0

22.5

23.0

23.5

24.0

24.5

25.0

25.5

Investment(Expressed as a percent of GDP)

1994 1995 1996 1997 1998 1999 200058.5

59.0

59.5

60.0

60.5

61.0

61.5

62.0

62.5

58.5

59.0

59.5

60.0

60.5

61.0

61.5

62.0

62.5

Consumption(Expressed as a percent of GDP)

Figure 4: United States: Stylized Facts (1994q1-2000q4)

1994 1995 1996 1997 1998 1999 20000.8

0.9

1.0

1.1

1.2

1.3

1.4

0.8

0.9

1.0

1.1

1.2

1.3

1.4

All Manufacturing

Durable Goods

Services

Productivity - Tradable and Non-Tradable(Indices; 1996q1=1)

1994 1995 1996 1997 1998 1999 20000.90

0.95

1.00

1.05

1.10

1.15

1.20

1.25

0.90

0.95

1.00

1.05

1.10

1.15

1.20

1.25

Services/Durable Goods

Services/All Manufactured Goods

Relative Price of Tradables(Indices: 1996=1)

Figure 5: Balassa Samuelson Effect on the Real Exchange Rateof a Ten Percent Increase in Productivity

(Increase indicates appreciation; Percentage deviation from baseline)

0.5 1.01 1.5 2 2.5 3 3.5 4 4.50.75 1.25 1.75 2.25 2.75 3.25 3.75 4.25 4.75

-4

-2

0

2

4

6

8

10

12

-4

-2

0

2

4

6

8

10

12

Elasticity of Substitution Between Home and Foreign Tradable Good

Figu

re 6

: Exp

ecte

d G

DP

Gro

wth

Rat

e Fi

ve Y

ears

Ahe

ad(Y

ear-

on-y

ear;

In

perc

ent)

Q4

Q1

Q2

Q3

Q4

Q1

Q2

Q3

Q4

Q1

Q2

Q3

Q4

Q1

Q2

Q3

Q4

Q1

Q2

Q3

Q4

1996

1997

1998

1999

2000

-0.4

-0.20.0

0.2

0.4

0.6

0.8

1.0

1.2

-0.4

-0.20.0

0.2

0.4

0.6

0.8

1.0

1.2

Hig

h va

rian

ce o

f pe

rsis

tent

com

pone

nt

Low

var

ianc

e of

per

sist

ent c

ompo

nent

Tim

e-va

ryin

g va

rian

ce o

fpe

rsis

tent

com

pone

nt Fore

cast

s

Figure 7: United States: Stylized Facts and Model Simulation Paths (1994q1-2000q4)Productivity Shock

(Solid - Actual data, Dashed - Tradable plus nontradable good version under uncertainty about persistence of shock)

1994 1995 1996 1997 1998 1999 200090

95

100

105

110

115

120

125

90

95

100

105

110

115

120

125

Real Effective Exchange Rate(Index; 1990=100)

1994 1995 1996 1997 1998 1999 2000-4.5

-4.0

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

-4.5

-4.0

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

Trade Balance(Expressed as a percent of GDP)

1994 1995 1996 1997 1998 1999 2000-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

Difference in GDP Growth From 1980-95 Average (Year-on-year; In percent)

1994 1995 1996 1997 1998 1999 2000-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

Difference in Inflation From 1992-95 Average(CPI all items less energy; Year-on-year; In percent)

1994 1995 1996 1997 1998 1999 200022.0

22.5

23.0

23.5

24.0

24.5

25.0

25.5

22.0

22.5

23.0

23.5

24.0

24.5

25.0

25.5

Investment(Expressed as a percent of GDP)

1994 1995 1996 1997 1998 1999 200059.0

59.5

60.0

60.5

61.0

61.5

59.0

59.5

60.0

60.5

61.0

61.5

Consumption(Expressed as a percent of GDP)

Figure 8: United States: Stylized Facts and Model Simulation Paths (1994q1-2000q4)Productivity Plus Risk Shock

(Solid - Actual data, Dashed - Tradable plus nontradable good version under uncertainty about persistence of shocks)

1994 1995 1996 1997 1998 1999 200090

95

100

105

110

115

120

125

90

95

100

105

110

115

120

125

Real Effective Exchange Rate(Index; 1990=100)

1994 1995 1996 1997 1998 1999 2000-4.5

-4.0

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

-4.5

-4.0

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

Trade Balance(Expressed as a percent of GDP)

1994 1995 1996 1997 1998 1999 2000-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

Difference in GDP Growth From 1980-95 Average (Year-on-year; In percent)

1994 1995 1996 1997 1998 1999 2000-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

Difference in Inflation From 1992-95 Average(CPI all items less energy; Year-on-year; In percent)

1994 1995 1996 1997 1998 1999 200022.0

22.5

23.0

23.5

24.0

24.5

25.0

25.5

22.0

22.5

23.0

23.5

24.0

24.5

25.0

25.5

Investment(Expressed as a percent of GDP)

1994 1995 1996 1997 1998 1999 200059.0

59.5

60.0

60.5

61.0

61.5

59.0

59.5

60.0

60.5

61.0

61.5

Consumption(Expressed as a percent of GDP)