WPS5174
Policy Research Working Paper 5174
Valuation Effects with Transitory
and Trend Productivity Shocks
Ha Nguyen
The World Bank
Development Research Group
Macroeconomics and Growth Team
January 2010
Policy Research Working Paper 5174
Abstract
In the past two decades, crossborder portfolio holdings critically on the nature of underlying productivity
of a large variety of assets have risen sharply. This has shocks. In response to transitory shocks, valuation effects
created an important role for changes in asset prices of are stabilizing; but in response to trend shocks, such
a country's external assets and liabilities (i.e. "valuation effects amplify the impact of the current account on
effects") in affecting the country's net foreign asset the net foreign asset position. These contrasting results
position. Valuation effects are commonly thought as arise because optimally smoothing consumers respond
stabilizing: they counteract current account movements differently to a transitory shock than to a trend shock
and mitigate the impact of the current account on the to income. The results are consistent with the pattern of
country's net foreign asset position. This paper shows that external imbalances between the United States and other
whether valuation effects are stabilizing or not depends G.7 countries since the 1990s.
This papera product of the Macroeconomics and Growth Team, Development Research Groupis part of a larger
effort in the department to understand external adjustment. Policy Research Working Papers are also posted on the Web
at http://econ.worldbank.org. The author may be contacted at hanguyen@worldbank.org.
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development
issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the
names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those
of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and
its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.
Produced by the Research Support Team
Valuation Effects
with Transitory and Trend Productivity Shocks
Ha Nguyen
Keywords: Valuation Effects, Current Account, External Imbalances, Net Foreign
Assets, Portfolio Choice.
JEL Classifications : F32, F41, G11, C68
This paper is based on my Ph.D. dissertation at the University of Maryland, College Park. I am
e
indebted to Anton Korinek, Enrique Mendoza and Carlos V´gh for supervising my work and for many
helpful discussions. Comments from Fabrice Collard, Pablo d'Erasmo, Fabio Ghironi, Constantino
Hevia, Karla Hoff, Nuno Limao, Alessandro Rebucci, John Shea and seminar participants at the
University of Maryland, the University of Adelaide, ESSEC Business School and the World Bank are
gratefully acknowledged. This paper reflects the author's views and not those of the World Bank,
its Executive Directors or the countries they represent. All errors are my own. Contact address: Ha
Nguyen, Development Economic Research Group, The World Bank, 1818 H Street, NW, Washington
D.C. 20433; Fax 2025223518; Email: hanguyen@worldbank.org.
1
1 Introduction
1.1 Contributions
In traditional balance of payments models, the evolution of a country's net foreign as
set (NFA) position is fully determined by the current account. For example, countries
that run a current account deficit experience a parallel reduction in their NFA position.
These models are based on the assumption that countries trade only a single bond of
constant real value. However, in the past two decades crosscountry portfolio holdings
of a large variety of assets have risen sharply. This has created a potentially impor
tant role for changes in asset prices, or"valuation effects", to play in a country's NFA
position (Lane and MilesiFerretti 2007). Valuation effects are changes in the value of
a country's gross external assets and liabilities due to asset price and exchange rate
fluctuations. Positive valuation effects arise when the capital gains on foreign assets
held by domestic agents are larger than those on domestic assets held by foreign agents.
Ceteris paribus, positive valuation effects enhance a country's external financial wealth
and improve its NFA position. Following this argument, Gourinchas and Rey (2007)
point out that large, persistent current account deficits of a country such as the U.S.
do not necessarily lead to a sharp deterioration in the NFA position if the country
experiences positive valuation effects. In such a situation, current account deficits can
be much more sustainable than was previously thought and valuation effects exert a
stabilizing role  they offset part of the current account deficit and mitigate the decline
in the country's NFA position.
This paper investigates theoretically if valuation effects do move to offset the cur
rent account and stabilize a country's NFA position. It shows that the impact of
valuation effects depends critically on the nature of underlying shocks. In response
to transitory shocks, valuation effects are stabilizing; they counteract current account
movements and help to soften the impact of the current account on a country's NFA
position. In response to trend shocks, valuation effects are amplifying; they move in
the same direction as the current account, and reinforce, or "amplify", the impact of
the current account on the NFA position. The theoretical predictions are illustrated
by the evolution of the NFA position of the U.S. with other G.7 countries since the
1990s: valuation effects (from stocks and bonds) were negative and amplifying before
2002 and have been positive and stabilizing since 2002.
The mechanism of valuation effects works as follows: in response to a positive
2
productivity shock, domestic asset prices appreciate (relative to foreign asset prices)
to reflect a better performance of the domestic economy. The appreciation of domestic
asset prices creates a negative valuation effect, in response to both a positive transitory
shock and a positive trend shock.
However, the role of the valuation effect in the two scenarios is very different. Fol
lowing a positive transitory shock, agents smooth consumption and save. Investment
also increases, but less than the increase in saving due to the presence of capital ad
justment costs. As a result, the domestic country runs a current account surplus. The
negative valuation effect hence moves in the opposite direction of the current account
and offsets the current account surplus. Valuation effects are said to have a stabilizing
property on NFA position as they counteract the fluctuations of the current account.
On the other hand, after a positive trend productivity shock, valuation effects are
amplifying. A positive trend productivity shock implies that growth is sustained, i.e.
higher output today will be followed by even higher output tomorrow. Put differently,
the increase in current income is lower than the increase in permanent income. Con
sumption smoothing implies that consumption rises more than output and the domestic
country runs a current account deficit. The negative valuation effect then moves in the
same direction as the current account, and reinforces the current account deficit. As a
result, the decrease in the NFA position is now more than the current account deficit,
which means valuation effects are amplifying. Simulation results indicate sizable val
uation effects, especially in response to trend shocks because asset price appreciations
are more dramatic in this case.
Quantitatively, the model is calibrated and estimated to match secondorder mo
ments of U.S. output, consumption and investment series. The estimated model can
account for most of the volatility of the U.S.'s trade and current account, about two
thirds of the U.S.'s changes in NFAs, and onethird of the U.S.'s valuation effects.
The empirical literature has sought to identify if the U.S.'s valuation effects are
stabilizing. Gourinchas and Rey (2007) impute net foreign asset returns from 1952
to 2004, and interpret these as the "valuation channel" of changes in NFA position .
They find that the valuation channel is stabilizing and accounts for 27% of the U.S.'s
cyclical external adjustments. However, Curcuru, Dvorak, and Warnock (2008), after
correcting for measurement errors, find that the average return differential of U.S.
claims (in stocks and bonds) over U.S. liabilities is essentially zero during the period
from 1994 to 2006. Bertaut and Tryon (2007) do not associate valuation effects to
3
asset returns, but to relative changes in asset prices1 . Their data indicates that be
tween 19942006, the U.S.'s cumulative valuation effects are significant and positive.
From my calculation using their data, total valuation effects from stocks and bonds
during 19942006 period were $1295 billion, offsetting about 22.8% of the size of the
U.S.'s total current account deficits. My calculation is consistent with the finding of
Curcuru, Dvorak, and Warnock (2008), because the U.S.'s external assets had a lower
average return than its liabilities before 2002, but higher after 2002 (Figure 42 , Ap
pendix A). Since after 2002, the total holdings of foreign assets on which the U.S.
experienced positive valuation effects are larger, the aggregate U.S.'s valuation effect
in 19942006 is positive and stabilizing (Figure 5, Appendix A).
On the theoretical front, Devereux and Sutherland (2009b) investigate valuation
effects in a twocountry dynamic stochastic general equilibrium model. They relate
valuation effects to return differentials. My paper however associates valuation ef
fects with changes in asset prices. Ghironi, Lee, and Rebucci (2007) also explicitly
consider asset prices but they do not consider the impact of trend productivity shocks.
Coeurdacier, Kollmann, and Martin (2009) also briefly discuss valuation effects with
transitory shocks, although they focus on explaining equity home bias. One key con
tribution of my paper is that it identifies the contrasting role of valuation effects as
stabilizing after transitory shocks, and amplifying after trend shocks. Unlike the con
ventional wisdom that valuation effects are generally stabilizing, as showcased in em
pirical findings of Gourinchas and Rey (2007), and as implied by the theoretical results
of Ghironi, Lee, and Rebucci (2007), Coeurdacier, Kollmann, and Martin (2009), and
Devereux and Sutherland (2009b), this paper shows that valuation effects can be am
plifying too. This situation is illustrated by the evolution of NFA position between the
U.S. and other G.7 countries during the 1990s, which I discuss in section 1.2.
My paper follows Aguiar and Gopinath (2007) in its approach to introduce trend
shocks, and Tille and van Wincoop (2007) and Devereux and Sutherland (2007) in their
method of solving for portfolio choice. They develop an approximation method to char
acterize timevarying equilibrium portfolios in a twocountry dynamic general equilib
rium model, in which financial markets are incomplete3 . In my paper, market incom
1
Bertaut and Tryon (2007) calculated valuation effects from stocks and bonds between the U.S.
and every other country from 1994 to 2007.
2
For sources of data used in all the figures and tables, see Appendix A.
3
For different solution methods, see Evans and Hnatkovska (2007); Heathcote and Perri (2007);
Pavlova and Rigobon (2009).
4
pleteness, along with home bias in portfolio holdings, is assumed4 , by the presence of
an exogenous cost of investing in foreign equities.
The paper is related to a large literature on global imbalances5 . Also using expected
higher growth of the U.S. than other industrialized countries, Engel and Rogers (2006)
explain the U.S.'s current account deficit, but they do not examine valuation effects.
Caballero, Farhi, and Gourinchas (2006) use the growth gap between the U.S. and
Continental Europe in the 1990s to explain U.S.Europe capital flows.
1.2 U.S.'s external imbalances with other G.7 countries
The paper's theoretical results have some important implications for the U.S.'s ex
ternal imbalances with other G.7 countries. The U.S. experienced persistently higher
economic and productivity growth than other countries in the 1990s, arguably due to
the information and communication technology revolution that took place in the U.S.
in this period (Figure 1). The average annual growth rate of U.S. PPP GDP during
19902000 was 1.94%, compared to 1.47% for other G.7 countries (henceforth referred
to as G.6). At the same time, U.S.'s relative stock prices followed an upward trend
(whether adjusted for changes in exchange rates or not), while the U.S.G.6 current
account balance has continued to worsen (Figures 2, 3).
Figure 1: U.S.G.6 Normalized Total Factor Productivity ratios
4
For papers that seek to explain home bias in portfolio holdings, see
Kollman (2006); Engel and Matsumoto (2009); Heathcote and Perri (2007); Benigno (2007);
Coeurdacier, Kollmann, and Martin (2009).
5
See for example Obstfeld and Rogoff (2005); Caballero, Farhi, and Gourinchas (2006);
Engel and Rogers (2006); Mendoza, Quadrini, and RiosRull (2009) among others.
5
Figure 2: Log of normalized stock price index ratios (Jan1990=0), after incorporating
changes in exchange rates, 19902008
Figure 3: U.S.G.6 current account and nonFDI valuation effects, 19952007
The theoretical results imply that if the U.S indeed had a positive trend productivity
shock relative to other industrialized countries, the valuation effects between the U.S.
and these countries would be negative and they would worsen the impact of the current
account deficit on the U.S.'s NFA position. Figure 3 shows that from 1995 to 2001, U.S.
G6 valuation effects were generally negative (except in 19996 ), and they exacerbated
the impact of the current account deficit on the NFA position. After 2002, the U.S.'s
valuation effects became positive, while the U.S.'s current account remains in deficit.
These two phenomena are consistent with the view that the U.S. had (or at least was
perceived to have had) a negative transitory shock at that time.
6
In 1999 the dot com bubble in other countries was even more severe than that of in U.S., leading
to a positive valuation effect.
6
2 The Model
2.1 The framework
The framework is a onegood, twocountry DSGE model. Each country has a large
number of identical households and firms. Output is produced with labor and capital.
The technological progress is affected by a transitory and a trend shock, both of which
are AR(1) processes. There are two assets: equities of Home country's firms and of
Foreign country's firms. Households observe wages, output, dividend payments, equity
prices and choose how much to work, how much to consume and how to allocate
their wealth between the two assets in their portfolios. Firms choose labor inputs,
investment, and dividend payments.
In the model, financial assets serve two purposes: for intertemporal consumption
smoothing and for risksharing. Households would like to insure themselves against the
risks of undiversifiable labor income and domestic equity holdings. Ideally, in a fric
tionless asset market, agents would hold assets to completely insure themselves against
any countryspecific shocks (Lucas 1982). However, in reality, residents of most coun
tries exhibit home bias in their portfolio holdings (Tesar and Werner 1995). A number
of explanations for the homebias puzzle have been presented. In this paper I assume
that there is a small cost of investing abroad, as in Tille and van Wincoop (2007) and
Heathcote and Perri (2004). These costs reflect a lack of market knowledge, market
access and information, as well as cultural and language barriers. Such costs make
investing abroad less attractive and create home bias in portfolio holdings.
Note that there is only one good in the model, thus, we cannot explicitly account
for exchange rate movements. In practice, valuation effects consist of movements in
both nominal asset prices and in foreign exchange rates. However, to the extent that
exchange rate movements are equilibrium responses to fundamental shocks, the change
in relative real asset prices in our model reflects both movements in nominal asset
prices and exchange rates.
2.2 Technology and Firms
Denote the two countries Home (H) and Foreign (F ). Both countries i = H, F produce
an identical perishable good. Production of country i employs both capital and labor
in a standard CobbDouglas function. Capital stock can be adjusted with a cost, which
7
is typically introduced in the literature to match investment moments.
i
Yti = zt Kti (i Li )1
t t (1)
i
where 0 < < 1 is the capital share of output. zt is the transitory shock that follows
an AR(1) process
i i iz
log(zt ) = z log(zt1 ) + t (2)
where 0 < z < 1 and iz represents an iid draw from a normal distribution with zero
t
mean and standard deviation z .
The parameter i represents a combination of a cumulative product of the growth
t
shocks of country i (as in Aguiar and Gopinath (2007)) and a convergence process. In
particular:
i
t1
i
t = i
gt i
t1 (3)
i
t1
log(gt ) = (1  g )log(g) + g log(gt1 ) + ig
i i
t (4)
i can also be thought of as the "permanent" component of country i' technology. g
t
and are between 0 and 1. ig is iid normal with zero mean and standard deviation
t
g . g > 1 is the common long run growth rate. i is the permanent component
t1
i
of the other country's technology. t1
i
represents a convergence process: the two
t1
countries' technology and output levels are assumed to converge in the long run. Con
vergence is assumed so that a local solution method can be applied. This assumption
is not unrealistic, however, particularly among countries and regions with similar in
stitutions (for example, see Barro and Salai Martin (2003) for different states of the
U.S., and Dowrick and Nguyen (1989) or Madsen (2007) for OECD countries). Having
said that, it is important to note that the main results of the paper do not depend on
this assumption. In this paper, is set close to zero (implying a long convergence).
Every period, firms in country i, after paying labor costs, decide how much to rein
vest (subject to an adjustment cost), and how much to distribute back to shareholders
in dividends.
i 2
Kt+1
Dt = Yti  Wti Li  (Kt+1  (1  )Kti ) 
i
t
i
¯
g Kti (5)
2 Kti
where Dt , Wti , Li denote dividend payments, wages and labor inputs of country i's
i
t
firms. We assume that capital depreciates at rate , and the adjustment cost to capital
stock is quadratic, where is the adjustment cost parameter.
8
2.3 Assets
There are two assets: equities of the Home firms and those of the Foreign firms. The
price at time t of firm i's equity carried into the next period is denoted Qi , measured
t+1
in terms of the consumption good. The holder of this claim gets a dividend in period t
and can sell the claim for price Qi . The overall return to country i's equity, in terms
t+1
of the consumption good is:
i Qi
t+1
i
Dt
Rt = + i (6)
Qit Qt
The above equation states that the return to investment in domestic equity com
prises a dividend yield and an appreciation of the equity.
I assume a credit market friction. In particular, agents investing abroad receive the
gross return times a "local expert" cost e , as in Tille and van Wincoop (2007). The
cost captures expenses paid to local experts for local market access and information,
as well as expenses spent to overcome cultural and language barriers. This friction
generates a homebias in portfolio holdings and market incompleteness. The "local
expert" cost is paid in the host country; for instance, the cost could represent payments
to experts in the local economy.
2.4 Households
An infinitelylived representative household maximizes its expected discounted utility:
i 
C
(Cti (1  Li )1 )1
t1
=0 log i
Y t
Ui = E0 e t (7)
t=0
1
I assume an endogenous discount factor, as in SchmittGrohe and Uribe (2003) and
Devereux and Sutherland (2009a). This is a simple technical device to induce unique
ness of the deterministic steady state and stationary responses to temporary shocks.
Specifically, the endogenous discount factor decreases with the aggregate consumption
output ratio, which the representative household takes as given. will be set equal
to the long run consumptionoutput ratio so that the long run discount factor equals
. In addition, is set arbitrarily small so that in the short run, the deviations of the
endogenous discount factor from the standard discount factor are negligible.
i
Denote t the fraction of country i's wealth invested in that country's equity car
ried from the last period to the current period. Country i's wealth in terms of the
9
consumption good evolves according to the following law of motion:
i i i
Ai = t Ai Rt + (1  t )Ai Rt e + Wti Li  Cti + (1  t )At Rt (1  e )
t+1 t t
i
t
i
t
i
(8)
i
where Ai is the wealth of country i's households carried to the next period. t Ai Rt +
t+1 t
i
i i
i
(1  t )Ai Rt e is country i's income from equities (Rt is the return of the other
t
country's equity), and (1  i,t )Ai Rt (1  e ) is the local expert cost that country i
t
i
collects from the other country's investors. Following Tille and van Wincoop (2007), I
assume that is second order (i.e. proportional to the variances of the shocks) so that
the portfolio holding is wellbehaved.
The timing of the agent's problem is as follows: A representative agent enters the
period knowing his wealth, his domestic and foreign equity holdings, and the domestic
and foreign equity prices. Output is then observed. The agent then chooses consump
tion and portfolio holdings for the next period, taking the returns as given. However
in equilibrium, the returns are affected by the agent's portfolio choice.
2.5 Households' and firms' decisions, and marketclearing
Taking wages as given, country i's households choose labor supply, consumption, and
a portfolio to hold to maximize their discounted utility (7) subject to their budget
constraint (8). The firstorder conditions of the problem are in Appendix B.
Country i's firms choose labor demand, dividend payments and capital next period
to maximize the discounted stream of dividend payments subject to the firms' con
straint. Note that following Heathcote and Perri (2007), I assume the firms also use
the same discount factors as the households. Thus, the firms' problem is to solve:
i 
t1
log
C
=0 Y i
max E0
i i
e i
t Dt (9)
Lt ,Dt
t=0
The firstorder conditions of the firms' problem are also in Appendix B.
Clearing of the good and asset markets entails :
YtH + YtF = CtH + CtF + (Kt+1  (1  )KtH ) + (Kt+1  (1  )KtF )
H F
H 2 F 2
Kt+1 Kt+1
+  g KtH +
¯ g
¯ KtF (10)
2 KtH 2 KtF
QH
t+1
H F
= t+1 AH + (1  t+1 )AF
t+1 t+1 (11)
QF F F H H
t+1 = t+1 At+1 + (1  t+1 )At+1 (12)
10
2.6 Valuation effects
In standard intertemporal models, the change in the net foreign asset position equals
the current account. In this model, however, this equation needs not hold, because the
model explicitly considers capital gains or losses arising from changes in domestic and
foreign asset prices, that is, the "valuation effects". In the model, the valuation effects
for the Home country are:
QF 
t+1 QH 
t+1
V EtH = (1  t )AH
H
t e  1  (1  t )AF
F
t e 1 (13)
QFt QHt
QF
H
where (1t )AH
t
t+1 
QF
e  1 is the home country's capital gain from Foreign equity
t
QH
F
holdings, after adjusting for the "local expert" costs, and (1  t )AF
t
t+1 
QH
e  1 is
t
the foreign investors' capital gain from holding domestic equity.
The current account consists of the trade balance and net factor income:
H 2 F H
Kt+1 Dt  Dt
CAH
t = YtH CtH (Kt+1 (1)KtH )
H
¯
g KtH +(1t )AH
t e (1t )AF H e
F
t
2 KtH QF
t Qt
(14)
The change in NFA position equals:
H F H
N F AH = [(1  t+1 )AH  (1  t+1 )AF ]  [(1  t )AH  (1  t )AF ]
t t+1 t+1 t
F
t (15)
This equals the current account plus the valuation effects:
N F AH = CAH + V EtH
t t (16)
To see this, substitute (14) and (15) into (16), and use equation (6) for equities' returns,
and equation (8) for the households' budget constraints.
3 Solution of the model
3.1 Detrending the system
Given that a realization of g permanently affects , output is nonstationary with a
stochastic trend. For a home variable X H following Aguiar and Gopinath (2007), I
introduce a lowercase xH to denote its detrended counterpart.
XtH
xH =
t
Ht1
11
For any foreign variable X F , I also use introduce xF :
XtF
xF =
t
Ht1
i i
The variables that do not need to be detrended are Rt , Li and t ,
t
Appendix C presents the system in terms of detrended variables. Note that there
F
is now a new variable, t = t1
H
, which is the ratio of the two permanent technology
t1
components. t is a state variable and converges to one in the steady state.
It is wellknown that up to a firstorder approximation, the values of the port
H F
folio choice t+1 and t+1 are indeterminate, because at this level of approximation,
the two assets are perfect substitutes. Previous literature usually relies on perfect
market structures that make portfolio choice irrelevant. Following the approach of
Tille and van Wincoop (2007) and Devereux and Sutherland (2007), I solve for the
firstorder accurate solution of the detrended system above (including the long run
portfolio choice decisions). First I take the firstorder approximation of the system,
and solve for the firstorder accurate solution of the nonportfolio choice variables con
ditional on the long run steady state portfolio choice. Subsequently, the conditional
solution is substituted into the secondorder approximations of the portfolio choice
equations to pin down the values of the long run portfolio choice. I will show that
the current account, changes in NFA position and valuation effects can also be ap
proximated to first order. After solving for the detrended variables, level variables are
recovered.
Consider the firstorder approximation of the system in appendix C. The portfolio
choice decisions that enter the firstorder system are the steadystate portfolio H (=
^H ^F
F ) and the term (t+1  t+1 ) . They enter the system only through the firstorder
approximations of the budget constraint equation (C16) and the asset market clearing
condition (C7):
at+1 ^H ct at ^t ^H ^F
ga(^H + gt + ^t ) + c^H  aL(^H + LH ) = aRRt + (1  )aRRt + aR^H
at
(17)
q qt+1  a^H  (1  )a^F
^H at+1 ^H ^F
at+1 = a(t+1  t+1 ) (18)
^H ^F
t+1  t+1 enters the system as a choice variable and will be useful to approximate
the current account, valuation effects and the changes in net foreign asset position.
Here note that I drop the superscripts H, F for the steadystate values, because for
any pair of variables xH and xF , their steadystate values equal: xH = xF = x.
t t
12
The system (conditional on long run portfolio choice ) can be solved by any stan
dard solution method for linear rational expectations models. I use the package of
SchmittGrohe and Uribe (2004).
Next, I will substitute the solution (condition on ) into the secondorder approxi
mations of the two portfolio choice Euler equations (C13) for the two countries:
L ^H ^H
ct+1 ^ H
Et [((1  )  1)^H Rt+1  (1  )(1  )(1  L)(1)(1) L R ]=
1  L t+1 t+1
L ^H ^F
ct+1 ^ F
Et [((1  )  1)^H Rt+1  (1  )(1  )(1  L)(1)(1) L R  ](19)
1  L t+1 t+1
L ^F ^H
ct+1 ^ H
Et [((1  )  1)^F Rt+1  (1  )(1  )(1  L)(1)(1) L R  ] =
1  L t+1 t+1
L ^F ^F
ct+1 ^ F
Et [((1  )  1)^F Rt+1  (1  )(1  )(1  L)(1)(1) L R ](20)
1  L t+1 t+1
Subtracting one equation from the other, I obtain:
^H ^F
Et (Rt+1  Rt+1 )((1  )  1)(^H  cF )
ct+1 ^t+1
^H ^F L ^H ^ t+1
Et (Rt+1  Rt+1 )((1  )(1  )(1  L)(1)(1) (L  LF )] =  (21)
1  L t+1
Note that since the local expert cost is of second order, it does not appear in
the system of firstorder approximation , but does appear here. Equation (21) can
be interpreted as follows: the covariance between the excess return and the difference
in marginal utilities equals the local expert cost (note that up to second order, the
covariance is timeinvariant). If the cost is zero, the covariance is zero because
domestic and foreign agents will have the same level of marginal utility regardless
of the interest rate difference. In other words, both domestic and foreign investors
are completely insured against countryspecific risks (i.e. the market is effectively
complete). A positive makes foreign investment less attractive, thereby creating
homebiased portfolios and thus market incompleteness. As a result, the difference
in marginal utilities is negatively correlated with the realized excess return because a
country whose equity yields a higher return can afford to consume more, and has lower
marginal utility.
I solve for by substituting the conditional result of the system into (21).
Denote the normalized current account, NFA position and valuation effects as cat
CAt N F At V Et
t1
, nf at t1
, and vet t1
. The firstorder approximations of all the economic
13
variables of interest can be expressed in firstorder terms.
veH =(1  )a¯ (^H + qt+1  qt )  (^F + qt+1  qt )
^t g at ^F ^F a ^H ^H
^H ^F g
(1  )a(^H  aF )  (t  t )a(¯  1)
at ^ (22)
^ H
nf at ^H ^F
=(1  )a(^H  aF )  a(t  t )
at ^t
H
^
caH =nf at  veH
^t ^t (23)
^H ^F
Note that (t  t ) is a first order term and was solved in the firstorder system.
4 Quantitative Analysis
This section explains the calibration and estimation procedure of the parameters, doc
uments empirical and theoretical business cycle moments, and plots impulse responses
to both the transitory and trend productivity shocks.
4.1 Calibrations
I use a combination of calibrated and estimated parameters. The coefficients of risk
aversion (), consumption exponent () discount factor (), depreciation rate () and
capital share () are set as standards. I set both the convergence parameter () and
¯
the endogenous discount factor parameter () to 0.001. I set g to the average growth
rate of quarterly output from the data which is 1.0055 (i.e. 0.55% per quarter). The
investment cost is calibrated so that the home asset holding is 0.9 (about the
level of home bias of U.S. investors in 19902000). I estimate the remaining structural
parameters z , z , g , g and , using GMM estimation7 .
Calibrated parameters are in table 1 below:
H
I have the following parameters to estimate: z , z , g , g and . I also assume z =
F
z so that the model can account for the difference in U.S. and of G.6's output mo
ments. The six parameters are estimated by the GMM method, where the following the
H
yt F
yt cH cH yt H iH yt H cH
oretical moments std H
yt1
,std F
yt1
, std cH
t
,corr H , yF
t
yt
, corr H , yF
t
yt
,std t
H
yt
t1 t t
are matched with the corresponding empirical moments. The estimated parameters
are in table 2.
Historical quarterly data of U.S.'s GDP, consumption and investment are from the
Bureau of Economic Analysis. Historical G.7's PPP(Purchasing Power Parity) GDP
7
See Burnside (1991) for a description and applications of the GMM methodology.
14
Risk aversion 2
Consumption component (utility) .36
Discount factor 0.98
Capital share 0.34
Depreciation rate 0.04
Convergence rate 0.001
Elasticity of the discount factor 0.001
Foreign investment cost 1.397 × 104
g Long run growth rate 1.0055
Table 1: Calibrated parameters
data are from the OECD's statistics. G.6's average PPP GDP is calculated by taking
the total G.6's PPP GDP divided by total G.6's population. The output ratio is the
ratio of G.6's average PPP GDP and the U.S.'s PPP GDP obtained also from the
OCED database. Data is quarterly from 1970,QI 2000,QI8 .
Estimated values Standard errors
z Persistence of transitory shocks 0.8404 (0.0002)
g Persistence of growth shocks 0.5598 (0.0001)
H
z Standard deviation of Home transitory shocks 0.0070 (0.0000)
F
z Standard deviation of Foreign transitory shocks 0.0040 (0.0000)
g Standard deviation of growth shocks 0.0042 (0.0000)
Adjustment cost 1.5086 (0.0005)
Table 2: Estimated parameters
4.2 Impulse Responses and Business Cycle Moments
To gain insights into how valuation effects influence the NFA position, I study the
impulse responses to the two kinds of productivity shocks. Figure 6 in Appendix D
contrasts the impulse responses of consumption, investment, current account, valuation
effects and changes in net foreign assets to a 1% (i.e. z = 0.01) positive transitory
productivity shock and a 0.1% (i.e. g = 0.001) trend (growth) productivity shocks.
The ratio of current account to income has a positive response (of about 0.5%) to
8
I restrict the data until 2000 because after 2000, a significant part of U.S.'s consumption results
from trading with China.
15
a 1% transitory productivity shock. Investment increases, but not enough to offset
saving. Valuation effect response is negative because the domestic asset price appre
ciates. The size of the valuation effect response is relatively small compared to that
of the current account because the domestic asset price appreciates only modestly, as
investors know the positive shock to the home country is temporary. In contrast, in
the case of the trend shock, valuation effects are much larger because the domestic
asset price appreciates more, as investors know the domestic country will outperform
the foreign country for a longer time. Valuation effects are negative and reinforce the
movement of the current account.
Data Both shocks Only Only
Transitory Trend
H
Yt+1
std YtH
0.0105 0.0103 0.0100 0.0028
(U.S.) (0.0008) (0.0007) (0.0003)
F
Yt+1
std YtF
0.0067 0.0067 0.0061 0.0028
(G.6.) (0.0005) (0.0004) (0.0003)
H
Ct+1
std CtH 0.0071 0.0067 0.042 0.0052
(0.0005) (0.0003) (0.0004)
H
Ct YH
corr , t
YtH YtF
0.5731 0.5641 0.9577 0.2687
(0.2350) (0.0243) (0.2592)
H
Ct
std YtH
0.0104 0.0104 0.0085 0.0009
(0.0019) 0.0022 (0.0003)
H
It YH
corr , t
YtH YtF
0.122 0.1011 0.3857 0.1146
(0.2979) (0.2080) (0.3150)
H
N Xt
std YtH
0.011 0.0098 0.0078 0.0056
( 0.0019) (0.0016) 0.0012
CAH
std YtH
t
0.013 0.0091 0.0071 0.0054
(0.0016) (0.0012 ) (0.001)
H
V Et
std YtH
0.0148 0.0052 0.0010 0.0051
(0.0004) (0.0002) (0.0004)
N F AH
std YtH
t
0.0156 0.0121 0.007 0.096
(0.0016) (0.0012) (0.0011)
Table 3: Volatility of trade, current account, valuation effects and changes in NFA
position
I run a simulation exercise to investigate the quantitative importance of valuation
effects. In the simulation I generate 200 histories, each of 120 periods. Each period
16
corresponds to one quarter. I run three separate simulations. First I have both shocks,
then I shut off the trend shocks, and finally I shut off the temporary shocks.
Table 3 reports averaged simulated standard deviations of output growth, consump
tion growth, the trade balance, the current account, valuation effects and changes in
NFA position. Numbers in brackets are the standard deviations of the statistics. In
the first six rows, it is not surprising that the model can match the data, because I use
output, consumption and investment data to estimate the model's parameters. When
it comes to trade, current account and valuation effects, the model can account for
most of the volatility in the trade and current account of the U.S. economy, but only
about onethird of the volatility of the U.S.'s valuation effects.
When only transitory shocks are present, the change in the NFA position is slightly
less volatile than the current account because valuation effects offset some of the current
account's movements. However, when only trend shocks are present, the change in the
NFA position is much more volatile than the current account because valuation effects
here are strongly reinforcing.
5 Conclusion
In light of the U.S.'s persistent current account deficits, both empirical and theoretical
literature has pointed to "valuation effects" as a channel that could offset the deficits
and mitigate the decline of the NFA position, that is, valuation effects are stabilizing.
This paper shows that whether valuation effects are stabilizing or not depends on the
the nature of the underlying productivity shocks. In response to transitory shocks, val
uation effects are stabilizing; but in response to trend shocks, valuation effects amplify
the impact of the current account on NFA position. This situation is clearly illustrated
by the external imbalances between the U.S. and other G.7 countries during the late
1990s when the U.S. experienced both current account deficits and negative valuation
effects. Quantitatively, the model can explain for most of the volatility of the U.S.'s
trade and current account, but it only accounts for about onethird of the U.S.'s valua
tion effects. This quantitative result is obtained in a framework where agents are fully
rational, financial frictions are limited to only "local expert" costs, and information
about transitory and trend productivity shocks is perfect. Relaxing these restrictions
is worth exploring in future research.
17
References
Aguiar, M. and G. Gopinath (2007). Emerging market business cycles: The cycle is
the trend. Journal of Political Economy 115, 69102.
Barro, R. and X. Salai Martin (2003). Economic growth. MIT Press.
Benigno, P. (2007). Portfolio choices with near rational agents: A solution of some
internationalfinance puzzles. NBER Working Papers No. 13173 .
Bertaut, C. C. and R. W. Tryon (2007). Monthly estimates of u.s. crossborder
securities positions. Board of Governors of the Federal Reserve System (U.S.)
International Finance Discussion Papers No. 910 .
Burnside, G. (1991). Real business cycle models: Linear approximation and gmm
estimation. mimeo, The World Bank .
Caballero, R. J., E. Farhi, and P.O. Gourinchas (2006). An equilibrium model of
"global imbalances" and low interest rates. NBER Working Papers No. 11996 .
Coeurdacier, N., R. Kollmann, and P. Martin (2009). International portfolios, cap
ital accummulation and the dynamics of capital flows. Journal of Interntional
Economics forthcoming.
Curcuru, S. E., T. Dvorak, and F. Warnock (2008). Crossborder returns differentials.
Quarterly Journal of Economics 123 (4), 14951530.
Devereux, M. B. and A. Sutherland (2007). Country portfolio dynamics. CDMA
Conference Paper Series No. 0706 .
Devereux, M. B. and A. Sutherland (2009a, July). A portfolio model of capital flows
to emerging markets. Journal of Development Economics 89 (2), 181193.
Devereux, M. B. and A. Sutherland (2009b). Valuation effects and the dynamics of
net external assets. Journal of International Economics forthcoming.
Dowrick, S. and D.T. Nguyen (1989). Oecd comparative economic growth 195085:
Catchup and convergence. American Economic Review 79 (5), 101030.
Engel, C. and A. Matsumoto (2009, July). The international diversification puzzle
when goods prices are sticky: It's really about exchangerate hedging, not equity
portfolios. American Economic Journal: Macroeconomics 1 (2), 15588.
Engel, C. and J. H. Rogers (2006). The u.s. current account deficit and the expected
share of world output. Journal of Monetary Economics 53 (5), 10631093.
18
Evans, M. D. D. and V. Hnatkovska (2007). Solving general equilibrium models with
incomplete markets and many financial assets. Georgetown University Working
paper No. 0318 .
Ghironi, F., J. Lee, and A. Rebucci (2007). The valuation channel of external ad
justment. NBER Working Papers No. 12937 .
Gourinchas, P.O. and H. Rey (2007). International financial adjustment. Journal of
Political Economy 115, 665703.
Heathcote, J. and F. Perri (2004). Financial globalization and real regionalization.
Journal of Economic Theory 119 (1), 207243.
Heathcote, J. and F. Perri (2007). The international diversification puzzle is not as
bad as you think. NBER Working Papers No. 13483 .
Kollman, R. (2006). International portfolio equilibrium and the current account.
CEPR Discussion Papers No 5512 .
Lane, P. R. and G. M. MilesiFerretti (2007). The external wealth of nations mark
ii: Revised and extended estimates of foreign assets and liabilities, 19702004.
Journal of International Economics 73 (2), 223250.
Lucas, R. J. (1982). Interest rates and currency prices in a twocountry world. Journal
of Monetary Economics 10 (3), 335359.
Madsen, J. B. (2007). Technology spillover through trade and tfp convergence:
135 years of evidence for the oecd countries. Journal of International Eco
nomics 72 (2), 464480.
Mendoza, E. G., V. Quadrini, and J.V. RiosRull (2009). Financial integration,
financial deepness and global imbalances. Journal of Political Economy forth
coming.
Obstfeld, M. and K. S. Rogoff (2005). Global current account imbalances and ex
change rate adjustments. Brookings Papers on Economic Activity 71 (20051),
67146.
Pavlova, A. and R. Rigobon (2009). Equilibrium portfolios and external adjustment
under incomplete markets. Journal of International Economics forthcoming.
SchmittGrohe, S. and M. Uribe (2003). Closing small open economy models. Journal
of International Economics 61 (1), 163185.
19
SchmittGrohe, S. and M. Uribe (2004). Solving dynamic general equilibrium models
using a secondorder approximation to the policy function. Journal of Economic
Dynamics and Control 28 (4), 755775.
Tesar, L. L. and I. M. Werner (1995). Home bias and high turnover. Journal of
International Money and Finance 14 (4), 467492.
Tille, C. and E. van Wincoop (2007). International capital flows. NBER Working
Papers No. 12856 .
A Appendix A
In this appendix I provide the details about the data and methodology used to construct
aggregates for all of the figures and tables used in this paper.
In Figures 1, total factor productivity (TFP) series of the G.7 countries from 1995
2006 are from OECD statistics. In Figure 2, the historical data of S & P 500 index are
obtained Professor Robert Shiller's website http://www.econ.yale.edu/ shiller/data.htm.
The historical data of the Nikkei and FTSE are from Wren Research at the address
http://www.wrenresearch.com.au/downloads/index.htm. The historical data of DAX
and the exchange rate are from the German Bundesbank.
In Figures 3 and 5, the series of the U.S.G.6 current account are from the Bureau
of Economics Analysis (International Transactions). Data on bilateral valuation effects
are taken from Bertaut and Tryon (2007). Valuation effects are defined as the adjusted
valuation changes of stocks and bonds that the U.S. holds in other G.7 countries (U.S.'s
claims) minus the adjusted valuation changes of stocks and bonds other G.7 countries
hold in the U.S. (U.S.'s liabilities).
Data used in Figure 4 is from Curcuru, Dvorak, and Warnock (2008), kindly pro
vided by Stephanie E. Curcuru.
In table 3, data for output levels, investment, consumption are the same as those
used in the GMM estimation. U.S.'s GDP, consumption and investment historical quar
terly data are from the Bureau of Economic Analysis. Historical G.7.'s PPP(Purchasing
Power Parity) GDP data are from the OECD. G6's average PPP GDP is calculated by
taking the total G6's PPP GDP divided by total G6's population. I restrict the data un
til 2000 because after 2000, a significant part of U.S.'s consumption results from trading
with China. For trade and current account, since bilateral quarterly data on trade and
current account between the U.S. and G.6. countries are not available, I use trade and
20
current account between the U.S. and the rest of the world in the period of 1970,QI
2000,QI. Data on valuation effects and changes in net foreign assets are quarterly
U.S.G.6. data from 1994 QII2000 QIV, obtained from Bertaut and Tryon (2007). If
we use quarterly U.S.G.6. data from 1994,QII2007,QIV, the standard deviations of
V EtH N F AH
YtH
and of YtH
t
are 0.020 and 0.0187 respectively.
Figure 4: U.S.'s return differentials in stocks
Figure 5: U.S.'s valuation effects and the current account
21
B Appendix B
FOCs of the household's problem:
Cti Wti (1  Lt )i
= (B1)
1
 i
(Cti (1  Li )1 )1
t Cti (Ct+1 (1  Li )1 )1 i
t+1
= Et Rt+1
Cti Yti i
Ct+1
(B2)
i i
(Ct+1 (1  Li )1 )1 i
t+1 (Ct+1 (1  Li )1 )1 i 
t+1
Et i
Rt+1 = Et i
Rt+1 e (B3)
Ct+1 Ct+1
FOCs of the firm's problem:
(1  )zt Kti (t Li )1
t
Wti = i
(B4)
Lt
i i 1 1 i
(Ct (1  Lt ) ) Kt+1
1+ ¯
g =
Cti Kti
 i 1
Cti (Ct+1 (1  Li )1 )1
t+1 i Li
t+1 t+1
Et zt+1 +1 (B5)
Yti i
Ct+1 i
Kt+1
C Appendix C
Production:
H H H H
yt = zt kt LH1 (gt t )1
t (C1)
F F F F 1
yt = zt kt LF 1 (gt t )1
t
i i iz
log(zt ) = z log(zt1 ) + t (C2)
i
i = gt i1 i
t t1 t1 (C3)
i i ig
g
log(gt ) = g log(gt1 ) + (1  g )log(¯) + t (C4)
F
where t = t1
H
t1
Convergence:
F
gt 12
t+1 = (C5)
gt t
H
22
Market clearings:
H F
aH + aF = qt + qt
t t (C6)
i i i
qt+1 = t+1 ai + (1  t+1 )ai
t+1 t+1 (C7)
i i
q dt
Rt = t+1 gt t + i
i
i
i
(C8)
qt qt
i 2
kt+1 i
i i
di = yt  wt Li  (kt+1 gt t  (1  )kt ) 
t t
i i i
¯ i
g  g kt (C9)
2 kt t
i
H F
yt + yt t t
H H H F F
= cH + cF + (kt+1 gt t  (1  )kt ) + (kt+1 gt t  (1  )kt )
H 2 F 2
kt+1 H H kt+1 F
+ ¯
g g kt + g g
¯
F t
kt (C10)
2 kt t
H
2 kt
Firstorder conditions of the consumer's problem:
ci
t wi (1  Li )
= t t
(C11)
1

(ci (1  Li )1 )1
t t ci
t (ci (1  Li )1 )1 i
t+1 t+1
= Et i
Rt+1 (gt t )(1)1
ci
t yt i
ci
t+1
(C12)
(ci (1  Li )1 )1 i
t+1 t+1 (ci (1  Li )1 )1 i 
t+1 t+1
Et Rt+1 = Et Rt+1 e (C13)
ci
t+1 ci
t+1
Firstorder conditions of the producer's problem:
i i i i
wt = (1  )zt kt Li (gt t )1
t (C14)
(ci (1  Li )1 )1
t t
i
kt+1 i
1+ ¯
g g =
ci
t kt t t
i
 1
ci
t (ci (1  Li )1 )1 i (1)1
t+1 t+1 i Li
t+1
Et i i
(gt t ) zt+1 i
i
(gt+1 t+1 )1 + 1 
yt ct+1 kt+1
(C15)
Budget constraint:
i i i i
ai gt t = t ai Rt + (1  t )ai Rt e  ci + wt Li + (1  t )ai Rt (1  e ) (C16)
t+1 t t
i
t
i
t
i
t
Changes in NFA position, Valuation Effects and the Current Account:
i
nf ai = [(1  t+1 )ai gt t  (1  t+1 )ai gt t ]  [(1  t )ai  (1  t )ai ]
t t+1
i i
t+1
i i
t
i
t
(C17)
i i
qt+1  i qt+1  i
vei =
t
i i
(1  t )at i e gt  1  (1  t )ai
i
t i
e g t t  1 (C18)
qt qt
cai =
t nf ai  vei
t t (C19)
23
D Appendix D: Impulse responses
1% positive transitory shock 0.1% positive trend(growth) shock
1.04 1.005 1.002 1.0022
1.02 1 1 1.002
1 0.995 0.998 1.0018
0 10 20 30 0 10 20 30 0 10 20 30 0 10 20 30
% of Home Output % of Home Output
% of Home Output
Home/Foreign Output Ratio Home/Foreign Asset Price Ratio Home/Foreign Output Ratio Home/Foreign Asset Price Ratio
1.05 19.8 1.005 19.59
1 19.7 1 19.58
0.95 19.6 0.995 19.57
0 10 20 30 0 10 20 30 0 10 20 30 0 10 20 30
Home/Foreign Dividend Payment Home Investment Home/Foreign Dividend Payment Home Investment
% of Home Output
% of Home Output
% of Home Output
78 0.5 77.8 0
77.5 77.75 0.05
77 0 77.7 0.1
0 10 20 30 0 10 20 30 0 10 20 30 0 10 20 30
Home Consumption Home Current Account Home Consumption Home Current Account
0.6
Home Valuation Effects 0
0.5 Home Current Account
Home Change in NFA
% of Home Output
% of Home Output
0.4
0.05
0.3
0.2
0.1
0.1
Home Valuation Effects
0 Home Current Account
0.15 Home Change in NFA
0.1
0 5 10 15 20 25 30 0 10 20 30
Figure 6: Impulse Responses to 1% transitory shock and 0.1% in trend shock
24