Nominal revaluation of cross-border assets, terms-of-trade changes, international portfolio diversification, and international risk sharing.
Kim, Soyoung
1. Introduction
All nominal assets are subject to nominal risks. The real value of
nominal debt decreases under inflation. In open economies, nominal
cross-border assets are subject to nominal risks, such as inflation
risks and exchange rate risks. That is, when the price level and
exchange rates fluctuate unexpectedly, the real value and real interest
income of nominal cross-border assets change, and wealth is
redistributed internationally. This is called the "nominal
revaluation of cross-border assets." (1)
This international wealth redistribution or international wealth
transfer is enormous when substantial nominal cross-border assets are
held. In major industrial countries, foreign assets and liabilities have
reached their GDP levels. Holdings of foreign assets by the United
States were 73% of its GDP, and its foreign liabilities were 95%, in
2000. The ratios for the United Kingdom were even larger, 260% and 276%,
respectively, in 1999.2 In these circumstances, substantial wealth is
transferred internationally through the "nominal revaluation of
cross-border assets." In the United Kingdom, the annual average of
this wealth redistribution was more than 5% of its annual GDP during the
period 1987-2000. (3)
This "nominal revaluation of cross-border assets" can
work as international risk sharing under some restrictive conditions.
When income and the price level move inversely, the real value and real
return on nominal assets are proportional to income. Thus, by
cross-owning or trading nominal assets internationally, countries can
share some country-specific risks. In his simple two-period model where
the only sources of uncertainty are endowment shocks, Svensson (1989)
showed that even a perfect pooling equilibrium can result by trading
only nominally risk-free bonds under a monetary policy that generates
negative correlation between endowment and the price level. However, he
did not emphasize the role of the mechanism in overall international
risk sharing, and possibly for this reason, the result is not well
known. In this paper, I apply the idea to the aggregate level of
international risk sharing by considering all types of nominal
cross-border assets as opposed to limiting the study to only nominal
bonds them selves.
The mechanism can be thought of as a nominal analogy to Cole and
Obstfeld (1991). In Cole and Obstfeld's (1991) model, changes in
the terms of trade can automatically transfer wealth to insure country-specific risks. In the nominal revaluation, the relative
"nominal" price (nominal exchange rate) changes between
countries, instead of relative "real" price (terms of trade)
changes, make international risk sharing possible. (4)
Cole and Obstfeld (1991) further suggested that the welfare gains
from international portfolio diversification may be small, and the
"home bias" in international portfolio investments may be
justified since changes in the terms of trade can insure some
country-specific risks. (5) Similarly, if the nominal revaluation works
as international risk sharing, it may serve as another justification for
home bias in equities since equities are only parts of total
cross-border nominal assets, and the nominal revaluation of other
cross-border assets (such as bonds, direct investments, currencies,
loans, and so on) can provide risk sharing. (6)
On the other hand, the nominal revaluation has some interesting
implications on the comparison between the flexible and the fixed
exchange rate regimes. If it works as (or against) international risk
sharing, it provides another merit (or drawback) of the flexible
exchange rate regime since the changes in the nominal exchange rate can
provide international risk sharing (or increase the country-specific
risks).
This paper empirically examines three international risk-sharing
channels: the nominal revaluation of cross-border assets, the
terms-of-trade channel suggested by Cole and Obstfeld (1991), and
cross-border security ownership (or international portfolio
diversification) that is thought of as a natural way of sharing
country-specific risks. First, I examine the magnitude of the wealth
transfers by each channel to examine whether it is substantial enough to
have an economic importance.
Second, I examine whether it works as international risk sharing.
In this respect, I estimate the correlation between returns (or wealth
transfers) of each channel and consumption differentials (the difference
between per capita consumption growth rates of a country and the rest of
the world), that is, whether each channel actually pools
country-specific consumption risks. The empirical methods are informal
but quite intuitive and different from previous studies. Consequently,
this study provides some new perspectives on international risk-sharing
research.
Section 2 develops a simple theoretical model to illustrate the
operation of the nominal revaluation since the channel is not well
known. In the model, there are two sources of disturbances: endowment
shocks and monetary policy shocks. The nominal revaluation works as
international risk sharing in the presence of endowment shocks as in
Svensson's (1989) model, but it works against international risk
sharing in the presence of monetary policy shocks, which is not
considered in Svensson (1989). The theoretical model shows the operation
of the nominal revaluation in the world of incomplete risk sharing (or
incomplete markets), in contrast to Svensson's (1989) model
describing the world of complete risk sharing (or complete markets). The
theoretical model is also used to motivate the empirical part.
Section 3 estimates the magnitude of wealth transfers through three
risk-sharing channels. Section 4 empirically examines whether the
nominal revaluation contributes to pooling country-specific consumption
risks. Section 5 examines whether the terms-of-trade channel and
cross-border security ownership work as international risk sharing.
Section 6 discusses implications of the findings in relation to previous
literature and future research directions.
2. Nominal Revaluation of Cross-Border Assets
The following model illustrates the operation of the nominal
revaluation of cross-border assets. In this model, the only assets
traded internationally are nominally risk-free bonds, which represent
general nominal cross-border assets, not just nominal bonds themselves.
Equity trading, which is a natural way to share country-specific risks,
is not allowed. In addition, by assuming only one consumption good and
purchasing power parity, the terms of trade is constant. Thus, the
risk-sharing mechanism suggested by Cole and Obstfeld (1991) is not
available. I show that, even in this world, some country-specific risks
can be shared by the nominal revaluation of cross-border assets.
There are several differences between Svensson (1989) and the
following model. In addition to endowment shocks (which is considered by
Svensson) that make the nominal revaluation an international
risk-sharing mechanism, there are monetary shocks (which are not
considered by Svensson) that generate the nominal revaluation but have
adverse effects on international risk sharing. This is an example in
which the nominal revaluation does not work as an international
risk-sharing mechanism. In addition, while the nominal revaluation on
interest income is emphasized in Svensson (1989), the nominal
revaluation on the value of existing assets, which is the dominant part
in the real world, is emphasized in the following model. Finally, I
examine the operation of the mechanism in incomplete markets in contrast
to Svensson's (1989) complete market model.
The following model has several simplifications that may not be
very realistic. Those simplifications are made to derive simple analytic solutions and to illustrate the operation of this possible international
risk-sharing mechanism. The empirical studies in section 3 are based on
more general conditions, and the empirical works examine whether this
possible mechanism works as international risk sharing in the real
world. Since the main purpose of the model is the illustration of the
channel, I present the model only briefly. Detailed analyses are
reported in the Appendix.
Simple Model with One-Period Nominal Bonds (Debts)
Income is endowed in each period. As a world economy, there are no
real savings, but each country can trade intertemporally by holding
foreign nominal bonds and issuing one-period nominal bonds to
foreigners. For the simplest international setting, several assumptions
are made. Each country has its own money, and private agents hold only
domestic money issued by their government. There is only one consumption
good. The nominal exchange rate is defined as e = p/[p.sup.*], where
p([p.sup.*]) is the domestic (foreign) price level. Each country issues
nominal bonds (debt) denominated in its currency to the other; that is,
one country holds nominal bonds of the other denominated in the
other's currency. Money holdings are motivated by transaction mode
which depend on consumption velocity.
Consumer Optimization
Home
Each individual in the home country maximizes his lifetime utility
subject to his intertemporal budget constraints. There are several
sources of income: endowment ([Y.sub.t]), transfer from the government
([[tau].sub.t]), gross interest income receipts (interest and principal)
from foreign nominal bonds holdings denominated in foreign currency
([e.sub.t][r.sup.*.sub.t-1][B.sup.*.sub.t-1]\[P.sub.t], where
[r.sup.*.sub.t-1] is the gross interest rate of the foreign bonds), and
sales of domestic nominal bonds denominated in the home currency
([B.sub.t]\[P.sub.t]). He allocates his income to consumption
([C.sub.t](1 + [gamma][Florin]([V.sub.t])) where
[gamma][Florin]([V.sub.t]) is the transactions cost term, which is a
function of consumption velocit, [V.sub.t] =
[P.sub.t][C.sub.t]\[M.sub.t]), changes in money holdings (([M.sub.t] -
[M.sub.t-1])/[P.sub.t]), gross interest payments (interest and
principal) to nominal bonds (denominated in home currency) held by
foreigners ([r.sub.t-1][B.sub.t-1]/[P.sub.t], where [ r.sub.t-1] is the
gross interest rate of the domestic bonds), and foreign nominal bonds
holdings denominated in foreign currency
([e.sub.t][B.sup.*.sub.t]/[P.sub.t]). Thus, each individual in the home
country solves the following problem:
[max.sub.[C.sub.t],[B.sub.t],[B.sup.*.sub.t],[M.sub.t]] [summation over ([infinity]/t=1) [[beta].sup.t] log ([C.sub.t])] s.t.
[C.sub.t][1 + [gamma]f([V.sub.t])] + [M.sub.t] - [M.sub.t-1] /
[P.sub.t] - [B.sub.t] - [r.sub.t-1] [B.sub.t-1] / [P.sub.t] + [e.sub.t]
([B.sup.*.sub.t] - [r.sup.*.sub.t-1] [B.sup.*.sub.t-1]) / [P.sub.t] =
[[tau].sub.t] + [Y.sub.t],
where [M.sub.t] [greater than or equal to] 0, [B.sub.t] [greater
than or equal to] 0, [B.sup.*.sub.t] [greater than or equal to] 0,
[e.sub.t] = [P.sub.t]/[P.sup.*.sub.t], [V.sub.t] =
[P.sub.t][C.sub.t]/[M.sub.t], and [Y.sub.t] = Y + [[epsilon].sub.yt].
Foreign
Each individual in the foreign country faces a similar problem:
[max.sub.[C.sup.*.sub.t],[B.sub.t],[B.sup.*.sub.t],[M.sup.*.sub.t]]
[summation over ([infinity]/t=1) [[[beta].sup.t] log ([C.sup.*.sub.t])]
s.t.
[C.sup.*.sub.t][1 + [gamma]f([V.sup.*.sub.t])] + [M.sup.*.sub.t] -
[M.sup.*.sub.t-1] / [P.sup.*.sub.t] - [B.sup.*.sub.t] -
[r.sup.*.sub.t-1] [B.sup.*.sub.t-1] / [P.sup.*.sub.t] + [B.sub.t] -
[r.sub.t-1] [B.sub.t-1] / [e.sub.t][P.sup.*.sub.t] = [[tau].sup.*.sub.t]
+ [Y.sup.*.sub.t],
where [M.sup.*.sub.t] [greater then or equal to] 0, [B.sup.*.sub.t]
[greater then or equal to] 0, [e.sub.t] = [P.sub.t] / [P.sup.*.sub.t],
[V.sup.*.sub.t] = [P.sup.*.sub.t] [C.sup.*.sub.t] / [M.sup.*.sub.t] ,
and [Y.sup.*.sub.t] = [Y.sup.*] + [[epsilon].sup.*.sub.yt].
Monetary Policy and Government Budget Constraint
The monetary authorities of both countries are assumed to follow
the constant money growth rate rule with random disturbances
([[epsilon].sub.mt]):
[M.sup.t]/[M.sup.t-1] = 1 + [[epsilon].sub.mt]
[[M.sup.*].sub.t]/[M.sup.*].sub.t]/[[M.sup.*].sub.t-1] = 1 +
[[epsilon].sup.*.sub.mt].
The government is assumed to transfer seigniorage to consumers in
each period:
[M.sub.t] - [M.sub.t-1]/[P.sub.t] = [[tau].sub.t]
[M.sup.*.sub.t] - [M.sup.*.sub.t-1]/[P.sup.*.sub.t] =
[[tau].sup.*.sub.t].
Equilibrium and Nominal Revaluation
I define [b.sub.t] = [B.sub.t]/[P.sub.t], [[b.sup.*.sub.t] =
[B.sup.*.sub.t]/[P.sup.*.sub.t], and k = 2b(1 - [beta]/[beta]. Then the
system of equation is linearized around a symmetric steady state. (7)
The solutions for the consumption process follow: (8)
[FORMULA NOT REPRODUCIBLE IN ASCII] (1)
[FORMULA NOT REPRODUCIBLE IN ASCII] (2)
where variables with subscript t are deviations from their
steady-state values and variables without subscripts are the
steady-state values.
In Equation 1, the last term on the right-hand side,
1/2([[epsilon].sub.yi] + [[epsilon].sup.*.sub.yi]), represents the
perfect pooling equilibrium where all country-specific consumption risks
are shared and the consumption growth rates of the home and foreign
countries are equalized (([C.sub.t] - [C.sub.0]) - ([C.sup.*.sub.t] -
[C.sup.*.sub.0]) = 0 in Epn. 2), while the first two terms show the
deviation from the perfect pooling equilibrium. The wealth transfer
through the nominal revaluation (the changes in net foreign asset
position of the home through changes in two nominal variables--the price
level and the exchange rate) is
[NR.sub.t] = [e.sub.t][[B.sup.*.sub.t-1] - [B.sub.t-1]/[P.sub.t] -
[e.sup.t-1][B.sup.*.sub.t-1] - [B.sup.t-1]/[P.sub.t-1]. (3)
By linearizing Equation 3 around the steady state, we can decompose the wealth transfer through the nominal revaluation into two parts, the
part due to exchange rate change and the part due to price level change:
[NR.sub.t] = [b.sup.*] ([e.sub.t] - [e.sub.t-1] - ([b.sup.*] - b)
[P.sub.t] - [P.sub.t-1]/p. (4)
In the symmetric steady state where b = [b.sup.*], the wealth
transfer is due solely to exchange rate change, and the size of the
wealth transfer depends on exchange rate change and the steady-state
cross-border assets; that is,
[NR.sub.t] = b([e.sub.t] - [e.sub.t-1]) (5)
= k/2(k + Y) ([[epsilon].sup.*.sub.yt] - [[epsilon].sub.yt]) +
kY/2(1 - [beta])(k + Y) ([[epsilon].sub.mt] - [[epsilon].sup.*.sub.mt]).
(6)
Equation 6 is derived using the solution of the system.
In the presence of the asymmetric endowment shocks, when the steady
state cross-border asset holdings (b or k) are nonzero, the wealth
redistribution through the nominal revaluation works as international
risk sharing. (9) For example, when there is a positive shock to home
endowment, the wealth effects of the nominal revaluation are negative
for the home country. The increase in the home endowment appreciates the
home exchange rate, which decreases the real value of net foreign assets
of the home country. As the steady-state cross-border assets (b or k)
increase, wealth transfers through the nominal revaluation increase, the
consumption differential decreases, and the equilibrium consumption path
approaches the perfect pooling consumption path. In the extreme case
where an infinite amount of cross-border assets is held, the perfect
pooling consumption path is achieved. (10)
In the presence of the monetary policy shocks, the nominal
revaluation works against international risk sharing when there are some
cross-border asset holdings. A home monetary expansion (positive
[[epsilon].sub.mt]) depreciates the exchange rate. Therefore, some
wealth is transferred from the foreign country, the consumption
differential increases, and the equilibrium consumption path moves away
from the perfect pooling. This suggests another channel for real effects
of monetary policy shocks under a flexible price assumption. (11)
3. Magnitude of Wealth Transfers
In this section, I estimate the magnitude of wealth transfers
through three risk-sharing channels: the nominal revaluation of the
cross-border assets, the terms-of-trade channel suggested by Cole and
Obstfeld (1991), and the cross-border security ownership. Finding the
right indicators or calculating the exact estimates of wealth transfers
through each channel (especially the nominal revaluation and
cross-border security holdings) is not easy. In the case of the United
States and the United Kingdom, some suitable indicators are available.
However, it should be noted that the raw data (therefore, the estimates
reported here) can be only an approximation because of the (data
collecting agency's and our) lack of accurate information about the
exact location and currency denomination of cross-border assets and the
type of assets involved. They should therefore be interpreted as
indicative of broad movements only. Also, note that the estimates simply
show the magnitude of wealth transfers through each channel, not the
magnitude of wealth transfers that actually worked as risk sharing.
Measures
In general, the net wealth changes of a country (in terms of home
currency) from holding cross-border assets (between time t and t + 1)
can be simplified to
[([Q.sup.1.sub.t+1] - [Q.sup.1.sub.t][B.sup.1.sub.t] +
([e.sub.t+1][Q.sup.2.sub.t+1] - [e.sub.t][Q.sup.2.sub.t])[B.sup.2.sub.t]
+ [[pi].sup.1.sub.t+1] + [e.sub.t+1][[pi].sup.2.sub.t+1], (7)
where B, Q, and it are vectors of cross-border assets, their
prices, and their net interest/dividends receipts, respectively. The
subscript 1 represents assets and liabilities denominated in home
currency, and 2 represents assets and liabilities denominated in foreign
currencies. Note that assets and liabilities are arranged in the same
vector. (Liabilities are with a negative sign.) Also note that some
cross-border assets are nonsecurities and may not provide interest or
dividends. There are two major sources of the net wealth changes. First,
([Q.sup.1.sub.t+1] - [Q.sup.1.sub.t])[B.sup.1.sub.t] + ([e.sub.t] +
1[Q.sup.2.sub.t+1] - [e.sub.t][Q.sup.2.sub.t])[B.sup.2.sub.t] shows the
change in the value of outstanding cross-border assets. Asset price
changes (from [Q.sub.t] to [Q.sub.t+1]) affect the value of assets.
Also, exchange rate changes (from [e.sub.t] to [e.sub.t+1]) affect the
home currency value of assets denominated in foreign currency. Second,
[[pi].sup.1.sub.t+1] + [e.sub.t+1][[pi].sup.2.sub.t+1] is net receipt of
interests and dividends. Note that the exchange rate in the next period
can also affect the domestic currency value of net receipts of interests
and dividends of assets denominated in foreign currency.
Therefore, exchange rate changes affect the net wealth of
cross-border assets in two ways. First, they affect the value of
outstanding cross-border assets. Second, they affect the value of net
interest/dividends receipts. In principle, wealth transfers through the
nominal revaluation channel should include both. However, in practice,
the latter effects are difficult to estimate since separating exchange
rate effects from interest payments or dividends is not easy. In
addition, such effects are probably relatively small compared to the
former effects. Therefore, I include only valuation changes in
outstanding cross-border assets due to exchange rate changes in my
estimates of wealth transfers through the nominal revaluation channel.
(12)
Each year, Survey of Current Business and Quarterly Bulletin (by
the Bank of England) report the international investment position
(assets and liabilities, separately) of the United States and the United
Kingdom at year's end. (13) In Survey of Current Business and
Quarterly Bulletin, changes in assets and liabilities are attributed to
capital flows and valuation adjustments. Valuation adjustments are
basically divided into two categories in the data: "price
changes" and "exchange rate changes." I use
"exchange rate changes" (in their definition, gains or losses
on foreign currency-denominated assets due to their revaluation at
current exchange rate). (14)
For wealth transfers through cross-border security holdings, I use
the sum of net capital gains and net interest/dividends receipts from
cross-border security (nonbank private) ownership. That is, I include
both components in Equation 7. However, only parts of cross-border
assets are securities; that is, only some elements of Bs in Equation 7
are securities. Cross-border assets also include direct investments,
loans, official reserve assets such as foreign currencies, reserve
position in the International Monetary Fund, special drawing rights, and
so on.
For net capital gains, I use total revaluations of cross-border
security holdings due to both "asset price changes" and
"exchange rate changes," which are available from the Survey
of Current Business and the Quarterly Bulletin. The data on net
dividends/interest payments from cross-border security ownership are
also available, although sometimes only for current periods. The Survey
of Current Business reports details of international transactions each
year. "Investment income" (a component of the current account)
is divided into two categories: "direct investment" and
"other private income." Among "other private
income," I use two components: dividends and interest on bonds from
nonbank private cross-border security ownership. Quarterly Bulletin also
reports earnings and payments from nonbank private portfolio investment.
The estimates of wealth transfers through the nominal revaluation
include some wealth transfers through cross-border security ownership
since the latter includes revaluation due to exchange rate changes. I
also calculate wealth transfers through the nominal revaluation that are
not included in those for cross-border security holdings, that is, the
wealth transfers through the nominal revaluation of nonsecurity
cross-border assets.
In Cole and Obstfeld's (1991) models, wealth effects (not
substitution effects) from changes in terms of trade are the source of
sharing country-specific risks. (15) Low endowment of the home country
relative to the foreign country improves the terms of trade, which
increases the value of exports and/or decreases the value of imports. As
a result, wealth is transferred from the foreign country to the home
country, and country-specific risks are pooled. For the terms-of-trade
channel, I estimate wealth effects from export and import price changes.
The following formula is used:
[P.sub.e,t+1] - [P.sub.e,t]/[P.sub.e,t][EX.sub.t] - [P.sub.i,t+1] -
[P.sub.i,t]/[P.sub.i,t][IM.sub.t], (8)
where [P.sub.e] is the price of exports, [P.sub.i] is the price of
imports, EX is exports, and IM is imports. (16)
Results
I report the estimates of the average value of wealth transfers for
the United States and the United Kingdom in Table 1. Each number shows
the percentage of each country's GDP, and it is the average
absolute net value. I construct each measure for a one- to five-year
span. In the first and second columns, the estimation period and the
data span are reported, respectively. In the first and second rows, I
denote the name of each channel under consideration and give more
detailed explanations. (17)
Wealth transfers through the nominal revaluation of cross-border
assets are substantial. Even though they are moderate for the overall
period in the United States (0.4% of GDP in the period after 1973 for a
one-year span), they increase as time passes, which is probably due to
increases in cross-border assets. In the period after 1996, they amount
to 1.3% of GDP for a one-year span. They are about two-thirds of wealth
transfers through cross-border security holdings for a one-year span.
They are about the same as wealth transfers through cross-border
security holdings for two- and three-year spans. For the United Kingdom,
the magnitude of wealth transfers through the nominal revaluation is
quite substantial, over 5% of GDP for a one-year span and over 10% for a
two-year span. They are more than two times larger than wealth transfers
through cross-border security holdings.
Wealth transfers through the terms-of-trade channel are smaller
than those through the other two channels, especially in the recent
periods. In the period after 1996, they are 0.4% of GDP in the United
States and 1.7% in the United Kingdom, or less than a third of wealth
transfers through the nominal revaluation channel. (18)
4. Does Nominal Revaluation Work as International Risk Sharing?
Methodology
In this section, I examine whether the nominal revaluation,
overall, works to share country-specific consumption risks in the real
world. If a suggested channel works to pool country-specific risks at
the aggregate level, then this channel should decrease country-specific
consumption risks that each country faces. In this respect, I examine
the correlation between the wealth transfers through the nominal
revaluation and consumption differentials between home and the rest of
the world. If overall international risk sharing is complete, then we
may not observe any systematic correlation since the consumption
differentials will always be at the perfect pooling point. (19)
However, if overall international risk sharing is incomplete (as
suggested by many previous studies, e.g., Obstfeld 1994 and Backus et
al. 1992) but a channel provides partial international risk sharing, we
should find a negative correlation; that is, if the nominal revaluation
works as international risk sharing, then the wealth transfers through
the nominal revaluation should hedge or pool some country-specific
consumption risks. Therefore, a positive wealth transfer should be
observed when consumption is relatively low compared to the rest of the
world.
The previously described empirical methodology is not structural.
Therefore, we cannot identify the exact underlying mechanism that
generates the correlation (or international risk sharing). However, as
long as a negative correlation is found, the channel (wealth transfers
through the nominal revaluation) works as international risk sharing
since it hedges country-specific consumption risks regardless of the
underlying mechanism. In addition, the test is valid under more general
conditions than the assumptions of the theoretical model in the previous
section. (20) The empirical test is appealing in these regards.
I illustrate how the empirical test works based on the previous
theoretical analysis. Under the assumption that structural shocks are
not correlated with each other, the correlation between the consumption
differential (([C.sub.t] - [C.sub.0]) - ([C.sup.*.sub.t] -
[C.sup.*.sub.0])) and the wealth transfers through the nominal
revaluation ([NR.sub.t]) in the model is -[Yk(1 - [beta])/2[(k +
Y).sup.2]]([[sigma].sup.*.sub.yt] + [[sigma].sub.yt]) - [[k.sup.2]Y/2(1
- [beta])[(k + Y).sup.2]]([[sigma].sup.*.sub.mt] + [[sigma].sub.mt]),
where [[sigma].sub.y], [[sigma].sup.*.sub.y], [[sigma].sub.m], and
[[sigma].sup.*.sub.m] are the standard deviations of home and foreign
endowment and monetary policy shocks. Therefore, the nominal revaluation
works as (or against) international risk sharing when the correlation is
negative (or positive), as in the case of endowment shocks (monetary
policy shocks).
Since it is difficult to construct the data on the wealth transfers
through the nominal revaluation for many countries, I use nominal
exchange rate changes as the measure of the direction of the wealth
transfers through the nominal revaluation. In Equation 5, the wealth
transfers through the nominal revaluation and exchange rate changes have
a perfect positive correlation. Therefore, I estimate the correlation
between exchange rate changes and the consumption differential to
examine whether the nominal revaluation works as international risk
sharing.
In deriving Equation 5, two key simplifying assumptions are used.
First, net foreign asset position is zero (i.e., b = [b.sup.*]), Second,
all cross-border assets are assumed to be denominated in the issuer s
currency. However, even in more general settings, the direction of
exchange rate changes can represent the direction of wealth transfers
through the nominal revaluation. First, even though the net foreign
asset position is not exactly zero in the real world, the foreign assets
or liabilities are far greater than the net foreign asset position. (21)
Then, in Equation 4, the exchange rate change dominates the price level
change. Moreover, exchange rate changes are far more volatile than price
level changes in most countries under the flexible exchange rate regime.
(22) Therefore, exchange rate changes are a reasonable measure for the
direction of wealth transfers through the nominal revaluation, even if
net foreign asset is not exactly zero. Second, in the real world, some
cross-border assets are denominat ed in the buyer's currency.
However, as long as the majority of the cross-border assets are
denominated in the issuer's currency, exchange rate changes are
positively correlated with wealth transfers through the nominal
revaluation. (23,24)
Empirical Results
For the consumption differential, I use the residuals from a
regression of the growth rate of per capita domestic consumption on the
growth rate of per capita consumption of the rest of the world. (25)
For the consumption of the rest of the world, I use the U.S.
consumption. For the exchange rate changes, I use changes in the nominal
exchange rate against the United States. In the case of the United
States, the correlation between the estimates of wealth transfers
through the nominal revaluation (see section 5) and the consumption
differential against the rest of the world is reported. (26)
Table 2 reports the correlations for 20 industrial countries. The
estimation period is from 1973 to 1992. The data spans are from one to
three years (nonoverlapping). The * and ** imply that the correlations
are different from zero at the 5% and 1% significance levels,
respectively. Correlation is negative in most cases, so the nominal
revaluation seems to work as an international risk-sharing mechanism.
For a one-year span, correlations are all negative (seven are
significant at the 5% level) except for two countries with very small
positive correlations. For two- and three-year spans, correlations are
negative (six and five correlations, respectively, are significant at
the 5% level) except for three and four countries, respectively, with
nonsignificant positive correlations. (27)
5. Terms-of-Trade Channels and the Cross-Border Security Ownership
Terms-of Trade Channel
I examine the international risk-sharing channel suggested by Cole
and Obstfeld (1991) using a similar empirical method. Again, if a
suggested channel works to pool country-specific risks at the aggregate
level, then the correlation between the wealth transfers through the
channel and the consumption differential should be negative when the
overall international risk sharing is incomplete.
In Cole and Obstfeld's (1991) models, wealth effects from
changes in terms of trade are the source of sharing country-specific
risks. (28) Relatively low endowment improves the terms of trade, wealth
is transferred from foreign countries, and country-specific risks are
pooled. Since changes in the terms of trade and wealth effects from the
changes are generally positively correlated, a negative correlation
between the consumption differentials and the terms-of-trade changes (in
percentage) implies that their channel works as an international
risk-sharing mechanism in general. (29)
Table 3 reports the correlations. (30) The wealth effects from
terms-of-trade changes do not seem to work as an international risk-
sharing mechanism, especially for one- and two-year horizons. More
positive correlations are found than negative ones in the estimation
using one- and two-year data spans. For a one-year span, correlations
are positive except for four countries, and only positive correlations
(seven countries at the 5% significance level) are significant. For
two-year data spans, correlations are all positive except for three
cases. For three-year spans, more than half the correlations are
negative, but we still find several positive correlations.
One reason that the terms-of-trade channel fails as an
international risk-sharing mechanism may be its procyclical behavior, in
contrast to the theoretical prediction of Cole and Obstfeld (1991). I
estimate the correlations between percentage changes in terms of trade
and the growth rate difference in domestic per capita GDP and the rest
of the world's per capita GDP. In most countries where we observe
negative correlations between the percentage changes in terms of trade
and the consumption differentials, terms of trade is procyclical, though
correlations are not significantly different from zero in most cases.
The effect of terms-of-trade changes on investment decisions may be an
another possible reason.
Cross-Border Security Ownership
One of the most frequently studied channels of international risk
sharing is cross-border security (stocks and/or bonds) holdings (or
international portfolio diversification). (31) If a claim on each
country's GDP is available in the real world, each country may own
a hypothetical portfolio that is constructed by buying a claim on the
rest of the world's GDP and selling a claim on domestic GDP and
thus share country-specific consumption risks. (32) However, in the real
world, such a claim is not available, and cross-border security holdings
may not provide international risk sharing at the aggregate level.
I list two reasons cross-border security (stocks and/or bonds)
holdings may not (or only partially) provide international risk sharing
at the aggregate level. First, some risks may not be marketable, or some
risks cannot be hedged by combinations of existing securities. In this
case, even though the market portfolio of each country is cross-owned by
the other countries, they may not pool all risks. Second, the foreign
securities owned by domestic consumers may differ from the foreign
market portfolio. (33) If the foreign (domestic) securities owned by
foreign (domestic) investors are negatively correlated with the foreign
(domestic) market portfolio, then cross-border security holdings may
work against sharing country-specific risks. (34)
To evaluate whether cross-border security holdings in the United
States work as an international risk-sharing mechanism at the aggregate
level, I examine the correlation between the consumption differentials
mentioned in the previous section and the wealth transfers through
cross-border security holdings estimated in section 3. Again, a negative
correlation implies that this channel pools country-specific consumption
risks. During the 1984-1992 period, the correlation (considering both
stocks and bonds) is 0.37 in the United States. When wealth transfers
through only cross-border stock holdings are considered, we still get
0.15, a positive correlation. (35) These correlations suggest that
cross-border security holdings may not work as international risk
sharing at the aggregate level. Note that this result may be due to the
fact that other risk-sharing mechanisms (such as the nominal
revaluation) are enforced before cross-border securities are chosen. In
section 6, I discuss further the implications of this r esult in
relation to past research.
6. Implications
First, I suggested a possible international risk-sharing mechanism:
the "nominal revaluation of cross-border assets." Then I
examined this mechanism and other risk-sharing channels empirically. I
found that the nominal revaluation of cross-border assets contributes to
pooling country-specific consumption risks in the real world and that
international wealth transfers through this channel are substantial. I
also found that the terms-of-trade channel suggested by Cole and
Obstfeld (1991) and cross-border security ownership do not seem to pool
the country-specific consumption risks at the aggregate level. In the
following, I discuss implications of the results.
International Risk Sharing
First, the result of the nominal revaluation can serve as a
possible justification for the home bias in equities (more generally,
both equities and bonds). Research on international portfolio
diversification, which has found a home bias toward domestic securities
when compared to the theoretical models' predictions (the
"international portfolio diversification puzzle"), does not
fully incorporate the nominal revaluation since it concentrates only on
cross-border security holdings, which are only small parts of total
cross-border asset holdings. In this respect, I estimate the magnitude
of wealth transfers through the nominal revaluation that is not captured
in wealth transfers through cross-border security holdings (i.e., wealth
transfers through the nominal revaluation of nonsecurity cross-border
assets). As shown in the last column of Table 1, substantial amounts of
wealth transfers through the nominal revaluation are not captured by
those through cross-border security holdings. They are about a third to
a half of the wealth transfers through cross-border security holdings in
the United States and more than twice the wealth transfers through
cross-border security holdings in the United Kingdom. This result
suggests that the degree of home bias from previous research may be
different once the nominal revaluation is incorporated.
On the other hand, the terms-of-trade channel suggested by Cole and
Obstfeld (1991) does not work as international risk sharing. Therefore,
the terms-of-trade channel cannot be a possible justification for the
home bias puzzle. In addition, the argument that welfare gains from
international risk sharing are small due to the terms-of-trade channel
may be inappropriate.
Fixed versus Flexible Exchange Rate Regimes
The results provide interesting implications for the comparison of
the fixed and the flexible exchange rate regime. The conventional
discussion on the comparison between the flexible and the fixed exchange
rates is based on the role of the exchange rate in macroeconomic adjustment procedures. (36) However, the results in this paper suggest
another dimension for the comparison, based on the role of the exchange
rate in international risk sharing.
Based on the results in this paper, the nominal revaluation works
as international risk sharing at the aggregate level. Also as suggested,
the changes in the nominal exchange rate play the key role in the
nominal revaluation. Under the flexible exchange rate regime, the
changes in the exchange rate provide international risk sharing through
the nominal revaluation. However, under the fixed exchange rate regime,
the nominal revaluation cannot work, and the world economy as a whole
loses this built-in risk-sharing mechanism. Therefore, the presence of
the nominal revaluation as an international risk-sharing mechanism
suggests an additional merit (or drawback) of the flexible (or fixed)
exchange rate regime. (37)
Future Research Agenda
There are several directions for further research. First, more
rigorous empirical research may be fruitful. The empirical method
employed in this paper provides an overall picture of international risk
sharing through each channel, but it does not provide the actual extent
of risk sharing achieved through each channel. It seems to be important
to examine the actual extent of risk sharing in future studies. In
addition, more detailed examinations for each channel--for example,
studies on the role of cross-border security holdings for international
risk sharing at the aggregate level--may be worthwhile. Second, some
aspects regarding the nominal revaluation of cross-border assets other
than international risk sharing are worth studying. For example, the
magnitude of wealth transfers or inflation taxes that some industrial
countries (especially the United States) can collect from other
developing countries by an inflation is an aspect worthy of further
study. Third, to show the practical importance of the nomina l
revaluation as an international risk-sharing mechanism, it is necessary
to study how much of the home bias for international portfolio
diversification can be justified by the nominal revaluation and how
different the extent of the incompleteness of overall international risk
sharing is once this channel is incorporated. Fourth, it seems to be
worthwhile to examine the welfare costs (or gains) of European Monetary
Union in terms of the nominal revaluation.
Appendix: Details on Theoretical Model
First-Order Conditions
First-order conditions of the consumer optimization follow:
[FORMULA NOT REPRODUCIBLE IN ASCII] (A.1)
1 - [gamma]f'([V.sub.t])[V.sup.2.sub.t] = [r.sup.-1.sub.t]
(A.2)
[Z.sub.t][e.sub.t]/[M.sub.t] =
[r.sup.*.sub.t][beta][E.sub.t][[Z.sub.t+1][e.sub.t+1]/[M.sub.t+1]] (A.3)
[FORMULA NOT REPRODUCIBLE IN ASCII] (A.4)
1 - [gamma]f' ([V.sup.*.sub.t]) [V.sup.*2.sub.t] =
[r.sup.*-1.sub.t] (A.5)
[Z.sup.*.sub.t]/[M.sup.*.sub.t][e.sub.t] =
[beta][r.sub.t][E.sub.t][[Z.sup.*.sub.t+1]/[M.sub.t+1][e.sub.t+1]].
(A.6)
Equations A.2 and A.5 represent liquidity preference relations.
Equations A.1 and A.4 are Fisher relations. We can replace Equations A.3
and A.6 with the following equations describing the relation between the
domestic interest rate and the foreign interest rate:
[FORMULA NOT REPRODUCIBLE IN ASCII]
[FORMULA NOT REPRODUCIBLE IN ASCII]
The last terms of the right-hand sides of these two equations
include the risk premium and convexity term.
Social Resource Constraint
The social resource constraint for the home country is
[C.sub.t][1 + [gamma]f([V.sub.t])] + [e.sub.t]([B.sup.*.sub.t] -
[r.sup.*.sub.t-1][B.sup.*.sub.t-1])/[P.sub.t] - [B.sub.t] -
[r.sub.t-1][B.sub.t-1]/[P.sub.t] = [Y.sub.t].
The social resource constraint for the foreign country is
[C.sup.*.sub.t][1 + [gamma]f([V.sup.*.sub.t])] + [B.sub.t] -
[r.sub.t-1][B.sub.t-1]/[e.sub.t][P.sup.*.sub.t] - [B.sup.*.sub.t] -
[r.sup.*.sub.t-1][B.sup.*.sub.t-1]/[P.sup.*.sub.t] = [Y.sup.*.sub.t].
The social resource constraint for the world economy is
[C.sub.t][1 + [gamma]f([V.sub.t])] + [C.sup.*.sub.t][1 +
[gamma]f([V.sup.*.sub.t])] = [Y.sub.t] + [Y.sup.*.sub.t].
Linearized System
The system of equations is linearized around a symmetric steady
state with nfa = 0. After substituting, using the steady-state relation,
and defining [m.sub.t] = [M.sub.t]/[M.sub.t-1], [b.sub.t] =
[B.sub.t]/[P.sub.t], [[pi].sub.t] = [P.sub.t]/[P.sub.t-1],
[m.sup.*.sub.t] = [M.sup.*.sub.t]/[M.sup.*.sub.t-1], [b.sup.*.sub.t] =
[B.sup.*.sub.t]/[P.sup.*.sub.t-1], [[pi].sup.*.sub.t] =
[P.sup.*.sub.t]/[P.sup.*.sub.t-1], [nfa.sub.t] = [b.sup.*.sub.t] -
[b.sub.t], and e = [e.sub.t]/[e.sub.t-1], the system can be reduced to
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where [[eta].sub.t] is [e.sub.t] - [E.sub.t-1][[e.sub.t]].
Variables with subscript t are deviations from their steady-state
values, and variable without subscripts are the steady-state values.
Generalized eigenvalues of this sytem are 0, 0, 1, and 1/[beta].
Since the number of roots greater than 1 is equal to the number of
equations with the expectation terms, a unique solution exists. (This
condition is from Blanchard and Kahn 1980.) Stability conditions of the
system are
[e.sub.t] = [[eta].sub.t] = 1 - [beta]/k + Y (-[[epsilon].sub.yt] +
[[epsilon].sup.*.sub.yt]) + Y/2b 1-[beta]/beta + Y ([[epsilon].sub.mt] -
[[epsilon].sup.*.sub.mt]),
where k = 2b(1 - [beta])/[beta] and
[nfa.sub.t] = [beta]Y/2(1 - [beta])C[[C.sub.t]-[C.sup.*.sub.t]].
Solutions
The complete solutions of the system follow:
[C.sub.t] = [summation over (t/i=1)] C/2 [1 - [beta]/k + Y
([[epsilon].sub.yi] - [[epsilon].sup.*.sub.yi]) + k/k + Y
([[epsilon].sup.*.sub.mi] - [[epsilon].sub.mi])] + C/2Y
([[epsilon].sub.yi] - [[epsilon].sup.*.sub.yi]) + [C.sub.0]
[FORMULA NOT REPRODUCIBLE IN ASCII]
[FORMULA NOT REPRODUCINLE IN ASCII]
[FORMULA NOT REPRODUCIBLE IN ASCII]
[FORMULA NOT REPRODUCIBLE IN ASCII]
Table 1
Magnitude of Wealth Transfers: Average of Absolute Value (% of GDP)
Nominal Revaluation
(Revaluation Due Terms of Trade
to Exchange Rate) (Wealth Effects)
Span
Period Years U.S. UK U.S. UK
1973- 1 0.4 -- 0.7 3.0
2 0.5 -- 1.4 5.9
3 0.6 -- 2.0 8.4
4 0.5 -- 2.0 8.7
5 1.0 -- 1.7 6.4
1984- 1 0.6 -- 0.4 1.7
2 0.9 -- 0.5 2.9
3 1.0 -- 0.7 2.8
1987- 1 0.7 5.9 0.4 1.4
2 0.9 10.8 0.6 2.6
1990- 1 0.8 6.5 0.3 1.6
2 1.1 12.2 0.4 2.8
1996- 1 1.3 5.6 0.4 1.7
Securities Nominal Revaluation
Capital Gains, Interest (from Nonsecurity
Income [NR included]) Cross-Border Assets)
Period U.S. UK U.S. UK
1973- -- -- -- --
-- -- -- --
-- -- -- --
-- -- -- --
-- -- -- --
1984- 0.9 -- 0.3 --
0.9 -- 0.5 --
1.1 -- 0.6 --
1987- 1.1 -- 0.4 --
0.9 -- 0.5 --
1990- 1.2 3.0 0.5 6.6
1.0 3.7 0.6 13.1
1996- 1.8 -- 0.6 --
Each number shows the estimate for average of absolute value of wealth
transfers through each channel as a percentage of GDP. The estimation
period for the United States is up to 2000, except for terms of trade
(up to 1998). The estimation periods for the United Kingdom are up to
1999, 1998, 1997, and 1997 for the nominal revaluation, terms-of-trade,
security, and nominal revaluation (from nonsecurity) channels,
respectively.
Table 2
Correlations between Exchange Rate Changes and the Consumption Growth
Differential
Span (Years) 1 2 3
Australia -0.46 * -0.36 -0.77 *
Austria -0.10 -0.09 -0.17
Belgium -0.34 -0.60 * -0.90 **
Canada -0.21 0.17 -0.07
Denmark -0.12 -0.17 -0.01
Finland -0.34 -0.23 -0.05
France -0.36 -0.49 -0.09
Germany -0.59 ** -0.72 ** -0.78 *
Iceland -0.34 -0.41 0.30
Ireland -0.49 -0.53 -0.83 *
Italy -0.28 -0.38 -0.67
Japan 0.02 -0.19 -0.07
Netherlands -0.46 * -0.55 * -0.55
New Zealand -0.10 -0.39 -0.39
Norway -0.06 0.15 0.15
Spain -0.57 ** -0.69 * -0.69
Sweden -0.44 * -0.82 ** -0.82 *
Switzerland 0.01 0.18 0.18
United Kingdom -0.64 ** -0.62 * -0.62
United States -0.14 -0.29 -0.54
Each number shows correlation between exchange rate changes and
consumption growth differential for the period 1973-1992. The data spans
are from one to three years (nonoverlapping). * and ** imply that the
correlations are different from zero at the 5% and 1% significance
levels, respectively.
Table 3
Correlations between Terms-of-Trade Changes and the Consumption Growth
Differential
Span (Years) 1 2 3
Australia 0.42 * 0.64 * 0.94 **
Austria -0.06 0.14 -0.28
Canada 0.38 0.27 -0.05
Denmark 0.53 ** 0.39 0.74 *
Finland 0.47 * 0.60 * 0.51
France 0.42 * 0.07 -0.45
Germany 0.15 0.12 -0.40
Iceland 0.66 ** 0.66 * -0.42
Ireland -0.29 -0.56 * -0.73 *
Italy -0.36 -0.13 -0.64
Japan 0.22 0.34 -0.88 **
Netherlands -0.34 -0.40 -0.14
New Zealand 0.15 0.03 0.50
Norway -0.10 0.06 -0.20
Spain 0.20 0.39 0.56
Sweden 0.39 * 0.85 ** 0.44
United Kingdom 0.18 0.12 -0.22
United States 0.69 ** 0.68 0.60
Each number shows correlation between terms-of-trade changes and
consumption growth differential for the period 1973-1992. The data spans
are from one to three years (nonoverlapping).
* and ** imply that the correlations are different from zero at the 5%
and 1% significance levels, respectively.
Received April 2001; accepted March 2002.
(1.) The term "nominal" is emphasized because I focus on
revaluations through "nominal" channels rather than
"real" channels. For example, by owning foreign equities, the
home country can receive income from foreign countries when the
equities' prices in real terms increase (when high growth is
expected for the foreign countries or firms). This represents changes in
the real value of cross-border assets through a "real"
channel. In contrast, inflation can decrease the real value of debt if
the debt is not indexed to the price level, a "nominal"
channel.
(2.) The data sources are Survey of Current Business for the United
States and Quarterly Bulletin by the Bank of England for the United
Kingdom.
(3.) In section 3, I explain how we obtain this estimate. In
severely indebted developing countries, the wealth transfers through the
nominal revaluation of the cross-border assets are even more dramatic.
For example, in Nicaragua and Guyana, the estimated annual average
(1989-1992) of the ratios of the changes in real value of debt to the
real GNP (in absolute terms) are 94.5% and 117.9%, respectively. See Kim (1996).
(4.) Later I explain why nominal exchange rate changes are the
major sources of the nominal revaluation.
(5.) See French and Poterba (1991) and Tesar and Werner (1992) for
the home bias puzzle. See also Lewis (1995) and Obstfeld (1995) for the
literature on international risk sharing.
(6.) In the United States, total foreign assess amounted to $2,765
billion, and private equity holdings were only $313 billion at the end
of 1994. Total foreign liabilities amounted to $3,349 billion, and
foreign holdings of the U.S. equities were only $338 billion.
(7.) Under the monetary policy and the transaction technology
specified previously, Z, [Z.sup.*], V, and [V.sup.*] become constant.
More precisely, I consider the transaction cost technology with which Z,
[Z.sup.*], V, and [V.sup.*] become constant and the other paths are
excluded by transversality and feasibility conditions. See Sims (1994)
for details. This constant velocity result is not very unrealistic
compared to a simple cash-in-advance constraint, which also implies a
constant velocity.
(8.) In the solutions, I ignored steady-state transaction costs for
simple presentation, that is, C = Y is assumed. See the Appendix for
precise solutions. There are two points to mention regarding
linearization of this model with a unit root. First, there is a unit
root in the system. However, the linearization is valid around the
steady-state manifold. Second, the unit root in the system implies that
net foreign assets drift. In the long run, one country may default, but
this system does not explicitly consider default risks. Therefore, its
solution may be different from the solution of the model, which
explicitly considers default risks. One justification is that, near
steady state, net foreign asset is close to zero, so there is only a
small probability of default risks; thus, the solution near steady state
can be regarded as a reasonable approximation.
(9.) In the following text, explanations are given as if we know
the separate distributions of b and [b.sup.*] even though, in the
present linearized model, only the distribution of net foreign assets is
determined but the separate distributions of b and [b.sup.*] are nor. We
can derive the distribution of b and [b.sup.*] separately by assuming
another equation that describes the allocation between domestic and
foreign bond holdings. More formal approaches that can determine the
separate distributions of b and [b.sup.*] are using different
approximations than linearization or using preferences with increasing
risk aversion. See Telmer (1993). Here I do not take those approaches
since the motivation for the theoretical model is to illustrate the
operation of the nominal revaluation.
(10.) We can show that the steady state with an infinite amount of
bond holdings is not necessarily the equilibrium in this model. Even
though it is optimal for the country as a whole, since all
country-specific endowment risks can be pooled (without monetary policy
shocks), for each individual risks become infinite with infinite bond
holdings.
(11.) Note that each country can improve its wealth and net foreign
asset position by a monetary expansion. Therefore, each country has an
incentive to inflate unexpectedly. It seems to be worthwhile to
investigate this situation carefully in future research. If both
countries repeatedly inflate, they will reach an equilibrium where the
cost of inflation is equal to the benefit of net asset position
improvements. Or they may want their cross-border assets to be indexed
to inflation.
(12.) The price level changes can also change the real value of
cross-border assets. However, as shown in my theoretical model, the
price level changes may be disregarded under some simplifying
assumptions. Further, I estimate the revaluation due to price level
changes, hut this revaluation effect is very small relative to other
revaluations. On the other hand, changes in expectations of the price
level change the term structure of interest rates, so the real value of
international investment positions changes. This is another source of
the nominal revaluation. (This mechanism can be another real effect of
monetary policy.) As in the corporate finance literature concerning
duration matching or immunization, the real value of international
investment position can change if the term structure of interest rates
changes when maturity of assets is different from that of liabilities.
In addition, when interest rate parity does not hold, changes in the
interest rate differentials between countries (after converting to the
same currency) can result in real value changes even when the term
structures are the same.
(13.) In Survey of Current Business, U.S. assets abroad include
U.S. official reserves, U.S. government assets (other than official
reserve assets), U.S. private assets (direct investment abroad [at
market value], foreign securities, U.S. claims on unaffiliated
foreigners reported by U.S. nonbanking concerns, and U.S. claims
reported by U.S. banks [not included elsewhere]). Foreign assets in the
United States include foreign official assets in the United States,
direct investment (at market value), U.S. Treasury securities, U.S.
currency, bonds, stocks, U.S. liabilities to unaffiliated foreigners
reported by U.S. nonbanking concerns, and U.S. liabilities reported by
U.S. banks (not included elsewhere). In Quarterly Bulletin, assets and
liabilities include direct investments, nonbank portfolio investment, UK
bank assets and liabilities in foreign currency and sterling, reserves
(assets) and official foreign currency borrowing, British government
stocks (liabilities), and other net public sector assets.
(14.) In the raw data, there is another component of valuation
adjustment--"other changes." It includes changes in coverage,
statistical discrepancies, and so on. I do not include this item in any
of my analyses.
(15.) Cole and Obstfeld (1991) showed that a perfect risk-pooling
equilibrium can be reproduced when export and import goods are not
substitutable. As substitutability of both goods increases, wealth
transfers to insure country-specific shocks decrease. That is, the
sources of international risk sharing are wealth effects from
terms-of-trade changes, not substitution effects.
(16.) Data series are obtained from International Financial
Statistics by the International Monetary Fund.
(17.) The estimation period for the United States is up to 2000,
except for the terms of trade channel (up to 1998). The estimation
periods for the United Kingdom are up to 1999, 1998, 1997, and 1997 for
the nominal revaluation, the terms-of-trade, the security, and the
nominal revaluation (from nonsecurity) channels, respectively.
(18.) For all these wealth transfers, I also calculated the
estimates from detrended values. Detrending may exclude bias in wealth
transfers from level and trend differences in asset and liability
holdings. The major implications are similar.
(19.) As shown in previous research, including Obstfeld (1994), in
complete international financial markets, ex post marginal rates of
intertemporal substitution between countries are equalized for all
states of nature. Under the isoelastic utility function where
nonseparability in the utility function between consumption and leisure
and nontradability of consumption are not allowed, the growth rates of
per capita consumption are equalized across countries, and we cannot
find any systematic correlation with them in complete markets (or
complete international risk sharing).
(20.) In general, the analysis is valid under the assumptions
discussed in footnote 12. Such assumptions are used by Obstfeld (1994),
Townsend (1994), and Sorensen and Yosha (1998), among others. See
footnote 10.
(21.) From the international investment position data in footnote
2, we can see that it holds for most countries.
(22.) For example, see Mussa (1986).
(23.) When some cross-border assets are denominated in the
buyer's currency, Equation 5 becomes [NR.sub.t] = ([b.sup.*.sub.a]
- [b.sub.a])([e.sub.t] - [e.sub.t-1]), where [b.sup.*.sub.a] is the
steady-state foreign assets denominated in the foreign currency and
[b.sub.a] is the steady-state foreign liabilities denominated in the
foreign currency. Therefore, if each country has more foreign assets
denominated in the foreign currency than foreign liabilities denominated
in the foreign currency (if [b.sup.*.sub.a] - [b.sub.a], is greater than
0), wealth transfers through the nominal revaluation and exchange rate
changes are perfectly positively correlated. In Germany, [b.sup.*] was
920 billion DM, while b was only 218 billion DM at the end of 1991 (data
from Statistical Supplements to the Monthly Reports by the Deutsche
Bundesbank).
(24.) Unexpected movements of nominal variables generate wealth
redistribution through the nominal revaluation. However, expected
movements do not if they are reflected in assets prices or the terms
structure of interest rates and in uncovered interest rate parity. If
the term structure of interest rates reflects expected changes in the
price level, there would be no nominal revaluation for this expected
part since it is already incorporated in bond prices. If interest rate
differentials between countries reflect changes in the exchange rates,
then these changes in the exchange rates cannot generate the nominal
revaluation since wealth transfers through the changes in exchange rates
would be offset by the differences in interest payments of foreign
assets and liabilities. In this respect, exchange rate changes are more
important than the price level changes since it is well known that most
parts of exchange rate changes are unpredictable, in particular, using
the interest differential. On the other hand, we a ssume that
cross-border assets are subject to exchange rate risks. If all exchange
rate risks are hedged, then there will be no wealth redistribution
effects. In reality, however, a substantial amount of cross-border
assets are subject to some nominal risks. Even though some foreign
portfolio investments at the individual level are hedged against
exchange rate risks, these kinds of assets are a relatively small
portion of all cross-border assets. Further, mere hedging at the
individual level does not necessarily imply hedging at the aggregate
level since there may be some domestic speculators who bet against them.
(25.) By using the residuals from the regression, the analysis is
valid when the steady-state per capita consumption growth rates are
different among countries and we can allow different discount rates and
different risk aversions between countries. See Obstfeld (1994) for
details.
(26.) Following Obstfeld (1994), I construct the world as 60
countries in the Penn world table that were graded at least a C- by
Summers and Heston (1991).
(27.) All empirical results in sections 3 and 4 are robust in the
presence of a linear trend. When we construct each value as a deviation
from a linear trend and then reestimate the correlations, the results
arc similar. I also examine the correlation between the effective
nominal exchange rate against 17 industrial countries and the
consumption differential against the rest of the world, to most cases,
negative correlations are found.
(28.) Cole and Obatfeld (1991) showed that a perfect risk-pooling
equilibrium can be reproduced when export and import goods are not
substitutable. As substitutability of both goods increases, wealth
transfer a to insure country-specific shocks decrease. That is, the
sources of international risk sharing are wealth effects from terms of
trade changes, not substitution effects.
(29.) Based on Equation 8, if the value of exports and imports is
different, the terms-of-trade changes are not always positively related
to the wealth effects from the changes.
(30.) Since the terms-of-trade data are against the rest of the
world, the consumption differential is constructed against the rest of
the world, not against the United States.
(31.) For example, French and Poterba (1991) and Tesar and Werner
(1992).
(32.) The consumption differential and the return on such a
portfolio (negative of the GDP differential) are negatively correlated.
This implies that it is possible for each country to share
country-specific consumption risks by constructing such a portfolio.
Shiller (1993) suggested the construction of such a claim in the real
world.
(33.) Kang and Stulz (1997) reported that foreign investors in the
Japanese stock market do not own the Japanese market portfolio.
(34.) A tax increase on repatriated equity income or a change in
the menu of foreign assets available may generate such a positive
correlation. See Asdrubali and Kim (2002).
(35.) I also examine the correlations with wealth transfers through
cross-border security holdings due to exchange rate changes (this
corresponds to wealth transfers through the nominal revaluation on
cross-border security holdings) in order to confirm the previous result
on the nominal revaluation and to examine whether the results using
wealth transfers are similar to those using returns. Negative
correlations are found, -0.21 and -0.18 for securities (stocks and
bonds) and stocks, respectively. That is, the nominal revaluation on
cross-border securities works as international risk sharing.
(36.) One may find this kind of discussion in most textbooks of
international economics, for example, Krugman and Obstfeld (1991). For
the more formal level, there is a wealth of literature, the method of
which is extended from Poole (1970), for example, Buiter and Eaton
(1985).
(37.) Each country may have an incentive to inflate unexpectedly as
discussed in footnote 11. In this regard, the fixed exchange rate regime
seems to he more stable. This may be a potential benefit of the fixed
exchange rate.
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Soyoung Kim *
* Department of Economics, University of Illinois at
Urbana-Champaign, 225b DKH, 1407 W. Gregory Drive, Urbana, IL 61801,
USA; E-mail
[email protected].
I thank Christopher Sims, Nouriel Roubini, Koichi Hamada, Gian
Carlo Corseiti, Robert Shiller, T. N. Srinivasan, How Pill, Javier
Valles, Enrique Alberola, Pierfederico Asdrubali, and an anonymous
referee for helpful discussions and comments and Michael Mecozzi and
Junsuk Yang for editorial help. I am also grateful to seminar
participants at Yale University, Bank of Spain, Universidad Pompeu
Fabra, the Annual Meeting of Society for Economic Dynamics and Controls,
and the Econometric Society European Meeting. All remaining errors are
mine.