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 Kim11@uiuc.edu.

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.