Welfare and public policy: the role of internationalized production.

Chu, Hsiao-Lei

I. INTRODUCTION

Micro foundations of the "new open macroeconomics" framework (see Lane 2001 for a comprehensive survey) provide a well-grounded welfare criterion to evaluate public policies. Contributions in this line of research suggest that whether a monetary or a fiscal innovation is detrimental or beneficial in terms of national welfare depends on various characteristics of the world economy under consideration. (1) The complexity of this problem warrants further investigation on economic features along this line of research to sort out policy implications. In this article I focus on a prevalent feature of the real world--firms hiring both domestic and foreign production factors to produce national goods--and call it internationalized production. (2)

Production factors contribute to foreign production through various ways of globalized production processes. For instance, a country can utilize foreign factors through importing intermediate goods, and firms can directly hire foreign production factors through establishing foreign-owned firms and foreign direct investment abroad. (3) The extent of internationalized production is not easy to measure, however, yet empirical evidence indicates that its scale and importance have been on the rise in recent years for many countries. Table 1 shows the imported inputs as a share of the value of production for selected countries, computed by Campa and Goldberg (1997). In all the four countries, except Japan, the shares of imported inputs have increased considerably in the last two decades.

Hummels et al. (1998) consider the imported inputs that are used to manufacture goods for export. They call the trade of these inputs vertical trade. Table 2 summarizes some of their results. Although vertical trade accounts for a relatively small fraction of total trade (as shown in the second and the third columns), its contribution to total export growth (as shown in the fifth column) far exceeds its share of total trade in all countries except Japan, indicating its increasing importance. In particular, for Canada and the Netherlands, almost 50% of the growth of exports from the first to the last year in the sample are due to growth in vertical trade.

Table 3, taken from Jungnickel and Keller (2003), presents the scales of sales and employment of foreign-owned firms in selected countries and years. In the listed countries, the sales and employment in percentage of the respective values for total manufacturing increase from 1985 to 1998, except in Japan and Italy (the figures for Germany are quite stable over time). In particular, foreign-owned firms employed more than a quarter of the total employment in the manufacturing sectors of France and Belgium in the year 1998.

As demonstrated, the factor markets have been increasingly connected across borders in production, and it is therefore important to investigate the implications of public policies to the world economy in which internationalized production matters. In this article I incorporate internationalized production into the model of Corsetti and Pesenti (2001), denoted CP hereafter, and investigate its role played on the welfare effects of public policies. This model generates many welfare implications different from CP's. In particular, an expansionary monetary shock can be beggar-thy-neighbor, and a fiscal shock can improve national welfare in this model. The ranges of parameter values which give rise to different welfare outcomes are derived. I also derive the transmission mechanism of public policy, which is quite different from theirs. In particular, in this model a fiscal shock affects the exchange rate and produces long-run welfare effects even if it is temporary. It is shown that internationalized production may not only cause tensions between countries but also widen the welfare gap between citizens in a country. This opens up a discussion on the issues of international retaliation and coordination, which I will discuss in the concluding remarks.

The article is structured as follows. Section II outlines the environment of the model. Section III derives the equilibrium outcomes of the model. Section IV analyzes the transmission mechanisms and welfare effects of public policies. Section V concludes.

II. ENVIRONMENT

Time is discrete. The model includes two countries, Home and Foreign. There are two traded consumption goods, x and y. Consumption-good markets are perfectly competitive. Home specializes in the production of x, and Foreign specializes in producing y. Consumers are defined over a continuum of unit mass in each country. Each consumer owns one of the two types of labor services, type x and type y, which are specific to manufacturing good x and good y, respectively. Each type of labor consists of differential brands of labor services. Governments issue money, collect taxes, and maintain balanced budgets.

At each date, an agent monopolizes one distinct brand of labor services with a nominal wage rate contracted in terms of the buyer's currency. The current nominal wage rates are predetermined at the end of the previous period. The choice of a currency to denominate wages of imported labor services affects the pass-through of exchange rate changes to labor income. Bacchetta and van Wincoop (2002) argue that the market share of an exporting country in a foreign market and the extent to which products of domestic firms can be substitutes for those of competing foreign firms are the two key factors empirically relevant to invoicing choice. Specifically, they show that the lower the exporter's market share is in an industry and the less differentiated the products are, the more likely that firms will price in the importer's currency. (4) In this article, labor service is the counterpart of the traded goods in Bacchetta and van Wincoop's paper. (5) Because the ratio of imported labor services to domestic labor services is lower than one in general and the intra-industry substitution of labor services is much higher than interindustry substitution of labor services, we assume that the wage rate of imported labor services is contracted in terms of the domestic currency.

In the following, notation [N.sup.j.sub.k,t](z) refers to the value of a variable N at time t attached to an individual z with type k labor services in a country j, for k = x, y and where j = h(Home), f(Foreign).

Technology

Let a fraction [[theta].sup.j.sub.k] of labor force be type k in country j. The aggregate production function of Home at date t is given by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

where x is the aggregate output; [l.sup.h.sub.x] (z) and [l.sup.f.sub.x,t] (z) are respectively the amount of labor services employed from a type x agent z of Home and Foreign; and [phi] denotes the elasticity of input substitution, [phi] > 1. Similarly, the production technology in Foreign is given by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

Let [p.sup.j.sub.k] denote the unit price of good k and [w.sup.j.sub.k](z) denote the nominal wage rate for type k agents in country j. Profit maximizations of firms imply that the labor demand functions are

[l.sup.j.sub.x](z) = [[w.sup.j.sub.x](z)/[p.sup.h.sub.x]].sup.-[theta]]x and [l.sup.j.sub.y](z) = [[w.sup.j.sub.y](z)/[p.sup.f.sub.y]].sup.-[theta]]y.

Consumers

The lifetime utility of an agent z with type k labor in country j is represented by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

where 0 < [beta] < 1, [rho] > 0, [chi] > 0, and a > 0. Here, [beta] is the discount rate, 1/[rho] is the elasticity of intertemporal substitution, [m.sup.j.sub.k,t](z) is the money holding, [l.sup.j.sub.k,t](z) is the quantity of labor supplied, and [c.sup.j.sub.k,t](z) is the consumption index defined by the consumption of good x, [x.sup.j.sub.k](z) and the consumption of good y, [y.sup.j.sub.k](z) according to [c.sup.j.sub.k](z) [equivalent to] [x.sup.j.sub.k][(z).sup.[gamma]][y.sup.j.sub.k] [(z).sup.1-[gamma]], 0 < [gamma] < 1.

The corresponding consumption-based price indices [p.sup.j] are determined as

[p.sup.j] = [[[[gamma].sup.[gamma]][(1 - [gamma])].sup.1-[gamma]]].sup.-1] [([p.sup.j.sub.x]).sup.[gamma]][([p.sup.j.sub.y]).sup.1-[gamma]].

No market segmentation ensures that

E[p.sup.f] = [p.sup.h],

where E is the exchange rate.

Agents hold two assets, national money m and an international bond b. For simplicity, we only introduce a Home type x agent's budget constraint as follows, as the analog for other agents are similar:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

where i is the nominal yield of the bond and [tau](z) is the lump sum taxes per capita. (6) Replacing [w.sup.h.sub.x](z)[l.sup.h.sub.x](z) with [p.sup.h.sub.x] [([l.sup.h.sub.x](z)).sup.([phi]-1)/[phi]][x.sup.1]/[theta]], an agent takes nominal wages and prices of consumption goods as given and chooses [x.sup.h.sub.x,t], [y.sup.h.sub.x,t], [c.sup.h.sub.x,t], [m.sup.h.sub.x,t], [b.sup.h.sub.x,t+1] and [l.sup.h.sub.x,t] to maximize utility.

In any case, no agent will supply labor services to an extent that the marginal benefit from working is less than the marginal cost from working. Accordingly, I can write the participation conditions of consumers as

[w.sup.j.sub.x,t]/[p.sup.h.sub.t] [greater than or equal to] a[l.sup.j.sub.x,t][([c.sup.j.sub.x,t]).sup.[rho]] and [w.sup.j.sub.y,t]/[p.sup.f.sub.t] [greater than or equal to] a[l.sup.j.sub.y,t][([c.sup.j.sub.y,t]).sup.[rho]].

Government and Resource Constraints

Each government implements a balanced budget by way of equating its revenue from both seigniorage and taxes to its spending. I assume that a government only consumes home-made final goods. Thus, the government's budget is given by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

where k = x if j = h and k = y if j = f.

The world resource constraints require that the aggregate output is no less than the world consumption for any good k, k = x if j = h; k = y if j = f,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

and the international bond is in zero net supply:

[b.sup.h.sub.t] + [b.sup.f.sub.t] = 0,

where [b.sup.j.sub.t] = [[theta].sup.j.sub.x][b.sup.j.sub.x,t] + [[theta].sup.j.sub.y][b.sup.j.sub.y,t].

III. EQUILIBRIUM

In the equilibrium, all consumers and firms solve their maximization problems and workers' participation constraints, and all resource constraints as well as government budget constraints are not violated. The world economy is initially in an equilibrium indexed by a subscript 0 where both government spendings are zero and neither country is a net debtor. The short-run equilibrium, where the nominal wages are not able to respond to current shocks, is not indexed. The long-run equilibrium, where the economy reaches a new steady state after shocks, is indexed by upperbars. In the appendix (available on request) I show that in the equilibrium agents with the same type of labor choose the same amounts of consumption and leisure. The solutions derived in the appendix are summarized in Table 4.

IV. WELFARE ANALYSIS

I assume that the social welfare U is the aggregation of the individual welfare, where

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Using Table 4, I derive the welfare impacts of small unanticipated permanent monetary shocks and fiscal shocks. Due to the symmetric setup of the model, I need only to consider public policies of the Home country, and the results apply to the Foreign country. The welfare impacts are listed in Table 5. For the purpose of comparison, I also summarize CP's results in Table 6.

One key feature of the equilibrium is that given initially a zero current account in each country, none of the shocks will induce international lending and borrowing. This is because the elasticity of relative net output demand (x - [g.sup.h])/(y - [g.sup.f]) with respect to relative price. ([p.sup.h.sub.x]/[E[p.sup.f.sub.y]]) is equal to 1. (7) When there is a monetary shock or a fiscal shock, the current account variation induced by a change in relative net output demand and that induced by a change in relative price offset each other so that the current account remains zero in each country. That is to say, neither country is a net debtor in equilibrium. This key feature is crucial for this model to generate a closed-form solution. To restrict the initial national debt position to be zero, I have to specify each individual's initial debt position, which in general is not zero, and it will influence individuals' debt positions later if a policy shock occurs. Nonetheless, individuals' debt positions do not affect their consumption and work decisions in equilibrium, assuming there is a perfect capital market. Therefore, I can focus on agents' consumption and work behaviors to investigate the transmission mechanism and welfare effects of policy shocks.

Monetary Shocks

I first consider an expansionary monetary shock at Home. As shown in Table 5, the welfare effect of an expansionary shock depends on the sign of {[[theta].sup.-2.sub.x] - [([theta]-1)/[theta]][1 + [rho](1 - [gamma])/[gamma]]} and the sign of [[[theta].sup.-2.sub.x] - (1 - [rho])([theta] - 1)/[theta]], which indicate the direction of welfare change for type x and type y agents, respectively. Because both signs can be positive or negative, the direction of national welfare variation is ambiguous in each country. If there is no internationalized production, that is, [[theta].sup.f.sub.x] = [[theta].sup.h.sub.y] = 0, then I return to CP's results listed in the first two rows of Table 6, indicating that this shock is prosper-thy-neighbor for sure, but it can be beggar-thyself. CP find that due to the deteriorating terms of trade, the benefits from a domestic monetary expansion accrue primarily to foreigners.

This article's welfare implication differs from CP's not only because the national welfare is defined by the aggregation of domestic type x agents' and type y agents' utility (in CP's model there is only one type of agents in each country) but also because the size of the two sectors, [[theta].sub.x] and [[theta].sub.y], matters. In particular, this shock hurts both countries when [[theta].sub.x], is sufficiently large, [theta] is large, and when [rho] < 1; that is, x and y are complements. To give an intuitive explanation of the welfare effects in this model, I discuss the transmission mechanism of monetary shocks assuming that the shock raises Home monetary stock by 1%.

The short-run transmission mechanism of the agents' consumption and leisure behaviors in response to the shock is as follows. On the one hand, because the exchange rate moves one to one with the Home monetary stock, the shock decreases the relative price of good x and induces an intratemporal consumption adjustment of raising the relative demand for good x. On the other hand, because the real interest rate decreases as the shock stimulates world real income to move upward, the shock induces an intertemporal consumption reallocation--increasing short-run consumption in both good x and good y. (8) Thus, in total, world demand for good x increases, but it is indeterminate whether the world demand for good y also increases. Note that world demand for goods directly affects agents' leisure. An agent may become worse off by supplying more labor, even though by doing so he or she acquires more real income and a higher consumption index.

First consider the welfare effect on type y agents. Type y agents consume more due to higher real income, however, their aftershock welfare rises only if they did not get too much disutility from longer hours of working. If [rho] > 1, that is, the intertemporal elasticity of consumption, 1/[rho], is less than the elasticity of intratemporal substitution between good x and good y, which is 1, then the higher demand for good y in the intertemporal adjustment is dominated by the lower demand for y in the intratemporal adjustment. Therefore, [rho] > 1 implies world demand for good y decreases by the shock and I say good y and good x are substitutes. In this case, type y agents get more leisure and their welfare rises for sure. On the other hand, if [rho] < 1, that is, good y and good x are complements, then world demand for good y increases. Type y agents get hurt when [rho] < 1 unless the labor force in sector y is sufficiently large, [[theta].sub.y] > 2 - [square root of [phi]/[([phi] - 1)(1 - [rho])]] (it is equivalent to saying that unless the labor force in sector x is sufficiently small, [[theta].sub.x] < [square root of [phi]/[([phi] - 1)(1 - [rho])]]). If sector y is large enough, then type y agents do not have to offer too much extra labor to cope with the increased market demand, and therefore the increased utility from higher consumption more than compensate for the disutility from supplying more labor. Note that when [rho] < 1 I get [square root of [phi]/[([phi] - 1)(1 - [rho])]] > 1. Thus, in CP's model type y agents become better off for sure.

I next consider the welfare effect on type x agents. Although type x agents' real income also increases by the shock, the change of relative price reduces the real value of their unit labor service. Contrary to the case of type y agents, a type x agent gains less real income for a given labor supply due to the deteriorating terms of trade. Each type x agent needs to supply sufficiently more labor service so that he or she may earn enough extra consumption to compensate for the disutility from working more. Thus, for type x agents to benefit from this shock, their labor force should not be too large, [[theta].sub.x] < [square root of [[phi]/[([phi] - 1)][[gamma]/[gamma] + [rho][1 - [gamma]])]] On the other hand, given [[theta].sub.x], if 7 is not too large (i.e., if good y represents a substantial share of total consumption), or [phi] is not too small (i.e., monopoly distortions in sector x are relatively weak), or p is not too large (i.e., good x and good y are complements), then it is more likely that type x agents suffer from domestic monetary expansion; that is, [[theta].sup.2.sub.x] - [[phi]/([phi] - 1)][1 + [rho](1 - [gamma])/[gamma]] is more likely to be negative. Note that in CP's model type x agents become worse off for sure if [[phi]/([phi] - 1)][1 + [rho](1 - [gamma])/[gamma]] > 1.

In the long run, prices fully react to the shock. Because there is no international borrowing and lending in the short run, the world economy returns to its initial equilibrium and the expansionary monetary shock has no welfare impact in the long run.

In summary, I depict the impact of an unexpected Home monetary expansion on national welfare in Figure 1. Given [phi] and [gamma], the shock is beneficial to both countries and all agents when [[theta].sub.x] < [square root of [[phi]/([phi] - 1)][[gamma]/([gamma] + [rho][1 - [gamma]])], as indicated in area A; the shock is detrimental to both countries and all agents when [rho] < 1 and [square root of [phi]/[phi] - 1)(1 - [rho])] < [[theta].sub.x] < 2, as indicated in area B. In the area C of Figure 1, a country is better off if domestic type y agents' welfare gain dominates domestic type x agents' welfare loss, and vice versa. In contrast to CP's result, an unexpected monetary expansion can be beggarthy-neighbor in this model when the range of parameter values is area B or area C.

In CP's model, Foreign always benefits from the shock and Home may be hurt, whereas in the present model Foreign may also be hurt by the shock. To understand more about the role of internationalized production, a benchmark case where [[theta].sup.j.sub.k] = 0.5, k = x, y, j = h, f and [gamma] = 0.5 is investigated and I can derive

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.].

In the benchmark case, the national welfare gain is unambiguously positive for both Home and Foreign. It seems that the existence of multitype national agents helps reduce the cross-country difference in the impact of the shock by sharing the benefit and detriment from the shock between countries. In the benchmark case Home and Foreign equally share the benefit and detriment from the shock where the benefit dominates the detriment due to the fact that the expansionary monetary shock eliminates the monopoly distortion in the economy as it works in a closed economy. The composition of workers is a critical variable. In the benchmark case, domestic and foreign welfare respond identically to the shock and domestic welfare is aligned perfectly with world welfare. By Table 5, if the two countries share the same sign, that is, if sign [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.], then I get

(1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.].

Equation (1) gives the parametric restriction that leads to domestic and foreign welfare responding in the same direction. It is straightforward to verify that if [[theta].sup.j.sub.k] = 0.5, k = x, y, j = h, f, then (1) always holds; if I further assume 7 is also 0.5, then the sign of national welfare change is always positive. Given the values of [phi], [rho], and [gamma], I can apply equation (1) to derive the set of world composition of workers, [[theta].sup.j.sub.k]'s, that ensures domestic and foreign welfare will respond to the shock in the same direction. An example given [phi] = 2, 7 = 0.5, and [rho] = 1 is presented in Figure 2, where the horizontal axis indicates [[theta].sup.h.sub.x] and the vertical axis indicates [[theta].sup.f.sub.y] (recall that [[theta].sup.f.sub.x] = 1 - [[theta].sup.f.sub.x] and [[theta].sup.h.sub.y] = 1 - [[theta].sup.h.sub.x] The line in Figure 2 is the locus of equation (1) with equality. When the world composition of workers is in the area above this line, then Home and Foreign welfare will respond to a monetary shock in the same direction. This implies that international coordination of monetary policy may not be necessary to improve world welfare, because both countries' welfare are aligned to each other with the presence of internationalized production.

Fiscal Shocks

In this subsection I consider the welfare effect of a permanent expansionary fiscal shock. CP show that an expansionary fiscal shock launched by Home hurts both countries. Their arguments are as follows. In the short run, without affecting terms of trade, this shock raises the output of good x to satisfy the unexpected demand and reduces the real interest rate to reflect the expected lower future consumption. In the long run, all agents consume less, because higher government spending crowds out part of world consumption. Home agents are hurt by the shock, because they not only consume less but also work more to cope with the fiscal expansion. Foreign output may or may not increase, but in general the crowding-out effect dominates and Foreign hurts. CP's results are listed in the last two rows of Table 6.

In this model if Home implements a permanent expansionary fiscal shock, then the directions of welfare change of type x and of type y agents are determined by the signs of [[Z.sub.x] + ([phi] - 1)(1 - [rho])/2[phi] - 1 - ([phi] - 1)(2[delta] + 1)(1 + [rho])/2[gamma][phi]] and [[Z.sub.y] + ([phi] - 1)(1 - [rho])/2[phi] - 1], respectively, as indicated in the last row of Table 5. Thus, the effect of an expansionary fiscal shock on national welfare depends on the relative magnitudes of the model parameters, which will be discussed shortly.

The transmission mechanism of fiscal shocks in this model is rather different from CP's view. In particular, in the short run the exchange rate rises along with the shock; whereas in CP the exchange rate is independent of government spending. In addition, the real interest rate may become either higher or lower, but it is lower in CP's paper. These differences result in more complicated short-run production and consumption behaviors in this model, which imply that even if the shock is temporary, the economy will in general deviate from its initial equilibrium in the long run. In contrast, in CP's model only one period after a temporary fiscal shock the demand for x and the employment in sector x go down to their preshock levels and the economy returns to its initial equilibrium.

To give an intuitive explanation, I present the effects of the shock on some key variables in Table 7. I also present the corresponding results in CP's work in the last column of Table 7.

One key feature in the present model is that the exchange rate responds to a fiscal shock. The crux of the matter is that given internationalized production a government's spending raises foreign workers' nominal income, but the taxes that finance it are borne entirely by its own citizens. Once the shock raises the demand for good x, Foreign type x agents immediately receive more labor income. This raises the demand for Foreign currency when the income flows back to the Foreign country, stimulating the exchange rate to move upward. The exchange rate variation induces consumption variations that alter production and employment in each sector. At the same time, the demand for Home and for Foreign currency in the foreign exchange market vary correspondingly with the change in importing of labor services and final goods. Given that the current account is always zero, the initial higher demand for Foreign currency dominates the later on induced changes in the foreign exchange market. Thus, this shock raises the equilibrium exchange rate.

If there is no internationalized production in Home, that is [[theta].sup.f.sub.x] = 0, then the expansionary fiscal spending financed by taxing Home agents all becomes Home agents' income and it will not affect the demand for Home and for Foreign currency in the foreign exchange market hereafter. As shown in Table 7, when [[theta].sup.f.sub.x] = 0, none of the values of E, [c.sub.x], [c.sub.y], and y are affected by [G.sup.h], and the results of this model reduce to CP's in Table 5.

Suppose that [G.sup.h] increases by 1% for convenience. The variation of exchange rate, listed in Table 7, is derived to be [rho][[theta].sub.3]([[theta].sub.1] - [[theta].sub.2])/(1 - [gamma]) percent, where [[theta].sub.3] = [[theta].sup.f.sub.x][[theta].sub.y] [([[theta].sup.h.sub.y][[theta].sup.f.sub.x] - [[theta].sup.h.sub.x][[theta].sup.f.sub.y]).sup.-1], and [[theta].sub.1] and [[theta].sub.2] are the fractions of type y agents' real balance held at Home and at Foreign in the initial equilibrium, respectively. It can be shown that [[theta].sub.3] and ([[theta].sub.1] - [[theta].sub.2]) have the same sign and thus the exchange rate rises. (9)

I next consider the effect of an expansionary fiscal shock on short-run outputs of goods. The unexpected government spending immediately raises demand for x by 1%. At the same time, the exchange rate variation induces an intratemporal consumption adjustment, changing demand for x and for y by [rho][[theta].sub.3]([theta].sub.1] - [[theta].sub.2]) and -[gamma][rho][[theta].sub.3]([[theta].sub.1] - [[theta].sub.2])/ (1 - [gamma]) percent, respectively. In addition, agents also adjust their intertemporal demands for goods as the real interest rate varies by [rho][-[gamma]/(1 + [rho]) + [[theta].sub.3] - [[theta].sub.3][[gamma][[theta].sub.1] + (1 - [gamma])[[theta].sub.2]]/ (1 - [gamma])] percent in which [rho] is the reciprocal of the elasticity of intertemporal substitution. The -[gamma]/(1 + [rho]) term comes from the expectation of a lower future consumption due to the crowding-out effect of government spending, and the [[theta].sub.3][[gamma][[theta].sub.1] + (1 - [gamma])[[theta].sub.2]]/(1 - [gamma]) - [[theta].sub.3] term indicates the magnitude of intertemporal consumption adjustment. In response to this real interest rate variation, type x agents and type y agents change their short-run consumption by [[theta].sub.3][[gamma][[theta].sub.1] + (1 - [gamma])[[theta].sub.2]]/ (1 - [gamma]) and [theta].sub.3][[gamma][[theta].sub.1] + (1 - [gamma])[[theta].sub.2]]/ (1 - [gamma]) percent, respectively.

For the long-run effect on outputs of goods, first note that the preceding analysis indicates that the ratio x/y increases in the short run. In the long run, this higher relative demand for x raises the relative price of x and Home's terms of trade improves by 0.5%. This terms of trade variation results in the demand for goods x and y to change by [1 - [gamma](1 - [rho])/2(1 + [rho])] and -[gamma](1 - [rho])/2(1 + [rho]) percent, respectively, where the 1% change in [bar.x] comes directly from the Home government spending itself. In addition, the long-run demand for goods is affected by agents' intertemporal consumption adjustment, that is; the -[rho][[theta].sub.3]/2 percent change in [bar.x] and the -[rho][[theta].sub.3]/2(1 - [gamma]) percent change in [bar.y].

According to the analysis, I summarize the total change in short-run and long-run consumptions and leisure for each type of agents in Table 7. Because none of the directions of these changes are determinate, an expansionary fiscal shock can be beneficial or detrimental to each country. In spite of these indeterminacies, it is certain that the consumption gaps and leisure gaps between the two types of agents are bigger than those in CP. Specifically, the gap within each pair of ([c.sub.x], [c.sub.y]), ([[bar.c].sub.x], [[bar.c].sub.y]), ([l.sub.x], [l.sub.y]), and ([[bar.l].sub.x], [[bar.l].sub.y]) increases in the absolute value of [[theta].sub.3].

When [[theta].sub.3] < 0, these changes in consumption and leisure gaps are good for type y agents, but bad for type x agents, because internationalized production pulls type y agents' consumption and leisure upward, while dragging type x agents' consumption and leisure downward. On the other hand, when [[theta].sub.3] > 0 and ([[theta].sub.1] - [[theta].sub.2]) is sufficiently small, these changes are to type x agents' advantage but to type y agents' disadvantage. Recall that [[theta].sub.3] = [[theta].sup.f.sub.x][[theta].sub.y][([[theta].sup.h.sub.y] [[theta].sup.f.sub.x] - [[theta].sup.h.sub.x] [[theta].sup.f.sub.y]).sup.-1]. Thus, if the domestic agents employed in foreign firms are outnumbered by those employed in domestic firms for each country ([[theta].sup.h.sub.y] < [[theta].sup.h.sub.x] and [[theta].sup.f.sub.y] > [[theta].sup.f.sub.x]), then the model yields the former result.

V. DISCUSSION AND CONCLUDING REMARKS

The present article generates very a different perspective on public policy from that in CP. With regard to monetary policy, when internationalized production matters, an unexpected monetary expansion can be beneficial or detrimental to both domestic and foreign agents. This implies that the welfare effects of related issues in retaliation or coordination between countries are not straightforward. Consider that Home launches an unexpected monetary expansion and Foreign retaliates by injecting money as if in a depreciation competition. If the range of the parameter values is the area C of Figure 1, then the retaliation may reverse the directions of welfare variations in both countries. Recall that in area C an unexpected domestic monetary expansion hurts agents working in domestic firms and benefits agents working for foreign firms. A country is worse off by an expansionary monetary shock if the welfare loss from some of its citizens is more than the welfare gain from the rest and vice versa. An effective retaliation gives countries an incentive to coordinate their monetary policies, rather than acting alone. In CP's paper, an expansionary monetary shock is always prosper-thy-neighbor, and there is no need for retaliation. If the range is the area B where an unexpected monetary expansion hurts all, then after the retaliatory depreciation both countries are worse off than their preshock welfare status. In fact, a country should never launch this kind of shock in the very beginning because it is beggar-thyself. If the range is the area A, then individual countries can simply implement unilateral shocks and welfare in both countries will rise. The areas A and B imply that the need for international coordination of monetary policy may be reduced when both countries' welfare are aligned to each other. The extent of internationalized production or the world composition of workers critically affects the extent of alignment between national welfare. An example demonstrated in Figure 2 implies that if the extent of internationalized production can be chosen, then a trade policy regarding it might be a substitute for international monetary coordination.

As to fiscal shocks, in contrast to CP, an unexpected fiscal expansion, even if it is temporary, triggers a change in the short-run exchange rate, which induces consumption and production variations in both the short run and the long run. Although there are indeterminacies about the magnitudes of these short run and long-run variations, I show that the short-run and long-run consumption gaps and leisure gaps between types of agents are bigger when there is internationalized production. Therefore, a fiscal innovation not only produces tensions between countries (because it can be beggar-thy-neighbor), but also stimulates a conflict of interests among citizens within a country (because internationalized production widens the welfare gap between different types of agents). The related welfare impacts of retaliation and coordination are opaque, because a fiscal shock produces both short-run and long-run welfare effects, however, the role that internationalized production plays on the change of relative welfare status between different types of agents shows a clue. For example, suppose that the domestic agents employed in foreign firms are outnumbered by those employed in domestic firms for each country. It is shown that in addition to the welfare effects found by CP, internationalized production results in welfare gains for type y agents and welfare loss for the others when Home launches an expansionary fiscal shock. Therefore, government transfers by taxing type y agents and subsidizing type x agents might alleviate the negative welfare impacts found by CP. On the other hand, it might be in the Foreign country's interests to make an international transfer to avoid a contractionary fiscal shock abroad if the welfare gains from its type x citizens is not enough to compensate for the welfare loss from its type y citizens after the shock.

In sum, this model sheds some light on further research regarding the issues of international retaliation and coordination when internationalized production is prevalent. Furthermore, the general setup of internationalized production in this model enables us to investigate the welfare effects in an environment where a country only exports or only imports intermediate goods as a special case.

APPENDIX

In the following, we define [PHI] = ([phi] - 1)[(a[phi]).sup.-1], [??] = [gamma][(1 - [gamma]).sup.-1], [[theta].sub.y] = [[theta].sup.h.sub.y] + [[theta].sup.f.sub.y], [[theta].sub.x] = [[theta].sup.h.sub.x] + [[theta].sup.f.sub.x], [PHI] = [[theta].sub.y]/[[theta].sub.x], [G.sup.h] = x/(x - [g.sub.h]), and [G.sup.f] = y/(y - [g.sup.f]). For a variable N, we define [N.sub.R] = [N.sup.h]/[N.sup.f] and [N.sub.w] = [([N.sup.h]).sup.[gamma]][([N.sup.f]).sup.1-[gamma]].

The profit maximization of firms imply

(A1) [l.sup.j.sub.x,t] = [([w.sup.j.sub.x,t]/[p.sup.h.sub.x,t]).sup.-[theta]][x.sub.t], and [l.sup.j.sub.y,t] = [([w.sup.j.sub.y,t]/[p.sup.f.sub.y,t]).sup.-[theta]][y.sub.t].

Let [[lambda].sup.j.sub.k] denote the Lagrange multiplier for type k agents in country j. The first-order conditions of utility maximization for type k agents in country j are

(A2) [gamma][([c.sup.j.sub.k,t]).sup.1-[rho]][([x.sup.j.sub.k,t]).sup.-1] = [[lambda].sup.j.sub.k,t][p.sup.j.sub.k,t],

(A3) (1 - [gamma])[([c.sup.j.sub.k,t].sup.1-rho]][([y.sup.j.sub.k,t]).sup.-1] = [[lambda].sup.j.sub.k,t][p.sup.j.sub.y,t],

(A4) [([c.sup.j.sub.k,t]).sup.-[rho]] = [[lambda].sup.j.sub.k,t][p.sup.j.sub.t],

(A5) [chi][([m.sup.j.sub.k,t]).sup.-1] = [[lambda].sup.j.sub.k,t+1] - [beta][[lambda].sup.j.sub.k,t+1],

(A6) [[lambda].sup.j.sub.k,t] = [beta](1 + [i.sup.j.sub.t+1])[[lambda].sup.j.sub.k,t+1],

(A7) [([l.sup.j.sub.x,t]).sup.[1+[phi]]/[phi]] = ([phi] - 1) [(a[phi]).sup.-1][[lambda].sup.j.sub.x,t][p.sup.j.sub.x,t][x.sup.1/ [phi].sub.t] and [([l.sup.j.sub.y,t]).sup.[1+[phi]]/[phi]] = ([phi] - 1)[(a[phi]).sup.-1][[lambda].sup.j.sub.y,t][p.sup.j.sub.y,t] [y.sup.1/[phi].sub.t].

Zero profit conditions imply that

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

and

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

Individual budgets imply that

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

Good markets clearing implies that

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

Debt markets clearing is

[b.sup.h.sub.t + [b.sup.f.sub.t] = 0

where [b.sup.j.sub.t] = [[theta].sup.j.sub.x][b.sup.j.sub.x,t] + [[theta].sup.j.sub.y][b.sup.j.sub.y,t].

A government's budget is balanced at each date,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] and k = y if j = f.

All of these equations determine the equilibria in the world economy where initially [b.sup.j.sub.k,0] = 0 and [g.sup.j.sub.0] = 0. In the following, the initial equilibrium is indexed by a subscript 0; the short-run equilibrium, where the nominal wages are not able to respond to current shocks, is not indexed; the long-run equilibrium, where the economy reaches a new steady state after shocks, is indexed by overscores. I solve the equilibria according to the following steps.

Step 1

Prove [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.], and [[bar.y].sub.k] = [[bar.y].sup.j.sub.k].

Given [b.sup.j.sub.k,0] = 0 and [g.sup.j.sub.0] = 0, condition (1) implies [l.sub.k] = [l.sup.j.sub.k]. Condition (1) and equation (7) imply that [[lambda].sup.h.sub.k,t] equals [E.sup.-1][[lambda].sup.f.sub.k,t]. Therefore, [c.sup.h.sub.k,t] equals [c.sup.f.sub.k,t] by equation (4), and [i.sup.h] equals i by equation (6). Equations (2), (3), and (4) imply [p.sup.j][c.sup.j.sub.k] = [[gamma].sup.-1][p.sup.j.sub.x][x.sup.j.sub.k] = [(1 - [lambda]).sup.-1][p.sup.j.sub.y][y.sup.j.sub.k]. The relationship of [c.sup.h.sub.k,t] = [c.sup.f.sub.k,t] and the law of one price implies that [x.sup.h.sub.k] equals [x.sup.f.sub.k] and [y.sup.h.sub.k] equals [y.sup.f.sub.k]. Therefore, we can write

(A8) [([c.sub.k]).sup.-[rho]] = [beta](1 + r) [([[bar.c].sub.k]).sup.-[rho]],

(A9) [[bar.m].sup.j.sub.k]/[p.sub.j] = [chi] [[1 + i]/i][([c.sub.k]).sup.[rho],

(A10) [[bar.m].sup.j.sub.k]/[[bar.p].sub.j] = [chi][[1 + [delta]]/[delta]] [([[bar.c].sub.k]).sup.[rho],

(A11) [([l.sub.x]).sup.[1+[phi]]/[phi] = [PHI][([bar.c].sub.x]).sup.-[rho]]/ [[bar.p].sup.h] and [([l.sub.y,t]).sup.[1+[phi]]/[phi] = [PHI][([bar.c].sub.y]).sup.-[rho]]/ [[bar.p].sup.h][p.sup.h.sub.y][y.sup.1/[phi]].

Step 2

Prove i = [delta]

By equations (8), (9), and (10), we get

[p.sup.j]/[[bar.p].sub.j] = [[beta](1 + r)] [[(1 + [delta])i]/[(1 + i)[delta]]].

Since [beta] = 1/(1 + [delta]) and [p.sup.j]/ ([[bar.p].sup.j])(1 + i) = (1 + r), we have i = [delta].

Step 3

Prove E = [bar.E].

By ([[bar.m].sup.h.sub.x]/[p.sup.h])/ ([[bar.m].sup.h.sub.x]/[[bar.p].sup.h]) = (([[bar.m].sup.f.sub.x]/[[bar.p].sup.f])/ [[bar.m].sup.f.sub.x]/[[bar.p].sup.f] and [p.sub.j]/[[bar.p].sub.j] = [beta](1 + r), we get (E/[p.sub.h])/([bar.E]/[p.sub.h]) = [beta](1 + r). Therefore, E = [bar.E].

Step 4

Prove [b.sup.j] = [[bar.b].sup.j] = 0.

Aggregating the individuals' budget constraints in the first period after a shock at Home, we get

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

In the long run, we can write

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

Thus, by [[bar.b].sup.h] - (1 + i)[b.sup.h] = -[delta][[bar.b].sup.h] and i = [delta], we have [b.sup.h] = [bar.h].

The short-run current account balance [b.sup.h]/[p.sup.h][c.sub.x] is

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

and the long-run current account balance -[delta][[bar.b].sup.h]/ [[bar.p].sup.h][[bar.c].sub.x] equals

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

Therefore, by x good and y good markets clearing conditions, we get the difference between the short-run and long-run current account balance as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

Since equation (8) implies [c.sub.x]/[c.sub.y] = [[bar.c].sub.x]/ [[bar.c].sub.y], thus, we get [b.sup.h] = 0. Similarly, we can write [b.sup.f] = 0.

Step 5

Solve for [c.sub.x]/[c.sub.y] and prove [c.sub.x]/[c.sub.y] = [??][THETA] if [G.sup.h] = [G.sup.f] = 1.

The short-run current account balance implies that

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

Therefore, we get

[c.sub.x]/[c.sub.y] = A,

where

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

Note that if [G.sup.h] = [G.sup.f] = 1, then [c.sub.x]/[c.sub.y] = [[bar.c].sub.x]/[[bar.c].sub.y] = A = [??][THETA].

Step 6

Solve for [b.sup.j.sub.k] and [[bar.b].sup.j.sub.k].

Using individual budget constraints, we can write

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

and

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

where [[theta].sup.j.sub.x][b.sup.j.sub.x0] + [[theta].sup.j.sub.y][b.sup.j.sub.y0] = 0 and e = 1 if j = f, e = 0 if j = h. That is,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

and

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

Step 7

Derivation of the long-run equilibrium.

Good markets clearing implies

(A12) [bar.x]/[G.sub.h] = [[gamma][[bar.p.sup.h]/ [[bar.p].sup.h.sub.x]]([[theta].sub.x][[bar.c].sub.y]) and [[bar.y]/[G.sup.f] = [(1 - [gamma])[[bar.p].sup.h]/ [[bar.p].sup.h.sub.y]] ([[theta].sub.x][[bar.c].sub.y]).

Thus, we can write

(A13) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

Firms' zero profit conditions and equation (11) imply

(A14) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

Thus, we can write

(A15) [bar.x]/[bar.y] = [[THETA].sup.[1+[phi]]/[1-[phi]]] [[[bar.p].sup.h.sub.x]/[[bar.p].sup.h.sub.y]][A.sup.-[rho]].

Equations (A13) and (A15) imply

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

Thus, equations (A12) and (A14) imply that

(A16) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

and

(A17) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

By (A16), and (A17), the solutions to [[bar.c].sub.x] and [bar.x] are derived as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

where

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

Similarly, we can get [[bar.c].sub.y] and [bar.y].

The exchange rate is solved by using ([[bar.M].sup.h]/[[bar.p].sup.h])/([[bar.M].sup.f]/[[bar.p].sup.f]) = [[bar.M].sub.R][[bar.E].sup.-1], where [[bar.M].sup.j] = [[theta].sup.j.sub.x][[bar.m].sup.j.sub.x] + [[theta].sup.j.sub.y][[bar.m].sup.j.sub.y].

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

Thus, we get

[bar.E] = [[[[theta].sup.f.sub.x] + [[theta].sup.f.sub.y][A.sup.-[rho]]]/[[[theta].sup.h.sub.x] + [[theta].sup.h.sub.y][A.sup.-[rho]]]][[bar.M].sub.R].

Since

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

we can write

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

Step 8

Derivation of the short-run equilibrium.

Because in the short run [p.sup.h.sub.x] and [p.sup.f.sub.y] are fixed at the previously contracted levels, we get

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

and

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

where [c.sub.x0] equals [[bar.c].sub.x] given [G.sup.h] = [G.sup.f] = 1. Note that when [G.sup.h] = [G.sup.f] = 1 we get [c.sub.x] = [[bar.M].sup.1/ [rho].sub.w][M.sup.-1/[rho].sub.w0][c.sub.x0].

The short-run terms of trade is determined by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

By good markets clearing conditions, we can show that

[p.sup.h]/[p.sup.h.sub.x] = x/[[gamma][G.sup.h][c.sub.x] ([[theta].sub.x] + [[theta].sub.y][A.sup.-1])] and [p.sup.f]/[p.sup.f.sub.y] = y/[(1 - [gamma])[G.sup.f][c.sub.x] ([[theta].sub.x] + [[theta].sub.y][A.sup.-1])].

Therefore, we can write

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

and

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

By [([c.sub.k]).sup.-[rho] = [beta](1 + r)[([[bar.c].sub.k]).sup.-[rho]], we get

1 + r = [[bar.c].sup.[rho].sub.x]/[[beta][c.sup.[rho.sub.x]].

Note that when [G.sup.h] = [G.sup.f] = 1 we get 1 + r = [[beta].sup.-1]/ [[bar.M].sup.-1.sub.w][M.sub.w0].

The long-run and short-run equilibria are summarized in Table 4.

TABLE 1
Imported Input Share of Total Values of
Production for Manufacturing Industries in
Selected Years

U.S. Canada U.K. Japan

4.1(1973) 15.9(1974) 13.4(1971) 8.2(1974)
6.2(1985) 14.4(1984) 19.0(1984) 7.3(1985)
8.2(1995) 20.0(1993) 21.7(1993) 4.1(1993)

Source: Campa and Goldberg (1997).

TABLE 2
Contributions of Vertical Trade and Horizontal Trade to
Change in Export Share of Gross Output from First to
Last Year of Sample: Selected Countries

 Vertical Trade as a
 Percentage of Gross
 Output (Exports Only)

 Change in Export Share
Country First Year Last Year of Gross Output

Australia 0.8 (1968) 1.6 (1989) 0.06
Canada 4.4 (1971) 8.1 (1990) 0.08
Denmark 7.7 (1972) 12.4 (1990) 0.17
France 2.3 (1972) 5.4 (1990) 0.11
Germany 3.0 (1978) 4.7 (1990) 0.09
Japan 0.6 (1970) 0.7 (1990) 0.03
Netherlands 12.3 (1972) 16.8 (1986) 0.10
U.K. 2.6 (1968) 6.9 (1990) 0.15
U.S. 0.2 (1972) 1.0 (1990) 0.07

 Percentage of Change Due
 to Increase in

Country Vertical Trade Horizontal Trade

Australia 13.4 86.6
Canada 43.7 56.3
Denmark 27.3 72.7
France 28.4 71.6
Germany 19.4 80.6
Japan 3.2 96.8
Netherlands 47.4 52.6
U.K. 29.6 70.4
U.S. 11.9 88.1

Note: Horizontal trade occurs when the production of
each traded good is made entirely in one country.

Source: Hummels et al. (1998).

TABLE 3
Share of Foreign-Owned Firms in the Manufacturing Sector of
Selected Countries (a)

 1985 1990

Host
Country Sales Employment Sales

Germany 26 16 26
France 27 21 28
UK (b) 19 15 25
Italy (b) 17 14 14
Belgium
The Netherlands 39 15 33
U.S. 7 15
Japan 4.6 1.6 2.4

 1990 1998

Host
Country Employment Sales Employment

Germany 17 25 16
France 24 36 (b) 30 (b)
UK (b) 16 33 19 (c)
Italy (b) 10 12 (c) 9 (c)
Belgium 35 (g) 27 (g)
The Netherlands 19 47 (d) 19 (d)
U.S. 11 15 14
Japan 1.1 1.2 (c) 0.8 (c)

(a) Sales and employment in % of the respective values for total
manufacturing.

(b) Majority holdings only.

(c) 1996.

(d) 1994.

(e) 1995.

(f) 1996.

(g) 1997.

Source: Jungnickel and Keller (2003).

[TABLES 4-7 OMITTED]

(1.) For example, based on the benchmark model of Obstfeld and Rogoff (1995), Tille (2001) shows that the relation between the elasticity of substitution between goods produced in a country and the elasticity of substitution between goods produced in different countries are critical; Betts and Devereux (2000), assuming pricing to the market, show that the deviation from the law of one price is primarily important; and finally Hau (2000) adds nontraded goods in the model to derive different welfare implications.

(2.) A related work is Devereux and Engel (1998). They, however, do not tackle the issue of beneficial effects versus adverse effects from monetary policies. Instead, they focus on the optimal choice of an exchange-rate regime.

(3.) Foreign workers hired on a seasonal or temporary basis is another way that foreign inputs contribute to domestic production. Although many foreign workers do not maintain residences in their home countries while working abroad, the nonpermanent property may make them a channel of policy transmission.

(4.) The invoicing choice has been found by Devereux and Engle (1998), Bacchetta and van Wincoop (2000), Corsetti and Pesenti (2002), and others to play a critical role for optimal monetary policy and the choice of exchange rate regime. For related empirical analysis, see Feenstra et al. (1996) and Yang (1997).

(5.) We may think of the environment as follows. Each type of consumption good is produced by employing differential brands of semi-finished goods. Each brand is produced by monopolized labor services. One unit of labor services is required to produce one unit of a distinct semi-finished good. The semi-finished-good markets are monopolistically competitive. Thus, a country exports some semi-finished products and the export prices are contracted in the currency of the importing country. In this article the labor service is the counterpart of the semi-finished good in the above scenario and the wage rate of the exported labor service is the counterpart of the exporting price of the semi-finished good. For brevity, the semi-finished good sector is skipped, and trading in semi-finished goods is directly expressed by trading in labor services.

(6.) A Home type y agent's budget constraint is [b.sup.h.sub.y,t+1](z) + [m.sup.h.sub.y,t](z) - [m.sup.h.sub.y,t-1](z) [less than or equal to] (1 + [i.sup.h.sub.t])[b.sup.h.sub.y,t](z) + [E.sub.t][w.sup.h.sub.y,t](z)[l.sup.h.sub.x,t](z)-[p.sup.h.sub.t] [[tau].sub.t](z)-[p.sup.h.sub.t][c.sup.h.sub.y,t](z). Due to internationalized production, the type y agent earns labor income [w.sup.h.sub.y,t](z)[l.sup.h.sub.x,t](z) (which is the analog of the revenue from exporting the semi-finished good in note 5) in terms of Foreign currency. He changes the income into Home currency, [E.sub.t][w.sup.h.sub.y,t](z)[l.sup.h.sub.x,t](z), and then chooses allocations to maximize his utility.

(7.) By Table 4 I get (x - [g.sup.h])/(y - [g.sup.f]) = [??] [n.sup.-1.sup.8]C[M.sub.R] and [p.sup.h.sub.x]/(E[p.sup.f.sub.y]) = [n.sub.8][C.sup.-1][M.sup.-1.sub.R]. It is apparent that the elasticity is 1.

(8.) It is derived by using Table 4 that, for Home type x agents, [[differential]([w.sup.h.sub.x][l.sub.x]/[p.sup.h])/ [differential][M.sup.h]]([p.sup.h][M.sup.h]/[w.sup.h.sub.x] [l.sub.x]) = [gamma]/[rho] and [[differential]([M.sup.h]/ [p.sup.h])/[differential][M.sup.h]]([p.sup.h][M.sup.h]/ [M.sup.h]) = [gamma]. I can get the similar result for other agents. Thus, this shock raises each agent's real labor income as well as real balances. The world real income increases along with the shock.

(9.) Using Table 4, we can write [[theta].sub.1] - [[theta].sub.2] = [[theta].sub.1]([[theta].sup.h.sub.y][[theta].sup.f.sub.x] - [[theta].sup.h.sub.x][[theta].sup.f.sub.x])/([[theta].sup.y.sub.y] ([[theta].sup.f.sub.x] + [[theta].sup.f.sub.y][[??][THETA].sup.-[rho]]]), where [??][THETA] = [[gamma]/(1 - [gamma])]([[theta].sub.y]/[[theta].sub.x]).

REFERENCES

Bacchetta, P., and Eric van Wincoop. "Does Exchange Rate Stability Increase Trade and Welfare?" American Economic Review, 90, 2000, 1093-109.

--. "A Theory of the Currency Denomination of International Trade." European Central Bank Working Paper, No. 177, 2002.

Betts, C., and M. B. Devereux. "Exchange Rate Dynamic in a Model of Pricing-to-Market." Journal of International Economics, 50, 2000, 215-44.

Campa, J., and L. Goldberg. "The Evolving External Orientation of Manufacturing Industries: Evidence from Four Countries." Federal Reserve Bank of New York Economic Policy Review, 3, 1997, 53-81.

Corsetti, G., and P. Pesenti. "Welfare and Macroeconomic Interdependence." Quarterly Journal of Economics, 116, 2001, 421-46.

--. "International Dimensions of Optimal Monetary Policy." National Bureau of Economic Research Working Paper, No. 8230, 2002.

Devereux, M., and C. Engel. "The Choice of Exchange-Rate Regime: Price-Setting Rules and Internationalized Production." Mimeo, University of British Columbia and Hong Kong University of Science and Technology, University of Washington, and National Bureau of Economic Research, 1998.

Feenstra, R. C., J. E. Gagnon, and M. M. Knetter. "Market Share and Exchange Rate Pass-Through in World Automobile Trade." Journal of International Economics, 40, 1996, 187-207.

Hau, H. "Exchange Rate Determination: The Role of Factor Price Rigidities and Nontradeables." Journal of International Economics, 50, 2000, 421-47.

Hummels, D., D. Rapoport, and Kei-Mu Yi. "Vertical Specialization and the Changing Nature of World Trade." Federal Reserve Bank of New York Economic Policy Review, 4, 1998, 79-99.

Jungnickel, R., and D. Keller. "Foreign-Owned Firms on the German Labor Market." Hamburgisches WeltWirtschafts-Archiv Discussion Paper, 233, 2003.

Obstfeld, M., and K. Rogoff. "Exchange Rate Dynamics Redux." Journal of Political Economy, 103, 1995, 624-60.

Lane, P. R. "The New Open Economy Macroeconomics: A Survey." Journal of International Economics, 54, 2001, 235-66.

Tile, C. "The Role of Consumption Substitutability in the International Transmission of Shocks." Journal of International Economics, 53, 2001, 421-64.

Yang, J. "Exchange Rate Pass-Through in U.S. Manufacturing Industries." Review of Economics and Statistics, 79, 1997, 95-104.

HSIAO-LEI CHU, I thank an anonymous referee for helpful comments. All mistakes are my alone.

Chu: Assistant Professor, Department of Economics, National Chi-Nan University, 1 University Road, Puli, Nantou, Taiwan. Phone 886-492-910-960 ext. 4918, Fax 886-492-914-435, E-mail hlchu@ncnu.edu.tw