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Global Rebalancing with Gravity: Measuring the Burden of Adjustment

Author(s):
International Monetary Fund. Research Dept.
Published Date:
August 2008
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The United States’ chronic current account deficit will inevitably reverse, and the reversal could be quite sudden. What would this reversal mean for the United States itself and for other countries? There are possible major effects on relative GDPs, real wages, and real absorption, not only across countries but also across individuals within countries.

We explore this question using a gravity model of trade and production. Because it represents the major component of trade, we focus on manufactures, asking what happens if manufacturing is the sector that bears the burden of rebalancing trade. We pursue this analysis using data for 2004 for the world, dividing it into 42 countries. Table 1 lists the countries, their GDPs, and three different deficit measures: the current account deficit, the overall trade deficit, and the deficit in manufactures.1

Table 1.GDP and Deficit Measures, 2004
Deficits
CountryCodeGDPCurrent accountTradeMfg
Algeriaalg85–11.2–7.211.8
Argentinaarg153–3.6–11.09.5
Australiaaul65939.221.857.5
Austriaaut293–1.2–4.47.3
Belgium/Luxembex392–16.6–20.552.6
Brazilbra604–12.5–26.1–8.8
Canadacan992–22.5–35.722.5
Chilechl96–1.7–8.1–2.4
China/HKchk2106–87.2–54.0–119.4
Colombiacol980.80.88.2
Denmarkden245–6.3–11.39.3
Egyptegy82–4.00.81.1
Finlandfin189–9.9–9.6–17.1
Francefra20604.17.4–3.3
Germanyger2740–105.4–122.9–278.3
Greecegre26413.113.929.2
Indiaind689–7.814.5–11.9
Indonesiaino254–1.9–10.1–25.1
Irelandire1830.8–25.5–68.8
Israelisr122–3.30.1–2.2
Italyita172013.4–4.0–46.6
Japanjap4580–178.1–72.4–385.1
Koreakor680–29.1–26.3–146.4
Ma/Phi/Singmps312–43.2–45.9–58.3
Mexicomex6835.817.820.2
Netherlandsnet608–55.2–44.48.9
New Zealandnze986.31.110.0
Norwaynor255–35.1–34.916.0
Pakistanpak1130.76.5–0.9
Peruper70–0.1–1.62.5
Portugalpor17812.714.39.8
Russiarus592–59.4–69.6–11.7
South Africasaf2167.22.61.0
Spainspa104053.544.861.7
Swedenswe349–27.9–27.4–26.2
Switzerlandswi360–57.1–32.8–13.4
Thailandtha161–7.1–6.0–21.1
Turkeytur30215.212.518.0
United Kingdomunk215032.374.2103.5
United Statesusa11700649.7667.0438.4
Venezuelaven112–14.0–17.36.0
Rest of worldrow3025–53.4–171.3341.9
Note: All data are in billions of U.S. dollars. Negative numbers indicate surplus. Ma/Phi/Sing is a combination of Malaysia, the Philippines, and Singapore.

In 2004 the United States ran a current account deficit of $650 billion, nearly 6 percent of its GDP.2 Aggregating the surpluses of the three largest surplus countries, Japan, Germany, and China, gets us to only $370 billion, little more than half the U.S. deficit. Note that for each of these four countries with the largest imbalances, the manufacturing deficit is by far the largest component of the overall deficit.

We build on previous work that integrates factor-market equilibrium into a model of international production and trade with heterogeneous goods and barriers to trade. Contributions include Eaton and Kortum (2002); Alvarez and Lucas (2007); and Chaney (forthcoming). We pursue a particular specification of gravity relationships, which we introduced in Dekle, Eaton, and Kortum (2007). Rather than estimating such a model in terms of levels, we specify the model in terms of changes from the current equilibrium. This approach allows us to calibrate the model from existing data on production and trade shares. We thereby finesse having to assemble proxies for bilateral resistance (for example, distance, common language, etc.) or inferring parameters of technology. A particular virtue is that we do not have to impose the symmetry in bilateral trade flows implied by these measures but spurned by the data. China, for example, runs the largest bilateral surplus with the United States, while running substantial deficits with some of its Asian neighbors, Japan in particular. Our approach recognizes and incorporates these bilateral asymmetries.

Our earlier work considered the effect of eliminating current account deficits in a world in which factors could seamlessly move between manufacturing and other activities. Although this assumption might apply to the very long run, it probably fails to capture barriers to internal factor mobility that are likely to loom large for some time. Here we pursue the opposite extreme of treating factors as fixed in either manufacturing or nonmanufacturing activity. For comparison purposes, we present our results for the case of perfect factor mobility as well.

In either case we allow adjustment to take the form of changes in the range of goods that countries exchange (the extensive margin) as well as changes in the amounts of each good traded (the intensive margin). But adjustment at the extensive margin may take time. Hence, to capture very short-run effects we consider a case in which both the allocation of labor and the extensive margin are fixed.

Both this paper and our previous one return to a venerable topic, the potential for a secondary burden of a transfer. A question we can answer is the extent to which the elimination of the giant U.S. current account deficit entails a loss in real resources beyond the loss of the transfer itself. Our model recognizes the importance of nontradability, so that it delivers Keynes’ prediction that the elimination of a transfer entails a worsened terms of trade. But as our model also incorporates nontraded goods whose prices decline, the burden of paying more for imports is mostly offset by the benefit of cheaper nontraded goods. With an active extensive margin, the offset is nearly complete. Our numbers thus come down on the side of Ohlin: the elimination of the transfer entails a loss in real absorption of virtually the same magnitude.3

This prediction emerges under either extreme assumption about factor mobility. But factor immobility introduces a major additional consideration: The internal redistribution of income implied by global rebalancing. We find that, with resource immobility, eliminating the current account deficit raises the returns to U.S. factors working in manufacturing to those working elsewhere by about 30 percent (with or without adjustment at the extensive margin).

Obstfeld and Rogoff (2005) also employ a static trade model to examine the implications of eliminating current account imbalances. Their focus is on real exchange rates and the terms of trade, rather than real wages and welfare, our interest here. They employ a stylized three-region model. With labor mobility our results are closest to what Obstfeld and Rogoff call a “very gradual” unwinding, or a decade-long adjustment, but labor immobility (with or without an operative extensive margin) connects better with their baseline scenario.4

I. A Model of the World

We consider a world of i = 1, …, N countries. Country i is endowed with labor Li.5 Labor is allocated between two sectors, manufacturing LiM and nonmanufacturing LiN, with

Throughout we assume that all production is at constant returns to scale and that all markets are perfectly competitive.6

Income and Expenditure: Some Accounting

We relate production and trade in manufactures to aggregate income, expenditure, and wages. We have to do some accounting to draw these connections.

We denote country i’s gross production of manufactures as YiM, of which a share βi is value-added. With perfect competition, value added corresponds to factor payments ViM=wiNLiM,wherewiM, is the manufacturing wage.

Similarly, wiN is the nonmanufacturing wage, so that nonmanufacturing value added is ViN=wiNLiN and GDP is

If we define the average wage as

then GDP is simply Yi=wi Li. Our notation is designed to admit: (i) sectoral labor mobility, in which case LiM and LiN are endogenous with wiM=wiN=wi and (ii) immobile labor, in which case LiM and LiN are fixed with wages typically differing by sector.

We denote country i’s gross absorption of manufactures as XiM and its manufacturing deficit as DiM. They are connected with YiM via the identity:

Manufactures have two purposes: as inputs into the production of manufactures and to satisfy final demand. We denote the share of manufactures in final demand as αi so that demand for manufactures in country i is

where Xi is final absorption, equal to GDP Yi plus the overall trade deficit Di, and γ is the share of nonmanufactures (hence 1–γ the share of manufactures) in manufacturing intermediates.7

Combining Equations (3) and (4) we obtain

Rearranging, we obtain equations for manufacturing production and absorption:

These equations will allow us to connect world equilibrium in manufactures to various deficits.

International Trade

Manufactures consist of a unit continuum of differentiated goods indexed by j. We denote country i’s efficiency making good j as zi(j). The cost of producing good j in country i is thus ci/zi(j), where ci is the cost of an input bundle in country i. Given the production structure introduced above,

where pi is an index of manufacturing input prices in country i, to be determined below. The term ki is a constant that depends on γ, βi, and the productivity of labor in nonmanufacturing.8

We make the standard assumption of “iceberg” trade barriers, implying that to deliver one unit of a manufactured good from country i to country n requires shipping dni≥1 units, where we normalize dii = 1. Thus, delivering a unit of good j produced in country i to country n incurs a unit cost:

Ricardian Specialization

Here we set up the model assuming that buyers purchase any good from its lowest cost source, so that the extensive margin is active. We turn to what happens if this margin is shut off later in the paper.

As in Eaton and Kortum (2002) country i’s efficiency z:(j) in making good j is the realization of a random variable Z with distribution:

which is drawn independently across i. Here Ti>0 is a parameter that reflects country i’s overall efficiency in producing any good and θ is an inverse measure of the dispersion of efficiencies. The implied distribution for pni (j)is

Buyers in destination n will buy each manufacturing good j from the cheapest source at a price:

The distribution Gn (p) of prices paid in country n is

where:

The probability π¯ni that country i is the cheapest source is its share of this sum:

Invoking the law of large numbers, this probability becomes the measure of goods that country n purchases from country i. Thus π¯ni is a bilateral trade share measured by numbers of goods. To obtain a trade share measured by expenditures we must specify demand.

Demand for Manufactures

We assume that the individual manufacturing goods, whether used as intermediates or in final demand, combine with constant elasticity σ>0. Spending in country n on good j is therefore

where pn is the manufacturing price index in country n, which appeared previously in expression (7) for the cost of an input bundle. We compute this price index by integrating over the prices of individual goods:

where

and Γ is the gamma function, requiring θ > σ–1.

We can express bilateral trade shares in expenditure terms mechanically as

where X¯niM is average spending per good in country n on goods purchased from i.

To compute X¯niM we need to know the distribution Gni(p) of the prices of goods that country n buys from country i because

As shown in Eaton and Kortum (2002), among the goods that n buys from i,, the distribution of prices is the same regardless of source, so that Gni(p)=Gn(p). It follows that X¯niM=XnM and hence Equation (10) becomes

The two measures of the bilateral trade share reduce to the same thing.

Trade Elasticities

How do trade shares and prices respond to changes in input costs around the world? Say that the costs of input bundles in each country k move from ck to ck We can represent this change in terms of the ratio c^k=ck/ck.

Extensive Margin Operative

We first consider the case in which a buyer can switch to any new source country that can deliver a good more cheaply. The resulting bilateral trade shares are

The parameter determining how changes in costs translate into trade shares is θ, which reflects the extent of heterogeneity in production efficiency. It captures how changes in costs bring about a change in international specialization in production and delivery to various markets, the extensive margin.

We also need to consider how price indices adjust to a change in costs around the world. Starting from Equation (9), with the extensive margin active, the price index resulting from a change in costs is

Note that σ is nowhere to be seen.

Extensive Margin Inoperative

Say instead that after input costs change, countries are stuck buying each good from the same source as before, so that adjustment is only in how much is spent on each good, the intensive margin. To see what happens to trade shares, return to Equation (10), this time shutting down the extensive margin by fixing the π¯nks.

The price of any good that country n had bought from country i at price p now costs pc^i. If country n goes on buying each good from its original source, the resulting bilateral trade shares (with a superscript SR to denote the short run) are

Assuming that we started with a situation in which country n bought every good from the lowest cost source, so that Gni(p) = Gn(p), the resulting trade shares simplify to

The parameter now determining how changes in costs translate into trade shares becomes σ–1, as in the Armington model. Because θ>σ–1, the effective trade elasticity is lower when we shut down the extensive margin.

Parallel to Equation (12) above, we also need an expression for the change in the price index in each country that results from a change in input costs. To derive this expression, recall that we can construct the price index from source-specific blocks:

Therefore, in response to a change in costs:

The elasticity σ–1 again replaces θ as the relevant parameter when we shut down the extensive margin. In all other ways, the analysis is exactly parallel.

We will return to this result in our simulations where we interpret σ–1 as the short-term trade elasticity. This interpretation is motivated by the dynamic two-country analysis of Ruhl (2005), in which firms choose not to adjust their extensive margin in response to temporary fluctuations in costs. In this case, all adjustment takes place via expenditure per good resulting from changes in prices and incomes.

Equilibrium

The conditions for equilibrium in world manufactures are

This set of equations determines relative wages across countries. To see how, plug in the expressions above for manufacturing production (5) and absorption (6) to obtain

We obtain an expression for the trade shares by substituting Equation (7) into Equation (11):

From Equations (7) and (9), the price index for manufactures is

The size of the nonmanufacturing sector (and hence of the manufacturing sector) is nailed down by

World equilibrium is a set of wages and price levels wiM, wiN and pi and labor allocations LiM and LiN for each country i that solve Equations (1), (2), and (16)–(19) given parameters including labor endowments and deficits, Di and DiM. To complete the description of equilibrium, we have to take a stand on labor mobility.

We consider the two extreme assumptions regarding internal labor market mobility. In the mobile labor case, which we take as reflecting the long run, the wage equilibrates between sectors, so that wiM=wiN=wi with LiM and LiN determined endogenously. In the immobile labor case, which we take as reflecting the short run, workers are tied to either manufacturing or nonmanufacturing. For this case we take LiM and LiN as given and solve for wiN and ViM separately.

Our counterfactual experiments calculate the response of all endogenous variables to an exogenous change in deficits around the world.

II. Quantification

Data

We created our sample of 42 countries as follows. We began with the 50 largest as measured by GDP in 2000, and combined the others into a “country” labeled ROW. Incomplete data forced us to move Saudi Arabia, Poland, Iran, the United Arab Emirates, Puerto Rico, and the Czech Republic into ROW as well. Because of peculiarities in the data suggestive of entrepôt trade, which our approach here is ill-equipped to handle, we combined (1) Belgium and Luxembourg (which we pulled out of ROW), (2) China and Hong Kong SAR, and (3) Malaysia, Philippines, and Singapore into single entities. The result is 42 entities, which we refer to as countries, which constitute the entire world.

To solve for the counterfactual, we need data on GDP (for Yi), manufacturing value added (for (ViM), gross manufacturing production (for YiM), overall and manufacturing trade deficits (Di and DiM), and bilateral trade flows in manufactures (for XniM), including purchases from home XiiM..

Wherever possible we take data for 2004 with all magnitudes translated into U.S.$ billions. We take GDP Yi and manufacturing value added YiM from the United Nations National Income Accounts Database (2007). We calculate value added in nonmanufacturing as a residual, ViN=YiViM..

The overall trade deficit in goods and services Di and current account deficits CAi, used for our counterfactual experiments below, are from the IMF (2006). We calculate total final spending as Xi=Yi+Di.9

Our handling of production and bilateral trade in manufactures is more involved. Our goal is a matrix of values X¯niM of the manufactures that country n buy from i. We begin with Comtrade data on bilateral trade from the United Nations Statistics Division (2006). We define manufactures as SITC trade codes 5, 6, 7, and 8. We measure trade flows between countries using reports of the importing country. We netted out trade within the three entities containing multiple countries.

Bilateral trade data do not contain an entry for the value of manufactures that country i purchases from local producers, X¯niM. We calculate these diagonal elements of the bilateral trade matrix as follows: (1) For each country i we calculate the share of value added in manufacturing βi as the ratio of value added in manufacturing to total manufacturing production for the most recent year for which each is available (and not imputed) from the United Nations Industrial Development Organization Industrial Statistics Database (2006).10 (2) We create a value of YiM for 2004 as YiM=ViM/βi using the 2004 value for YiM. (3) We calculate XiiM=YiMEiM, where EiM is country i’s manufacturing exports EiM=ΣniXniM.

With our bilateral trade matrix, we can calculate the trade deficit in manufactures, DiM. Except for the numbers used to calculate Pi all data are for 2004, the most recent year for which we could get complete data.

Calibration

In principle, computing the world equilibrium requires knowing the parameters dni, κ, αi, βi, γ, Ti, Li (LiM and LiN separately in the case of factor immobility), and θ (or σ in the case with no extensive margin) as well as the actual and counterfactual overall and manufacturing deficits Di, Di, DiM, and DiM. As explained below, however, because we only consider changes from the current equilibrium, all we need to know about dni, Ti, and κi is contained in the current trade shares πni but all we need to know about LiM and LiN is contained in value added ViM and ViN.

We set θ = 8.28, the central value Eaton and Kortum (2002) report based on bilateral trade and cross-country product-level price data. We also report the implications of shutting down the extensive margin by replacing θ with σ–1. There are a wide range of estimates of s that we might consider.

Bernard Eaton, Jensen, and Kortum (2003) find that σ = 3.79 (and θ = 3.60) explains the size and productivity of advantage of U.S. plants that export. Ruhl (2005) finds that σ = 2.0 can reconcile the time-series data regarding the degree of adjustment in trade balances to temporary changes in relative costs. To create a sharper contrast with simulations in which the extensive margin is active, and because our approach of shutting down the extensive margin is inspired by Ruhl (2005), we go with the lower value.

We calculate the share of nonmanufactures in manufacturing inter mediates γ from input-output tables. We do not have enough input-output tables to calculate g for each country. Instead we calculate γ = 0.43 from the 1997 input-output use table of the United States, and apply this value for all countries (Organization for Economic Cooperation and Development, 2007).11

Using Equations (3) and (4), we calculate αi as

Table 2 presents the values of αi and βi for our 42 countries, along with data on the share of manufacturing value added in GDP and the share of exports in manufacturing gross production. Of our countries, Algeria has the smallest share of manufacturing value added (at 0.06) and China/Hong Kong (henceforth China) the largest (0.38). Argentina and Egypt have the least outwardly oriented manufacturing sector (10 percent exported), and Malaysia/Philippines/Singapore the most outwardly oriented (94 percent exported). The share of value added in manufacturing P averages about one-third, with India having the lowest value (0.19), and Brazil the highest (0.53). The calculated share of manufactures in final demand ranges from a low of 0.06 in Ireland to a high of 0.78 in China/Hong Kong. In spite of these outliers, the values of α are each typically between 0.25 and 0.50.

Table 2.Manufacturing Share of GDP, Export Share of Manufacturing, Share of Manufacturing in Final Demand (Alpha), and Share of Value Added in Manufacturing Gross Output (Beta)
CountryShares
Vmfg/GDPExports/YmfgAlphaBeta
Algeria0.060.140.260.34
Argentina0.220.100.520.33
Australia0.110.150.260.39
Austria0.170.570.340.35
Belgium/Luxembourg0.150.830.480.27
Brazil0.220.220.300.53
Canada0.170.470.320.38
Chile0.160.460.260.40
China/Hong Kong0.380.230.780.27
Colombia0.150.190.310.46
Denmark0.120.680.230.45
Egypt0.180.100.410.27
Finland0.200.440.320.32
France0.120.300.310.22
Germany0.200.440.310.31
Greece0.080.150.250.34
India0.150.120.380.19
Indonesia0.280.280.390.39
Ireland0.240.930.060.34
Israel0.140.720.230.35
Italy0.170.270.350.26
Japan0.210.250.290.36
Korea0.260.640.230.38
Ma/Phi/Sing0.270.940.440.29
Mexico0.160.470.320.35
Netherlands0.130.630.310.27
New Zealand0.150.180.370.34
Norway0.100.270.310.30
Pakistan0.170.180.310.31
Peru0.150.150.300.37
Portugal0.140.350.320.28
Russia0.160.260.280.38
South Africa0.170.250.350.29
Spain0.150.240.360.27
Sweden0.180.580.270.34
Switzerland0.190.660.300.39
Thailand0.350.670.450.40
Turkey0.200.320.390.38
United Kingdom0.130.300.290.32
United States0.130.220.220.48
Venezuela0.170.160.340.51
Rest of world0.150.450.420.34
Note: Vmfg is value added in manufacturing, Ymfg is gross production in manufacturing, beta is the share of value added in gross production, and alpha is the share of manufactures in final absorption. Ma/Phi/Sing is a combination of Malaysia, the Philippines, and Singapore.

Counterfactual Deficits

Our counterfactual is a world in which production and trade in manufactures has adjusted to eliminate all current account imbalances. Not modeling nonmanufacturing trade, we hold nonmanufacturing trade deficits at their 2004 level as a share of world GDP. We thus set for each country i

where CAi is the 2004 current account surplus. We correspondingly set the new trade deficit at

Table 3 reports the actual and counterfactual trade deficits both overall and in manufactures. Notice that the United States must run a surplus in manufactures of over two hundred billion dollars to balance its current account.

Table 3.Actual and Counterfactual Trade Deficits(Overall and Manufactures)
CountryActual DeficitCounterfactual Deficit
TotalMfgTotalMfg
Algeria–7.2411.804.0023.03
Argentina–11.029.52–7.3913.15
Australia21.8457.53–17.3518.34
Austria–4.367.25–3.218.41
Belgium/Luxembourg–20.5252.58–3.9069.19
Brazil–26.12–8.84–13.583.71
Canada–35.7022.53–13.2345.00
Chile–8.05–2.43–6.34–0.71
China/Hong Kong–53.97–119.3633.22–32.18
Colombia0.808.21–0.017.40
Denmark–11.269.28–5.0015.54
Egypt0.791.124.825.15
Finland–9.56–17.080.39–7.13
France7.41–3.273.34–7.34
Germany–122.90–278.28–17.47–172.85
Greece13.8629.180.7116.03
India14.46–11.8722.22–4.10
Indonesia–10.13–25.14–8.23–23.25
Ireland–25.48–68.85–26.31–69.69
Israel0.13–2.193.451.13
Italy–3.99–46.57–17.42–60.00
Japan–72.41–385.08105.74–206.94
Korea–26.29–146.382.79–117.30
Ma/Phi/Sing–45.94–58.26–2.71–15.03
Mexico17.7920.1612.0014.37
Netherlands–44.388.9010.8464.12
New Zealand1.079.99–5.263.67
Norway–34.9115.960.1451.01
Pakistan6.52–0.935.85–1.60
Peru–1.622.47–1.542.55
Portugal14.349.811.61–2.92
Russia–69.57–11.67–10.1947.71
South Africa2.641.01–4.52–6.15
Spain44.7961.73–8.698.24
Sweden–27.42–26.190.531.76
Switzerland–32.76–13.3824.3043.68
Thailand–5.98–21.061.09–13.99
Turkey12.5318.01–2.672.81
United Kingdom74.19103.5041.8771.18
United States666.97438.4017.23–211.34
Venezuela–17.275.97–3.2919.95
Rest of world–171.29341.91–117.85395.34
Note: All data are in billions of U.S. dollars. Ma/Phi/Sing is a combination of Malaysia, the Philippines, and Singapore.

Formulation in Terms of Changes

As for Ti, κi, dni, direct observations are hard to come by. Instead of attaching numbers to them, and to Li as well, we reformulate the model to express the equilibrating relationships in terms of aggregates of these parameters that are readily observable. We then solve for the proportional changes in wages and prices needed to eliminate current account deficits. We use χ′ to denote the counterfactual value of variable x and χ′ to denote χ′/x. We will repeatedly use the fact that factor payments correspond to value added, so that wikLik=w^ikwikLik=w^ikVik in each sector k = M, N as well as in the aggregate wiLi=w^iwiLi=w^iYi.

Starting with the equation for the average wage (2), we have

where the sectoral shares are siM=ViM/YiandsiN=ViN/Yi.. The goods market-clearing condition (16) becomes

The trade share Equation (17) becomes

The price Equation (18) becomes:

Finally, the sectoral share Equation (19) becomes

In the case of mobile labor,V^iN=L^iN with

In the case of immobile labor,

with L^iN=0.

In the case of immobile labor with no extensive margin we simply replace θ with σ–1 in Equations (22) and (23).

The parameters Ti, dni, κi, LiM and LiN no longer appear. Instead we have manufacturing value added ViM nonmanufacturing value added ViN, and manufacturing trade shares πni, not the counterfactual values but the actual (factual) ones, XniM/XnM.. We can thus use data on VnM,VnN, and XniM/XnM., along with the parameters αi, βi, γ, and θ (or σ with no extensive margin) to solve the counterfactual equilibrium changes w^iM,w^iN,V^iN,andp^i that arise from moving to counterfactuals deficits Dn and DnM.

Computation

Simple iterative procedures solve Equations (20)–(24) for changes in wages, employment, and prices, with Equations (26) and (25) employed appropriately for the case at hand. With 42 countries, a good quality laptop running GAUSS can deliver the solutions almost immediately. In this algorithm, world GDP is the numéraire,

For each of our 42 countries we present the change in a set of outcomes, as the ratio of the counterfactual value to its original value.

In the case of factor immobility, we present the change in manufacturing wage w^iM, nonmanufacturing wage w^iN, and the change in the overall wage w^i using Equation (20). The change in the overall wage corresponds to the change in GDP, because Yi=w^iYi. With factor mobility we simply solve for w^i.

Because we solve for the change in the manufacturing price index pi, we can calculate the change in the cost of living as p^iL=(p^i)αi(w^iN)1αi. We can thus calculate the changes in real wages and real GDP.

Taking into account the static gain or loss of the transfers themselves, we get the change in real absorption in country i as

The counterfactual bilateral trade share of country i in n, πni, can be constructed from the original shares using expression (22). The counterfactual bilateral trade flow of n’s imports from i is

Finally, the change in the share of manufacturing value added in GDP is

We now turn to the results.

III. Results

In discussing the results, we work backwards. Because it is conceptually simplest and relates to our earlier work, we start with the longest run in which both the allocation of labor and the extensive margin can adjust. We then look at a medium run in which labor is locked into its initial sector but the extensive margin still operates. We conclude with the very short run in which neither margin can adjust: labor is immobile and there is no change in the set of goods that countries buy from each other, only how much they buy. Our tables report all results in terms of relative changes, so that if a variable changed from x to χ′ the table reports x^=x/x..12

Labor Mobility

Table 4 reports the results for the mobile-factor case. With labor mobility, there is a single national wage whose change equals the change in GDP. The changes in wages are reported in the first column. As noted above, they are calculated so that world GDP remains the same.

Table 4.Changes in Wages (GDP), Manufacturing Price Index, Aggregate Price Index, Real Wages (Real GDP), Manufacturing Share, and Real Absorption(Factor Mobility)
CountryWage

(GDP)
Price IndicesReal Wage

(Real GDP)
Mfg

Share
Real

Absorption
MfgAggregate
Algeria1.2051.0551.1641.0350.4691.176
Argentina1.0201.0161.0181.0020.9781.029
Australia0.9460.9690.9520.9941.2350.935
Austria1.0151.0161.0151.0000.9931.004
Belgium/Luxembourg1.0211.0131.0171.0040.9441.049
Brazil1.0191.0151.0181.0010.9521.023
Canada0.9910.9830.9881.0030.9431.026
Chile1.0171.0091.0151.0020.9501.023
China/Hong Kong1.0151.0151.0151.0000.9891.042
Colombia1.0000.9990.9991.0001.0250.992
Denmark1.0331.0221.0311.0030.9011.030
Egypt1.0521.0431.0481.0030.9311.049
Finland1.0371.0271.0341.0030.9051.059
France1.0091.0091.0091.0001.0040.998
Germany1.0251.0181.0231.0020.9301.043
Greece0.9580.9840.9640.9931.2320.946
India1.0161.0151.0161.0000.9821.011
Indonesia1.0121.0121.0121.0000.9881.008
Ireland1.0061.0031.0061.0001.0050.996
Israel1.0111.0081.0101.0010.9161.028
Italy1.0071.0101.0080.9991.0130.991
Japan1.0331.0271.0311.0020.9201.040
Korea1.0231.0151.0211.0020.9151.046
Ma/Phi/Sing1.0491.0081.0311.0180.8601.184
Mexico0.9770.9800.9780.9991.0180.991
Netherlands1.0531.0201.0431.0100.7931.108
New Zealand0.9580.9730.9630.9941.1390.929
Norway1.1311.0631.1101.0190.6511.182
Pakistan1.0011.0031.0020.9991.0120.994
Peru1.0001.0001.0001.0000.9971.001
Portugal0.9750.9910.9800.9951.1680.929
Russia1.0971.0661.0881.0080.7561.124
South Africa0.9910.9970.9930.9981.0630.965
Spain0.9840.9950.9880.9961.1040.946
Sweden1.0501.0301.0441.0050.8181.092
Switzerland1.0791.0271.0631.0150.6671.186
Thailand1.0151.0141.0151.0000.9551.046
Turkey0.9911.0020.9960.9961.0890.948
United Kingdom1.0001.0051.0010.9981.0430.984
United States0.9550.9730.9590.9961.2280.944
Venezuela1.1041.0521.0861.0170.7251.170
Rest of world1.0171.0151.0161.0010.9721.020
Note: Simulation results are expressed as a ratio of the counterfactual to the actual value. Simulation based on θ = 8.28. Ma/Phi/Sing is a combination of Malaysia, the Philippines, and Singapore.

Note that relative wage changes are quite modest. Taking one of the largest swings, the U.S. wage (and hence GDP) falls relative to Japan’s by less than 8 percent. Because most goods are not traded, price indices, reported in the second and third columns, move in the same direction as wages, resulting in changes to real wages (equivalently real GDPs), reported in the fourth column, nearly always a fraction of a percent.

In countries initially in deficit, labor shifts from nonmanufacturing to manufacturing. The change in the manufacturing share is shown in the fifth column. Note that the shifts can be substantial, with the share for the United States rising by almost 23 percent (about 3 percentage points). The manufacturing sector in Japan declines by 8 percent.

The last column of Table 4 shows the change in real absorption. This change is dominated by the primary burden of eliminating the deficit. The United States experiences a 6 percent decline in real absorption but Japan’s and Germany’s rise by around 4 percent. The change in real absorption corresponds almost exactly to the change in the transfers involved in eliminating current account deficits. Quantitatively, then, Ohlin was right. There is no discernible secondary burden to eliminating the transfer.

To what extent could we have predicted the changes in wages (and GDPs) from the size of the current account surplus that had to be eliminated? Figure 1 plots the change in the wage reported in the first column of Table 4 against the initial current account deficit as a share of GDP (with country codes as listed in Table 1). Note that there is a definite negative relationship. Mexico and Canada are a bit below other countries with similar deficits, reflecting their proximity to the United States whose relative GDP has declined substantially. There is also a systematic positive relationship between the initial deficit and the change in the size of the manufacturing sector. Figure 2 plots the change in the size of the manufacturing sector (column 5 of Table 4) against the initial current account as a share of GDP. These results closely match those in Dekle, Eaton, and Kortum (2007).

Figure 1.Change in GDP, Mobile Labor

Figure 2.Change in Manufacturing Share, Mobile Labor

Labor Immobility

Behind the mild price effects of eliminating the deficits just reported are big movements in labor across sectors. What if instead a worker is stuck in the sector where she is initially employed? The first two columns of Table 5 report the changes in relative wages that our model says are needed for manufacturing to balance current accounts, the results for and , respectively. Again, these changes leave world GDP unchanged. The third column indicates what happens to each country’s GDP.

Table 5.Changes in Wages, GDP, and Manufacturing Prices(Factor Mobility)
CountryWagesGDPMfg Price

Index
MfgNon-Mfg
Algeria0.9511.4021.3781.059
Argentina1.0271.0551.0491.036
Australia1.0640.8550.8770.995
Austria1.0321.0411.0391.036
Belgium/Luxembourg1.0061.0681.0591.032
Brazil1.0191.0831.0691.033
Canada0.9771.0431.0321.003
Chile1.0111.0731.0631.028
China/Hong Kong1.0241.0431.0361.034
Colombia1.0301.0061.0101.021
Denmark1.0121.1171.1051.039
Egypt1.0231.1131.0961.062
Finland0.9921.1281.1011.045
France1.0331.0281.0281.030
Germany0.9971.0961.0761.037
Greece1.0810.8880.9041.010
India1.0221.0431.0401.035
Indonesia1.0251.0421.0371.032
Ireland1.0341.0151.0191.024
Israel0.9791.0821.0681.026
Italy1.0371.0201.0231.030
Japan1.0031.1191.0951.046
Korea0.9811.1301.0921.034
Ma/Phi/Sing0.9561.1741.1141.029
Mexico1.0020.9820.9851.001
Netherlands0.9361.1811.1501.037
New Zealand1.0480.9090.9300.997
Norway0.9431.3221.2831.071
Pakistan1.0281.0121.0151.023
Peru1.0181.0221.0221.020
Portugal1.1030.9150.9411.014
Russia0.9831.3001.2501.077
South Africa1.0520.9750.9881.018
Spain1.0700.9540.9711.017
Sweden0.9531.2101.1641.046
Switzerland0.9091.3681.2821.041
Thailand1.0051.0801.0541.034
Turkey1.0600.9530.9751.024
United Kingdom1.0440.9971.0031.026
United States1.0650.8270.8580.998
Venezuela1.0171.3161.2671.061
Rest of world1.0221.0531.0481.034
Note: Simulation results are expressed as a ratio of the counterfactual to the actual value. Simulation based on θ = 8.28. Ma/Phi/Sing is a combination of Malaysia, the Philippines, and Singapore.

Except for Canada, the GDP changes are always in the same direction as in the case of mobile labor, but the magnitudes of the changes are much larger. The United States shrinks relative to Japan by 22 percent (as opposed to 8 percent in the previous case). Figure 3 plots the change in GDP against the initial current account deficit as a share of GDP, using the same scale as Figure 1. Note that the relationship is again negative and about twice as steep as in the case of labor mobility. Hence eliminating countries’ ability to reallocate resources requires substantially more adjustment in relative GDPs.

Figure 3.Change in GDP, Immobile Labor

Nearly as systematic is the tendency of the wage in manufacturing relative to nonmanufacturing to rise in countries initially in deficit with the opposite in surplus countries. In the United States, the relative wage in manufacturing rises by 29 percent. The change for Australia, another large deficit country, is nearly as large. In Japan and Germany, the largest surplus countries, the relative wage of manufacturing workers declines by around 10 percent. Looking across countries, changes in nonmanufacturing wages contribute much more to changes in relative GDP. Figure 4 plots the change in the manufacturing share against the initial current account deficit as a share of GDP. Note the systematically positive relationship.

Figure 4.Change in Manufacturing Share, Immobile Labor

Because of the pervasiveness of nontradedness, both the price index of manufactures (reported in the fourth column of Table 5) and the overall price index (reported in the fourth column of Table 6) move in line with relative GDP. As a consequence, changes in real GDP (reported in the third column of Table 6) are much smaller than the changes in relative GDP. Although the secondary burden of eliminating current account deficits is about twice what it was with labor mobility, it remains a tiny percentage of the initial deficit.

Table 6.Changes in Real Wages, Real GDP, Aggregate Price Index, and Real Absorption(Factor Immobility)
CountryReal WagesReal

GDP
Aggregate

Price Index
Real

Absorption
MfgNon-Mfg
Algeria0.7301.0761.0571.3031.195
Argentina0.9831.0101.0041.0451.032
Australia1.1970.9610.9870.8890.926
Austria0.9931.0021.0001.0391.005
Belgium/Luxembourg0.9581.0171.0081.0511.054
Brazil0.9541.0141.0011.0681.024
Canada0.9481.0131.0021.0301.026
Chile0.9531.0111.0021.0611.026
China/Hong Kong0.9881.0071.0001.0361.042
Colombia1.0190.9950.9991.0100.991
Denmark0.9211.0161.0051.0991.034
Egypt0.9371.0191.0041.0921.048
Finland0.9011.0250.9991.1011.055
France1.0040.9991.0001.0280.998
Germany0.9251.0170.9981.0781.039
Greece1.1790.9690.9860.9170.939
India0.9831.0031.0001.0401.010
Indonesia0.9871.0040.9991.0381.008
Ireland1.0180.9991.0041.0151.002
Israel0.9161.0120.9991.0691.024
Italy1.0130.9971.0001.0240.992
Japan0.9131.0200.9971.0981.035
Korea0.8861.0200.9861.1071.030
Ma/Phi/Sing0.8631.0611.0061.1071.171
Mexico1.0150.9940.9970.9880.989
Netherlands0.8261.0421.0141.1341.111
New Zealand1.1140.9660.9880.9410.922
Norway0.7611.0671.0361.2391.201
Pakistan1.0130.9970.9991.0150.993
Peru0.9961.0011.0001.0221.002
Portugal1.1660.9680.9950.9460.930
Russia0.7971.0541.0131.2341.133
South Africa1.0630.9850.9990.9900.966
Spain1.0960.9770.9950.9760.945
Sweden0.8191.0401.0011.1641.087
Switzerland0.7211.0851.0181.2601.178
Thailand0.9491.0200.9951.0591.040
Turkey1.0820.9730.9950.9800.947
United Kingdom1.0380.9920.9981.0050.983
United States1.2370.9600.9960.8610.944
Venezuela0.8311.0761.0361.2231.196
Rest of world0.9781.0071.0031.0451.024
Note: Simulation results are expressed as a ratio of the counterfactual to the actual value. Simulation based on θ = 8.28. MA/Phi/Sing is a combination of Malaysia, the Philippines, and Singapore.

Although aggregate changes are small, the redistributional effects are substantial. Column 1 of Table 6 shows real gains to labor in the manufacturing sector in countries that are initially in deficit. In the United States, the real wage in manufacturing rises by 24 percent but declines by 4 percent outside manufacturing. In Japan, the real manufacturing wage declines by 9 percent with a 2 percent gain in nonmanufacturing. In every country the real wage moves in opposite directions in the two sectors.

No Extensive Margin

Sticking with a situation of labor immobility, we now take the further step of eliminating the extensive margin of adjustment. We interpret this case as applying to the very short run. Implementing this case amounts to replacing θ with σ–1 in our solution algorithm described above. As mentioned, we follow Ruhl (2005) in setting σ= 2.0. There are thus two interpretations of what we are doing in this case. One is that the parameter = 8.28 is as above, but with no adjustment on the extensive margin, the parameter σ = 2 becomes the relevant one governing adjustment. Another interpretation is that we are simply repeating the immobile labor case, now using the much lower value of θ= 1.

The results are shown in Tables 7 and 8. Focusing on relative GDP changes (in column 3 of Table 7), we see that they are magnified considerably when the extensive margin is inoperable. U.S. GDP falls by about 30 percent, but Japan’s rises by 26 percent relative to the world. Figure 5 plots the change in GDP against the initial deficit as a share of GDP, again using the same scale as Figure 1. Note that the relationship has become twice as steep again as that portrayed in Figure 3. Note also that U.S. neighbors Canada and Mexico have fallen further below the rest.

Table 7.Changes in Wages, GDP, and Manufacturing Prices(Factor Immobility, No Adjustment on Extensive Margin)
CountryWagesGDPMfg Price

Index
MfgNon-Mfg
Algeria1.3821.5611.5511.177
Argentina1.1021.1141.1121.087
Australia0.8650.7240.7400.899
Austria1.0941.0971.0961.093
Belgium/Luxembourg1.0761.1141.1081.072
Brazil1.0741.1391.1251.075
Canada0.8760.9570.9430.911
Chile1.0621.1251.1151.050
China/Hong Kong1.0681.0901.0821.082
Colombia1.0301.0081.0111.014
Denmark1.1171.1991.1901.108
Egypt1.2261.3111.2951.226
Finland1.1331.3101.2741.152
France1.0641.0591.0601.060
Germany1.0851.2151.1881.105
Greece0.9350.8070.8170.970
India1.0711.0961.0931.083
Indonesia1.0731.1021.0941.085
Ireland1.0421.0301.0331.027
Israel0.9731.0761.0611.038
Italy1.0601.0451.0481.061
Japan1.1351.2961.2621.169
Korea1.0391.2501.1961.087
Ma/Phi/Sing1.0741.3361.2641.053
Mexico0.8610.8520.8530.903
Netherlands1.0811.3091.2801.093
New Zealand0.8840.7980.8110.908
Norway1.3361.5731.5491.250
Pakistan1.0070.9880.9911.013
Peru1.0001.0081.0071.006
Portugal1.0040.8260.8510.977
Russia1.3331.6341.5871.315
South Africa1.0070.9300.9430.996
Spain0.9950.8900.9050.992
Sweden1.1041.3971.3461.144
Switzerland1.0861.5551.4681.117
Thailand1.0501.1411.1101.084
Turkey1.0230.9220.9431.027
United Kingdom1.0390.9941.0001.039
United States0.8890.6730.7010.891
Venezuela1.3521.5311.5021.213
Rest of world1.0781.0901.0881.083
Note: Simulation results are expressed as a ratio of the counterfactual to the actual value. Simulation based on σ = 2. Ma/Phi/Sing is a combination of Malaysia, the Philippines, and Singapore.
Table 8.Changes in Real Wages, Real GDP, Aggregate Price Index, and Real Absorption(Factor Immobility, No Adjustment on Extensive Margin)
CountryReal WagesReal

GDP
Aggregate

Price Index
Real

Absorption
MfgNon-Mfg
Algeria0.9531.0771.0701.4501.205
Argentina1.0021.0131.0111.1001.042
Australia1.1290.9460.9650.7660.901
Austria0.9991.0011.0011.0951.006
Belgium/Luxembourg0.9841.0191.0141.0941.060
Brazil0.9591.0171.0051.1201.029
Canada0.9301.0161.0010.9421.024
Chile0.9611.0181.0091.1051.036
China/Hong Kong0.9861.0060.9981.0841.039
Colombia1.0200.9981.0021.0100.993
Denmark0.9491.0181.0101.1781.040
Egypt0.9611.0271.0151.2761.051
Finland0.9011.0421.0131.2581.069
France1.0041.0001.0001.0590.998
Germany0.9201.0301.0081.1791.049
Greece1.1070.9550.9680.8440.922
India0.9821.0051.0011.0911.010
Indonesia0.9791.0060.9991.0961.009
Ireland1.0121.0001.0031.0301.003
Israel0.9121.0080.9951.0671.021
Italy1.0090.9950.9971.0510.990
Japan0.9021.0301.0031.2581.038
Korea0.8571.0320.9871.2111.031
Ma/Phi/Sing0.8931.1111.0521.2021.225
Mexico0.9920.9820.9830.8680.978
Netherlands0.8741.0581.0351.2371.132
New Zealand1.0570.9530.9680.8370.895
Norway0.9121.0741.0571.4651.225
Pakistan1.0110.9920.9950.9950.990
Peru0.9921.0010.9991.0081.001
Portugal1.1520.9480.9760.8720.913
Russia0.8671.0621.0321.5381.156
South Africa1.0580.9760.9900.9520.957
Spain1.0750.9610.9780.9250.929
Sweden0.8331.0551.0161.3251.104
Switzerland0.7711.1041.0421.4081.200
Thailand0.9421.0240.9951.1151.040
Turkey1.0640.9590.9800.9620.932
United Kingdom1.0320.9870.9931.0060.979
United States1.2430.9400.9800.7160.929
Venezuela0.9561.0831.0621.4141.231
Rest of world0.9911.0031.0011.0871.023
Note: Simulation results are expressed as a ratio of the counterfactual to the actual value. Simulation based on σ = 2. Ma/Phi/Sing is a combination of Malaysia, the Philippines, and Singapore.

Figure 5.Change in GDP, Immobile Sourcing

As in the previous case, most of the GDP adjustment occurs through the nonmanufacturing wage. Figure 6 plots the change in the manufacturing share against the initial current account deficit. It looks very similar to Figure 4.

Figure 6.Change in Manufacturing Share, Immobile Sourcing

Again, prices tend to move in line with relative GDP, so that changes in real GDP are small. They are, nonetheless, substantially larger than in the previous two cases. Note that U.S. real GDP falls by about 2 percent, about a third of the initial deficit. Hence with a very low response of trade shares to costs, a nontrivial secondary burden appears.

Qualitatively the consequences of adjustment for real wages are much as in the previous case, with the manufacturing real wage rising in deficit countries and falling in surplus countries. For the United States, at least, the burden of the inability to adjust at the extensive margin is born by workers outside manufacturing. The increase in the manufacturing real wage is as in the previous case, but the decline in the nonmanufacturing wage is greater.

IV. Conclusion

We have revisited the question of the secondary burden of transfers using a 42–country gravity model of international production and trade in manufactures. Our motivation is to assess the implications for relative wages, relative GDPs, real wages, and real absorption in the major countries of the world should the current transfers implied by existing current account deficits come to a halt. How much relative GDPs need to change depends on flexibility of two forms, factor mobility between manufacturing and nonmanufacturing, and the ability of trade to adjust at the extensive margin. With perfect mobility and an active extensive margin, the GDP of the United States (running the largest deficit) must fall about 8 percent relative to that of Japan (running the largest surplus). Without mobility, however, the decline is 22 percent. If there is no adjustment in supplier sourcing (the extensive margin) either, the decline is 44 percent.

Because of the pervasiveness of nontraded goods, however, prices move largely in sync with relative GDPs so that aggregate real changes are much more muted. Regardless of the degree of labor mobility, the decline in U.S. real GDP is only 0.4 percent if the extensive margin is operative. Without an extensive margin, the drop rises to 2 percent of GDP. So only with extreme inflexibility does a secondary burden of eliminating the transfer inherent in the U.S. current account deficit show up.

Although the overall real effects are small, with factor immobility redistributional effects are substantial. Regardless of whether the extensive margin is operative, eliminating current account deficits leads to a rise in the U.S. wage in manufactures relative to nonmanufactures of around 30 percent, reflecting a 24 percent real increase for manufacturing workers and a decline of around 5 percent for nonmanufacturing workers. In the long run in which labor is mobile, this wage difference induces an increase in the manufacturing share of employment of 23 percent.

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Robert Dekle is professor of economics at the University of Southern California; Jonathan Eaton is professor of economics at New York University; and Samuel Kortum is professor of economics at the University of Chicago. The authors have benefitted from comments by our discussant, Doireann Fitzgerald. Eaton and Kortum gratefully acknowledge the support of the National Science Foundation.

We describe how we created this sample and where our data come from in Section II.

This number is not only very large absolutely, it is also large relative to U.S. GDP. Australia, Greece, and Portugal have larger deficit-to-GDP ratios. Some small countries run current account surpluses that are much larger fractions of their GDP. The Bureau of Economics Analysis reports the U.S. current account deficit in 2006 as $857 billion, 6.1 percent of GDP.

While our framework can quite handily deal with a multitude of countries, its analytic essence derives from the two-country model of trade and unilateral transfers of Dornbusch, Fischer, and Samuelson (1977).

Corsetti, Martin, and Pesenti (2007) develop a symmetric two-country model in which adjustment can also occur across both the intensive and extensive margins. They examine the long-run consequences of the effects of improving net export deficits of 6.5 percent of GDP in one country to a balanced position. In the version of the model in which all adjustment takes place at the intensive margin, the authors find that closing the external imbalance requires a fall in long-run consumption (of the country undergoing the adjustment) by around 6 percent and a depreciation of the real exchange rate and the terms of trade by 17 and 22 percent respectively. When adjustment can also occur at the extensive margin, there is a much smaller depreciation in the real exchange rate and in the terms of trade, of 1.1 percent and 6.4, respectively. The changes in consumption and welfare under the two versions of the model, however, are similar.

To generalize our analysis to incorporate multiple factors of production one may think of Li as a vector of factors.

See Eaton, Kortum, and Kramarz (2008) to see how the model could be respecified in terms of monopolistic competition with heterogeneous firms, as in Melitz (2003) and Chaney (forthcoming).

More precisely, the parameter αi captures both manufactures used in final absorption and manufactures used as intermediates in the production of nonmanufactures. For simplicity, we ignore this feedback from the manufacturing sector to the nonmanufacturing sector. As we discuss below, this feedback appears to be small.

If the unit cost function in nonmanufactures is wiN/ai, reflecting productivity ai, then ki=(ai)γ(1βi)βiβi[γ(1βi)]γ(1βi)[(1γ)(1βi)](1γ)(1βi).

We have to confront the problem that the data imply nonzero current account and trade balances for the world as a whole. Our procedures cannot explain this discrepancy so we allocated the deficits to countries in proportion to their GDPs. Because we use only importer data to measure bilateral trade in manufactures, world trade in manufactures balances automatically.

For each country i other than ROW a measure of P is available in some year in the interval 1991–2003. Our measure of P for ROW is the simple average of the Ps across countries not in ROW.

As mentioned earlier, we do not take account of the use of manufactures as intermediates in the production of nonmanufactures. According to the 1997 input-output use table for the United States, the share of intermediates in the gross production of nonmanufactures is 8.5 percent.

In the text, we refer to a percentage change in x as 100(x^=1) and the percentage change in x2 relative to x1 as 100[(x^2/x^i)1].

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