Here is a quick summary of an article by Mike Kouparitsas. The article helps us to think about the consequences of running current account deficits, and how at some point if net foreign assets get small enough, the country will have to start exporting goods abroad: running a surplus on the net exports of merchandise. Many argue that now, the U.S. is a net debtor nation, which suggests that the U.S. will need to start sending merchandise abroad on net in order to service its liabilities. Mike Kouparitsas does some simple algebra which suggests this is not true. The algebra is reproduced below.

First, some simple national income accounting. Let GDE denote gross domestic expenditures. This is purchases of domestic and foreign consumption goods, plus purchases of domestic and foreign investment goods, plus government purchases of domestic and foreign goods (i.e., the C+I+G in class!). Also, let GNP denote gross national product. Let A denote the foreign assets owned by U.S. residents, and let D denote the U.S. assets owned by foreign residents. Then,

NFA = A-D,

where NFA denotes net foreign assets. A basic accounting identity says,

GNP = GDE + NX + NFI + UT.

Here, NX denotes net exports of goods and services, NFI denotes net foreign income (income of U.S. residents on foreign investments – that is, dividends and interest income, as well as earnings of domestically owned firms operating abroad) minus income earned by foreign residents on U.S. investments, plus wage and salary earnings abroad by U.S. residents minus wage and salary earnings in the U.S. by foreign residents), and UT denotes ‘unilateral transfers’. The last three terms in the above expression are just the current account, CA:

(1) CA = NX + NFI + UT.

Recall that the current account must equal the financial account. That is, CA must be equal to the change in net foreign assets:

(2) CA = NFA – NFA(-1),

Where (-1) means the value of the variable in the previous year.

Ignoring the wage component of NFI, which is small in any case, NFI is earnings on investments abroad earned by U.S. residents minus earnings of foreigners on U.S. investments:

NFI = r^AA(-1) – r^DD(-1).

Here, r^A denotes the return earned by U.S. residents on their foreign assets and r^D denotes the return earned by foreign residents on U.S. assets. It is convenient to rewrite this expression a little:

(3) NFI =[ r^A - r^D ]A(-1) + r^D[A(-1)-D(-1)] = [ r^A - r^D ]A(-1) + r^DNFA(-1)

This says that net foreign income is the excess of U.S. over foreign interest rate times foreign assets held by U.S. residents, plus net foreign assets times the interest rate earned by foreigners.

Substitute out for CA in (1) from (2), to obtain:

NX = NFA – NFA(-1) - NFI - UT .

Now, substitute out for NFI from (3) into this expression:

NX = NFA – NFA(-1) - [ r^A - r^D ]A(-1) - r^DNFA(-1) - UT

= NFA – (1 + r^D)NFA(-1) - [ r^A - r^D ]A(-1) - UT

Having derived these accounting identities, in the second step, we express all the terms in the previous expression as a ratio to GNP. Thus, we divide this expression by GNP:

(NX/GNP) = (NFA/GNP) – (1 + r^D)[NFA(-1)/GNP] - [ r^A - r^D ][A(-1)/GNP] – UT/GNP

Let a variable with a * denote division by GNP. Thus, NX/GNP = NX* . Then,

NX* = NFA* – (1 + r^D)[NFA(-1)/GNP(-1)][GNP(-1)/GNP] - [ r^A - r^D ][A(-1)/GNP(-1)][GNP(-1)/GNP] – UT*

Note here that

NFA(-1)/GNP = [NFA(-1)/GNP(-1)][GNP(-1)/GNP]=NFA*(-1)/(1+g),

where g denotes the growth rate of GNP, that is, GNP/GNP(-1) = 1+g. Then,

NX* = NFA* – (1 + r^D)NFA*(-1)/(1+g) - [ r^A - r^D ]A*(-1)/(1+g) – UT*

We can now ask the following question: if U.S. assets remained at A*, and U.S. liabilities remained at, D*, then what quantity of net merchandise exports could the U.S. maintain indefinitely? This can be obtained from the previous equation, simply by dropping (-1) from the variables:

NX* = NFA*[1 – (1 + r^D)/(1+g)] - [ r^A - r^D ]A*/(1+g) – UT*

= NFA*(g – r^D) - [ r^A - r^D ]A*/(1+g) – UT*,

after using the fact that [1 – (1 + r^D)/(1+g)] is, approximately, g - r^D. There is one complication that needs to be addressed before we can compute NX*, the net merchandise exports to GNP ratio that can be sustained forever. The expression on the right side of the equality has oversimplified in that there are several different types of assets, and they earn different rates of return. In particular a part of NFA and A reflect foreign direct investment (when a U.S. firm directly acquires productive resources in a foreign country, such as when Nike builds a shoe factory in Mexico). We denote this by DI. Other private foreign investment is denoted PI and government or official investment is denoted G. Then,

(4) NX* = NFA_DI*(g – r^D_DI) - [ r^A_DI - r^D_DI ]A_DI*/(1+g)

+ NFA_PI*(g – r^D_PI) - [ r^A_PI - r^D_PI ]A_PI*/(1+g)

+ NFA_G*(g – r^D_G) - [ r^A_G - r^D_G ]A_G*/(1+g)

- UT*

According to Kouparitsas, the data suggest that in 2003:

NFA_DI*=0.05, NFA_PI*=-0.08, NFA_G*=-0.19, A_DI*=0.19, A_PI*=0.44, A_G*=0.02

These numbers are themselves quite interesting. Note that in the case of foreign direct investment, the U.S. has more holdings abroad than foreigners have in the U.S., by 5 percent of US GNP. At the other extreme, U.S. holdings of foreign government debt is very small compared to foreigners’ holdings of U.S. government debt, by 20 percent of GNP. Gross assets obtained by U.S. foreign direct investment is 19 percent of GNP. The biggest part of foreign assets held by U.S. citizens is other private foreign investment, at 44 percent of U.S. GNP.

To complete the calculations, we require rates of return. Kouparitsas argues that the evidence suggests

r^D_DI = 0.039, r^A_DI = 0.103, r^D_PI = 0.067, r^A_PI = 0.073, r^D_G = 0.074, r^A_G = 0.056, g=0.069.

Note that in all cases but government assets, the return earned by U.S. citizens exceeds that earned by foreigners. The most extreme case is the return on direct investment, where the return earned by U.S. citizens is estimated to be 10.3 percent, while the return earned by foreigners is 3.9 percent. These rates of return are estimated by computing the ratio of the relevant income flows to the asset stocks. Some argue that the return discrepancies are just too big to make any sense. Still, these are close to the conventional numbers.

Substitute the above numbers into (4) (also, UT*=-0.005) to obtain NX*=-0.9% of GNP. Thus, given current assets and liabilities, the U.S. could enjoy a deficit in net exports of goods and services equal to 0.9 percent of GNP. Despite the concerns about all the foreign liabilities the U.S. has accumulated, there is a sense in which the U.S. is still not a net debtor because it has enough assets to finance net imports of goods and services forever.