## APPENDIX: The Large Open Economy

When analyzing policy for a country such as the United States, we need to combine the closed-economy logic of Chapter 3 and the small-open-economy logic of this chapter. This appendix presents a model of an economy between these two extremes, called the large open economy.

## Net Capital Outflow

The key difference between the small and large open economies is the behavior of the net capital outflow. In the model of the small open economy, capital flows freely into or out of the economy at a fixed world interest rate r *. The model of the large open economy makes a different assumption about international capital flows. To understand this assumption, keep in mind that the net capital outflow is the amount that domestic investors lend abroad minus the amount that foreign investors lend here.

Imagine that you are a domestic investor—such as the portfolio manager of a university endowment—deciding where to invest your funds. You could invest domestically (for example, by making loans to U.S. companies), or you could invest abroad (by making loans to foreign companies). Many factors may affect your decision, but surely one of them is the interest rate you can earn. The higher the interest rate you can earn domestically, the less attractive you would find foreign investment.

Investors abroad face a similar decision. They have a choice between investing in their home country and lending to someone in the United States. The higher the interest rate in the United States, the more willing foreigners are to lend to U.S. companies and to buy U.S. assets.

Thus, because of the behavior of both domestic and foreign investors, the net flow of capital to other countries, which we’ll denote as CF, is negatively related to the domestic real interest rate r. As the interest rate rises, less of our saving flows abroad, and more funds for capital accumulation flow in from other countries. We write this as

CF = CF(r).

This equation states that the net capital outflow is a function of the domestic interest rate. Figure 6-15 illustrates this relationship. Notice that CF can be either positive or negative, depending on whether the economy is a lender or borrower in world financial markets.

Figure 6.17: FIGURE 6-15: How the Net Capital Outflow Depends on the Interest Rate A higher domestic interest rate discourages domestic investors from lending abroad and encourages foreign investors to lend here. Therefore, net capital outflow CF is negatively related to the interest rate.

To see how this CF function relates to our previous models, consider Figure 6-16. This figure shows two special cases: a vertical CF function and a horizontal CF function.

Figure 6.18: FIGURE 6-16: Two Special Cases In the closed economy, shown in panel (a), the net capital outflow is zero for all interest rates. In the small open economy with perfect capital mobility, shown in panel (b), the net capital outflow is perfectly elastic at the world interest rate r*.

The closed economy is the special case shown in panel (a) of Figure 6-16. In the closed economy, there is no international borrowing or lending, and the interest rate adjusts to equilibrate domestic saving and investment. This means that CF = 0 at all interest rates. This situation would arise if investors here and abroad were unwilling to hold foreign assets, regardless of the return. It might also arise if the government prohibited its citizens from transacting in foreign financial markets, as some governments do.

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The small open economy with perfect capital mobility is the special case shown in panel (b) of Figure 6-16. In this case, capital flows freely into and out of the country at the fixed world interest rate r*. This situation would arise if investors here and abroad bought whatever asset yielded the highest return and if this economy were too small to affect the world interest rate. The economy’s interest rate would be fixed at the interest rate prevailing in world financial markets.

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Why isn’t the interest rate of a large open economy such as the United States fixed by the world interest rate? There are two reasons. The first is that the United States is large enough to influence world financial markets. The more the United States lends abroad, the greater is the supply of loans in the world economy, and the lower interest rates become around the world. The more the United States borrows from abroad (that is, the more negative CF becomes), the higher are world interest rates. We use the label “large open economy” because this model applies to an economy large enough to affect world interest rates.

There is, however, a second reason the interest rate in an economy may not be fixed by the world interest rate: capital may not be perfectly mobile. That is, investors here and abroad may prefer to hold their wealth in domestic rather than foreign assets. Such a preference for domestic assets could arise because of imperfect information about foreign assets or because of government impediments to international borrowing and lending. In either case, funds for capital accumulation will not flow freely to equalize interest rates in all countries. Instead, the net capital outflow will depend on domestic interest rates relative to foreign interest rates. U.S. investors will lend abroad only if U.S. interest rates are comparatively low, and foreign investors will lend in the United States only if U.S. interest rates are comparatively high. The large-open-economy model, therefore, may apply even to a small economy if capital does not flow freely into and out of the economy.

Hence, either because the large open economy affects world interest rates, or because capital is imperfectly mobile, or perhaps for both reasons, the CF function slopes downward. Except for this new downward-sloping CF function, the model of the large open economy resembles the model of the small open economy. We put all the pieces together in the next section.

## The Model

To understand how the large open economy works, we need to consider two key markets: the market for loanable funds (where the interest rate is determined) and the market for foreign exchange (where the exchange rate is determined). The interest rate and the exchange rate are two prices that guide the allocation of resources.

The Market for Loanable Funds An open economy’s saving S is used in two ways: to finance domestic investment I and to finance the net capital outflow CF. We can write

S = I + CF.

Consider how these three variables are determined. National saving is fixed by the level of output, fiscal policy, and the consumption function. Investment and net capital outflow both depend on the domestic real interest rate. We can write

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Figure 6-17 shows the market for loanable funds. The supply of loanable funds is national saving. The demand for loanable funds is the sum of the demand for domestic investment and the demand for foreign investment (net capital outflow). The interest rate adjusts to equilibrate supply and demand.

Figure 6.19: FIGURE 6-17: The Market for Loanable Funds in the Large Open Economy At the equilibrium interest rate, the supply of loanable funds from saving S balances the demand for loanable funds from domestic investment I and capital investments abroad CF.

The Market for Foreign Exchange Next, consider the relationship between the net capital outflow and the trade balance. The national income accounts identity tells us

NX = SI.

Because NX is a function of the real exchange rate, and because CF = SI, we can write

NX(ε) = CF.

Figure 6-18 shows the equilibrium in the market for foreign exchange. Once again, the real exchange rate is the price that equilibrates the trade balance and the net capital outflow.

Figure 6.20: FIGURE 6-18: The Market for Foreign-Currency Exchange in the Large Open Economy At the equilibrium exchange rate, the supply of dollars from the net capital outflow, CF, balances the demand for dollars from our net exports of goods and services, NX.

The last variable we should consider is the nominal exchange rate. As before, the nominal exchange rate is the real exchange rate times the ratio of the price levels:

e = ε × (P*/P).

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The real exchange rate is determined as in Figure 6-18, and the price levels are determined by monetary policies here and abroad, as we discussed in Chapter 5. Forces that move the real exchange rate or the price levels also move the nominal exchange rate.

## Policies in the Large Open Economy

We can now consider how economic policies influence the large open economy. Figure 6-19 shows the three diagrams we need for the analysis. Panel (a) shows the equilibrium in the market for loanable funds; panel (b) shows the relationship between the equilibrium interest rate and the net capital outflow; and panel (c) shows the equilibrium in the market for foreign exchange.

Figure 6.21: FIGURE 6-19: The Equilibrium in the Large Open Economy Panel (a) shows that the market for loanable funds determines the equilibrium interest rate. Panel (b) shows that the interest rate determines the net capital outflow, which in turn determines the supply of dollars to be exchanged into foreign currency. Panel (c) shows that the real exchange rate adjusts to balance this supply of dollars with the demand coming from net exports.

Fiscal Policy at Home Consider the effects of expansionary fiscal policy—an increase in government purchases or a decrease in taxes. Figure 6-20 shows what happens. The policy reduces national saving S, thereby reducing the supply of loanable funds and raising the equilibrium interest rate r. The higher interest rate reduces both domestic investment I and the net capital outflow CF. The fall in the net capital outflow reduces the supply of dollars to be exchanged into foreign currency. The exchange rate appreciates, and net exports fall.

Figure 6.22: FIGURE 6-20: A Reduction in National Saving in the Large Open Economy Panel (a) shows that a reduction in national saving lowers the supply of loanable funds. The equilibrium interest rate rises. Panel (b) shows that the higher interest rate lowers the net capital outflow. Panel (c) shows that the reduced capital outflow means a reduced supply of dollars in the market for foreign-currency exchange. The reduced supply of dollars causes the real exchange rate to appreciate and net exports to fall.

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Note that the impact of fiscal policy in this model combines its impact in the closed economy and its impact in the small open economy. As in the closed economy, a fiscal expansion in a large open economy raises the interest rate and crowds out investment. As in the small open economy, a fiscal expansion causes a trade deficit and an appreciation in the exchange rate.

One way to see how the three types of economy are related is to consider the identity

S = I + NX.

In all three cases, expansionary fiscal policy reduces national saving S. In the closed economy, the fall in S coincides with an equal fall in I, and NX stays constant at zero. In the small open economy, the fall in S coincides with an equal fall in NX, and I remains constant at the level fixed by the world interest rate.

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The large open economy is the intermediate case: both I and NX fall, each by less than the fall in S.

Shifts in Investment Demand Suppose that the investment demand schedule shifts outward, perhaps because Congress passes an investment tax credit. Figure 6-21 shows the effect. The demand for loanable funds rises, raising the equilibrium interest rate. The higher interest rate reduces the net capital outflow: Americans make fewer loans abroad, and foreigners make more loans to Americans. The fall in the net capital outflow reduces the supply of dollars in the market for foreign exchange. The exchange rate appreciates, and net exports fall.

Figure 6.23: FIGURE 6-21: An Increase in Investment Demand in the Large Open Economy Panel (a) shows that an increase in investment demand raises the interest rate. Panel (b) shows that the higher interest rate lowers the net capital outflow. Panel (c) shows that a lower capital outflow causes the real exchange rate to appreciate and net exports to fall.

Trade PoliciesFigure 6-22 shows the effect of a trade restriction, such as an import quota. The reduced demand for imports shifts the net exports schedule outward in panel (c). Because nothing has changed in the market for loanable funds, the interest rate remains the same, which in turn implies that the net capital outflow remains the same. The shift in the net-exports schedule causes the exchange rate to appreciate. The rise in the exchange rate makes U.S. goods expensive relative to foreign goods, which depresses exports and stimulates imports. In the end, the trade restriction does not affect the trade balance.

Figure 6.24: FIGURE 6-22: An Import Restriction in the Large Open Economy An import restriction raises the demand for net exports, as shown in panel (c). The real exchange rate appreciates, while the equilibrium trade balance remains the same. Nothing happens in the market for loanable funds in panel (a) or to the net capital outflow in panel (b).

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Shifts in Net Capital Outflow There are various reasons that the CF schedule might shift. One reason is fiscal policy abroad. For example, suppose that Germany pursues a fiscal policy that raises German saving. This policy reduces the German interest rate. The lower German interest rate discourages American investors from lending in Germany and encourages German investors to lend in the United States. For any given U.S. interest rate, the U.S. net capital outflow falls.

Another reason the CF schedule might shift is political instability abroad. Suppose that a war or revolution breaks out in another country. Investors around the world will try to withdraw their assets from that country and seek a “safe haven” in a stable country such as the United States. The result is a reduction in the U.S. net capital outflow.

Figure 6-23 shows the impact of a leftward shift in the CF schedule. The reduced demand for loanable funds lowers the equilibrium interest rate. The lower interest rate tends to raise net capital outflow, but because this only partly mitigates the shift in the CF schedule, CF still falls. The reduced level of net capital outflow reduces the supply of dollars in the market for foreign exchange. The exchange rate appreciates, and net exports fall.

Figure 6.25: FIGURE 6-23: A Fall in the Net Capital Outflow in the Large Open Economy Panel (a) shows that a downward shift in the CF schedule reduces the demand for loans and thereby reduces the equilibrium interest rate. Panel (b) shows that the level of the net capital outflow falls. Panel (c) shows that the real exchange rate appreciates and net exports fall.

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## Conclusion

How different are large and small open economies? Certainly, policies affect the interest rate in a large open economy, unlike in a small open economy. But, in other ways, the two models yield similar conclusions. In both large and small open economies, policies that raise saving or lower investment lead to trade surpluses. Similarly, policies that lower saving or raise investment lead to trade deficits. In both economies, protectionist trade policies cause the exchange rate to appreciate and do not influence the trade balance. Because the results are so similar, for most questions one can use the simpler model of the small open economy, even if the economy being examined is not really small.

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