Open-Economy Macro and the Real Exchange Rate

Trade balance as the mirror of saving minus investment; how the real exchange rate adjusts to keep the two sides equal; what tariffs actually do (and don't do).

The fundamental identity

In the simplified national-income framework used here, what a country saves and does not invest at home becomes net acquisition of foreign assets. Abstracting from international income and transfers, the current account is net exports, so:

S - I = NX.

If the US saves more than it invests, $S - I > 0$ , so $NX > 0$ : the US runs a trade surplus and accumulates foreign assets. If the US invests more than it saves, $NX < 0$ : a trade deficit financed by foreigners acquiring domestic debt, equity, real estate, or other assets—not only by bank lending. In fuller balance-of-payments accounts, $S-I$ maps to the current account, which also includes net income and transfers.

The real exchange rate is the price that clears trade

The real exchange rate $\varepsilon$ is how many units of foreign goods trade for one unit of US goods. A higher $\varepsilon$ (a stronger dollar in real terms) makes US exports more expensive and imports cheaper, reducing $NX$ .

The simulation uses a positive-domain trade schedule:

NX(\varepsilon) = \overline{NX} - b\ln(\varepsilon), \qquad b > 0,\; \varepsilon > 0.

Its loanable-funds side is explicit as well (all flow amounts are annual USD billions, and $r^*$ is entered in percentage points):

S(r^*,m_S)=1500m_S+20r^*, \qquad I(r^*)=1700-40r^*.

Thus the world-rate slider raises saving by $20B and lowers investment by $40B per percentage point; the saving-multiplier slider changes the intercept. The calibrated trade schedule starts from $\overline{NX}=200$ billion USD and $b=700$ billion USD.

Equilibrium $\varepsilon^*$ is whatever value makes $NX(\varepsilon) = S - I$ . If saving rises, the right-hand side rises, so $NX$ must rise, which requires $\varepsilon$ to fall — a weaker real dollar.

The nominal broad US dollar index, daily, from 2006 to 2024. — Nominal dollar index against a basket of major trading-partner currencies since 2006. This is context, not the model's real exchange rate: with E measured as foreign currency per dollar, the modeled object is ε = EP/P*, so relative price levels are also required. The nominal index is therefore only an imperfect short-run proxy.Source: FRED, St. Louis Fed (DTWEXBGS)

World real rate r*: 5.00%Domestic saving multiplier: 1.00xTariff/protection wedge: $0B

Saving S

$1600B

Investment I

$1500B

Net capital outflow (S − I)

$100B

Real exchange rate ε*

1.15

Current parameters: r* = 5.00%, saving multiplier = 1.00x, and trade-policy wedge = $0B. Annual flows are USD billions: S = $1500B × saving multiplier + $20B × r*, and I = $1700B − $40B × r*, with r* in percentage points. The calibrated trade curve is NX(ε) = $200B − $700B ln(ε), whose positive domain guarantees ε > 0. A small open economy takes the world real rate as given. Higher domestic saving raises S − I (more capital flowing abroad), which requires a weaker domestic currency (lower ε) to generate the offsetting trade surplus. Tariffs shift the NX curve upward but, in this experiment, don't change the equilibrium quantity of NX because S and I are held fixed with respect to the tariff. Channels through saving, investment, income, expectations, or retaliation are outside this benchmark.

Try raising the world real rate (slider) and watch what happens. Higher world $r$ pulls capital out of the US, lowers investment, raises $S - I$ , and weakens the dollar to boost net exports.

Tariff neutrality in the benchmark model

Try sliding the tariff lever. In this experiment the tariff shifts $NX(\varepsilon)$ upward while holding $S$ and $I$ fixed. Equilibrium $NX$ therefore remains $S-I$ , and $\varepsilon$ rises until the stronger real dollar offsets the initial trade-schedule shift. This is a trade-balance-neutrality result, not a claim about who bears the tariff.

Outside the benchmark, tariffs can change government saving, investment, income, expectations, pass-through, and foreign retaliation. Any of those channels can move $S-I$ or reshape the trade schedule, so neither a fixed trade balance nor complete consumer pass-through is a universal empirical prediction.

Learning objectives

The fundamental identity

The real exchange rate is the price that clears trade

Tariff neutrality in the benchmark model