§14 The Goods Market in the Open Economy

Uncovered Interest Parity Condition

• “Arbitrage” implies that:

  $$(1 + i_t) = E_t(1 + i^*_t)\frac{1}{E^{e}_{t+1}}$$

• This relation is known as the (uncovered) interest parity condition.

• This means that in equilibrium financial investors must be indifferent between holding the two bonds. If not, investors would flock to the one with highest expected return.

• With some algebra and approximations:

  $$i_t \simeq i^*_t - \frac{E^{e}_{t+1} - E_t}{E_t}$$

• Arbitrage by investors implies that the domestic interest rate must be equal to the foreign interest rate minus the expected appreciation rate of the domestic currency.

The IS in the Open Economy

• When the economy is open, we need to distinguish between the demand for domestic goods and the (total) domestic demand for goods.

• The former corresponds to the demand for domestically produced goods, which is the driver of domestic production (because in the short run output is demand determined in the IS-LM model).

• Domestic demand remains the same as before (but part of this demand goes to foreign goods):

  $$D \equiv C(Y - T) + I(Y, r) + G$$

• The new concept is the demand for domestic goods:

  $$Z \equiv D + X - \frac{IM}{\epsilon}$$

Export and Import Functions

• Exports is positively related to foreign income, $Y^*$, and negatively related to the real exchange rate, $\epsilon$:

  $$X = X(Y^*, \epsilon); \quad X_{Y^*} > 0, X_\epsilon < 0$$

• Imports is positively related to domestic income, $Y$, and positively related to the real exchange rate:

  $$IM = IM(Y, \epsilon); \quad IM_Y > 0, IM_\epsilon > 0$$

Equilibrium Output and the Trade Balance

• The equilibrium condition is $Y = Z$ :

  $$Y = C(Y - T) + I(Y, r) + G + X(Y^*, \epsilon) - \frac{IM(Y, \epsilon)}{\epsilon}$$

The Role of the Exchange Rate

• Next export function:

  $$NX(Y^*, Y, \epsilon) = X(Y^*, \epsilon) - \frac{IM(Y, \epsilon)}{\epsilon}$$

  $$NX_{Y^*} > 0, NX_Y < 0, NX_\epsilon?$$

• Marshall-Lerner condition: $NX_\epsilon < 0$ . A real appreciation leads to a decline in net exports. This is a realistic condition except for the very-very-very short run. We will assume it holds in the rest of the course (no trick-questions in quizzes and psets!)

Depreciation, the Trade Balance, and Output

• Suppose you want to reduce the trade deficit without changing equilibrium output. One way to do it is to reduce $G$ and $\epsilon$ .
• Rely on foreign rather than domestic demand to support the current level of output.
• Incidentally, it reduces the fiscal deficit as well! No wonder countries like the recipe…

Summary

• Demand for domestic goods is no longer equal to domestic demand for goods. Part of the latter goes to foreign goods, and part of the former comes from foreign demand.
• Equilibrium output is determined as before, but with a smaller multiplier (because imports rise with domestic income) and a new shifter (foreign demand).
• All these differences are reflected in the Trade Balance.
• A depreciation improves the trade balance and increases the demand for domestic goods.
• For a given exchange rate, changes in AD demand in one (large) country (induced by policy or by the private sector) affect other countries.

— Apr 22, 2025

§14 The Goods Market in the Open Economy by Lu Meng is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. Permissions beyond the scope of this license may be available at About.