# Open Economy Macroeconomics

# The Balance of Payments

The balance of payments and the international investment position are designed to measure and present an economy’s external activity engaged with the rest of the world, such as flows of goods, services and capital during certain periods and the accumulated stocks of assets or liabilities at certain times.

## National Accounts with an External Sector

In a closed economy involving no government activity, the following accounting identities hold:

\[\begin{aligned} GDP &= C+I \\ GDP &= C+S \end{aligned}\]

where \(GDP\) is gross domestic product, \(C\) is consumption expenditure, \(I\) is investment and \(S\) is savings. The first equation is the compositions of spending, the second equation is the compositions of income, and total spending is equal to total income. The above equations imply:

\[S = I\]

which states that investment is equal to savings in a closed economy without a government.

Incorporating government activities, the equations become:

\[\begin{aligned} GDP &= C+I + G \\ GDP &= C+S + T \end{aligned}\]

where \(G\) is government spending, \(C\) is consequently confined to private consumption, \(I\) is consequently confined to private investment, \(T\) is taxation or government income, and \(S\) is consequently confined to private savings.

Still, total spending must equal total income. A relationship:

\[S-I = G-T\]

is derived, which states that government budget deficit must be offset by surplus in private savings.

In an open economy, national spending does not necessarily always equal na- tional income. National spending can be in excess of national income at times or over a not too long period. Further incorporating an external sector, the equations become:

\[\begin{aligned} GDP &= C+I + G + X -M \\ GDP &= C+S + T - NYF - NCT\end{aligned}\]

where \(X\) stands for exports of goods and services, \(M\) stands for imports of goods and services, and \(X – M\) is balance on goods and services; \(NYF\) stands for net income from abroad, and \(NCT\) stands for net current transfers.

*\(X – M > 0\): the economy is a net exporter and has produced more than it has spent, and
*\(X – M < 0\): the economy is a net importer and has spent more than it has produced.

Moreover, a nation’s total income in an open economy, due to income receipts from abroad, income payments to foreigners, and current transfers, can be different from its GDP and is the sum of GDP, NYF and NCT.

\[(S-I)-(G-T) = (X-M) + NYF + NCT = CAB\]

where \(CAB\) stands for current account balance. This equation indicates that if government budget deficit is not offset by private savings surplus, the country must run a current account deficit, or must be a net importer of goods and services when net income from abroad and net current transfers are negligible.

From the balance of payments identity, it can be worked out that:

\[(S-I)-(G-T) = NFI - NKT + NAN\]

where \(NFI\) is net foreign investment including official and private investment, \(NKT\) is net capital transfers and \(NAN\) is net acquisition of non-produced, non-financial assets. \((NKT – NAN)\) together is balance on the capital account. The sign of \(NFI\) is reversed from that for the financial account, with \(+\) indicating net foreign investment abroad of the reporting country or capital outflow, and \(–\) indicating net foreign investment in the reporting country or capital inflow.

This equation shows that if a country saves more than it invests domestically by the private sector and the government, the country will have surplus capital to invest abroad; and if a country invests more domestically by the private sector and the government than it saves, the extra capital has to be flowed in from the rest of the world.

The international economic linkages can be summerized as follows:

*If a country has spent more than it has produced, the country must acquire the excess through international trade as a net importer of goods and services, and becomes a net importer of capital in the meantime with more foreign investment inflow. Accompanied by capital inflows, more domestic assets, financial and real, fall in the hands of foreigners.
*If a country has produced more than it has spent, the country is a net exporter of goods and services and exports the excess through international trade to the rest of the world, and increases its net foreign investment abroad in the meantime. The larger the excess, the more claims the country is to make on the rest of the world. Accompanied by capital outflows, the country acquires more real and/or financial assets abroad.

From the budget perspective, spending is related and constrained by savings.

*When savings are less than the sum of domestic private investment and government budge deficit, the country has to import capital from the rest of the world in the form of foreign investment to fill the overall domestic private and government budgetary shortfall financially, and then to implement foreign investment physically through imports.
*When a country saves more than the sum of domestic private investment and government budge deficit, the country exports capital to the rest of the world in the form of foreign investment abroad financially, and then to implement foreign investment physically through exports.

In a closed economy, private savings surplus must have the same sign as government budget deficit with an equal amount. In an open economy, they do not necessarily offset each other completely, since the balance can be made up through international trade and foreign investment. So, it is possible that a country runs both a private savings deficit and a government budgetary deficit. When this happens, it is said that the country experiences **twin deficits**. Obviously, when a country experiences twin deficits, it runs an overall budgetary deficit. While an overall budgetary deficit may or may not be associated with twin deficits, e.g., when private savings are in surplus but the surplus is not large enough to offset government budget deficit completely.

# IS-LM Analysis

There are two parts in IS–LM analysis, one is the IS plane for investment and savings, and the other is the LM plane referring to liquidity of money. The former the equilibrium on the goods market and the latter is the equilibrium on the money market. General equilibrium attains when both the goods market and the money market clear or are in equilibrium. This happens when the IS curve and the LM curve cross on the \(Y-r\) plane. The level of income and the level of the interest rate can therefore be determined. When the IS curve and/or the LM curve shift due to changes in the value of the exogenous variables, the level of income and the corresponding interest rate will also change accordingly to settle down at a new equilibrium point.

## The goods market

The goods market equilibrium and the corresponding IS curve are derived from analysing the following equation:

\[S+T-I= G+TB\]

Taking derivatives of these variables with respect to the interest rate, income and the real exchange rate, the partial derivatives indicate that

*Savings are an increasing function of the interest rate \(r\);
*Investment is a decreasing function of the interest rate \(r\);
*Both savings and investment increase with the level of income \(Y\) (\(GDP\)), but savings increase more than investment for a same size of increase in \(Y\);
*Government tax revenue is an increasing function of income \(Y\);
*Trade balance is an increasing function of the real exchange rate \(Q\) (An increase in \(Q\) means the depreciation of the domestic currency in real terms) - depreciation in the real exchange rate boosts exports and deters imports by making domestic goods cheaper and more competitive abroad and imported foreign goods more expensive and less competitive on the domestic market; and
*Trade balance is a decreasing function of income \(Y\) – domestic residents will spend more on imported goods with income increases.

The IS curves and the goods market equilibria at various levels of the exogenous variables, government spending, \(G\), and the real exchange rate, \(Q\) is as follows: \[r = -\frac{\beta}{\lambda}Y + \frac{h}{\lambda}Q + \frac{1}{\lambda}G\]

It is clear that the slope the curve is \(-\beta/\lambda\), which is down sloping. Both increases in government spending and the real exchange rate shift the entire IS curve in the up right direction.

## The money market

The money market equilibrium and the corresponding LM curve are derived from analysing the following equation:

\[\frac{M^D}{P} = \frac{M^S}{P} = L(r,Y)\]

where \(M^D\) is demand for money and \(M^S\) is money supply and they are equal when the money market is in equilibrium; \(P\) is price; and \(L\) stands for liquidity of money, which is a function of the interest rate \(r\) and income \(Y\). \(L(r,Y)\) is a measure of the **velocity** of money in circulation. With a fixed amount of money supply, the lower the price level, the more liquid is the money market.
*\(L(r,Y)\) is a decreasing function of the interest rate \(r\) – a higher level of the interest rate will induce more savings and reduce demand for money; and
*\(L(r,Y)\) is an increasing function of income \(Y\) – with the price level and money supply unchanged, a higher level of income means the same money has to circulate for more times in a given period, or the velocity of money has to increase.

With \(M^D=M^S=M\) it yields:

\[r = \frac{k}{\gamma}Y - \frac{1}{\gamma}\frac{M}{P}\]

The equation suggests that the LM curve is up sloping with the slope being \(k/\gamma\). An increase in money supply will move the entire LM curve downwards or rightwards; and an increase in the price level will shift the entire LM curve upwards or leftwards.

# IS-LM-BP Analysis

In the above IS–LM analysis, the foreign exchange rate is treated as an exogenous variable, so is trade balance. While this treatment works for domestic policy analysis, it is not appropriate for the analysis of issues in international finance and trade where foreign exchange, international trade and capital flows are amongst major considerations. Therefore, this section adds another dimension to the IS–LM framework by incorporating the balance of payments (BP) into the analysis, in which the foreign exchange rate and trade balance are endogenous. Under this extended framework of IS–LM–BP analysis, income, the interest rate, the exchange rate, and the balance of payments accounts are jointly determined, e.g., the implementation of a specific policy may firstly have effect on the level of the interest rate and income, which passes onto the exchange rate, which in turn impacts trade balance, income and the interest rate.

In the same spirit as for IS–LM analysis, the balance of payments accounts are expressed as functions of income, \(Y\), the real foreign exchange rate, \(Q\), and the interest rate, \(r\):

\[BP = CAB(Q,Y)+KAB(r)\]

where \(BP\) stands for the balance of payments, \(CAB\) stands for the current account balance, and \(KAB\) stands for the capital and financial account balance. As suggested earlier, our analysis concentrates on trade balance, \(TB = (X–M)\), so we re-write the equation as follows:

\[BP = TB(Q,Y)+KAB(r)\]

Taking derivatives of TB and KAB with respect to the foreign exchange rate, income and the interest rate respectively indicates that

*Trade balance is an increasing function of the real foreign exchange rate \(Q\) (it can be the nominal exchange rate and the analysis is the same) – depreciation in the real exchange rate boosts exports and deters imports by making domestic goods cheaper and more competitive abroad and imported foreign goods more expensive and less competitive on the domestic market;
*Trade balance is a decreasing function of income \(Y\) – domestic residents will spend more on imported goods with income increases; and
*Capital and financial account balance is an increasing function of the level of interest rate \(r\) – a higher level of the interest rate will induce more capital inflows and reduce capital outflows. Capital is perfectly mobile when \(KAB'_r = \infty\) , which is usually applicable to a small open economy, and capital is completely immobile when \(KAB'_r = 0\).

Same as with IS–LM analysis, we express TB and KAB as linear functions of and Y, Q and r:

\[\begin{aligned}TB(Y,Q) = hQ-\theta Y \\ KAB(r) = \kappa (r-r^*) \end{aligned}\]

where \(0\le \kappa <\infty\), and \(r^*\) is the equilibrium interest rate. Noting that the two balances sum to zero, it therefore yields:

\[hQ - \theta Y + \kappa (r-r^*)=0\]

# Assumptions on Price Attributes

Economists make different assumptions on the properties of prices. Analysis based on different assumptions may proceed with different approaches and reach different conclusions. Depending on the circumstances, one assumption or one set of assumptions can be more appropriate and relevant than others. There are three assumptions on the attributes of prices, based on which three major models of foreign exchange rate determinations were developed, and presents their implications respectively.

With the **flexible prices assumption**, aggregate supply curve is vertical. This means that a shift in aggregate demand has no whatsoever effect on output. The level of output cannot be easily changed as it is mainly determined by supply side factors. Since a shift in demand will not cause shifts in aggregate supply or output, the shift in aggregate demand will only cause prices to change. e.g., since a shift to a higher aggregate demand level will not lead to a higher aggregate output level, the price level has to and will rise.

The figure above demonstrates what may happen under the flexible prices assumption. For example, if initially the aggregate supply curve is at the position \(AS_1\) and the aggregate demand curve is the position \(AD_1\). Output is at the level of \(Y_1\), the price level is at \(P_1\), and the aggregate demand curve and the aggregate supply curve cross at point \(A\) in equilibrium. If for some reason the aggregate demand curve shifts to a new position \(AD_2\), then \(A\) is no longer the equilibrium point. The aggregate supply curve and the new aggregate demand curve cross at point \(B\) in a new equilibrium where output remains \(Y_1\) but the price level increases from \(P_1\) to \(P_2\). Only a shift in aggregate supply will change the level of output, e.g., from \(Y_1\) to \(Y_2\). The price level can be lowered in a new equilibrium at point \(C\) or higher at point \(D\), depending on whether aggregate demand shifts as well and how it shifts.

**The flexible price monetary model** of foreign exchange rate determination adopts this assumption on price attributes. Since there is not much role for the goods market equilibrium, the monetary model, unlike the Mundell-Fleming model, does not follow the IS–LM framework. If it dose in some sense, it works with the LM part only.

When **fixed prices** are assumed, the aggregate supply curve is fairly flat or horizontal in the extreme. This suggests that a shift in aggregate demand is almost everything to concern. Changes in aggregate supply or output are almost entirely induced by shifts in aggregate demand. In contrast to the flexible price case, the level of output can be easily adjusted in response to shifts in aggregate demand so the price level need not change.

The figure shows the fixed prices case. Since the aggregate supply is flat, the amount of supply changes, increase or decrease, induced by a shift in demand can be enormous, indicating supply side factors can be easily mobilised. Assuming the initial equilibrium has been reached at point \(A\), a shift of the aggregate demand curve from \(AD_1\) to \(AD_2\) induces aggregate supply to increase so the level of output increases from \(Y_1\) to \(Y_2\), with little effect on the price level, since the consequences of the shift in demand are almost absorbed by adjustments in output.

With the fixed prices assumption, demand analysis is important and, consequently, the IS–LM framework or its international extension, IS–LM–BP analysis, is usually adopted. **The Mundell-Fleming model** adopts this assumption on price attributes.

Flexible prices and fixed prices are two extreme assumptions on price attributes. A more appropriate assumption may be that prices are neither totally flexible nor totally fixed, which leads to the **sticky price assumption**. The aggregate supply curve is flat in the short-term, the slope of the aggregate supply curve gradually becomes steeper and steeper with increases in time horizon, and the curve is vertical in the long-run. In the short-term, increases in output are induced by shifts in aggregate demand; in the medium-term, increases in output are caused by shifts in aggregate demand or shifts in aggregate supply or both; and in the long-run, only a shift in aggregate supply changes output. The stick price is the assumption adopted by **the Dornbusch model** of foreign exchange rate determination.

The figure exhibits the short-term, medium-term and long-run features of aggregate supply with the sticky prices assumption. In the short-term, the aggregate supply curve \(AS_S\) is flat or horizontal, so a shift of the aggregate demand curve from \(AD_1\) to \(AD_2\) induces aggregate supply to increase so the level of output increases from \(Y_1\) to \(Y_2\), while the price is unchanged or fixed at \(P_1\). Assuming the initial equilibrium has been reached at point \(A\), the shift of the aggregate demand curve from \(AD_1\) to \(AD_2\) will lead to the temporary equilibrium point \(B\). In the medium-term, the aggregate supply curve \(AS_M\) is neither horizontal nor vertical and output is determined by both aggregate demand and aggregate supply. At point \(C\), the price level is between \(P_1\), the fixed price, and \(P_2\), the flexible price with the aggregate demand shift; and the increase in output is lower than that in the fixed price case. In the long-run, the aggregate supply curve \(AS_{L1}\) is vertical, so at point \(D\) there is only increase in the price level but no change in output. Only a shift in aggregate supply from \(AS_{L1}\) to \(AS_{L2}\) increases output from \(Y_1\) to \(Y_2\).