This chapter seeks to provide a general overview of the respective theories of exchange rate determination and includes a review of some of the empirical evidence that seeks to test these theories. Exchange rate determination is a topic that is of importance to financial economists, financial institutions, foreign currency traders, and all the other participants that are involved in the foreign exchange market. In this lecture we will consider a number of schools of thought that relate to exchange rate determination. These include the asset market view that may be used to solve complex problems. We will also explore the different determinants of exchange rates and the theories that deal with its determination. These theories include (a) the monetary approach and (b) the portfolio balance approach, where the monetary approach incorporates the monetarist model (flexible prices) and the overshooting model (sticky prices). Other related issues will be discussed, such as efficiency in the foreign exchange market, exchange rate expectations and the effect of “News”, as well as the interaction between the money market and exchange rate.^{1}

The theoretical literature on the asset market view of exchange rate determination continues to expand after it was initially formulated in the mid-1970s. This theory has a number of practical implications and generations of economists and practioners continue to apply this theory in theoretical research and trading practices. Note that the theoretical foundations of this view assume that there is an absence of substantial transaction cost, capital control, and other impediments to the flow of capital between nations. After formulating the theoretical model, one could then consider the implications of incorporating these rigidities. Thus, we initially assume that there is perfect capital mobility among countries. In this case, the exchange rate will adjust instantly to equilibrate the international demand for stocks of national assets. The empirical implication is that floating exchange rates exhibit high variability, which goes beyond the variability of their underlying determinants. Econometric analysis gives specific empirical implications for the various theories.

Before we consider the asset market view for exchange rate determination, we can consider the traditional Balance of Payments view that was used to describe the value of the exchange rate. This view suggests that the exchange rate is the price of a currency that is determined in the foreign exchange market by the demand and supply forces for foreign exchange. Hence, it assumes that the exchange rate moves (if free to do so) to equate the demand and supply for foreign exchange to restore equilibrium in the balance of payments.

That flexible exchange rates are determined in the foreign exchange market by demand and supply forces for foreign exchange is an irrefutable fact (we do, of course, exclude economies with administrative exchange controls). However, the manner in which one seeks to determine the extent of these demand and supply forces is a source of disagreement. The traditional Balance of Payments view regards the demand and supply of foreign exchange as pure flows, which are largely derived from imports and exports of goods, which in turn depend on the exchange rate. In addition, such flows could also be influenced by national income. The introduction of capital movements as a further component of the demand and supply forces for foreign exchange does not alter this view insofar as these movements are also regarded as pure flows.

This approach has however been criticised for several shortcomings, among which is the fact that it neglects stock adjustments. For example, when the price of a currency changes then this could affect the wealth of an investor or country, which could influence the relative demand and supply for a particular currency. In addition, when the central bank adds to the monetary stock then the price of the currency would also need to adjust. Note however that while this view may not provide significant insight into the identification of potential factors that influence the demand and supply of foreign exchange, it is still the case that the interaction between these demand and supply forces will ultimately determine the value of the exchange rate.

To consider a practical application of the Balance of Payments view to exchange rate determination we could make use of setting where the demand for and supply of foreign currency is going to be influenced by the demand for imports and the supply of exports. Whenever trade takes place, the demand and supply schedules shift up or down, as shown in Figure 1.

Note : An increase in the demand for euros (€) shifts the demand schedule from \(D_€\) to \(D_€^\prime\) and the original equilibrium exchange rate \(S_0\) (at the intersection of the demand and supply schedules) increases to \(S_1\). In this case, the euro appreciates and the US dollar depreciates. A subsequent reduction in the supply of euros results in a shift of the supply schedule to the left from \(S_€\) to \(S_€^\prime\) (from points \(E_1\) to \(E_2\)).

By using a balance of payments equation, we can determine the factors that affect these two schedules:

\[\begin{eqnarray} BP_t = CA \left( \frac{S_t P_t^\star}{P_t}, Y_t , Y_t^\star , \Pi_t , \Pi_t^\star \right) + FA \left( i_t - i_t^\star \right) \tag{1.1} \end{eqnarray}\]

where, \(CA\) = current account, \(S_t\) = spot exchange rate, \(P_t\) = domestic price level, \(P_t^\star\) = foreign price level, \(Y_t\) = real income, \(\Pi_t\) = shift factor (tariffs, subsidies, interventions, etc.), \(FA\) = financial account, \(i_t - i_t^\star\) = interest rate differential, and an asterisk (\(\star\)) denotes the foreign variables. In the case of floating exchange rates, the balance of payments equilibrium is maintained by the continuous adjustment of the exchange rate.

Therefore, from (1.1), solving for the exchange rate (\(S_t\)) and expressing all the variables in natural logarithms (\(s_t\)), except interest rates (since variables that are measured as percentages per annum are not transformed to logarithms), we have:

\[\begin{eqnarray} s_t = \alpha_0 + \alpha_1 \left( p_t - p_t^\star \right) + \alpha_2 \left( y_t - y_t^\star \right) + \alpha_3 \left( i_t - i_t^\star \right) + \alpha_4 \left( \Pi_t - \Pi_t^\star \right) + \varepsilon_t \tag{1.2} \end{eqnarray}\]

- \(\alpha_1 > 0\) when an increase in \(p_t\) reduces exports (\(x_t\)), the \(CA_t\) deteriorates and the country loses its competitive position; this will results in a depreciation of the domestic currency (spot rate will increase, \(s_t \uparrow\)).

- \(\alpha_2 > 0\) when a rapid growth in domestic real output tends to increase imports (\(m_t\)) and the \(CA_t\) deteriorates; then, domestic currency depreciates (\(s_t \uparrow\)).

- \(\alpha_3 < 0\) when an increase in the domestic interest rate, holding the foreign interest rate constant, caused capital inflows into the country, which will increase the demand for domestic currency, and the domestic currency will appreciate (\(s_t \downarrow\)).

- \(\alpha_4 < 0\) when any kind of intervention (domestic trade policy) seeks to improve the \(CA_t\), which will result in an appreciation in the value of the currency (\(s_t \downarrow\)).

Equation (1.2) can be expanded by using other pairs of variables (i.e., national debt differential: \(nd_t - nd_t^\star\), investment differential: \(\log I_t - \log I_t^\star\), saving differential: \(\log S_t - \log S_t^\star\), wage differential: \(w_t - w_t^\star\), etc.).

The asset market view for the determination of floating exchange rates assumes that the exchange rate is the relative price of a commodity. Such a commodity could take the form of monies, which is a concept that is consistent with the monetary approach of exchange rate determination. Alternatively, it could be regarded as the relative price of bonds, which would be consistent with the portfolio approach. The two approaches differ with regards to the assumptions made on the substitutability between domestic and foreign bonds, given the common hypothesis of perfect capital mobility. The monetary approach assumes perfect substitutability between domestic and foreign bonds, so that asset holders are indifferent as to which they hold, and the issuers of bonds do not influence the outcome. Conversely, in the portfolio approach, domestic and foreign bonds are imperfect substitutes, which implies that the issuers of these instruments are relevant.

The theoretical assumptions that all these asset-market models share include the suggestion that there is an absence of substantial transaction cost or other impediments to the flow of capital between countries. Therefore, assuming that there is also no risk of default or future capital controls, perfect capital mobility implies covered interest parity,

\[\begin{eqnarray} i_t - i_t^\star = fd_t \;\;\; \text{or} \;\;\; fp_t = f_t - s_t \tag{2.1} \end{eqnarray}\]

where, \(fd_t\) = forward discount, \(fp_t\) = forward premium, \(f_t\) = the natural logarithm of the forward rate, and \(s_t\) = the natural logarithm of spot exchange rate. Perfect substitutability between domestic and foreign bonds is a much stronger assumption that asset holders are indifferent to the composition of their bond portfolios, as long as the expected rate of return on the two countries’ bonds is the same, when expressed in any common numéraire and implies uncovered interest parity,

\[\begin{eqnarray} i_t - i_t^\star = \Delta s_t^e = s_{t+1}^e - s_t \tag{2.2} \end{eqnarray}\]

where, \(s_t^e\) = expected change in the spot rate and \(s_{t+1}^e\) = expected spot rate in the next period.

To avoid confusion it would be worthwhile to make a clear distinction between (perfect) capital mobility and (perfect) substitutability. Perfect capital mobility means that the actual portfolio composition instantaneously adjusts to the desired one. This would imply that if we assume that there is no risk of default or future capital controls then *covered interest parity* must hold. Perfect substitutability is a stronger assumption, as it means that asset holders are indifferent as to the composition of their bond portfolios (provided of course that both domestic and foreign bonds have the same expected rate of return expressed in a common numéraire). This indifference between holding bonds in different countries would imply that *uncovered interest parity* would hold.

It is important to note that according to some writers (see, for example, Helliwell and Boothe (1983)), the condition of covered interest parity itself becomes a theory of exchange-rate determination (the *interest parity model*, where interest parity may be expressed either in nominal or real terms), if one assumes that the forward exchange rate is an accurate and unbiased predictor of the future spot rate: it would in fact suffice, in this case, to find the determinants of the expected future spot exchange rate to be able to determine, given the interest rates, the current spot rate.

If we assume that uncovered interest parity holds (\(i_t - i_t^\star = s_{t+1}^e - s_t\)), the supply of bonds becomes irrelevant. In such a case, the responsibility for determining the value for the exchange rate is shifted to money markets. Such models belong to the monetary approach of exchange rate determination, which focuses on the demand for and supply of money. Instead of emphasizing tradeflows and capital movements, the monetary approach focuses on the monetary stock equilibrium condition in each country’s money market.

The monetarist model assumes there are no transaction costs, no capital controls, and no segmentation in international capital markets (domestic and foreign bonds are also perfect substitutes). Therefore, it is similar to having only one bond in the world. In addition, there are no transportation costs, no trade controls, and no segmentation in the international goods markets (domestic and foreign goods are perfect substitutes). Therefore, it is also similar to having only one good in the world. This assumption implies that purchasing power parity (PPP) will hold, such that \(P_t = P_t^\star S_t\); where, \(P_t\) = the domestic price level, \(P_t^\star\) = the foreign price level, and \(S_t\) = the spot exchange rate. Since perfect price flexibility is maintained in this model, it is called the monetarist model. The fundamental equations for this model would then include:

The PPP equation in logarithm form,

\[\begin{eqnarray} s_t = p_t - p_t^\star \tag{2.3} \end{eqnarray}\]

where, \(s_t\) = the natural logarithm of the spot exchange rate (i.e., $/€), \(p_t\) = the natural logarithm of the domestic price level (CPI), and \(p_t^\star\) = the natural logarithm of the foreign price level (\(CPI^\star\)).

The domestic real demand for money,

\[\begin{eqnarray} m^d_t - p_t = \alpha + \beta y_t - \gamma i_t + \varepsilon_{1,t} \tag{2.4} \end{eqnarray}\]

where, \(m^d_t\) = the natural logarithm of the domestic money demand, \(p_t\) = the natural logarithm of the domestic price level, \(y_t\) = the natural logarithm of domestic real income, \(i_t\) = the domestic short-term interest rate, and \(\varepsilon_{1,t}\) = the error term.

The foreign real demand for money,

\[\begin{eqnarray} m^{\star d}_t - p_t^\star = \alpha + \beta y_t - \gamma i_t^\star + \varepsilon_{2,t} \tag{2.5} \end{eqnarray}\]

where, asterisks (\(^\star\)) denote foreign variables and elasticities are assumed to be the same in both countries (constrained model).

Assuming equilibrium in the money markets, we have,

\[\begin{eqnarray} m^d_t - p_t = m^s_t - p_t = m_t - p_t \tag{2.6} \end{eqnarray}\]

and

\[\begin{eqnarray} m^{\star d}_t - p_t^\star = m^{\star s}_t - p_t^\star = m_t^\star - p_t^\star \tag{2.7} \end{eqnarray}\]

By combining equations (2.4), (2.5), (2.6) and (2.7) to (2.3), we have,

\[\begin{eqnarray} s_t = \left( m_t - m^\star_t \right) - \beta \left( y_t - y_t^\star \right) + \gamma \left( i_t - i_t^\star \right) + \varepsilon_t \tag{2.8} \end{eqnarray}\]

Equation (2.8) gives a constrained model of exchange rate determination (with three constraints); the unconstrained one is when we allow the elasticities to be different in each country,

\[\begin{eqnarray} s_t = \alpha_0 + \alpha_1 m_t + \alpha_2 m^\star_t + \alpha_3 y_t + \alpha_4 y_t^\star + \alpha_5 i_t + \alpha_6 i_t^\star + \varepsilon_t \tag{2.9} \end{eqnarray}\]

where, \(\alpha_0\) = the constant term, \(\alpha_1 > 0\) = the domestic money elasticity of the exchange rate, \(\alpha_2 < 0\) = the foreign money elasticity of exchange rate, \(\alpha_3 < 0\) = the domestic real income elasticity of exchange rate, \(\alpha_4 > 0\) = the foreign real income elasticity of exchange rate, \(\alpha_5 > 0\) = the domestic interest rate semi-elasticity of the exchange rate, \(\alpha_6 < 0\) = the foreign interest rate semi-elasticity of the exchange rate, and \(\varepsilon_t\) = the error term or residual or disturbance.

Under the alternative unconstrained equation (eq. (2.9), we can test the hypothesis that elasticities are the same in both countries (null hypothesis), constrained equation (eq. (2.8))]. By solving both models, we can determine the log likelihood statistic (\(\log L^c\)) of the constrained model and the log likelihood statistic (\(\log L^u\)) of the unconstrained model. The resulting likelihood ratio statistic,

\[\begin{eqnarray} -2 \left( \log L^c - \log L^u \right) \sim \chi^2_q \tag{2.10} \end{eqnarray}\]

is distributed asymptotically as \(\chi^2_q\), where, \(q\) =the number of constraints (three constraints, in this case). Comparison of this statistic with the critical \(\chi^2_q\) then, tests the null hypothesis (i.e., the same elasticities in both countries).

Also, by taking into consideration other economic and financial relationships between the two countries, we can create alternative specifications of the basic monetarist model, equation (2.8).

- The
*uncovered interest parity*:

\[\begin{eqnarray} i_t - i_t^\star = \Delta s_t^e = s_{t+1}^e - s_t \tag{2.11} \end{eqnarray}\]

- The
*covered interest parity*:

\[\begin{eqnarray} i_t - i_t^\star = fd_t \text{or} fp_t = f_t - s_t \tag{2.12} \end{eqnarray}\]

- Expected depreciation of the currency is equal to expected inflation differential:

\[\begin{eqnarray} \Delta s_t^e = \pi_t^e - \pi_t^{\star e} \tag{2.13} \end{eqnarray}\]

- The monetarist view: the expected growth of money (\(\dot{m}^e_t\)) is equal to the expected inflation (\(\pi_t^{e}\)):

\[\begin{eqnarray} \dot{m}^e_t - \dot{m}^{\star e}_t = \pi_t - \pi_t^{\star e} \tag{2.14} \end{eqnarray}\]

Thus, based on equations (2.11), (2.12), (2.13) and (2.14), we have alternative specifications of the basic model, equation (2.8):

\[\begin{eqnarray} & & s_t = \left( m_t - m^\star_t \right) - \beta \left( y_t - y_t^\star \right) + \gamma \left( s_{t+1}^e - s_t \right) + \varepsilon_t \tag{2.15} \\ &\text{or}& s_t = \left( m_t - m_t^\star \right) - \beta \left( y_t - y_t^\star \right) + \gamma \left( f_t - s_t \right) + \varepsilon_t \tag{2.16}\\ &\text{or}& s_t = \left( m_t - m_t^\star \right) - \beta \left( y_t - y_t^\star \right) + \gamma \left( \pi_t^{e} - \pi_t^{\star e} \right) + \varepsilon_t \tag{2.17}\\ &\text{and}& s_t = \left( m_t - m_t^\star \right) - \beta \left( y_t - y_t^\star \right) + \gamma \left( \dot{m}^e_t - \dot{m}^{\star e}_t \right) + \varepsilon_t \tag{2.18} \end{eqnarray}\]

The first factor affecting exchange rate is the money differential between the two countries. An increase in the domestic money supply increases the supply of domestic currency (rands) and the South African currency depreciates, which is reflected by an increase in the spot rate (\(s_t \uparrow\)). The second factor refers to relative income levels. A boost in domestic real income (*ceteris paribus*) creates an excess demand for the domestic money stock. In an attempt to increase the real money balances, domestic residents may also reduce expenditure, and prices fall until the money market equilibrium is achieved. Through PPP (\(p_t \downarrow - \bar{p}^\star_t = s_t \downarrow\)), the fall in domestic prices (with foreign prices constant) implies an appreciation of the domestic currency (\(s_t \downarrow\)).

The third factor is the relative short-term interest rate in the two countries. An increase in the domestic interest rate denotes the market expectation of the exchange rate. The domestic currency is expected to depreciate and the country increases the interest rate to cover the forward discount with its higher interest rate, so it could attract investment. Thus, the causal effect is from: \(s_{t+1}^e \uparrow \Rightarrow \left( i_t \uparrow - \bar{i}^\star_t \right)\).

The monetarist model assumes instantaneous adjustment in all markets, which has been the subject of a number of critiques, and subsequent work by Dornbusch (1976), showed that it was possible to modify some of these assumptions to describe the short-run dynamics of most exchange rates. This model assumes that asset markets adjust instantaneously, whereas prices in goods markets adjust slowly (gradually). The resulting exchange rate model retains all the long-run equilibrium or steady-state properties of the monetary approach, but in the short-run, the real exchange rate and the interest rate can diverge from their long-run levels. The inclusion of these rigidities in the goods market would also ensure that monetary policy can influence the behaviour of the real variables in the system. Thus, exchange rate dynamics or overshooting can occur in any model, in which some markets do not adjust instantaneously.

Such a sticky price model adopts Keynesian features to the monetary approach and while it may be assumed that purchasing power parity (\(p_t = s_t p_t^\star\)) may be a good approximation in the long-run, it does not necessarily hold in the short-run. For example, there may be long-term contracts, imperfect information, a high cost of acquiring information, inertia in consumer habits, and other restrictions, which do not allow prices to change instantaneously. These features would provide a model of exchange rate determination, in which changes in the nominal money supply result in changes to the real money supply \(\left( \frac{M^s \uparrow}{\bar{P}} = \frac{M^s}{P} \uparrow \right)\), since prices are sticky:

\[\begin{eqnarray*} \frac{M^s \uparrow}{\bar{P}} \Rightarrow \frac{M^s}{P} \uparrow \Rightarrow D_{Bonds} \uparrow \Rightarrow P_{Bonds} \uparrow \Rightarrow i \downarrow \Rightarrow K_{outflow} \Rightarrow S_{S-R} \uparrow \uparrow\uparrow \Rightarrow X \uparrow \end{eqnarray*}\]

In the short run, since prices are sticky, a monetary expansion has a liquidity effect; thus, the interest rate falls, generating a capital outflow, which causes the currency to depreciate instantaneously and by an amount that is greater than the long-run depreciation. This is shown in Figure 2, where the expected rate of future appreciation precisely cancels out the interest differential. This is known as overshooting of the spot exchange rate and its dynamics will be explored in greater detail. The overshooting results are consistent with perfect foresight or the behaviour of rational agents.

Note that in this model the prices of goods are sticky in the short-run, while the prices of currencies are flexible. It is assumed that asset markets have exploited arbitrage opportunities, such that uncovered interest parity holds and expectations of exchange rate changes are anticipated by rational agents. However, the initial shocks that influence exchange rates are unanticipated. For example, an unanticipated increase in the domestic money supply in period \(t_1\) would temporarily lower the domestic interest rate (liquidity effect). Due to price stickiness in the goods market, the short-run equilibrium will be achieved through shifts in financial market prices. As prices of goods increase gradually toward the new equilibrium in period \(t_2\), the foreign exchange continuous repricing approaches its long-term equilibrium level. After a period of time, a new long-run equilibrium will be attained in the domestic money, currency exchange, and goods markets. As a result, the exchange rate will initially overreact (overshoot), due to a monetary shock. Over time, goods prices will eventually respond, allowing the foreign exchange rate to appreciate to reclaim some of the overreaction and the economy will reach its new long-run equilibrium in all markets in period \(t_2\). This behaviour is displayed in Figure 2.

Note: \(m_t\) = money supply, \(i_t\) = interest rate, \(y_t\) = real output (production), \(p_t\) = price level, and \(s_t\) = spot exchange rate. \(M^s \uparrow \Rightarrow (\bar{P}) \Rightarrow \frac{M^s}{P} \uparrow \Rightarrow D_{Bonds} \uparrow \Rightarrow P_{Bonds} \uparrow \Rightarrow i \downarrow \Rightarrow \text{capital outflows} \Rightarrow\) currency depreciates instantaneously more than it will in the long term.

The overshooting model can be presented with the following equations:

The money demand function,

\[\begin{eqnarray} m_t = \bar{p}_t + \alpha + \beta y_t - \gamma i_t + \varepsilon_{1,t} \tag{2.19} \end{eqnarray}\]

The uncovered interest parity,

\[\begin{eqnarray} i_t - i_t^\star = \Delta s_t^e = s_{t+1}^e - s_t \tag{2.20} \end{eqnarray}\]

The long-run PPP,

\[\begin{eqnarray} \bar{s}_t = \bar{p}_t - \bar{p}^\star_t \tag{2.21} \end{eqnarray}\]

The bars (i.e., \(\bar{p}\)) over the variables mean that the relationship holds in the long run.

The long-run monetarist exchange rate equation,

\[\begin{eqnarray} \bar{s}_t = \left( \bar{m}_t - \bar{m}^\star_t \right) - \beta \left( \bar{y}_t - \bar{y}^\star_t \right) + \gamma \left( \Delta \bar{p}^e_t - \bar{p}^{\star e}_t \right) + \varepsilon_t \tag{2.22} \end{eqnarray}\]

We could then assume that expectations are rational and the system is stable, where income growth is exogenous, with \(\mathbb{E}(g_y) = 0\), and that monetary growth follows a random walk. Thus, the relative money supply and, in the long-run, the relative price level and exchange rate, are all rationally expected to follow paths that increase at the current rate of relative money growth \((g_{m_t} - g_{m^\star_t}\) or \(\dot{m}_t - \dot{m}_t^\star)\).

Then, equation (2.22) becomes,

\[\begin{eqnarray} \bar{s}_t = \left( m_t - m^\star_t \right) - \beta \left( y_t - y_t^\star \right) + \gamma \left( g_{m_t} - g_{m^\star_t} \right) + \varepsilon_t \tag{2.23} \end{eqnarray}\]

In the short run, when the exchange rate deviates from its equilibrium path, it is expected to close that gap with a speed of adjustment of \(\Theta\). In the long run, when the exchange rate lies on its equilibrium path, it is expected to increase at \((g_{m_t} - g_{m^\star_t})\).

\[\begin{eqnarray} \Delta s_t^e = -\Theta \left( s_t - \bar{s}_t \right) + g_{m_t} - g_{m^\star_t} \tag{2.24} \end{eqnarray}\]

By combining (2.24) with (2.20), we obtain,

\[\begin{eqnarray} i_t - i_t^\star = -\Theta \left( s_t - \bar{s}_t \right) + g_{m_t} - g_{m^\star_t} \tag{2.25} \end{eqnarray}\]

and putting the growth of money equal to the expected inflation,

\[\begin{eqnarray} g_{m_t} - g_{m^\star_t} = \pi_t^{e} - \pi_t^{\star e} \tag{2.26} \end{eqnarray}\]

we have,

\[\begin{eqnarray} s_t - \bar{s}_t = - \frac{1}{\Theta} \left[ \left( i_t - \pi_t^{e} \right) - \left( i_t^\star - \pi_t^{\star e} \right) \right] \tag{2.27} \end{eqnarray}\]

Equation (2.27) shows that the gap between the exchange rate and its equilibrium value is proportional to the real interest rate differential. When a tight domestic monetary policy causes the interest differential to rise above its equilibrium level, a capital inflow causes the value of the domestic currency to rise (spot rate falls) proportionately above its equilibrium level.

Now, by combining equation (2.23), which represents the long-run monetary equilibrium path, with equation (2.27), representing the short-run overshooting effect, we can obtain a general monetary equation of exchange rate determination,

\[\begin{eqnarray} s_t = \bar{s}_t - \frac{1}{\Theta} \left[ \left( i_t - \pi_t^{e} \right) - \left( i_t^\star - \pi_t^{\star e} \right) \right] + \varepsilon_t \tag{2.28} \end{eqnarray}\]

and

\[\begin{eqnarray} s_t = \left( m_t - m^\star_t \right) - \beta \left( y_t - y_t^\star \right) + \gamma \left(g_{m_t} - g_{m^\star_t} \right) - \left[ \left( i_t - \pi_t^{e} \right) - \frac{1}{\Theta} \left( i_t^\star - \pi_t^{\star e} \right) \right] + \varepsilon_t \tag{2.29} \end{eqnarray}\]

Equation (2.29) is an expansion of the monetarist equation with the addition of the fourth variable, the real interest differential between the two countries. If the monetarist model is correct, the last variable must have a coefficient of zero, which means that the speed of adjustment (\(\Theta\)) is infinite. By considering that the level of the money supply, rather than the change in the money supply, is a random walk, the expected long-run inflation differential \((\pi_t^{e} - \pi_t^{\star e} )\) is zero.

Equation (2.29) becomes,

\[\begin{eqnarray} s_t = \left( m_t - m^\star_t \right) - \beta \left( y_t - y_t^\star \right) - \left( i_t - i_t^\star \right) + \varepsilon_t \tag{2.30} \end{eqnarray}\]

Equation (2.30) is the Dornbusch equation, which can be tested econometrically by estimating equation (2.29), where it is more likely that the variables will be stationary.

Note that we may also be interested in determining whether or not the domestic and foreign bonds are perfect substitutes. A violation of this assumption would imply that the interest differential will differ from the expected rate of currency depreciation. This difference may arise due to transaction costs, expectation errors, or a risk premium, which would be the case in most practical applications.

The correlation between current account deficits (\(CA_t\)) and exchange rates (\(s_t\)) has been undeniably strong (\(\rho_{CA,s} > 0\)). The current account developments over the last few decades have been largely dominated by imports of oil, and in the case of a number of small countries, the imports of industrial and manufacturing products. As the world oil trade is done in US dollars, a sharp increase in world oil prices raises the demand for the dollar at the expense of the other currencies (euro, yen, pound, etc.). On the other hand, some economists may argue that the huge US national debt, the Middle East crises, and the easy money policy of the Federal Reserve System following the Global Financial Crisis have depreciated the dollar.

When considering the relationship between the current account deficit and the exchange rate, the release of unexpected figures on the trade balance and the current account appear to have had large immediate “announcement effects” on the value of exchange rates. Such announcements relating to the current account reveal information about shifts in the long-run terms of trade. However, the important point is that only the unexpected component (\(CA^u\)) of the current account (\(CA = CA^e + CA^u\)) has a large effect; the expected component (\(CA^e\)) would have already been taken into account by the foreign exchange market:

\[\begin{eqnarray} CA_{t+1} = CA^e_{t+1} + CA^u_{t+1} \tag{2.31} \end{eqnarray}\]

where, \(CA_{t+1}\) = the actual current account balance, \(CA^e_{t+1}\) = the expected current account balance based on information today \(\left[ CA^e_{t+1} = \mathbb{E} \left( CA_{t+1} | I_t \right) \right]\), and \(CA^u_{t+1}\) = the unexpected part of the current account balance, the “surprise” or “news”, which equates to the the risky part of the \(CA_{t+1}\).

In addition, a current account surplus is a transfer of wealth from foreign residents to domestic residents (and a transfer of unemployment from the domestic economy to the foreign one). The increase in domestic wealth (\(W_t \uparrow\)) can appreciate the currency (\(S_t \downarrow\)).

- It can raise domestic expenditure by increasing domestic consumption:

\[\begin{eqnarray} C_t = f \left( \overset{+}{W_t} \right) \tag{2.32} \end{eqnarray}\]

where, \(C_t\) = consumption and \(W_t\) = domestic wealth.

Then, aggregate demand will increase, which will affect production and income. This higher income will increase the demand for money (\(M_t^d\)).

- It can raise the demand for domestic money directly if wealth enters the money demand function:

\[\begin{eqnarray} M_t^d = \alpha_0 + \alpha_1 W_t + \alpha_2 P_t - \alpha_3 i_t + \varepsilon_t \tag{2.33} \end{eqnarray}\]

where, \(M_t^d\) = demand for money, \(P_t\) = price level, \(i_t\) = nominal interest rate (opportunity cost of capital), and \(\varepsilon_t\) = the error term.

- If domestic bonds and foreign bonds are imperfect substitutes, domestic residents have a greater tendency to hold wealth in the form of domestic bonds; then, the increase in domestic wealth will raise the demand for domestic bonds:

\[\begin{eqnarray} B_t^d = f \left( \overset{+}{W_t} \right) \tag{2.34} \end{eqnarray}\]

where, \(B_t^d\) = demand for domestic bonds.

We assume that we have imperfect capital substitutability and there are no barriers segmenting international capital markets, it implies that we may introduce a risk premium (\(RP_t\)),

\[\begin{eqnarray} RP_t = fd_t - \mathbb{E} \left( s_t \right) = i_t - i_t^\star - \mathbb{E} \left( s_t \right) = \left(f_t - s_t \right) - \left( s_{t+1}^e - s_t \right) \tag{2.35} \end{eqnarray}\]

where, \(RP_t\) = risk premium, \(fd_t\) = forward discount, \(\mathbb{E}\left( s_t \right)\) = expected change in the spot exchange rate, \(i_t - i_t^\star\) = interest rate differential, and \(f_t\) = the natural logarithm of the forward exchange rate.

Therefore, investors allocate their bond portfolios between the two countries in proportions that are functions of the expected rates of return (\(i_t^e\) and \(i_t^{\star e}\)). The two assets are imperfect substitutes because there are differences between the two countries in liquidity, in tax rates, in default risk, in political risk, in exchange rate risk, and in other factors. We assume that there are perfect international bond markets and the two bonds differ, due to their currency denomination (i.e. one is in the domestic currency and the other is in a foreign currency).

Now in the presence of an economic shock that takes the form of a change in wealth, we would expect to observe a wealth effect that results in an increase in the demand for each financial asset, and a substitution effect, where the holding of high-return financial assets are substituted for the low-return alternative. Consequently, the exchange rate and interest rates have to adjust to ensure portfolio equilibrium. The portfolio balance approach states that the exchange rate and interest rates are determined simultaneously by the portfolio equilibrium conditions for asset holders in these two different countries.

A simple version of the portfolio balance model can be presented with the following equations:

Demand for money:

\[\begin{eqnarray} M_t^d = m \left( i_t , i_t^\star , W_t \right) \tag{2.36} \end{eqnarray}\]

Demand for domestic bonds:

\[\begin{eqnarray} B_t^d = b \left( i_t , i_t^\star , W_t \right) \tag{2.37} \end{eqnarray}\]

Demand for foreign bonds evaluated in the domestic currency:

\[\begin{eqnarray} S_t B_t^{\star d} = f \left( i_t , i_t^\star , W_t \right) \tag{2.38} \end{eqnarray}\]

The supply of these assets is given as follows: \(M_t^s\), \(B_t^s\), and \(B_t^{\star s}\), and we assume equilibria,

\[\begin{eqnarray} M_t^d = M_t^s = M_t \tag{2.39}\\ B_t^d = B_t^s = B_t \tag{2.40}\\ B_t^{\star d} = B_t^{\star s} = B_t^\star \tag{2.41} \end{eqnarray}\]

where, \(B_t^d\) = demand for bonds, \(B_t^s\) = supply of bonds, \(B_t\) = the equilibrium amount of bonds, and an asterisk (\(^\star\)) denotes the foreign variable.

The financial portfolio makes up the total wealth (\(W_t\)), which is equal to the sum of the three assets,

\[\begin{eqnarray} W_t = M_t + B_t + S_t B_t^\star \tag{2.42} \end{eqnarray}\]

At any point in time, the existing stocks of these assets are fixed, and the domestic interest rate (\(i_t\)) and exchange rate (\(S_t\)) must adjust so that the assets are willingly held by investors (maximization of their return). The stocks of financial assets change over time. When the budget deficit is increasing, the government issues bonds to finance it, which increases the supply of domestic government bonds (\(B_t\)). Autonomous growth of money supply (expansionary monetary policy) or monetization of the government debt (open market purchase) increases the stock of money (\(M_t\)). Current account surpluses increase the net domestic holdings of foreign(bonds) assets (\(B_t^\star\)).

Then, the exchange rate (\(S_t\)) of the portfolio balance model will be given from equation (2.38) and equation (2.42), as follows:

\[\begin{eqnarray} S_t = s \left( M_t , B_t , B_t^\star , i_t , i_t^\star \right) \tag{2.43} \end{eqnarray}\]

The foreign interest rate (\(i_t^\star\)) is determined by the foreign asset market,

\[\begin{eqnarray} i_t^\star = r \left( M_t^\star , B_t^\star \right) \tag{2.44} \end{eqnarray}\]

Substituting equation (2.44) and equation (2.43), we have,

\[\begin{eqnarray} S_t = s \left( \overset{+}{M_t} , \overset{+}{B_t} , \overset{+}{M_t^\star} , \overset{+}{B_t^\star} , \overset{+}{i_t} , \overset{+}{i_t^\star} \right) \tag{2.45} \end{eqnarray}\]

Equation (2.45) specifies the relationship between exchange rates, assets supplies, and interest rates (returns) in the two countries:

- An expansionary monetary policy, as an exogenous increase in money supply (\(M_t\)) means an increase in wealth. The wealth effect leads to excess demand for domestic and foreign bonds. With given foreign interest rate (\(\bar{i}^\star_t\)), excess demand for domestic bonds would raise their price, so the domestic interest rate will fall. The excess demand for foreign bonds will increase the demand for foreign currency (foreign currency will appreciate), leading to a depreciation of the domestic currency (spot rate will increase).
- An increase in domestic government bonds (\(B_t\)) will increase the domestic wealth and through a wealth effect, would increase the demand for foreign bonds and consequently, the demand for foreign currency will go up. This will lead to an appreciation of the foreign currency and a depreciation of the domestic currency. Also, an increase in domestic debt will increase the supply of bonds, which will reduce their price and increase the domestic interest rate. This higher domestic interest rate (\(i_t > i_t^\star\)) would make foreign bonds less attractive. If this substitution effect dominates the previous wealth effect, the domestic currency will appreciate, due to increase in investment on domestic bonds.
- An increase, now, in net holdings of foreign bonds (\(B_t^\star\)), induced by a current account surplus, increases the domestic wealth. This wealth effect will increase the demand for domestic assets, which will increase their prices and the interest rate will fall. This will depreciate the domestic currency (exchange rate will increase).

The monetary approach focuses only on a single asset (money). The portfolio balance approach deals with multi-assets, which integrates the analysis of the exchange rate behaviour with other financial assets (bonds,stocks, etc.). This second approach allows the current account imbalances (\(-CA = FA\)) to affect the exchange rate (where, \(CA\) = the current account and \(FA\) = the financial account). Thus, the portfolio balance model contains features provided by the monetary approach and the balance of payment approach. Residents of both countries hold assets issued by both countries. Domestic residents wish to hold a greater proportion of their wealth in domestic assets and foreign residents wish to hold a greater proportion in foreign assets (perfect local habitat). The current account will redistribute world wealth in such a way as to raise net world demand for the surplus country’s assets, thus, raising the price of its currency.

The efficient market hypothesis (EMH) in the financial literature has been developed by a number of influential authors and there appears to be consensus that financial markets are informationally efficient. This implies that one cannot consistently achieve returns in excess of average market returns on a risk-adjusted basis, given the information available at the time the investment is made. In this version of the efficient market hypothesis, all new information is quickly understood by market participants and becomes immediately incorporated into market prices. Thus, prices of financial assets provide signals for portfolio allocation and market efficiency is associated with the rationality of market expectations.

To examine market efficiency, we must determine whether market participants could systematically earn an excess profit. If we designate \(R_{t+1}\) as a series of asset returns next period and \(R_{t+1}^e\) as market expectations of these returns, the hypothesis suggest that we are not able to make systematic unexploited profits over a period of time. We could write such hypothesis as,

\[\begin{eqnarray} \mathbb{E} \left[ R_{t+1} - R_{t+1}^e | \Pi_t \right] = 0 \tag{3.1} \end{eqnarray}\]

where, \(R_{t+1}\) = the actual return next period, \(R_{t+1}^e\) = the expected return derived from forecasting it one period ahead, \(\mathbb{E}\) = is the expectations operator conditioned on the information set \(\Pi_t\) = very broad information available at the end of period \(t\).

Investors would then inspect the forecast errors (\(R_{t+1} - R_{t+1}^e = \varepsilon_{t+1}\)) to see whether there are unexploited patterns that may be used to improve their investment strategy. Thus, the systematic information will be exploited and the resulting error becomes “white noise”. To satisfy the efficiency condition, equation (3.1), an optimal forecast of asset prices is consistent with rational expectations behaviour.

In the foreign exchange markets, tests for the efficient markets hypothesis have been applied in the spot market and the forward market. Equation (3.1) can be used to express the spot exchange rate as follows,

\[\begin{eqnarray} \mathbb{E} \left[ s_{t+1} - s^e_{t+1} | \Pi_t \right] = 0 \tag{3.2} \end{eqnarray}\]

where, \(s_{t+1}\) = the natural logarithm of the spot exchange rate and \(s_{t+1}^e\) = the natural logarithm of the expected spot rate based on information available at time \(t\).

Equation (3.2) states that the expectation errors will be zero on average, so that no excess profits can be exploited in the foreign exchange markets. To test this hypothesis, the difficulty lies in the way that we form the optimal forecast value for which the most popular suggestions make use of a random-walk specification, the use of the forward rate (i.e. as in the unbiased forward rate hypothesis), a composite model that combines information from both of these sources, or various versions of the models that are incorporated under the asset market view for exchange rate determination.

In this lecture we discussed different theories for exchange rate determination before we briefly considered issues relating to the efficiency of the foreign exchange market. We started our discussion with a review of the balance of payments view, which focuses largely on tradable goods and services. Some of the models from the asset market were then introduced, which consider currencies as an asset class that are used to construct investment portfolios. Asset prices are influenced mostly by people’s willingness to hold the existing quantities of assets, which in turn depend on their expectations regarding the future worth of these assets. The asset market model of exchange rate determination states that the exchange rate between two currencies represents the price that equates the relative supplies of, and demand for, assets denominated in those currencies.

The world’s currency markets can be viewed as a huge asset market that are influenced by a large and ever-changing mix of current events, supply and demand factors, as well as information and expectations. This implies that both the price and risks that are associated with these assets are constantly shifting, since the supply and demand for any given currency, and thus its value, are not influenced by any single element, but rather by several. These elements generally fall into three categories: economic factors (fundamentals), political conditions (government and central bank interventions, public policies: fiscal, monetary, and trade policies, political stability, and uncertainty), and market psychology (expectations, information, and risk). For all these reasons, exchange rate determination is a difficult and dynamic process that needs continuous improvement.

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