International Finance Exchange Rate Economics: Asset Market Approach 1. Introduction During the Bretton Woods period the International Monetary System was organised in such a way that exchange rates were substantially pegged. The exchange rates among the currencies of the countries which had signed the Bretton Woods agreement could vary from their central parities by no more than 1%. Changes in the central parities were possible but infrequent as the agreement was interpreted strictly. The System was sustainable because for a long period most currencies were not convertible, and later capital controls were kept widespread and strict in most countries. In that period the international finance literature was dominated by two topics: external adjustment and international liquidity. Since exchange rates were fixed, economists were concerned with the conditions under which current account imbalances could be eliminated. A connected problem stemmed from the constraints on international capital flows: temporary external imbalances of single countries were difficult to finance because too little liquidity was available in the financial markets. In practice, exchange rates determination became an important issue only after the collapse of the Bretton Woods agreement. 1 With the passage to a system of floating exchange rates the literature turned to the determination of exchange rates. According to the traditional flows view, the equilibrium value of the exchange rate maintains the equilibrium of the Balance of Payments, i.e., it equilibrates the flows of imports and exports: in other words, the exchange rate is said to be the relative price of different national outputs. While this definition was substantially correct until strict capital controls were widespread among the industrialised countries, it was not longer applicable in a world of high capital mobility, which emerged after the demise of the Bretton Woods System. According to the asset market approach developed in the early seventies, instead, the exchange rate is the relative price of different national assets: under the assumption of perfect capital mobility, which rules out significant transaction costs, capital controls and generally any obstacle to capital movements, the exchange rate adjusts instantly to equilibrate the demand and supply for stocks of national assets. In other words, according to the new approach, the exchange rate will immediately move to clear the markets for national assets in response to changes in their demands or supplies. This means that all those factors which influence the desire of private investors to hold these assets will condition the exchange rate and should enter into its fundamental equation. From the point of view of financial investors the decision to hold domestic or foreign assets will depend on their expected returns. Therefore, in the determination of the exchange rate all factors which condition the expected values of these returns will be important. In particular, we will see that both monetary and real factors will be relevant in the determination of the demand and supply of domestic and foreign assets and will enter in the fundamental equation of the exchange rate. While all the asset market approach shares this definition of the exchange rate, there exists a wide range of alternative models. I will present a simple taxonomy of the various models of 1 The collapse of the Bretton Woods System was the consequence of the combination of political and economic factors. The economic factors were substantially the increased capital mobility and the accumulation of trade deficits on the part of the United States, which undermined the role of the US dollar as a reserve asset.
Asset Market Approach Perfect Capital Substitutability Monetary Approach Flexi-Price Monetarist Model Sticky-Price Overshooting Model Imperfect Capital Substitutability Portfolio Balance Approach Figura 1: A taxonomy of models of exchange rate determination the asset market approach: this taxonomy is based on some distinctive assumptions concerning real and financial aspects of the economy, which determine crucial dichotomies in exchange rate economics. A first crucial distinction concerns the substitutability of bonds denominated in different currencies in the portfolio holdings of private investors. The condition of perfect substitutability between domestic and foreign bonds implies that the composition of the investors portfolios is irrelevant as long as the expected returns of foreign and domestic bonds are equal when expressed in the same currency. 2 While this condition holds within the monetary approach, in models of the portfoliobalance approach domestic and foreign bonds are not perfectly substitute, in that investors have a preference towards assets denominated in the domestic currency. This preference is generally determined by several sources of risk, such as the risk of default, the volatility of exchange rates and the uncertainty on the fiscal treatment of foreign investors. The hypothesis of perfect substitutability has important implications for modelling exchange rates. In fact, according to the monetary approach domestic and foreign bonds are equivalent and can be considered as a unique asset. This means that if, simplifying, investors can hold in their portfolios only moneys and bonds, the equilibrium of the asset markets reduces to that of three markets: those for domestic and foreign moneys and that for international bonds. Then, we can appeal to Walras Law: as the equilibrium of the two money markets guaranties that of the bond market, we can exclude from the analysis both domestic and foreign bonds. This explains why we refer to this branch of the asset market approach as to the monetary approach: within its models the analysis of financial markets corresponds to that of the money markets. On the contrary, when the condition of perfect substitutability does not hold, models of exchange rate determination will consider a set of equilibrium conditions for all asset markets in line with the framework of Tobin. 3 2 Confusion should not be made between the condition of perfect capital mobility, which guaranties the continuous equilibrium of financial markets, and that of perfect substitutability, which concerns agents preferences towards the composition of their asset holdings. 3 See Tobin J., (1969) A General Equilibrium Approach to Monetary Theory, Journal of Money, Credit and Banking, 1, pp. 15-29.
Within the portfolio-balance approach investors are risk-averse and hold domestic and foreign assets in order to diversify the risk in their portfolios. Therefore, any capital movement, which changes the composition of domestic and foreign assets held by private investors, will be possible only if there is a change in the expected relative rate of returns of these assets, which compensates for the change in the risk they bear. In other words, according to the portfolio-balance effect foreign investors can be forced to hold a larger share of their wealth in domestic bonds, and hence to accept riskier portfolios, only if they obtain an increase in the expected rate of return on these assets through a devaluation of the domestic currency. A second important distinction between models of the asset market approach concerns goods markets. If goods prices are perfectly flexible an equilibrium condition known as purchasing power parity holds at all times. This condition characterises the class of monetarist models or flexible prices models within the monetary approach. On the contrary, within an important group of models prices are supposed to be sticky. This means that goods markets are not continuously in equilibrium and that the purchasing power parity holds only in the long-run. We will see this dichotomy generates different properties of the real exchange rates and real interest rates. In Figure 1 we have a graphical representation of our taxonomy. 2. Monetary Models Let us now consider in more details the monetary approach, discussing the formulation of its models of exchange rate determination. While there are several versions of the monetarist model, they all share four common elements: an equilibrium condition for the real exchange rate, known as the purchasing power parity (PPP), stable demand functions for domestic and foreign real money balances, the assumption of perfect substitutability, from which we derive a non-arbitrage condition for nominal interest rates and exchange rate expectations known as Fisher open, some treatment of exchange rate expectations, which are generally assumed to be rational. (i) While there is little doubt that the prices of commodities will always be the same when expressed in a common currency, within the monetarist framework the PPP is an equilibrium condition for the exchange rate. In the words of Frenkel (1976): The purchasing power doctrine (in its absolute version) states that the equilibrium exchange rate equals the ratio of domestic to foreign prices. 4 In logs the absolute version of the PPP can be expressed as follows: s t = p t p t, (1) where s indicates the spot exchange rate (units of domestic currency for one unit of the foreign currency), p the domestic price level, measured using the consumer price index, and the superscript a representative foreign country. This means that no movement in the real exchange rate is possible, a condition we know is continuously violated. 5 (ii) The core of the monetary approach is given by the equilibrium conditions for the money markets. While several versions have been considered in the literature, the basic element is that 4 According to the relative version of the PPP, the exchange rate depreciation equals the relative rate of inflation of domestic to foreign prices. Frenkel J.A., (1976) A Monetary Approach to the Exchange Rate: Doctrinal Aspects and Empirical Evidence, Scandinavian Journal of Economics, 78, pp. 200-08. 5 In fact, the real exchange rate in logs is: e t s t + p t p t.
the demands for real money balances are stable functions. Assuming identical specifications for domestic and foreign money demands, their most common formulations are as follows: m d t p t κy t λi t, (2) m d t p t κy t λi t, (3) where m d indicates the log of the demand for nominal money balances, y the log of the real income and i the nominal interest rate. Note that since real variables enter the specification of (2) and (3), the exchange rate is not a purely monetary phenomenon in that it is conditioned by real factors, such as the level of real income. 6 In equilibrium, the demand for money must equal its supply: m d t = m s t, m d t = m s t. (4) (iii) Since domestic and foreign bonds are perfect substitute, their expected rates of returns expressed in the same currency will be always equal, because arbitrage activity would immediately exploit and eliminate any wedge. This uncovered interest rate parity, known as Fisher open, states that the difference in the nominal interest rates of domestic and foreign bonds is equal to the expected rate of depreciation of the domestic currency: i t i t = s e t+1 s t, (5) where the superscript e indicates the expectation operator. 7 This equation suggests that the interest rate differential constitutes an unbiased estimator for the investors expectations of the exchange rate depreciation and brings about an important implication of the monetarist models: from the uncovered interest rate parity and the PPP we conclude that the domestic real interest rate is equal to the foreign one: r t = rt. (6) This is another implication which is generally violated. Indeed, equation (6) is a direct consequence of the assumption of perfectly flexible prices (1), 8 so the violation of the former is a direct consequence of the failure of the latter. (iv) From the PPP and the equilibrium conditions of the money markets we can derive the following relationship for the spot rate: s t = m t κy t + λ(i t i t ), where m = m m and y = y y. This indicates that, given the values for the foreign countries of m y and i, the domestic currency will depreciate if there is an expansion in the monetary base or an increase in the nominal interest rate and will appreciate if the domestic real income augments. Notice that general opinion is that an increase in the interest rate should be accompanied with an appreciation of the exchange rate, since higher returns on domestic assets should make the domestic currency more attractive. Although, in the monetarist model an increase of i is a consequence of higher inflation expectations. This make the domestic currency less attractive: the reduction of the demand for domestic money balances forces a devaluation of the currency. 6 Frenkel (1976) discusses a model in which only the expected rate of inflation enters among the determinants of the money demand. Its simpler formulation is reasonable when the economy is locked-in an hyperinflation. 7 For equation (5) to be a precise condition, the interest rates should be interpreted as the continuously compounded interest rates on the domestic and foreign bonds. 8 Substituting the PPP in the Fisher open, and considering that i t = rt + πe t, where πe t is the expected inflation rate, one can check that the domestic real interest rate is equal to the foreign one.
Substituting in this equation the Fisher open we obtain the final equilibrium condition for the spot rate: s t = m t κy t + λ(s e t+1 s t). (7) This equation clearly shows the centrality of the expectations on the future values of the spot rate for the determination of its current value. To solve this equilibrium condition, rational expectations are called for, so by recursive substitution we can write that: s t = 1 1 + λ γ j E[m t+j Ω t ] j=0 κ 1 + λ γ j E[y Ω t+j t ], (8) j=0 where γ = λ/(1 + λ) and Ω t is the investors information set at time t. Therefore, the current value of the spot rate will depend on the expectations of all future values of the relative money supply and the relative real income. These expectations will on turn depend on the underlying stochastic processes followed by m and y. Assuming these are stable processes, we can derive a closed form for the exchange rate. Bilson (1978) and Mussa (1976) discuss several examples, distinguishing between anticipated and unanticipated monetary shocks and between permanent and transitory changes in the real income. We consider here just a simple case. 9 Let us assume that for all t m t = y t = 0, and for all t y t = 0, while the domestic money supply respects the following stochastic process: m t = m + u t, with u t = ρu t 1 + ɛ t, where 0 ρ < 1 and ɛ t is a white noise process. Then, it is immediate to see that: s t = m + 1 1 + λ γ j E[u t+j Ω t ]. j=0 Since E[u t+j Ω t ] = ρ j u t, where u t = m t m, we conclude that: s t = m + u t 1 + λ(1 ρ). Thus, the spot rate will depreciate as a consequence of a positive monetary shock, ɛ t > 0. Nevertheless, since the increase in the money supply is only temporary, investors expect the spot rate to reappreciate in future. In fact the forward rate is: f t = E[s t+1 Ω t ] = m + ρu t 1 + λ(1 ρ). This reduces the initial depreciation of the domestic currency (see equation (7)), because it induces investors to hold larger domestic money balances, determining a phenomenon of undershooting of the exchange rate. 3. Sticky-Price Models In the seventies, the volatility of the exchange rates seemed to exceed that of the underlying real and monetary variables that entered their fundamental equation. This continuous overshooting of 9 Mussa M., (1976) The Exchange Rate, the Balance of Payments, and Monetary and Fiscal Policy Under a Regime of Controlled Floating, Scandinavian Journal of Economics, pp. 229-48.
exchange rates can be replicated within the monetarist model assuming particular specifications of the demand for money function and the underlying processes governing the fundamental variables. Nevertheless, this phenomenon was also connected to the violation of the PPP. In a model suggested by Dornbusch (1976), in which the PPP is abandoned while the hypothesis of perfect substitutability is retained, this phenomenon of overshooting is explained through the different speed of adjustment of the money and the goods markets. In his classical model, Dornbusch retains the hypothesis of perfect capital substitutability. This means that equation (5) withholds. Since the model is presented in continuous time, the uncovered interest rate parity is now expressed as follows: i i = x ds t dt, (9) where x is the instantaneous rate of depreciation of the domestic currency. 10 Dornbusch also preserves the same equilibrium condition for the demand for real money balances: m p = κy λi. (10) One of his central points is that expectations of exchange rate devaluation are regressive. In fact, the exchange rate tends to a long-run equilibrium level, s: x = θ( s s), (11) where θ is a parameter which guarantees the rationality of the investors expectations. We can insert (11) in the Fisher open and substitute the interest rate in equation (10) to obtain the following equilibrium condition: p m = κy + λi + λθ( s s). (12) Assuming that in the long-run the exchange rate is equal to its equilibrium value, s, we can calculate the corresponding price level: p = m + (λi κy). (13) Substituting this expression in equation (12) we obtain a useful formulation for the equilibrium condition of the money market involving the exchange rate and the price level: s = s 1 (p p). (14) λθ To determine the spot rate we now have to turn to the goods market. Here comes the second crucial point of Dornbusch s model: prices are sticky, in that an excessive demand for goods is not immediately eliminated through changes in their prices. The inflation rate, ṗ, is assumed to respect the following equation: ṗ = ν(d y), where d, the log of the demand for domestic output, depends on several factors, including public spending, the relative price of domestic goods, the real income and the interest rate. The demand for domestic output is: d = u + δ(s p) + φy σi, 10 For simplicity we drop the time subscript in the presentation of this model.
p p M E G... Q G M s s Figura 2: Equilibrium in the goods and money markets where u represents a shift parameter. It follows that: ṗ = ν[u + δ(s p) + (φ 1)y σi]. (15) Under the assumption that in the long-run ṗ = 0 and i = i, we obtain an expression for the long-run equilibrium level of the spot rate: s = p + 1 δ [σi + (1 φ)y u]. (16) Finally, reconsidering the Fisher open and the regressive expectations, i i = θ( s s) and inserting the expression for the long-run spot rate in equation (15) we obtain a final expression for the inflation rate: ṗ = µ(p p), (17) where µ = ν (δ + σθ + δλθ). λθ In Figure 2 we consider the adjustment process to the long-run equilibrium. The MM schedule corresponds to the equilibrium of the money market, given by equation (14), while the GG schedule represents the equilibrium of the goods market, ṗ = 0. The latter is obtained setting ṗ = 0 in equation (15), using the Fisher open and equation (16). 11 While the money market is always in equilibrium, so that we are always on a point on the MM, the condition ṗ = 0 is satisfied only in the long-run. Nevertheless, the dynamics of the price level conditions that of the spot rate. In effect, starting from a point Q we move towards the longrun equilibrium E ( s, p) along the schedule MM: in Q there is an excess demand for national goods which pushes up the price level; as this augments, the demand for money increases and consequently the domestic currency appreciates until both markets settle in E. 12 11 One can easely show that: ṗ = ν[δ(s s) (δ + σ )(p p)]. λ It is then obvious that the schedule ṗ = 0 is flatter than the 45 0 diagonal. 12 From equations (15) and (16) we can derive the simple dynamic system: ṗ = ν[δ(s s) (δ + σ )(p p)], λ ṡ = 1 (p p). λ Then, it is trivial to check that E is a stable equilibrium and that MM is the corresponding saddle path.
p p 1 p 0 M G G M E Q G E M G M... s 0 s 1 s 1 s Figura 3: Monetary expansion and exchange rate overshooting We can describe more precisely the dynamics of s and p along the schedule MM. In fact, solving equation (17) we have: p(t) = p + (p(0) p) exp( µt). Consequently, the dynamics of the exchange rate is: s(t) = s + (s(0) s) exp( µt). In conclusion, we need to check that exchange rate expectations are rational, because otherwise we do not have a consistent equilibrium. Since the model is non-stochastic, this condition corresponds to that of perfect foresight. From the dynamics of s we know that its rate of depreciation is given by µ, while the expected rate of depreciation is θ; then investors are rational if µ = θ. Since µ depends on θ and other parameters, this condition permits determining a consistent value for θ. We can now employ this model to show how a phenomenon of overshooting can emerge. Let us assume there is a monetary expansion at some moment in time, t. Until then all the fundamental variables, m, y, u and i, are kept constant and the exchange rate and the price level are at their long-run equilibrium values. In t there is a permanent increase in m. From the definition of the long-run equilibrium value of the price level and the spot rate, you can see that in the long-run there will be an equal increase of p and s: since the money expansion does not condition the output level, in the long-run a shift in the money supply will just augment the domestic prices and devalue the domestic currency. In the short-run the effect of the monetary expansion is more complex: since the goods market does not adjust immediately, the price level will not reach the new equilibrium level p 1 directly. p will move towards p 1 at the exponential rate µ. On the other hand, the money market is always in equilibrium: the exchange rate will adjust immediately to equate the demand and supply of money balances. Since at time t we have a positive shift in the money supply, given the price level, a new equilibrium in the money market can be achieved through a depreciation of the domestic currency. In effect, given the shift in m, and hence in p and s, the schedule MM moves to MM. As it is clear from Figure 3 the initial depreciation is greater than the final one, as s 1 exceeds s 1. The economic intuition of this overshooting of the exchange rate is that the monetary expansion determines a reduction in the interest rate, given that the price level initially does not move. As the foreign interest rate is constant, the uncovered interest rate parity holds if there are expectations of an appreciation of the domestic currency. This implies that initially the spot rate overshoots the new long-run equilibrium level.
The degree of overshooting of the exchange rate will depend on the semi-elasticity of demand for money to the interest rate, λ, and the coefficient of the regressive expectations, θ. Using equation (12) and the condition d s = dm = d p, you can show that the initial shift in the spot rate is: ds dm = 1 + 1 λθ. Thus, a large λ implies that the monetary expansion will have a small impact on i and hence s. A similar argument applies to θ. 13 After the initial jump, s and p move along the schedule MM. Since the price level moves towards p 1, the real money balances reduce and the interest rate moves back to the equilibrium value i. Simultaneously, the exchange rate appreciates consistently to the investors expectations. Finally the dynamic system settles in the new equilibrium E. 4. Portfolio-Balance Models Within the portfolio-balance approach the assumption of perfect substitutability is abandoned and equilibrium conditions for all asset markets have to be considered. We simplify and consider a single country in which investors can hold only three assets: domestic money, domestic and foreign bonds. The markets for these assets must be in equilibrium at all times, since the condition of perfect capital mobility withholds. The supplies of money, M, domestic bonds, B, and foreign bonds, F, are constant in the short-run, while their demands will depend on their expected returns and the total wealth of the domestic investors. While money does not yield any returns, domestic and foreign bonds pay respectively an interest i and i. The interest rate i is determined on international markets; for simplicity we assume it cannot be influenced by a single country and will be considered constant. On the contrary, i can change: even if exchange rates expectations are static, i can vary from i because domestic and foreign assets are not perfect substitute. In fact, in this case domestic bonds pay a risk premium, so the uncovered interest rate becomes: i = i + x + ρ, (18) where ρ is a risk premium on the domestic currency, that changes with the composition of the investors portfolios. We can assume the demands for money, domestic bonds and foreign bonds depend on these values (i,i, W) and write the following equilibrium conditions: where S = e s and W, the total wealth of domestic investors, is: M s = M d f M (i, i )W, (19) B s = B d f B (i, i )W, (20) SF s = SF d f F (i, i )W. (21) W B + M + SF, since F is measured in foreign currency. As the spot rate determines the investors wealth, any change in s will condition the demands for the three assets. The derivatives of the functions f M, f B
s F B s 0 E M... M F B i 0 i Figura 4: Exchange rate and interest rate in equilibrium and f F are intuitive: the demand for money is decreasing in both i and i ; while that for domestic bonds is increasing in i and decreasing in i ; the opposite is true for the demand for foreign bonds. In Figure 4 we present the schedules corresponding to these three equilibrium conditions in the space (i, s), considering the derivatives of the functions f M, f B and f F and the definition of total wealth. An increase in the spot rate augments the total wealth and hence the demand for money and domestic bonds. Given that the demand for money is decreasing in i, we have the positive slope of the schedule MM, which indicates the equilibrium of the money market. On the other hand, to requilibrate the market for domestic bonds a reduction in the interest rate will be necessary: this gives the negative slope of BB. An increase in the interest rate determines a reduction of the demand for foreign bonds and consequently of the spot rate. The schedule FF is flatter since the sensitiveness of the demand for domestic bonds is greater than that for foreign bonds. The intersection of the three schedules gives the equilibrium values of s and i in the short-run, E. Notice that by Walras s law, the equilibrium of the three markets is guaranteed if the markets for domestic and foreign bonds are in equilibrium, so we can just analyse the schedules FF and BB. These schedules move according to shifts in the supply of domestic or foreign bonds. In particular, consider that the exchange rate, the international interest rate, and the quantity of foreign bonds held by domestic investors determine the current account Z, which corresponds to the net accumulation of foreign bonds on the part of domestic investors. The current account is the sum of the trade balance and the net income from foreign bonds; therefore: Z df dt = NX(s p) + i F, where the trade balance, NX, is assumed to be an increasing function of the real exchange rate, (s p) (p = 0). If there is an imbalance in the current account, Z = 0, there will be a change in the quantity of foreign bonds held by domestic investors and hence the exchange rate will move. In particular, let us assume that for an initial value s 0, Z is positive. Investors, who hold an excessive quantity of foreign bonds given s and i, will try to sell them, forcing a reduction in the exchange rate. This corresponds to a shift on the left of FF in Figure 5. If the appreciation of the domestic currency is 13 The overshooting clearly depends on the stickiness of the goods prices. Nevertheless, the constancy of the domestic output is crucial as well for this result. If y moves in the short-run the overshooting of the exchange rate may not emerge. See Dornbusch (1976) for details.
s F B B F E E B F B F i Figura 5: Exchange rate and accumulation of foreign bonds equal to the increase in the stock of foreign bonds, there will not be a wealth effect, so W does not vary. The schedule BB will move to BB and the domestic interest rate will not change. In any case, effects of a increase in F on i are possible if the total wealth varies. In other words, because of the portfolio-balance effect, the equilibrium value of the exchange rate will vary as long as there is a deficit or a surplus in the current account. This introduces another question: Under which conditions the exchange rate will reach a long-run equilibrium when Z = 0? A first answer is relatively simple: The exchange rate will vary until the imbalance in the current account is eliminated. Anyway, this may not occur. In fact, if for Z > 0 the consequent appreciation of the domestic currency does not bring about a worsening of the current account, s keeps on decreasing. For the dynamics system to be stable we need a reduction in the current account surplus when the domestic currency appreciates. This implies the following two conditions: NX NX > 0, (22) s dḟ df NX s F + i < 0, (23) where s F, the derivative of the exchange rate with respect to F, is negative. The first equation represents the Marshall-Lerner condition, while the second is the actual stability condition. Assuming the stability conditions are satisfied, the exchange rate will always converge to a longrun equilibrium. In the case there is an initial surplus in the current account, the exchange rate declines along the convergence path, while the surplus Z progressively reduces and finally disappears when the long-run equilibrium s is reached. Along this convergence path foreign bonds accumulate in the domestic investors portfolios and hence in correspondence of s there must be a trade deficit. This also means that the long-run equilibrium level of the exchange rate is path dependent: in fact, the new s is different from the value of the exchange rate that would have assured the balance of the current account at the beginning of the adjustment process. 14 14 To understand this point a different situation can be considered. Suppose that at time t = 0 Z = 0. This means s 0 = s 0. Now suppose the central bank sells foreign bonds to domestic investors, determining an increase in F from F 0 to F 1 and a current account surplus. The adjustment process to a new equilibrium will start. When it terminates the quantity of foreign bonds held by domestic investors reaches the value F 2 > F 1. Thus, the new long-run exchange rate s 2 is different from the value of s such that: Z = NX(s p) + i F 1 = 0.
p 1 s 1 s, p p 0 = 1 s 0 = 1. t = 0 t = 1 t Figura 6: Adjustment process and monetary expansion To understand the implication of the portfolio-balance effect for the exchange rate consider a monetary expansion similar to that discussed within Dornbusch s model. As in his model we assume the domestic output is given and prices are sticky: when the money supply expands the new equilibrium value for the price level is not reached immediately. In any case, in the longrun the increase in the goods prices is proportional to the increase in the money supply. The convergence path of the price level to the new long run equilbrium level is exponential as in Dornbusch s model and is described in Figure 6. Suppose at time t = 0, immediately before the monetary expansion, the asset markets are settled in a long-run equilibrium, ( s 0, p 0 ). The increase in the money supply is carried out through an open market operation. This implies a shortfall in the quantity of domestic bonds held by private investors. As a consequence, domestic bonds become more expensive and the interest rate declines. Simultaneously, for s given, the demand for foreign bonds increases. This produces a devaluation of the domestic currency. 15 The exchange rate will overshoot the new long-run equilibrium s. In fact, since prices are sticky the initial devaluation produces a current account surplus. This means that domestic investors start accumulating foreign bonds and the exchange rate declines. As in the sticky-price model we have an adjustment path in which goods prices increase while the domestic currency appreciates. Nevertheless, while in Dornbusch s model this phenomenon is the effect of the combination of sticky prices with rational expectations and the Fisher open, here the Fisher open does not hold and expectations are not considered (in effect exchange rate expectations are static). The overshooting phenomenon is now a consequence of the portfolio-balance effect. In fact, at time t = 1 the exchange rate equates the price level. This value would correspond to the new long-run equilibrium within Dornbusch s model, while here the adjustment process is not complete: since the total quantity of foreign bonds is now larger than the initial value, the balance of the current account can be reached only if there is a trade deficit, so the appreciation of the domestic currency carries on until Z = 0. It is important to stress this point: the main difference with Dornbusch s model is the pathdependence. If the condition of perfect substitutability holds, a monetary contraction that returned M to its initial level would lead the exchange rate and the price level to their original long-run equilibrium values. This is not the case in the present context, since the accumulation 15 When M augments we have a shift of MM and BB on the left in Figure 4.
s P Z A E A P F Z Figura 7: Dynamic system for exchange rate and international assets (de-accumulation) of foreign bonds changes the value of the spot rate that maintains the balance of the current account. 5. Application So far we have discussed exchange rate determination for purely theoretical reasons. However, models of the asset market approach should be used to explain real facts, that is events experienced on international markets. An interesting example of the application of the models discussed so far is the analysis of the German reunification in 1989. We now discuss the effects of the German reunification on interest rates and currency values and provide an explanation of their movements in the period 1989-92. 16 During 1987-88 the German interest rates were 2-3 percentage points below the US rates. In 1989 the long-term interest rates started augmenting in both countries. German interest rates moved above the US rates and reached a peak in 1990. Subsequently, their trend reversed, but with German rates still above the US ones. In the same period, the German current account moved from a surplus of nearly 5% of GDP in 1989 to a small deficit in 1991. The German DM appreciated from late 1989 to early 1991 and then reversed in 1992. We can try to explain these movements using the portfolio-balance models discussed in the previous section. Anyway, some initial qualifications are necessary. Here we consider a two country model in which the home country corresponds to Europe or Germany and the foreign country represents United States. This means that the foreign interest rate, i, will not be fixed as it can be influenced by the home country variables. Furthermore, exchange rate expectations will be rational. 17 Consider Figure 7. In this Figure we represent two equilibrium schedules for the exchange rate and the net assets credit of the home country to the foreign one. The schedule ZZ is the loci of points in the space (s, F) for which there is a balance of the current account, Z = 0. The slope of ZZ is negative as the stability conditions (22) and (23) are met. 16 See Branson W, (1994), High World Interest Rates, in The International Monetary System, (eds) Kenen, Papadia and Saccomanni, CUP, Cambridge. 17 In the earlier discussion of the portfolio-balance effect we simplified in assuming static expectations.
s A P Z P E A E 1 A A P P F Z Figura 8: Unanticipated fiscal expansion in Europe The schedule AA is the loci of points for which the asset markets are in equilibrium, so that the exchange rate does not move, ds/dt = 0: it represents a reduced form of the equations (19), (20) and (21) when M, B are given. As we have already discussed, an increase in the quantity of foreign bonds held by domestic investors forces an appreciation of the domestic currency. This explains the negative slope. A reduction in the quantity of foreign bonds in the domestic investors portfolios brings about an increase in their prices. Hence the foreign interest rate, i, decreases and the domestic one, i, augments. An opposite substitution effect in the two countries will increase saving in Europe and decrease it in the United States. Given the fiscal deficits in the two countries, the European current account shall improve. Notice, in fact, that if f g ( f g ) and sa (sa ) are respectively the fiscal deficit and the level of private saving in the home (foreign) country, we have that: Z = sa f g = f g sa. (24) This improvement in Z will force a large devaluation, greater than that necessary to balance the current account, explaining why the schedule AA is steeper than the ZZ. The intersection of the schedules ZZ and AA gives a long-run equilibrium for the exchange rate and the net external position of the home country. To show that this equilibrium is stable consider the dynamics of F and s. Below the ZZ the current account is in deficit and F decreases; above the ZZ the current account is in surplus and F accumulates. Simultaneously, above the AA the exchange rate moves upward; the opposite applies below the AA. To explain this consider what happens when the exchange rate is above the AA. The first effect is an improvement of the current account. Through equation (24) you can see that this augments domestic saving, while reducing the foreign one. This is possible only if the interest rate differential, i i, increases inducing expectations of devaluation of the home currency through the modified uncovered rate parity (18). This means that, under the hypotheses of rational expectations, the exchange rate will devalues even more. In this way a graphical analysis of the dynamic system shows that there is a unique saddle path, PP, into the long-run equilibrium E. All other paths are speculative bubbles which can be ruled out at the outset, since they lead to unfeasible values of s or F. Let us see what happens when an unanticipated fiscal expansion in Europe takes place. Assuming that the greater fiscal deficit is financed with new bonds, domestic investors are forced to
s P Z A P E A 1 A 0 E P A F Z P Figura 9: Anticipated fiscal expansion in Europe hold a larger quantity of domestic bonds, B, for an higher interest rate: the schedule BB moves upward in Figure 4. The increase in the domestic interest rate reduces the demand for foreign assets, appreciating the domestic currency: 18 in Figure 7 there is a shift of the schedule AA to AA. The fiscal expansion is immediately accompanied by an appreciation of the domestic currency, since s moves on the new saddle path, PP. The jump of the exchange rate creates a current account deficit, while, the interest rate differential, i i, widens. Hence, the exchange rate and the net external position move long a new saddle path: the former depreciates until it reaches an higher long-run equilibrium value, while the latter de-accumulates. A different dynamics will emerge if the fiscal expansion is announced or anticipated by private investors. This seems to be the case for the German reunification, when its costs became clear nearly immediately to investors. Then, assume investors realise at time t = 0 that a credible fiscal expansion will take place at time t = 1. In practice investors know that in Figure 9 there will be a shift of the schedule AA to AA at time t = 1. The effect of the anticipation is an immediate jump of the exchange rate on a bubble path. This bubble path is selected in such a way that at the time of the fiscal expansion s and F will lie on the new saddle path PP. The described dynamics rules out any possibility of arbitrage. Let us assume in fact that until time t = 1 there is no change in the exchange rate and that this jumps on the new saddle path when the fiscal expansion takes place. Since this jump is fully anticipated speculators have a chance to gain profits by shorting the foreign currency just before the jump. This means that arbitrage activity will force an appreciation of the domestic currency well before the fiscal expansion. In effect in Germany, the DM appreciated and the interest rate differential widened before the reunification forced a large fiscal deficit. 6. Empirical Evidence From the models of the asset market approach we can derive closed form equations of exchange rate determination. In these equations the spot rate appears on the left hand side, while among regressors several monetary and real variables will be listed. The empirical fit of these models has 18 We disregard any significant wealth effect which would increase the demand for foreign bonds moving the FF on the right.
never been impressive as suggested by Frankel (1984). 19 In particular, coefficients of regressors were incorrectly signed with respect to theoretical prescriptions and generally of insignificant magnitude, coefficients of multiple correlation were also low for most of a series of empirical investigations of the asset market approach to the exchange rate. In any case, it is a series of papers by Meese and Rogoff (1983) which completely devastated the theory. 20 In their analysis Meese and Rogoff showed that all popular models of exchange rate determination, including those of Frenkel (1976), Bilson (1978), Dornbusch (1976), were of no use in predicting exchange rates outside the estimation samples. The strategy used by Meese and Rogoff is simple. Closed form equations for the various models are estimated over a fitting period using OLS, Cochrane-Orcutt and instrumental variables techniques. Then, the estimated models are used to predict the values of the exchange rate over a forecasting period. Forecasts are derived for various horizons, including one, three, six and twelve months, using rolling regressions. Despite in theory actual realised values of the future regressors should not be used, Meese and Rogoff employ them to calculate the exchange rate predictions. This should eliminate any bias due to errors in the prediction of the explanatory variables and support the theoretical models. Meese and Rogoff compare the exchange rate forecasts obtained from these regressions with those derived from a simple random walk. Forecasting errors from the random walk model are smaller than those of the asset market approach on average. This quite general result holds even if the estimates of the coefficients of the various models are replaced by entire grids of possible values. Furthermore, the random walk model performs better than simple univariate models, such as autoregressive processes and so on. All this evidence in favour of the random walk model is consistent with the condition of efficiency of financial markets, but the incapability of structural models to explain movements in exchange rate challenges the validity of the asset market approach. To conclude we should stress that unsatisfactory econometric results of the structural models of exchange rate determination are not an entire surprise. There are, in fact, several reasons why their empirical fit can be poor. For instance, in the case of the German reunification an important factor is the anticipation of the fiscal expansion. In that case the movement in the value of the DM anticipated its cause. In other words, it is practically impossible to treat news properly within these structural models: to endogenise them econometricians should be able to anticipate any shift in the expectations of investors of future values of the explanatory variables. Likewise, it is difficult to pin down any shift in the investors preferences. These external shocks invest in particular the demands for assets and money. For instance, some economists claimed that part of the increase in the interest rates in the United States in the early eighties was due to an exogenous shift in the demand for money. These exogenous movements may be frequent and are difficult to treat when estimating structural models of the exchange rates. In synthesis, it seems impossible to use the asset market approach to predict future movements of the exchange rates, but we can explain ex-post particular events involving exchange rates. 19 Frankel J.A., (1984) Monetary and Portfolio-Balance Models of Exchange Rate Determination, in Exchange Rate Theory and Practice, edited by J.F.O. Bilson and R.C. Marston, University of Chicago Press, Chicago. 20 Meese R.A., and K. Rogoff (1983) Empirical Exchange Rate Models of the Seventies: Do They Fit Out of the Sample?, Journal of International Economics, 14, pp. 3-24.