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Existing Theories of Exchange Rate Determination
We have seen that existing studies have produced a number of different estimates of the exchange rate of the renminbi. The reason behind the difference is that different theories, data and econometric methods are used. It is clear that not all the theories that are actually used are suitable for forecasting the movement of exchange rate. Some may be better than others. Thus, it is very important for researchers who study exchange rates to choose or create a better model with micro foundations for an empirical study. In this Chapter, we investigate existing theories, their preconditions, implications and advantages and disadvantages, which will be helpful to the modeling efforts to be made in the next part.
The exchange rate theories investigated in this part can be classified into three kinds: partial equilibrium models, general equilibrium models and disequilibrium or hybrid models. Partial equilibrium models include relative PPP and absolute PPP, which only consider the goods market; and covered interest rate parity (CIRP) and uncovered interest rate parity (UCIRP), which only consider the assets market, and the external equilibrium model, which states that the exchange rate is determined by the balance of payments. General exchange rate equilibrium models include the Mundell- Fleming model, which deals with the equilibrium of the goods market, money market and balance of payments, but lacks micro-foundations to some extent; the Balassa-Samuelson model, which is built on the maximization of firms profit; the Redux model, which was developed by Obestfeld and Rogoff, and the PTM (Pricing to Market) model, created on the maximization of consumer’s utility; A simple monetary model with price flexibility and the Dornbusch model (or Mundell-Fleming-Dornbusch model), are actually obtained by combining the monetary equilibrium with the adjustment of price and the adjustment of output toward their long run equilibrium, and can be called hybrids of monetary equilibrium with PPP or UCIRP. The balance of payments is covered in this investigation since many studies regards it as a foundation of equilibrium exchange rate determination.
3.1 Purchasing Power Parity
The starting point of exchange rate theory is purchasing power parity (PPP), which is also called the inflation theory of exchange rates. PPP can be traced back to sixteen-century Spain and early seventeencentury England, but Swedish economist Cassel (1918) was the first to name the theory PPP. Cassel once argued that without it, there would be no meaningful way to discuss over-or-under valuation of a currency.
Under this model, let i P and * i P denote, respectively, the price level of good i in the home currency and foreign currency. Letter “ S ” denotes the nominal exchange rate that expresses the price in foreign currency in terms of the domestic currency. According to the “law of one price,” the price of one good should be equal at home and abroad, say, * i i SP P = . If the prices of each good are equalized between the two countries and if the goods baskets and their weights in the two countries are the same, then, then absolute PPP holds: * SP P = (3.1)
Absolute PPP theory was first presented to deal with the price relationship of goods with the value of different currencies. The theory requires very strong preconditions. Generally, Absolute PPP holds in an integrated, competitive product market with the implicit assumption of a risk-neutral world, in which the goods can be traded freely without transportation costs, tariffs, export quotas, and so on. However, it is unrealistic in a real society to assume that no costs are needed to transport goods from one place to another. In the real world, each economy produces and consumes tens of thousands of commodities and services, many of which have different prices from country to country because of transport costs, tariffs, and other trade barriers.
Absolute PPP is generally viewed as a condition of goods market equilibrium. Under absolute PPP, both the home and foreign market are integrated into a single market. Since it does not deal with money markets and the balance of international payments, we consider it to be only a partial equilibrium theory, not the general one. Perhaps because absolute PPP require many strong impractical preconditions, it fails in explaining practical phenomenon, and signs of large persistent deviations from Absolute PPP have been documented.11
Although absolute PPP may contradict practical data, this does not imply market failure. It may simply reflect the inability, without expenses, to instantaneously move goods from one place to another. Thus, a more general version of PPP, called the relative purchasing power parity, was introduced to describe the relationship of prices with the exchange rate in different economies. Generally, relative PPP can be derived by assuming that transaction costs are proportionately related to price level. For example, assuming that a commodity’s home price at time t is t P , and the transport cost is t kP , where k is constant, the foreign price of the commodity is equal to the price of foreign currency multiplied by the exchange rate t P k) 1 ( + in terms of home currency, that is
By taking the logarithm and then carrying out a differential operation on each side of equation (3.2) with regard to time t, we get relative PPP expressed by
(3.3) states that the relative change of the exchange rate equals the difference of the inflation rate between the two economies.
can be reexpressedas
(3.3) Can also be derived by taking the logarithm and differential operation directly from (3.1). If the real exchange rate is denoted by the ratio of national price levels,
if absolute PPP holds, the, the real exchange rate equals one. If relative PPP holds, the real exchange rate should be a constant, but is not necessarily equal to one. If an economy adopts a fixed exchange rate regime, the relative PPP model forecasts that the home prices change at the same speed as foreign prices. Conversely, if the inflation rates in the two economies are the same, according to relative PPP, the exchange rate should be constant. Mundell has in fact taken the fact that the PRC and the US experience the same inflation rate as a rationale for supporting a renminbi peg to the dollar.
It is clear that absolute PPP is built on the assumption of a perfect market setting with high information efficiency in both foreign exchange and goods markets. Allowing for transport costs, tariffs and trade barriers, absolute PPP may not hold. Many empirical studies show that neither absolute nor relative PPP holds in the short run, since the adjustment is a time-consuming process. Though controversies over PPP remain, it seems that only relative PPP can hold in the long run (Pippenger, 1993). This may explain why PPP was thought by some to be a long-run equilibrium condition, instead of a casual relationship (Pongsak Hoontrakul, 1999). Relative PPP implies that the real exchange rate is constant. However, this theory itself does not explain why the real exchange rate should remain constant over a particular period of time.
Empirically, evidence against PPP may be caused by inaccuracy of the price index measuring the inflation rate for the countries studied (Frenkle, 1978; Genberg, 1978; and Thurow, 1997), the statistical procedure, or the problem of simultaneous determination of both price and exchange rate (Levi, 1976).
Theoretically, deviations of the PPP from its practical value may also be caused by differences in production technology and consumer’s preferences toward risk and uncertainty. For example, the Balassa-Samuelson model argues that a rise in the productivity rate in the home country relative to a foreign country can lead to a real appreciation of the home currency against the foreign currency. Many other models (Liu, Zhao and Ma, 2002) state that the real exchange rate is associated with the preferences of consumers. In addition, tax or tariff policy may also change the real exchange rate. For example, to offset the effect of the East Asia crisis, the PRC increased export tax refunding after 1998, and this had a similar impact as the real depreciation of home currency. Also, currently, the PRC plans to increase the tariff on textile exports to avoid sanctions by European countries, and this is equivalent to a real appreciation of home currency12.
As for whether PPP holds in the PRC, Chou and Shih (1998) showed that the renminbi was overvalued after the economic reform was launched in 1979, but that purchasing power parity holds in the long run. Using the ADF-test and Engle-Granger unit root test and integration test, Hu Yuancheng (2003) concluded that the real exchange rate of the renminbi was not stationary, and thus that at least in the short run, PPP does not hold.
3.2 Interest Rate Parity
As early as the period of the gold standard, monetary policymakers found that exchange rates were influenced by changes in monetary policy. The rise of the home interest rate is usually followed by the appreciation of the home currency, and a fall in the home interest rate is followed by a depreciation of the home currency. This indicates that the price of assets plays a role in exchange rate variations. The interest rate parity condition was developed by Keynes (1923), as what is called interest rate parity nowadays, to link the exchange rate, interest rate and inflation. The theory also has two forms: covered interest rate parity (CIRP) and uncovered interest rate parity (UCIRP). CIRP describes the relationship of the spot market and forward market exchange rates with interest rates on bonds in two economies.
UCIRP describes the relationship of the spot and expected exchange rate with nominal interest rates on bonds in two economies.
3.2.1 Covered Interest Rate Parity
Under this model, assume that the home country denotes the PRC and the foreign country denotes the US. The nominal interest rate at time t in the PRC is t i and that at time t in the US is * t i , the spot exchange rate is t S and the forward exchange rate at time t+1 is 1 + t S . If an investor in the PRC deposits one yuan in Chinese currency, he will get a return of t i at time t+1, and the sum of his principal and interest rate at time t+1 is t i + 1 . If this investor exchanges his one yuan renminbi into USD at time t and then deposits it in a US bank with interest rate * t i , the sum of his principal and interest in dollar terms is t t S i / ) 1 ( * + . However, since the forward change rate is 1 + t S , this sum of the principal and interest in yuan terms is t t t S S i / ) 1 ( 1 * + + . In a perfectly competitive market, it is generally recognized that it is less likely for the gap between the renminbi’s yield and that of the USD to persist for any length of time. In other words, the return from depositing renminbi in the PRC must be the same as the return from depositing USD in US. This relation can be expressed using the covered interest rate parity condition:
(3.6) is the precise form of the covered interest rate parity condition. CIRP can also be derived directly from the Fisher condition and PPP. Under the Fisher condition, the real interest rates at home and abroad are, respectively
Since the real interests rates are equal, the following formula holds:
or PPP holds, we again obtain the CIRP condition
To simplify the model, we introduce the sign:
is defined as the forward premium (discount), the proportion by which the forward exchange rate exceeds (falls below) its spot rate.
Using (3.7), (3.6) can be rewritten as
is such a small number that it can be omitted, (3.8) can be written approximately as
This is the normal form of the covered interest rate parity, which states that the domestic interest rate must be higher than the foreign interest rate by an amount equal to the forward premium (discount) on domestic currency. According to CIRP, if the exchange rate of, say, the renminbi against the USD is fixed, the interests of the two countries should be equal. Thus, a small country with a pegged exchange rate regime cannot carry out monetary policy independently. Empirically, using weekly observations from Jan. 1962 to Nov. 1967, Frenkle and Levich (1975) confirmed that CIRP held. Later (1977) they extended their studies into three periods: 1962–67, known as the “tranquil peg”; 1968–69, the “turbulent peg”; and 1973–1975, the managed float, and strengthened the findings of their previous study that CIRP still holds during these periods even when the effect of transaction costs is taken into account. Levi (1990) indicated that deviations from CIRP might occur due to four major reasons: (1) transaction costs, (2) political risk, (3) potential tax advantages, and (4) liquidity preference.
3.2.2 Uncovered Interest Rate Parity
However, investors face uncertainty over future events. In a rational expectation framework, the forward exchange rate may be strongly influenced by the market expectations about the future exchange rate if new information is taken into consideration. In an uncertain environment, an un-hedged interest rate parity condition may hold. Given that all other variables’ symbols do not change but that the forward exchange rate 1 + t S is substituted by the expected exchange rate ) ( 1 + t S E , the UCIRP condition can be written as
This is the precise form of uncovered interest rate parity. Like PPP, the UCIRP does not allow for investor’s preferences. In other words, (3.10) is derived under the condition that investors are risk neutral. This means that agents are indifferent between an investment yielding a completely secure return, on the one hand, and one offering the prospect of an identical return on average, but with the possibility of a much higher or lower return, on the other hand. In other words, they are concerned only with average returns.
Similarly, using the following approximate expression:
is the expected rate of appreciation of foreign currency, and then substituting (3.11) into (3.10) and ignoring the smaller number as we did previously, we get the formal uncovered interest rate parity condition:
Formula (3.12) states that the domestic interest rate must be higher than the foreign interest rate by an amount equal to the appreciation rate of foreign currency. As with PPP, uncovered and covered interest rate parity conditions are derived under the assumption of no transaction barriers, a perfectly competitive capital market and no arbitrage opportunities at equilibrium. Obviously, this kind of equilibrium is still partial, because only the assets market is considered.
Very few empirical studies support UCIRP. For example, Using a K-step-ahead forecasting equation and overlapping techniques on weekly data of seven major currencies, Hansen and Hodrick (1980) reject the market efficiency hypothesis for exchange.
We have indicated above that the Fisher Open condition can be a basis for covered interest rate parity. This condition implies that the expected real interest rates are equal in different countries, with the real interest rate defined as the nominal interest rate divided by the sum of one plus the expected inflation rate. The Fisher Open condition implies approximately that the difference of nominal interest rates equals the difference of expected inflation rate between two countries. Empirically, little evidence supports the Fisher Open hypothesis (Cumby and Obstfeld 1981, 1984). When the Fisher Open hypothesis is denied, real interest rate parity cannot hold.
3.3 The Mundell-Fleming Model
Money is important, because it serves as a medium of exchange, ruler of value, and means of storage. As a modern invention, paper money or currency plays an important role in reducing transaction costs. However, this role was not included in the previous section. Thus, the effect on the nominal exchange rate of monetary policy is not clear from previous models. The Mundell-Fleming model is developed by extending the IS-LM model to the case of an open economy, and thus provides understanding of how the exchange rate is determined. The IS-LM model considers three markets: goods, money and assets, and is mainly used to analyze the impacts of monetary policy and fiscal policy. When the goods market is not in full employment equilibrium level, it shows how to use fiscal policy and monetary policy to adjust an economy to a new full employment equilibrium. Since only two of the three markets are independent, the IS-LM model only establishes a linkage between the money market and goods market. In the Mundell-Fleming model, the balance of international payments is considered another equilibrium condition in addition to the money market and goods market.
Let us first define the goods market equilibrium as the IS curve
where Y denotes domestic national income; C = C(Y) denotes consumption which is a function of income; I = I(i) denotes investment, which is a decreasing function of nominal interest rate i ; G denotes government spending; X = X(Y*,q) denotes exports , which is an increasing function of foreign national income and real exchange rate. M = M(Y,q) denotes imports, an increasing function of domestic income and decreasing function of the real exchange rate.
The real exchange rate is defined by
where S is the nominal exchange rate; P,P* denote, respectively, domestic and foreign prices.
Second, we define the money market equilibrium through the LM curve. Let Md/P = L(Y,i) represent money demand, which is an increasing function of domestic income and decreasing function of the interest rate, and Ms represent money supply. The money market equilibrium condition can be expressed as
Ms/P = L(Y,i). (3.14)
Finally, the external equilibrium is denoted by the BP equation: BP = CA + KA = 0 (3.15)
where, current account CA = PX - SP*M and capital account
One of the most important issues addressed by the model is the so-called trilemma, which states that perfect capital mobility, monetary policy independence and a fixed exchange rate regime cannot be achieved simultaneously. Specifically, It argues that a country cannot sustain monetary policy independence in a fixed exchange rate regime with perfect capital mobility. However, this argument is made in a small country setting, and it is not necessarily true in a bigger economy, say, the PRC. What we have seen in the PRC is that it is not so small and is maintaining certain capital control and its monetary policy has seemed to be independent so far. The model also forecasts that the exchange rate level is perfectly correlated with the level of monetary supply in the long run, and thus that monetary policy may only play a trivial role. Another important implication is that devaluation may lead to further devaluation if fiscal discipline, inflation and balance of payments are not well managed or if the assets market produces a self-fulfilling bubble.
Finally, the impact of devaluation on the improvement of the current account may be weakened if an economy is heavily reliant on the reexport processing industry.
3.4 Exchange Rate and Productivity: The Balassa-Samuelson Model
From the discussion above, we conclude that PPP and CIRP (and UCIRP) only express forms of partial equilibriums and do not clearly relate producer behavior and consumer behavior. However, price levels are determined by the interaction between supply and demand. Since the supply of and demand for products are associated with producer and consumer’s behavior, a starting point for studying the determinants of the real exchange rate is to investigate producer’s behavior and consumer’s behavior, which are associated with the microeconomic foundations of exchange rate theory. In this section, from the angle of producer behavior, we investigate the Balassa- Samuelson model (Balassa, 1964; Samuelson, 1964). It allows us to see the role that productivity plays in the real exchange rate.
The standard version of the B-S model is presented using a single-factor aggregate production function in Obstfeld and Rogoff (1996). For simplicity, this model assumes that the production functions of tradable (T) and nontradable goods take the following form:
where Y is production, A is a constant describing technology, and L is labor force. Foreign economies employ the same kind of technology as the domestic economy, but may differ from it in the value of the technological parameter, A. the subscript T denotes the tradable sector, and the subscript N the nontradable sector. This model also assumes that the law of one price holds for tradable commodities and that the world price of tradable commodities is equal to one without a loss of generality. In addition, perfect labor mobility is assumed between sectors within an individual economy, but zero mobility of labor is assumed between economies. The mobility of labor insures that the wage rates w are equal in other sectors of the same economy. We define the price index as the weighted geometric average of prices of tradable and nontradable goods:
is the share of tradable goods in total outputs. If this share is the same at home as abroad, the relative price vis-a-vis the outside world is
the nominal GDP per employee can be expressed as
So the relative price can be transformed into
This formula states that the relative price is determined by relative GDP and the relative technological level or productivity in nontradable sector of the two economies. Given a level of productivity at home and abroad, a higher nominal GDP growth in home than abroad leads to an appreciation of the real exchange rate. On the other side, given an economic growth rate, higher productivity of nontradables in the home country than the foreign country will lead to depreciation of the real exchange rate.
This simplified model can be easily extended to a more general one that includes two production factors: labor and capital. Let us consider a small economy that produces two composite goods: tradables and nontradables. We assume that the production functions are functions of capital and labor with constant return to scale:
where K denotes capital. The other variables are the same as above. Through some manipulation, the log-differentiation of the relative price of tradable goods and nontradable goods can be expressed as
are respectively the labor share of the income generated in the tradable and nontradable goods sectors.
Provided that nontradables are relatively labor intensive, meaning
the model forecasts that the domestic economy will experience real appreciation if its productivity-growth advantage in tradables exceeds its productivity growth advantage in nontradables.
The Balassa-Samuelson model is one of the cornerstones of the traditional theory of the real equilibrium exchange rate. The key empirical observation underlying the model is that countries with higher productivity in tradables compared with nontradables tend to have high price levels. The B-S model hypothesis states that productivity gains in the tradable sector allow real wages to increase commensurately and, since wages are assumed to link the tradable to the nontradable sector, wages and prices also increase in the nontradable sector. This leads to an increase in the overall price level in the economy, which in turn results in an appreciation of the real exchange rate.
During the starting period of economic reform and opening up, productivity in both tradable and nontradable goods production in PRC was very low compared with developed countries. With the opening up and economic reform, the lag in the economic and technological level allowed the PRC to enjoy three advantages over developed countries, namely, cheap labor, high productivity growth and spillover effects of foreign direct investment. These advantages have allowed the PRC to enjoy much faster growth in productivity in the tradable sector than the nontradable sectors and at home than in foreign markets. According to the B-S model, this should result in the PRC experiencing real depreciation, and thus incurring nominal appreciation pressure in the long run.
However, the shortcomings of this model are clear. First, It assumes that the tradable price at home is the same as that abroad. This is clearly an unrealistic special form of PPP, but for tradable goods only. Under this setting, how the prices of tradables are determined remains unknown. Second, since it says nothing about the demand side, it is criticized by the Keynesian school, which regards price to be rigid or sticky. Third, without considering the behavior of consumers, or the demand side, it is difficult to interpret how market prices are formed. Last and most importantly, this model does not deal with the role of money; it can at best explain partly how the real exchange rate is determined.
Integrating the model with a model of accumulation of capital and with the demand side of the economy, Tomâŝ Holub and Martin Ĉihâk (2003) claimed that that the predictions of their model were generally consistent with empirical findings for Central and Eastern European countries. But the extended model still does not have room for money and the nominal exchange rate. This implies that money is assume out of this kind of model and that prices are assumed to be flexible enough to adjust to supply and demand.
3.5 A Simple Monetary Exchange Rate Model with Price Flexibility
Unlike the Mundell-Fleming model, which involves the balance of international payment, a simple monetary model was originally created in a frictionless world with only one good and one bond (Mussa, 1976, Frenkle, 1976), in which money market equilibrium, PPP and UCIRP are reached. This model includes three blocks.
The first block is the money market equilibrium equation given by
Where p is the log price level, i is nominal interest rate, y is the log of real output and m is the log of money supply. The second block is purchasing power parity. Let e be the log of the nominal exchange rate, defined as the price of foreign currency in terms of home currency; p*,p denote the log of the world foreign currency price of the goods basket and the log of the home currency price level. The purchasing power parity in log terms is
The third block is uncovered interest parity, which can be approximately expressed in the forms of logs:
Substituting (3.19) and the uncovered interest rate parity approximation equation (3.19) into money market equilibrium equation (3.18), we have
Given money supply, foreign interest rate and price, this simple monetary model demonstrates that the exchange rate depends on both current values as well as expected future values of related variables; that an increase in the domestic money supply and foreign interest rate raises both the domestic price level and nominal exchange rate level; and that changes in real domestic income and the foreign price level have a negative effect on the domestic level and nominal interest rate.
In the extreme case of a fixed exchange rate regime, the domestic interest rate and price level are equal to their foreign counterparts. The money supply is endogenously determined by domestic output, the foreign interest rate and foreign price level:
3.6 The Dornbusch Overshooting Model
Many studies document the fact that deviations from the law of one price are highly correlated with nominal exchange rate changes (for example, Isard, 1977; Giovannini, 1988). Evidence also shows that real exchange rates always seem much less volatile when nominal exchange rates are fixed than when they are floating (Mussa, 1986).
During the Bretton Woods period up until December 1971, the nominal exchange rate of the lira to the French franc was relatively fixed and real exchange rate volatility was fairly low. During the periods when the relative value of the two currencies was not effectively fixed (the early 1970s through 1987), real exchange rate movements were much more volatile and short-run real changes virtually mirrored short-run changes in the nominal exchange rate.
This indicates that the choice of exchange rate regime can have important effects on real variables. Such forms of evidence motivate a sticky price extension of the flexible exchange rate monetary model above, namely the Dornbusch Overshooting model, which was presented in the influential masterpiece “Expectations and exchange rate dynamics” by Rudiger Dornbusch (1976) (Kenneth Rogoff, 2002). Under the Dornbusch model, uncovered interest rate parity and the money equilibrium of the simple monetary model are retained. However, the assumption of flexible prices is replaced by sticky prices. Similarly, The first condition in Dornbusch’s model is monetary equilibrium:
where m is the money supply, p is the domestic price level, and y is domestic output, all in logarithms; η and φ are positive parameters. (3.22) implies that higher interest rates raise the opportunity cost of holding money and thereby lower the demand for money; on the other hand, a higher interest rate also means high costs of speculation, which lowers the demand of money as well. Conversely, an increase in output raises the transaction demand for money. Finally, the demand for money is positively related to the level of prices. The second condition is uncovered interest rate parity, which can be rewritten as
where e is the logarithm of the exchange rate (home currency price of foreign currency), and Et denotes market expectations based on information at time t.
are approximately correct. The foreign interest rate i* is taken as a given exogenous variable. In accordance with uncovered interest rate parity, the home interest rate must be equal to the foreign interest rate i* plus the expected depreciation rate of the home currency
Unlike under the perfectly flexible price model, the prices of goods are sticky and cannot adjust immediately to clear the market in the Dornbusch model. With sticky prices, an adjustment mechanism is needed for an economy to converge to its equilibrium path in which full employment is realized. Given the magnitude of the real exchange rate’s departure from its long-term equilibrium, the force to pull it back to equilibrium will increase. Dornbusch assumes that if the real exchange rate rises over its long-term equilibrium level, or if the foreign currency is overvalued or the domestic currency is undervalued, the demand for domestic goods will increase; contrarily, if the real exchange rate falls below its long-term equilibrium level, or the foreign currency is undervalued or domestic currency is overvalued, then the demand of domestic goods will fall. In this connection, the third condition is an adjustment mechanism of the demand for domestic goods, which can be expressed as
Where p and p* are, respectively, logarithms of the domestic price level P in domestic currency and foreign price levels P* in foreign currency, δ is a constant greater than zero,
is the real exchange rate at time t, and y and
The last or fourth condition is the price adjustment equation. Keynes assumed that the domestic price level p does not move instantaneously in response to unanticipated monetary disturbances, but adjusts only slowly over time. However, under Dornbusch’s model the feature of sticky prices is different from that in the Mundell-Flemming model where the domestic price level is basically assumed to be fixed.
Using the price adjustment mechanism proposed by Mussa (1982), which is better suited than Dornbusch’s original formulation to dealing with more complex exogenous shocks, the sticky-price adjustment process can be described as
The Dornbusch model is well known for its overshooting phenomenon, which states that one permanent change in the money supply must lead to a proportionate change in the price level and the exchange rate in the long run. But in the short run, the price level is fixed and the nominal exchange rate must overshoot its long-run equilibrium. That is, any initial disturbance of money supply will cause an even larger unanticipated rise in the instant exchange rate than in the long-term exchange rate.
Another significant conclusion of the Dornbusch model is that the impact on the exchange rate of a monetary shock is greater when prices are sticky than when they are flexible. The third conclusion is that the exchange rate converges to its flexible-price equilibrium value following an initial overshooting after a shock and that the nominal exchange rate is more volatile than the real exchange rate when ψδ < 1.
Fourth, the Dornbusch model tells not only a story of overshooting, but it has important policy implications for the exchange rate regime. A central conclusion of the model is that with sticky prices and flexible exchange rates, purely monetary shocks will have significance for the real economy, leading to large changes in prices and output and prolonged adjustment. If the exchange rate is fixed, the real effects of money demand shocks can be eliminated by setting money supply to money demand (so-called nonsterilized foreign exchange intervention).
The model also states that the exchange rate policy is to some extent inconsistent with the independence of monetary policy. When a real shock occurs, say a long-run rise in the real exchange rate, buffeting the economy, the model forecasts that a new full employment equilibrium adjustment will occur immediately under a floating exchange rate regime, and need not change the price level. If the exchange rate were fixed, in order to recover the real economy to equilibrium, the entire burden would have to be borne by the prices of goods. But because these prices are sticky, it is a time-consuming process for the economy to reach equilibrium.
Dornbusch’s model is not without deficiencies. For example, it is unable to deal adequately with the current account and fiscal policy dynamics or, more fundamentally, with welfare issues, because it lacks a micro foundation. In addition, it is premised on the assumption that capital is perfectly mobile and the market is clear. In cases where capital mobility is imperfect, or where capital control is stringent, as happened in the PRC and other developing countries, there is a lot of room for the model to be improved. Finally, a fixed exchange rate regime may not be a viable option in the long run, given the limited ability of an economy to endure pervasive speculative attacks on a fixed exchange rate.
It is worth mentioning that the above arguments are obtained in the context of a small country model. For a big economy, further studies are needed to determine whether these conclusions are applicable.
3.7 The Obstfeld and Rogoff Model
Probably from the awareness that previous models have an inadequate micro foundation, and are unable to deal adequately with current accounts and balances of international payments, economists have made considerable efforts to explore a new setup for exchange rate determination.
The modern models of Obstfeld and Rogoff were set up based on simple PPP, which implicitly assumes that nominal prices are producer’s currency of production (PCP). As a result, the exchange rate changes “pass-through” one hundred per cent to consumer prices and a flexible exchange rate is a perfect substitute for flexible goods price. In their pioneering work, based on PCP, Obstfeld and Rogoff (1995) developed a perfect-foresight two-country equilibrium monetary model with preset prices.
Their model assumes that the world is inhabited by a continuum of individual monopolistic producers, indexed by z ∈ [0,1], each of which produces a single differentiated good, also indexed by z. All producers reside in one of two countries, home or abroad. The home consists of producers on the interval [0,n], whereas foreign producers are on interval (n,1]. But this model revolves around the endogeneity of output of good z, y, (z).
One of the important contributions of the model is that it introduces a utility function consumer j, j ∈ [0,1], which depends on the consumption index, real money balances, and effort made in production:
Here, the real consumption index for individual j is defined as
where cj (z) is the j-th home individual’s consumption of good z, and θ > 1.
Let p(z) be the home-currency price of good z . Then the home money price level is
Let p*(z) be the home-currency price of good z . Then the foreign money price level is
The law of one price holds for individual goods, and the home and foreign price levels are related by purchasing power parity. That is P = ε P*
An individual’s budget constraint
rt denotes the real interest rate on bonds between t-1 and t, yt, (j) is the output of good j, and pt(j) is its domestic currency price. Because there is production differentiation, pt(j) need not be the same for all j. The M is agent j’s holdings of nominal money balances entering period t, and t τ denotes lump-sum taxes.
Compared with the Dornbusch model, the Obstfeld and Rogoff model has four advantages. First, it was developed on a firm micro foundation that maximizes the welfare of consumers. Second, though money the demand functions in the Dornbusch model and Obstfeld and Rogoff model have similar forms, the output variable in the former was substituted by consumption in the later. Third, a goods differential is allowed in the Obstfeld and Rogoff model, but Dornbusch’s model revolves around the market structure and the endogeneity of output. Fourth, in the Obstfeld and Rogoff model, a comparison of the impact of external shocks on consumer’s welfare is allowed, but it isn’t in Dornbusch model.
According to Obstfeld and Rogoff (1995, 1998, 2000a), the flexibility of the exchange rate is desirable in the PCP setting, because: (1) flexible exchange rates are a perfect substitute for flexible nominal prices. Relative price adjustment is achieved by exchange rate flexibility under PCP pricing; (2) the policy that achieves the flexible price allocation is a constrained Pareto optimum; (3) this optimal policy is completely self-oriented. No policy coordination across countries is required or desirable. In this sense, perfectly flexible exchange rates are optimal (Engle, 2002).
3.8 Price to Market and the Exchange Rate Regime
The modern models of Dornbusch and Obstfeld and Rogoff are based on simple PPP, which implicitly assumes that nominal prices are PCP. As a result, the “pass-through” of exchange rates to consumer prices is one hundred per cent and flexible exchange rates are a perfect substitute for flexible goods prices. However, a number of empirical studies and experiences of Japan (Chapter 6) indicate that in the short run, nominal exchange rate changes only partly pass through to consumer prices. To reflect this phenomenon, Devereux and Engle (2003) put forward another type of price-stickiness: prices are preset in the consumer’s currency (denoted by local currency pricing or LCP).
Under LCP, the short-run responses of consumer prices to exchange rate changes are very small. When prices are not very responsive to exchange rate changes, the monetary policymaker cannot rely on the exchange rate to provide the necessary adjustment to real shocks. Since consumers do not interpret exchange rate changes as relative price changes in the short run, it is not easy to control the relative demand for domestic goods and foreign goods through exchange rate changes. In the absence of strong expenditureswitching effects, the benefits of floating exchange rate are diminished. This implies that an optimum monetary rule would not utilize exchange rate movements at all and that welfare-maximizing monetary policies may entail a fixed exchange rate (Engle and Devereux 2003).
This theoretical framework can be viewed as a major challenge to the Friedman case for exchange rate flexibility, according to which floating exchange rates are helpful in cushioning national economies from real idiosyncratic shocks, and one that is applicable to industrial rather than emerging economies.
Otstfeld (2004) improved on the model of Devereux and Engle in two ways. First, he modeled the monetary policy as a choice of the nominal interest rate rather than a monetary aggregate. Second, he introduced non-traded goods in the LCP framework. However, his conclusion challenges that of Devereux and Engle. He declared that even when the exchange rate plays no role, countries may wish to have flexible exchange rates in order to free the domestic interest rate as a stabilization tool.
3.9 Balance of Payments Equilibrium and Exchange Rate Misalignment
Ronald Macdonald (2000) made an overview of the concepts for calculating equilibrium and discussed the advantages and disadvantages of various approaches to the estimating equilibrium exchange rate, such as BEERs (Behavioral Equilibrium Exchange rates), PEERs (Permanent and Transitory Decompositions of Real Exchange Rates), and FEERs (Fundamental Equilibrium Exchange Rates). All the approaches regard the balance of payments as a starting point. According to Ronald Macdonald, the standard balance of payments equilibrium condition holds under floating exchange rates in the absence of intervention in the foreign exchange market:
where cat and kat = 0 denote, respectively, the current account and capital accounts of the balance of payments. Ignoring some minor components, the current account is determined by:
where nxt denotes net exports and itnfat represents net interest payments on net foreign assets.
This model does not assume PPP to be true in all cases, but assumes that the real exchange rate or term of trade as a measure of competitiveness have an impact on net exports and the current account. It also assumes that a rise in domestic income worsens net exports through its effect on imports, while a rise in foreign income improves the net export position through its influence on domestic exports. Thus, net exports are determined by a standard relationship:
where st is the log of the spot exchange rate, pt is the log of the domestic price level, yt is the log of domestic income, pt* is the log of the foreign price level and y>t* is the foreign income. a's are elasticities.
In practice, the international capital markets are not necessarily perfect, and thus the uncovered interest parity may not hold everywhere. However, when the capital markets are not in equilibrium, a mechanism for adjusting the flows of capital will take effect. In other words, if other things are equal, a rise in the domestic interest rate raises capital inflow, while a rise in the foreign interest rate lowers capital inflow, leading to a rise in the expected exchange rate (domestic currency deprecation), which will encourage capital outflow.
where it denotes an interest rate yield of domestic deposits, and i*t an interest rate yield of foreign deposits, and ∆set+k is the expected change in the exchange rate. Substituting (3.34) into (3.33) and the resulting expression, along with (3.35) into (3.32) we obtain the balance of payments exchange rate equation:
This formula is usually thought to be a general expression of an equilibrium exchange rate in that it satisfies the balance of payments equilibrium under floating exchange rates.
It is clear that u → ∞ means that UCIRP is satisfied and a 1 → ∞ αmeans that PPP is satisfied.
Combining (3.36) and the definition of the real exchange rate
The real exchange rate at time t can be rewritten as:
3.10 Summary of Model Implications
In this section, we provide a brief review of exchange rate determination theories and their policy implications. This review demonstrates that each theory holds in a particular setting and explains some macroeconomic phenomena. No single theory contains all the factors that may have an impact on foreign exchange rates.
Purchasing power parity (PPP) theory, which is classified into two types (absolute PPP and relative PPP) is covered in this review as a starting point for understanding how exchange rates are determined in the goods market. It builds linkage between the exchange rate and prices of goods in two economies. This is why it is called the “inflation theory of exchange rates.” Since it deals only with the goods market, and not the assets market, it is a partial equilibrium theory. The minimum preconditions for absolute PPP include: (1) same production technology for individuals, (2) neutral-risk preferences, (3) perfectly competitive goods markets in two different economies, (4) no trader barriers such as transport costs, tariffs and trade quotas, and so on. It is established on the “law of one price.” Actually, the preconditions for absolute PPP do not hold since transport costs, tariffs, and technological and preferential differences exist at all times and places. Absolute PPP is rejected by most empirical surveys. Relative PPP allows exchange rates to deviate from absolute PPP. It is equivalent to the real exchange rate being constant. Empirically, both absolute PPP and relative PPP in the short run are rejected, but some studies find that relative PPP seems to hold in the long run.
Another popular partial equilibrium exchange rate theory, interest rate parity, examines how the exchange rates are determined in financial markets. Since interest rates change frequently in the short run, interest rate parity is thought of as “short run exchange rate theory.” Interest rate parity also has two types, CIRP and UCIRP, both of which are based on the assumption that asset markets are frictionless and that there is no arbitrage. A lot of evidence supports CIRP as a forward exchange rate pricing model. However, variations in monetary policy, degree of risk aversion, political risks, barriers to capital mobility, and microstructure variations in the market may cause persistent variations in the risk premium over time. UCIRP and the Fisher open condition are also covered in this review, but both lack support from empirical studies.
Three monetary models are presented to introduce the impact of monetary factor and real factor shocks on the exchange rate. The first model, known as the simple monetary model in the setting of flexible prices, forecasts how the exchange rate and price level change with current and expected future values of related variables, such as money supply, foreign interest rate, and income level.
The second model, the Mundell-Fleming model, is extended from a closed IS-LM model. Unlike the simple monetary model, in which prices are viewed as flexible, it assumes that prices are preset in the short run. In addition to the internal monetary market equilibrium, goods market equilibrium, and external equilibrium condition, the balance of payments is also considered in the Mundell- Fleming model. Thus, it can be viewed as a general equilibrium model. One of the most important forecasts of the model is the socalled trilemma, which states that perfect capital mobility, monetary policy independence and a fixed exchange rate regime cannot be achieved simultaneously. In the long run, the exchange rate level is perfectly correlated with the level of monetary supply, and monetary policy may only play a trivial role in economic growth. Another important forecast is that devaluation may lead to further devaluation if fiscal discipline, inflation and the balance of payments are not well managed, because a self-fulfilling bubble may be produced. Finally, the impact of devaluation on current account improvement may be weakened if an economy is heavily dependent on the re-export processing industry.
The third monetary model, Dornbusch model, loosens the condition that prices must be preset, but allows for slow price adjustments. A famous insight into policy implication of this model is the overshooting of the nominal exchange rate over its long-run equilibrium, when an economic system is shocked with monetary supply. This character is regarded as an advantage of a fixed exchange rate regime over a floating one. This model shows that once a real economic shock happens, markets may move to equilibrium either through a flexible exchange rate or change of prices. The difference between the two is mainly that in the latter, adjustment may consume more time and be less risky than in the former. If prices are relatively flexible and inflation can be controlled in a moderate range, a fixed change rate regime is desirable.
These models were criticized frequently for their lack of micro foundations, and for their failure to elucidate the effect of the balance of payment on the determination of the exchange rate. However, their clear implications for policymakers should not be underestimated. The Ballasa-Samulson model partly addressed the issue of the lack of a micro foundation in modeling work by incorporating productivity differentials or technological changes in production into a one-factor production technology model, which was then extended to a two-factor model. The main contribution of this kind model is that they built linkages between productivity, output and the real exchange rate (terms of trade) through the rational behavior of producers. However, they fail to incorporate paper money or nominal exchange rate and the behavior of the demand side that might have important impacts on the exchange rate.
The latest important development in exchange rate studies is the pioneering work in 1995 of Obstfield and Rogoff (Redux), whose model incorporates the demand side. However, this model still relied on PPP and price presetting. Though it allows the welfare effects of different shocks to be compared, it merely seems to be a Dornbusch model based on maximization behavior. There are still many deficiencies in the model. First, it does not consider investment and producer’ behavior; second, it regards absolute PPP as a precondition, but this has not been supported by empirical studies.
To address the unsuitability of PPP, recent modeling efforts have been formulated in the setting of consumer’s currency pricing or LCP. In the LCP setting, some implications are found to be different from that in the PCP setting, especially regarding the choice of the exchange rate regime. In PCP, perfectly flexible exchange rates are to some extent optimal. However, some economists argue that the LCP setting is more practical than PCP, at least in the short run. In the LCP setting, an optimum monetary rule does not utilize exchange rate movements at all and welfare-maximizing monetary policies may entail a fixed exchange rate. However, Otstfeld argues that if substituting interest rate for aggregate money demand in LCP, even when the exchange rate plays a trivial role, countries may wish to have flexible exchange rates in order to free the domestic interest rate as a stabilization tool.
Existing exchange rate models have done little regarding the role of fiscal policy and income policy in dealing with trade surpluses and deficits. For a perfect market economy, this may not be a problem, because fiscal policy and income policy are usually regarded as nonmarket measure and may cause distortions of the market. But for a country that is undergoing reform and marketization, structural factors may play a key role in the balance of trade and payments. PRC already had some experiences in this regard. For example, when it was suffering shocks from the Southeast Asian crises in 1998, many researchers forecasted that the PRC would have to devaluate the RMB, but in the end it decided to raise export tax rebates, which had a similar effect as a devaluation. Presently, though the PRC has a trade surplus and a large amount of foreign exchange reserves, it faces structural issues, involving social security funds, pensions, health insurance, labor security, implicit fiscal deficits, and an inefficient banking system, which are challenging policymakers. Thus, all those factors mentioned here may have an impact on government decisions. However, the following modeling work will start mainly from the macro aspect.
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