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# Equilibrium Exchange Rate Theoretical Research Review

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Published: Wed, 14 Mar 2018

## Literature review

3.1 equilibrium exchange rate theoretical research review

The equilibrium exchange rate (EER) is commonly defined in three ways .The first definition comes from the most common equilibrium concept in economics. When supply of foreign exchange equals the demand, the level of exchange rate is equilibrium exchange rate. The second definition of EER is the exchange rate which can be calculated by using some specific exchange rate determination models. The last definition refers to the exchange rate which is “consistent with the simultaneous achievement of internal and external balance”(Williamson,1985).In this paper, the second method will be adopted ,that is to say, the equilibrium exchange rate will be estimated by a theoretical model.

Different levels of equilibrium exchange rate can be obtained based on different theoretical models corresponding to specific theoretical assumptions. Currently, the most influential theories of estimating EER are mainly Purchasing power Parity (PPP) approach, the Macroeconomic Balance (MB) approach, Fundamental Equilibrium Exchange Rate (FEER) approach, Natural Real Exchange Rate (NATREX) approach, and Equilibrium Real Exchange Rate (ERER) approach, Behaviour Equilibrium Exchange Rate (BEER) approach. All models mentioned here will be discussed in the following pages.

3.1.1 the purchasing power parity (PPP) theory

The purchasing power parity theory popularized by Gustav Cassel (1992) is considered as a milestone theory of accessing equilibrium exchange rate. The theory is supported by “law of one price”, which states that “in absence of the cost of transaction and transportation, identical goods in any country must be sold at the same common currency price” (Copeland, 1997). According to PPP theory, the equilibrium exchange rate between any two countries can be determined by the relative purchasing power of their currencies, namely, their own price levels. We identify this theory as absolute PPP which will be improved by the relative PPP theory later. And the following equation 1 gives mathematical description of absolute PPP.

(1)

Where: E stands for nominal exchange rate expressed as units of domestic currency per unit of foreign currency. P and P* is the price index of domestic country and foreign country respectively. The types of commodity and the weight of each type should be absolutely the same when we calculate P and P*. However, there are great differences between any two countries in the level of national economic development, economic structure and consumption structure. Therefore, it is very difficult to measure P and P* in practice. What’s worse, the assumption of “law of one price” may not exist in real world. Because of these problems, the relative purchasing power parity is announced by researchers afterwards. The basic idea of relative PPP is that changes in exchange rate between the two countries in proportion to changes in price levels with the same period. It can be expressed in the following equation:

= (2)

Where: Et and E0 stand for nominal exchange rate expressed as units of domestic currency per unit of foreign currency in period t and base period. Pt and P0 donate the price index of domestic country in period t and base period respectively. And then, P*t and P*0 represent the price index of foreign country in period t and base period. According to relative PPP theory, the base period need to be determined at the beginning, which is judged in the macro-balance. The real exchange rate in base period is considered as equilibrium exchange rate. The nominal exchange rate in period t can be calculated by the equation 2. And then, the real exchange rate can be obtained after adjusting the nominal exchange rate. If there is a difference between the real exchange rate in period t and the real exchange rate in base period, which means that the exchange rate begins to deviate from the equilibrium exchange rate. Not difficult to find, the traditional purchasing power parity theory indicates that the real exchange rate has to remain unchanged to the equilibrium level. But the fact in real economic life tells us that the real exchange rate changes frequently in every country. A lot of empirical studies about exchange rate movements after the collapse of Bretton Woods system have shown that the purchasing power parity theory is not applicable to the majority of currencies in the world. However, the PPP theory has been valued by academics with the development of econometric technology and a large increase in sample data. Scholars have been using the new measurement methods to re-test its applicability which break the limit of traditional ways. Chou and Shih (1998) accessed the movements of equilibrium exchange rate of RMB based on PPP theory. They find that RMB is overvalued in 80’s and early 90’s , while most of the foreign researchers insisted that the yuan grossly underestimated (Overholt, 2003; Frankel, 2004; Goldstein, 2004). On the contrary, Chinese scholars are more inclined to believe that RMB is not undervalued or have not been seriously underestimated (Yu qiao, 2000; Tang guoxin & Xu jiangang, 2003; Dou xiangsheng & Yang xin, 2004). The reason why these conclusions differ greatly is that the selected exchange rate indicators and base period are different. The PPP theory did not take the effect of changes in economic fundamentals into account, so the results generally overestimate the degree of exchange rate misalignment. However, economic fundamentals change dramatically in developing and transition economies, for instance, the situations in china. Obviously, there would be a serious deviation of the conclusions drawn by ignoring the changes in equilibrium exchange rate due to changes in basic economic factors. What’s more, the theory itself does not contain the macroeconomic implications of internal and external balance (Driver and Westaway, 2004; Rogoff, 1996). Therefore, it is unreasonable to measure RMB’s equilibrium exchange rate by PPP model.

3.1.2 the Macroeconomic Balance theory

All theories mentioned above, except PPP approach, can be called “non-PPP” approach. From here, researchers begin to pay attention to the macroeconomic balance rather than just the changes in relatively price index. The expert in International Monetary Fund (IMF) Swan (1963) put forth the earliest MB theory based on the research of Nurkse (1945). The equilibrium exchange rate defined by Swan is the real rate which is consistent with internal and external balance. Furthermore, the internal equilibrium is defined as full employment and external equilibrium is balance of international payments. The author not only gave the conditions to achieve the equilibrium exchange rate, but also supplied the method to judge the characteristics and reasons of internal and external imbalances. The research of Swan made great contributions in the following areas. First of all, there is a clear distinction between internal and external balance, and the criterions are potential production capacity and balance of payments respectively. And then, the theory broadens the application field of Keynesian macroeconomic analysis method. What’s more, the author also divided the imbalances into different types, making a deeper understanding of the types and characteristics of imbalance. However, the shortcomings of this theory are also quite obviously. In the first place, the equilibrium exchange rate is static without consideration of currency itself and capital market. In the second place, the balance of international payments is represented by the current account in practice, which means that the capital account is not analyzed in that reason. Therefore, the theory is not comparatively feasible at that moment.

Williamson (1994) improved this approach by “running simulations using large macroeconomic models”. There are a lot of new troubles which need to be settled consequently, such as “a considerable amount of parameter estimation”, “time lags in comparative static models”, “the size of model specifications in simulation models”. Because of these defects, the use of MB approach for actual measuring of equilibrium exchange rate is limited.

3.1.3 the Fundamental Equilibrium Exchange Rate (FEER) theory

Williamson(1994) improved MB approach by redefining the internal balance as “economy operating at capacity output” and the external balance as “a sustainable current account position”. Compared to Swan’s concept of equilibrium, the new theory seems more reasonable since the capital account balance has been introduced into the determinants of exchange rate.The equilibrium exchange rate in this new definition can be estimated by a function of the fundamental economic variables, that is the reason why we call it the fundamental equilibrium exchange rate (FEER).

The theory focuses completely on medium-term and long-term economic conditions, not concerning the short-term fluctuations (Williamson, 1994). When we apply the FEER theory, the external balance is specified by “simply equating account balance (CA) to capital account (KA)” (Reza Y. Siregar & Ramkishen S. Rajan, 2006). The current account is determined by “net trade balance” and “returns on net foreign assets”(Reza Y. Siregar & Ramkishen S. Rajan, 2006). At the same time, the capital account is accessed by exogenous factors. Apparently, this approach need set a large number of parameters not only in the current and capital accounts part but also in the domestic capital and labour markets. This makes the model very difficult to operate. Besides, the measurements can be quite sensitive to the selected parameters. Researchers also argue that the equilibrium exchange rate based on FEER theory is “a rate consistent with some notion of ‘ideal’ economic circumstances of internal and external balances” (Reza Y. Siregar & Ramkishen S. Rajan, 2006). The definition of internal balance is not achieved consensus in the academic point of view. Apart from that, the criterion of external balance is considered as “too subjective in nature” (Reza Y. Siregar & Ramkishen S. Rajan, 2006). In a word , the conditions to achieve equilibrium are extremely hard to realize in practice. Furthermore, the FEER method does not involve the equilibrium of money market and asset market, therefore, the analysis is not completely. Foreign scholars mainly apply the FEER theory to measure the equilibrium exchange rate in developed countries, since the economic situation are comparatively more complicated in developing countries. Chinese scholars have not seen some attempts in this area.

3.1.4 the Natural Real Exchange Rate (NATREX) approach

The natural real exchange rate (NATREX) theory was proposed by stein in 1994, and then developed by the researches of the author himself and some other scholars. Form Stein’s point of view, the criteria of internal and external balance should be defined in a new way (stein, 2001). The internal balance is “a situation where the rate of capacity utilization is at its longer run stationary mean” (stein, 2001). At the same time, the external balance is “a situation where, at the given exchange rate, investors are indifferent between holding domestic or foreign assets” (stein, 2001). By the above definition, it is clear that NATREX-based equilibrium exchange rate is a moving rate consistent with movements of exogenous and endogenous fundamental economic factors. We adjust the real exchange rate by the calculated equilibrium exchange rate, but can never reach that “ideal” level.

Furthermore, in common with FEER approach, NATREX pay much attention to medium-term equilibrium achieved by a series of conditions: “the domestic securities market clear”, “cyclical and short-term speculative capital flows cancel out”, “any difference between investment and saving represents the excess flow of supply of tradable long-term securities” (Reza Y. Siregar & Ramkishen S. Rajan, 2006). Hence, there is no short-term analysis generated by FEER model.

Another point worth mentioning, the theory is not easy to practice. According to stein (2001), the equilibrium exchange rate depends on “relative thrift” and “relative productivity”. In addition to these two fundamentals, the “terms of trade” also be taken into consider for small open economy as a exogenous variable ( MacDonald, 2004). In a word, the selected fundamental factors may vary from the “size of economy” and the “development stages of the local economy” (Reza Y. Siregar & Ramkishen S. Rajan, 2006). So much more than this, the following things are that choose appropriate proxies for the selected fundamental variables and then test the model by solving a series of simultaneous equations. The results of measurement are largely influenced by estimating parameters and setting exact form for equations. But both of them are proved to be greatly difficult to operate by some empirical studies.

Last but not least, the same with FEER, the NATREX model is comparatively more applicable to advanced economies. Many important data are not available in developing countries. Empirical studies have shown that the results from transition economies and emerging markets are not the results predicting by model (Reza Y. Siregar & Ramkishen S. Rajan, 2006). For these reasons, no researcher adopt NATREX model to measure the equilibrium value of Chinese currency so far.

3.1.5 the Equilibrium Real Exchange Rate (ERER) approach

The equilibrium real exchange rate (ERER) approach was introduced by Edwards in 1989 for the first time. And then, it has been revised and expanded gradually by Edwards and Elbadawi. For estimating equilibrium value of exchange rate in developing countries, the ERER approach has made a big step forward in theory. The hypothesis of this theory which given by Edwards are as follows¼š

• There are three types of goods in the market, namely, exports, imports, and non-tradables. The estimated country need produce exports and non-tradables, and consume imports and non-tradables at the same time.
• Nationals hold assets in both home currency and foreign currencies. Private sector may have a certain number of foreign currencies.
• Dual exchange rate is adopted as a fixed nominal exchange rate applies to commodities trading and a free-floating nominal exchange rate applies to financial transactions.
• Government consume imports and non-tradables, while the income is generated by non-distorting tax and the creation of domestic credit. And there is no public debt.
• Neither government nor private sectors are allowed to have foreign loans.
• Only the import tariffs exist, and the revenue from tariffs has been used for public.
• There is no effect of capital controls on government.

Based on these assumptions, the theory considers the characteristics of transition economies in developing countries adequately. It holds that the equilibrium exchange rate may be influenced by some policy variables such as parallel exchange rate, trade restrictions, transaction restrictions, capital flows and so on. Here, the equilibrium exchange rate is defined differently as “the relative price of non-tradables to tradables that results in the simultaneous attainment of internal and external equilibrium” (Nikola Spatafora and Emil Stavrev, 2003).

However, there are some drawbacks cannot be ignored. First of all, there is a gap between the reality and the assumptions made in this model. Secondly, the division of non-tradables is in a strongly subjective way. Thirdly, there is a high correlation within the independent variables in the dynamic model, which has impact of poor quality on the estimated results.

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