# Literature Review focusing on China’s Foreign Reserves

The recent surge in foreign reserves of emerging market has revived old debates about the optimal level of reserves. China is a typical representative case for this buildup. In 1990 China hold 29.5 billion dollars foreign reserves around 8% of GDP denoted by dollars. During past 5 years the average reserves to GDP ratio surge dramatically to 42.5%. In 2006 China overtook Japan as the country with the largest foreign exchange reserves.

For the sake to solve the puzzle of recent buildup it is necessary to establish a quantity criterion to measure the optimal level of reserves. Therefore this dissertation mange to extent original Jeanne and r(2008) ‘s model in order to establish a more precise standard to evaluate the optimal level of foreign reserves.

This dissertation contributes to a long list of literature on reserves.

The dissertation is structured as follows. Section 2 present the position of china’s foreign reserve, moreover measure the adequacy of the level of reserves by reference to several conventional benchmark. Section 3 exhibit the extend model yielding a modified formula for the optimal reserves. Section 4 show the calibration of the model and investigate the model by using sensitive analysis. Section 5 estimate the probability of sudden stop by employing Ben-Bassat and Gottlieb’s approach. Section 6 present the conclusion and reveal possible limitation of this dissertation.

Literature review

Early theories

Under the gold standard money system, gold serve as the fundamental preparation for currency issue. Meanwhile in this period gold is the main form of the international reserves. Therefore the relationship between gold reserves and domestic money supply attracted great research attention for the politics and academics. According to Thornton (1802), the level of the gold reserve is determined by the potential benefits in smoothing domestic fluctuations. This theory, however, fails to accounted the external factors such as trade deficits (Keynes 1913,1930). In 1940’s the researcher come to an agreement that international reserves should consider to be an stock for international transaction rather than backing of domestic money supply(Badinger 2001). Hence in the following period the academics conduct their study of level of international reserves on the area of international trade.

The Benchmark or ratio approach

With the development of international trade, the requirement of payment for international truncation became the main function of the foreign reserve. Nevertheless after the Second World War major countries implement exchange controls for the reason that inadequate international liquidity. Therefore IMF was required to supervise exchange controls by employed some benchmark or yardstick. Triffin(1946) state that the adequacy of international reserves should be judged by the ratio of reserve to imports. According to Triffin’s(1946) research if the reserve ratio maintain the level of 30%, it allows the country to mitigate the effect of external deficit. Triffin(1960) demonstrate that reserves to imports ratio (R/M) serves as a good indicator of optimal reserve level. Through the analysis of data from 12countries from 1950-1957, Triffin(1960) point out that the appropriate R/M ratio should be 40%, moreover 25% is the floor boundary for the level of the reserve.

R/M ratio approach become prevalence in the monetary authorities duo to its simplicity and practical which is quite easy to adopt. In practice, the government maintains the level of reserve enough to cover three months import (Williamson 1973). Also this approach is employed by academics to measure the adequacy of the demand foreign reserve.

Although the practical of the Triffin’s ratio, it is criticized by researchers due to its flaws. Foremost the R/M ratio approach is based on international trade, however, this statement is not consistent with the definition of the function of foreign reserve. Nurkse(1944) emphasize that foreign reserves are consider to use as finance deficit payment rather than trade purpose. In other word authorities not only have the obligation but also impossible to make a payment for the private sector. The central bank serves simply as an agent for the private sector during exchange controls period.

Furthermore the R/M ratio fails to include strong theoretical support. Grubel (1971) indicated that the Triffin’s ratio approach is simply a transform of the relation of money demand and the volume of transactions. This implication implies that there is a stable relationship between requirement of foreign reserve and international transaction. In other word the R/M ratio is only a replicate of the theory of money quantity. Thus the ratio approach is not an sufficient evidence to discriminate the optimal level of foreign reserve.

In addition, the Triffin’s ratio implies the demand of reserve is solely determined by trade. It fails account other factors relevant to the reserve such as the fluctuation of international trade (Nukse, 1944 and Heller, 1968) Last but not the least, it is not appropriate that set a stable standard about 40% to all countries through different time. The R/M ratio is too rigid to serve as an benchmark (Badinger 2000).Accordingly, Triffin’s R/M ratio is insufficient served as criteria to determine the level of foreign reserve.

With the development of the theory for the optimal reserve, researchers have capture improvement for the ratio approach by employed other factors such as: reserves to short-term external debt, reserves to M2 ratio and reserves to GDP ratio.

After the domination of the Triffin’s ratio, the most prevalent ratio used by researcher and political is reserves to short-term external debt ratio also called “Greespan Guidotti Rule”. This ratio imply that for the sake of maintain an rational country’s operation, the authority should hold enough foreign reserves to resist the possibility of a massive withdrawal of short term debt. Compared with Trufin’s ratio, Greenspan Guidotti Rule lead to a shift of attention to the vulnerability of a country’s financial account. According to Bussiere and Mulder (1999) reserves to short-term debt ratio is a proper benchmark for the emerging economy community that with good fundamentals. In other word by reference to the ratio, the authority is easy to avoid contagion-related crises. Besides this approach is supported by recent empirical research ( Jeanne and Ranci 2005 Jeanne 2007). Accordingly, this ratio have already been incorporated as an benchmark by IMF to indicate financial crisis ( Berg et al 1999). l

Reserves to M2 ratio. Although the reserves to short-term debt ratio can be consider as an indicator for warning purpose of financial crisis. However, this ratio only represents a loose relationship between reserves and macroeconomic circumstance. Therefore reserves to M2 ratio is designed which is a measure of reserves and broad money supply. Researchers have demonstrate that there is a negative relationship between the level of the ratio and the probability of financial crisis (Kaminsky et al 1996, Berg et al 1999). Alternatively the higher ratio implies a lower probability of crisis. Furthermore this ratio is not only provides an benchmark for floating exchange rate countries but also serve as an appropriate indicator for pegged exchange rate countries since reserves to M2 ratio is a extraordinary yardstick to measure of potential foreign asset demand from domestic for pegged exchange rate countries (Calvo 1996). In addition, Wijnholds and Kapteyn(2001) provide two different level of ratio for countries with different exchange regime. For pegged exchange rate countries is 10%-20% and for floating exchange rates countries 5% to 10% is appropriate level.

Last the ratio of reserves to GDP is another alternative approach for the benchmark approach. This approach is criticizes by Torgerson (2007) that there is no clear logical relationship between reserves and GDP. Moreover, similar to the Triffin’s ratio, this ratio also lack of theoretical support until 2008, Jeanne and Ranci(2008) develop a model in a small open economy to capture the optimal the level of reserve. According the finding of their model, the optimal ratio of reserves to GDP is 9%.

The cost-benefit model

Apart from ratio approach, Heller (1966) developed a novel framework cost-benefit to investigate the demand of foreign reserves. Foremost Heller (1966) point out that transaction payment is not appropriate server as an motivation for holding reserves since authority are not involved in international trade in general. However, the precautionary consideration is recognized to be the dominated concern. Moreover, Heller suggests that the optimal level of reserves is determined by three factors: (1) the cost to mitigate the external imbalance (2) the opportunity cost of holding reserves and (3) the probability of imbalance.

To be more specific, Heller’s cost-benefit model imply that the authority financing the disequilibrium by foreign reserves other than adjusting national income level which lead to direct cost. Therefore the benefits bring out by holding reserves can be estimate by the cost caused by adjusting income level. However, holding certain level of reserves is not without cost which is measured by the opportunity cost given by the difference between return of capital investment and return of reserve related investment. Therefore after acquiring the probability of imbalance, it is possible to identify the total adjusting cost. Finally the optimal level of reserve is determined when the marginal benefits (adjusting cost) equals to the marginal opportunity cost. In other words in this moment the total cost of adjusting is minimized.

It is undeniable that Heller’s work extend the analysis framework for the optimal reserves not only formulating precautionary motivation of reserves but also involving probabilities of future deficits (Hamada and Ueda, 1977;Bahmani-Oskooee and Brown,2002) However Heller’s model failed to the external effect on the adjustment of the income and holding reserves. According to Haberler (1977), country in a floating exchange rate regime did not need foreign reserves since fluctuate of exchange rate would correct the imbalances of payment. Thus subsequent works make modification for the original model by including alternative adjustment policies. Kreinin and Heller (1973) extend the model by introducing exchange rate variations. Claassen (1975) seek to measure the cost induced by external disequilibrium by employed more than one means.

In addition there is another important extension introduced by Agarwal (1971) to developing country. Agarwal (1971) modify the measure of opportunity cost of holding reserves by introducing the proportion of imported necessary raw materials and other factors characterize the difference between developed country and developing country. Last a further refinement of the original Heller model is focus on the probabilistic aspect relative to adjustment to external disequilibrium (Hamada and Ueda, 1977; Frenkel and Jovanovic, 1981). This arose a new sort of model called buffer stock model.

The Buffer stock model

Since the imperfection of the Heller’s model, Hamada and Ueda (1977) further developed Heller formula by involving inventory management developed by Miller and Orr (1966). To be more specific their extended model captured drift effect, serial correlation , lag of policies and fluctuate of speculative capital. In addition Hamada and Ueda (1977) argue that the authority, in general, tend to adjust the domestic economy to accompany the external deficit until exhaust of foreign reserves.

Moreover there is another prominent model introduced by Frenkel and Jovanovic (1981). Similar to Hamada and Ueda’s work, Frenkel and Jovanovic’s model also based on the inventory approach developed by Miller and Orr (1966). Foremost this model implies that reserves server as a buffer stock against external transaction fluctuation. In other words the level of holding reserve is determined by the variability of international transaction. The most important contribution of their work is the involvement of the stochastic process to mimic the demand for reserves and a continuous time analysis framework for inventory (Frenkel and Jovanovic, 1980). According to the buffer stock model the optimal level of reserve is positive to volatility and imports and negative to the opportunity cost of holding reserves. These argument are consist to later empirical literature.()

Besides Jung (1995) make a refinement on the buffer stock model in theory by introducing the maximum limit of reserves. Jung(1995) advocate that without the upper bound of reserves ,Frenkel-Jovanovic’s model may lead to unrealistic infinity stochastic process.

The optimizing model of Ben-Bassat and Gottlieb

Even though there is sort of imperfection of the Frenkel-Jovanovic’s model, it still popular in the research area in optimal reserve before the emergence of Ben-Bassat and Gottlieb (1992) model. Ben-Bassat and Gottlieb’s model is consist to Heller (1966)’s assumption of the motivation of holding reserves is precautionary requirement. In addition, their model is focus on the sovereign risk and the cost of default. Ben-Bassat and Gottlieb (1992) argued that the optimal level of reserves is reached when the expected total opportunity cost of holding reserves is minimized.

Contrast to actual reserve data for Israel Ben-Bassat and Gottlieb (1992)’s model performance better than conventional model. In comparison to previous literature, Ben-Bassat and Gottlieb model made several improvement and modification. First Ben-Bassat and Gottlieb state that the cost of reserve depletion should be measured by output loss where Heller (1966) and Clark (1970) assert that the cost can be indicated by a function of the economy’s openness. Second Ben-Bassat and Gottlieb defined the opportunity cost of holding reserves as the differential between the countries marginal productivity of capital and the financial return on reserves. Finally an important improvement is the determination of the probability of a country’s default on external payment. Based on Feder and Just (1977), B-G model imply a stable relationship between deficit probability and economic variables such as the ratio of reserves to imports(R/M), propensity to import (M/Y) and the ratio external debt to exports(D/X). Though this approach it is possible to estimate the probability of default.

It is deniable that the B-G model is focus on borrowing countries’ reserve management. Ozyildirim and Yaman(2005) claim that the B-G model allows authority to calculate the optimal level of reserves by involving nation’s specific information. Furthermore B-G model take current account imbalance into consideration which is more appropriate for the case of emerging markets. In addition this model extended the cost of holding reserve to a more wider scope including economic or financial crisis. Accordingly the research framework developed by Ben-Bassat and Gottlieb (1992) has been employed by later researchers to analysis the optimal level of reserves in different countries such as Thailand (Vimolchalao 2003) Turkey (Ozyildirim and Yaman 2005) and India(Gupta 2008) etc.

Utility-maximizing model

Jeanne(2007) developed a utility-maxmizing approach in order to conduct the optimal level of foreign reserves. Heller(1966) argue that the optimal level of reserves reached when the sum of the expected cost of adjustment and the opportunity cost of holding reserves is minimized. Furthermore this model was mainly focus on the current account. The main spirit of Heller’s model was developed by Baumol- Tobin inventory model where the current account deficit followed a stochastic process. In the recent literature representative agent has been employed as the criterion to measure the adequacy of reserves. In other words these literatures imply welfare-based approach is involved in the measurement. Caballero and Panageas (2007) establish a dynamic equilibrium model which allows the country during sudden stop can invest in not only conventional reserves such as fixed income foreign assets but also derivatives assets whose payoffs are under the condition of sudden stop arrivals. They found that hedging strategies contributed to minimize the cost of sudden stop. Subsequently Durdu et al (2007) mange to estimate the optimal level of precautionary reserves in a small open economy by involving business cycle volatility, financial integration and the risk of sudden stop. They assert that financial integration and the risk of sudden stop serves as the key explanations of recent buildup of the foreign reserve.

Nevertheless the loosely relationship between reserves and domestic welfare result in the ambiguity in the definition. Therefore Jeanne (2007) establishes a welfare-based model features a open small economy vulnerable to external crisis which induce a fall in output. Another interesting part of the model is the economy is represented by a consumer holding a certain level of foreign assets. This capital is allowed to invest in liquid foreign assets or illiquid asset. Foreign assets yield benefits referring to crisis mitigation and crisis prevention, however holding these foreign assets entail an opportunity cost relative to illiquid investment with higher profit. Thus the optimal level of reserve is determined when the representative consumer’s utility maximize. Jeanne and Rancière(2008) extend the utility function of Jeanne(2007) from 3 separate period to infinite period. Moreover according to Aizenman and Marion(2003) many emerging market countries view holding reserves as a form of self-insurance against fluctuation of capital flow especially after international financial crises. However there are only limited academics focuses on the research of quantifying the level of reserves of that can be defined as an insurance contract. Jeanne and Rancière(2008) present their model as insurance rather than precautionary savings. However this modification did not change the assumption for accumulated reserves as precautionary consideration. Finally another contribution of this paper is that Jeanne and Rancière(2008) derived the optimal level of reserves as a ratio form (reserves-to-GDP ratio) which is close to Greenspan-Gridotti rule.

In a nut shell, there is a apparent shift refer to the motivation for holding foreign reserves from international transaction payments to precautionary purpose. The early benchmark approaches implicitly assume authority holding reserves to cover the payment requirement from international. However argument for international payment has changed after the appearance of Heller’s cost- benefit model. It is generally agreed that precautionary motivation of holding reserves serves as the intention. In addition accumulation of reserves is not costless since the foregone earning on those holding. Afterward the establishment of cost-benefit analysis framework, the researchers focus on identifies the optimal level of foreign reserves by minimizing the net holding cost. Subsequently the buffer stock model apply the inventory control measure to determinate the optimal reserves. This approach is quite appropriate for the industrial or developed countries which are supported by empirical literatures. However the buffer stock model fails to capture the character of the emerging market, the emergence of Ben-Bassat and Gottlieb’s model bridge the gap and extend the optimizing reserves by involving country risk and economic failure cost. Furthermore the utility approach strengthens the loose relationship between foreign reserves and domestic welfare, determining the optimal level reserves by maximizing the reprehensive consumer’s utility. This approach has already demonstrated the explanation power for analyzing the case of emerging market before recent reserves accumulation climb up. Nonetheless over the past several decades the expected utility theory was challenged by number of empirical literatures on human preference patterns (Neumann-Morgenstern, 1947). Moreover several non-expect utility models were developed to feature the evidence of empirical works (Fishburn, 1988, Camerer, 1989). The prospect theory is the most prominent model which explain violation of the traditional utility theory. Therefore, this dissertation will attempt to extend the original J-R model by introducing the prospect theory to measure the optimal level of foreign reserve.

## 2.1. Introduction for the prospect theory

## 2.1.1 Prospect Theory

According to the conventional economic theory, the value placed on outcome is called “utility” which is measured relative to states of wealth. Furthermore, the expected utility of an option is the sum of the products of utilities time probabilities, which is employed by Jeanne and r in their optimal foreign reserve model. However, actual selection often exhibit systematic deviations. In the scopes of behavior finance Tversky and Kahneman (1981) constructed prospect theory, which introduces the decision-making process under risk as a counterpoint to the expected utility theory. In their seminal work, they employ series of laboratory experiments and documented some choice problems that violate expected utility theory including certainty effect and reflection effect. They developed the prospect theory to capture these irrational decision-making processes based on laboratory experiments.

In their theory, the outcome of a “gain x with probability p and y with probability q” is captured by a value function (denoted by v(.) and a probability weighting function(denoted by(.))

(1)

It can be seen from above equation, prospect theory may be viewed as a modification of expected utility theory. One improvement regards the weights for the possible form. In this theory, the utility of each possible is multiplied by a probability weighting function (PWF) features as a non-linear transformation of the physical probabilities. According to Gregory et.al (2009) there are two major characteristic features: it over-weights low probabilities and under-weights high probabilities. Moreover, PWF is asymmetric and having a fixed point at a probability level of about 30%. It is also noticeable that the theory allows for different PWFs for gains and losses with above basic properties.

Nevertheless, the prospect theory is criticized that the PWF does not satisfy stochastic dominance which as an assumption that theorists applied. Furthermore, it failed to extend the theory with large number of outcomes Tversky and Kahneman (1992). Quiggin(1982) bridge the gap by employing the rank-dependent model. In addition Tversky and Kahneman (1992) developed cumulative prospect theory which generalized the original prospect theory to capture the situation with more than two outcomes.

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