Estimating Foreign Exchange Reserve Adequacy

INTRODUCTION The accumulation in foreign exchange reserves (FER) has been widely observed in, especially, developing countries in the last few years. FER is undoubtedly a very important variable in macroeconomics. Rodrik (2006) states that there has been a rapid increase since the early 1990s in foreign reserves held by developing countries. He also states that these reserves have climbed to almost 30 percent of developing countries’ GDP and 8 months of imports. A country needs to maintain FER for various purposes, such as to finance import, to maintain exchange rate at a certain range of levels, or to maintain a certain level of exchange rate when the economy applies a fixed exchange rate system (for further discussion, see Monetary and Capital Markets Department, 2013; and Elhiraika and Ndikuma, 2007, among others). Some strategies have been invented to organize the FER. Antal and Gereben (2011) discuss the strategies to maintain FER before and after the 1997 Asian crises. Moghadam et al. (2011) focus on the precautionary aspect of holding reserves that reflect the key distinguishing characteristics of reserves, namely the availability and liquidity for Vol. 6 | No. 1 ISSN: 2089-6271


INTRODUCTION
The accumulation in foreign exchange reserves (FER) has been widely observed in, especially, developing countries in the last few years.FER is undoubtedly a very important variable in macroeconomics.Rodrik (2006) states that there has been a rapid increase since the early 1990s in foreign reserves held by developing countries.
He also states that these reserves have climbed to almost 30 percent of developing countries' GDP and 8 months of imports.
A country needs to maintain FER for various purposes, such as to finance import, to maintain exchange rate at a certain range of levels, or to maintain a certain level of exchange rate when the economy applies a fixed exchange rate system (for further discussion, see Monetary and Capital Markets Department, 2013;and Elhiraika and Ndikuma, 2007, among others).Some strategies have been invented to organize the FER.Antal and Gereben (2011) discuss the strategies to maintain FER before and after the 1997 Asian crises.Moghadam et al. (2011) focus on the precautionary aspect of holding reserves that reflect the key distinguishing characteristics of reserves, namely the availability and liquidity for potential precautionary reasons.Barnichon (2009) models the optimal level of reserves for lowincome countries against external shocks.Borio et al. (2008) focus at trends and challenge to manage foreign exchange reserves.
Besides these benefits, holding FER comes with its price.There are costs need to be born by an economy for holding FER.One of them is the opportunity cost, in terms of the difference between domestic and foreign borrowing rates.
Another cost need to be born would be the loss due the value reduction in the denominated foreign exchange reserve.This phenomenon is now faced by China, which has accumulated a huge amount of funds, mostly in US dollar (USD).
China suffers loss when USD depreciates.China has now been diversifying the foreign exchange reserve, holding various currencies.The USD proportion in China foreign exchange reserves has declined from 69% to 49% in three years, from 2011-2014 (Ning, 2014).Gosselin and Parent (2005), investigating reserve accumulation by central banks in emerging Asia, suggest that overaccumulation of reserves entails domestic costs such as exchange rate misalignment, loss of monetary control, and sterilization costs.Taking these costs into account would reduce the desired level of international reserves.Yeyati (2006) numerically illustrates the cost of holding reserves that are estimated as sovereign spread on the riskfree return on reserves paid on the debt issued to purchase them.Rodrik (2006) highlights the social cost of foreign exchange reserves.He states that the income loss to most developing countries amounts to close to 1 percent of GDP.
Another aspect of FER is its impact on macroeconomic variables.Fukuda and Kon (2010) find that an increase in foreign exchange reserves raises external debt outstanding and shortens debt maturity.They further suggest that increased foreign exchange reserves may lead to a decline in consumption, but can also enhance investment and economic growth.Chaudry et al. (2011) investigate the relationships between foreign exchange reserves and inflation by conducting an empirical research on Pakistan since 1960 and find that the rise in FER leads to lower the rate of inflation in Pakistan.Sultan (2011) investigates the aggregate import demand function for India using Johansen's cointegration method.He finds that there is a long run equilibrium relationship between real imports and real foreign exchange reserves, and that imports are inelastic with respect to foreign exchange reserve.
Considering the benefits, costs, and impacts of holding FER, an economy should organize the FER wisely.There are at least two issues matter, namely, how much FER should be maintained, and the currencies composition of the FER.Regarding the first issue, Zeng (2012) investigates whether the Chinese foreign exchange reserves have been too large.He finds that the Chinese actual foreign exchange reserves greatly exceeded the 3-month import foreign exchange demands and also that the optimal foreign exchange reserves demands were calculated to be 40% of the total foreign debt balance.Antal and Gereben (2011) find that international reserves are likely to increase further, which might generate further tensions in the global financial system.To avoid global imbalances, international coordination and alternative sources of foreign exchange liquidity should be reinforced.Siregar and Rajan (2003) (Romero, 2005;Sianturi, 2011;and Alam and Rahim, 2013, among others), Granger causality test (Akdogan, 2010), and dynamic model averaging (DMA), dynamic model selection (DMS) random walk, recursive OLS-AR, recursive OLS with all predictive variables models, or Bayesian model averaging (BMA) (Gupta et al., 2014).
Various independent variables have also been used to explain FER such as export and import (Akdoban 2010 andSianturi, 2011), current account balance (Wijnholds and Kapteyn, 2001;Gupta and Agarwal, 2004;Romero, 2005;and Alam and Rahim, 2013), capital and financial account balance (Wijnholds and Kapteyn, 2001;Gupta and Agarwal, 2004;and Alam and Rahim, 2013), exchange rates (Wijnholds and Kapteyn, 2001;Gupta and Agarwal, 2004;Romero, 2005;and Alam and Rahim, 2013), interest rate differential or opportunity cost (Wijnholds and Kapteyn, 2001;Gupta and Agarwal, 2004;and Akdoban, 2010;and Gupta et al. 2013), economic size or GDP (Wijnholds andKapteyn, 2001 andGupta andAgarwal, 2004), possibility of capital flight (Wijnholds andKapteyn, 2001 andGupta andAgarwal, 2004), and average propensity to import, Romero (2005) According to rule of thumb, the position of foreign currency in a country is said to be safe if the FER is enough to finance the country's import for at least three months (see Gupta et al., 2013 andZheng, 2013;among others).If, to make it simple, each year we import an amount of USD 12, throughout the year we have to be ready with, at least, ¼ times USD 12 = 3 USD.The ratio, ¼, comes from 3 months divided by 12 months.In another word, the FER-to-import ratio should be at least 0.25.As an alternative, this paper proposes to find the risky ratio level assuming that the ratio follows a certain type of distribution.Assuming this distribution, the risky ratio can be calculated as the Value-at-Risk (VaR).The VaR is calculated as the mean of the distribution minus the product of statistical value (say 1.65 for 95% assuming normal distribution, one side estimate) and the standard deviation of the distribution.In this case, we assume that in common situation, foreign exchange reserves are always enough to support imports.In such a case, the ratio will be higher than the VaR.The ratio will be lower than the VaR only in non-common situation, namely when there are unexpected shocks.Such shocks might come from domestic or foreign sources.Therefore, during a crisis, we can expect that the ratio will be lower than the corresponding VaR.As of the saying, there is no such thing as free lunch, accumulating reserves also has its cost.
The opportunity cost is included in the model to measure the cost of accumulating the reserves.
This paper uses the difference between Indonesian lending rate and US lending rate.
The dependent variable in this paper is the ratio between total foreign reserve (TRM), assuming that one of the main goal in accumulating foreign reserves is to provide enough funds to import.
As discussed, this paper models the TRM using both conditional mean and conditional variance.The are given by a 1 (a 1 + g 1 ) .When the conditional shocks, h t , follow a symmetric distribution, the expected short-run persistence is a 1 + g 1 /2, and the contribution of shocks to expected long-run persistence is a 1 + g 1 /2 + b 1 (see McAleer (2005)).
All data are taken from The World Bank (2014), except for the ER, which is from fxtop.com, available at http://fxtop.com/en/historical-exchange-.TRM is calculated as the ratio of Total Foreign Exchange Reserve divided by Import.GG is the growth of GDP, calculated by the formula of GG t = 1n(GDP t / GDP t-1 ).This formula has less probability to become a non-stationary series.OC is the opportunity cost of accumulating total reserve, calculated as the difference between Indonesian lending rate and the US lending rate.ER is the exchange rate, which is IDR/USD in this case.DUM is a dummy variable which takes zero for years prior the crises (1987 -1997) and one for years post the crises (1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012).

RESULTS AND DISCUSSION
To make sure that the estimation is not spurious, this paper tests the variables included in the model.Using a Dickey-Fuller test, the results are presented in It can be learned that the higher the GDP growth, the higher the TRM, reflecting the need of more foreign reserves, assuming that import is constant.
It can be learned as well that the higher the exchange rates, the higher the TRM.This means that as Indonesian Rupiah is weaken against the USD dollar, the economy needs to accumulate more reserves, since perhaps more imports is expected.In addition, the higher the OC, the higher the foreign reserves.Last but not least, the dummy variable also suggests the positive impact on the TRM.This means that post the 1997 crises, the TRM increases.It is commonly understood that when a country moves from a fixed exchange rate rezim to a floating one, it will accumulate less foreign reserves.This is so because the country does not need to maintain a certain level of exchange rates.
The fact that Indonesia has higher TRM following the crises perhaps suggesting that the impact of the aforementioned three independent variables are so strong that the impact surpasses that impact of the crises.
The results of the conditional variance equation suggest that the ARCH and GARCH impacts on the conditional variance are significant.This means that the variance is volatile in both the short and long runs.In addition, the results also suggest that the asymmetry of the negative and positive impacts is evident.This means that the negative shock has stronger impact than that of the positive one.
To estimate the VaR, the following formula is applied where VaR t is Value-at-Risk at time t, and X t represents all independent variables in the model.
The z value is the standardized normal distribution value calculated using a certain confidence level.This z value can be replaced with t value if it is assumed that t-student distribution is considered as the more appropriate distribution.The result is in Table 4.

MANAGERIAL IMPLICATIONS
This paper models the Value-at-Risk of total foreign exchange reserves to import ratio.When the ratio is lower than the Value-at-Risk, this means that foreign exchange reserve is not enough to support imports in such a way that it might endanger the whole economic system of the country.Therefore, the model can be used as a precautionary warning about such situation.
, and consumption differentials (Akdoban, 2010).Most of these researches are able to explain the behaviour of FER.However, these models do not answer the question of how much foreign exchange reserves should be maintained.The IMF, through its Monetary and Capital Markets Department (2013) have made guidelines in 2001, which then revised in 2012, for foreign exchange reserve management.They meant for helping strengthen the international financial architecture, to promote policies and practices that contribute to stability and transparency in the financial sector, and to reduce external vulnerabilities of member countries.The objectives of the guidelines are to ensure, among others, adequate foreign exchange reserves are available for meeting a defined range of objectives.However, they do not specifically mention the need to save the import of goods and services from other countries.
VaR has been widely used in finance and other risk management system to measure the risky value of a certain distribution.With the invention of conditional volatility models such as GARCH or stochastic volatility models, it is now possible to calculate the conditional Value-at-Risk.This enables us to evaluate the risky value of a certain variable in daily basis.For discussion about VaR, please readBrooks et al. (2005),Bhattacharyya et   al. (2008), andBao et al. (2006), among others.For conditional VaR, please readChan et al. (2007),Jabr (2005), andKu and Wang (2008), among others.The standard deviation used in this paper is a conditional standard distribution assuming that the variance of the model is volatile.We can use the help of GARCH family models to model such volatility.Therefore, this paper uses conditional VaR to model and estimate such foreign exchange reserves.For the usefulness of GARCH family model in modelling volatility, volatility spillovers, and conditional correlations, please refer to McAleer (2005) and McAleer et al. (2007).METHODS From the above discussion, this paper models TRM uses some variables that influence total foreign reserve, namely gross domestic product, exchange rates, and opportunity cost.To avoid regressing nonstationary variables, this paper uses GDP growth (GG) instead of GDP.GDP is included in the model to represent the economic size, in which reserves are expected to rise with population and real per capita The exchange rate uses in this paper is USD/ IDR.This variable is included in the model because it influences the need of the reserves to be accumulated.The higher the exchange rate flexibility, the smaller the reserves that needs to be accumulated.
conditional variance is then employed to calculate the VaR.Different from non-conditional VaR, where the value is calculated as the mean plus or minus the distribution value times the standard deviation, this paper uses conditional VaR since the standard deviation (volatility) is a conditional volatility, modeled by a family of GARCH model.This paper uses GJR model by Glosten et al. (1993), a family of univariate GARCH model which, in addition to traditional GARCH model, also accommodates the possibility of asymmetric impact of negative and positive shocks on the conditional variance.The model can be written as follows: of positive (negative) shocks Figure 1.Comparing Actual, Fitte, VaR-z, and VaR-t Values

Table 2 .
It can be inferred that the

Table 1 .
Data to be AnalyzedThe estimation results of the model are presented in Table3.It can be inferred that all variables in