Optimum international reserves and sovereign risk: Evidence from India

Journal of Asian Economics 28 (2013) 76–86

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Journal of Asian Economics

Optimum international reserves and sovereign risk: Evidence from India Prabheesh K.P. * Department of Liberal Arts, Indian Institute of Technology Hyderabad, Ordnance Factory Estate, Yeddumailaram 502205, Andhra Pradesh, India

A R T I C L E I N F O

A B S T R A C T

Article history: Received 11 December 2012 Received in revised form 4 July 2013 Accepted 6 July 2013 Available online 15 July 2013

This paper empirically determines the optimal level of international reserves for India by explicitly incorporating the country’s sovereign risk associated with the default on external debt. The optimum level of reserves is determined by minimizing the central bank’s cost function, which consists of costs due to high reserve holdings and costs due to reserve depletion. The simulated optimum reserves for the period 1994–2010 indicate that actual reserves are higher than the optimum value across the sample period, except during 1997–1998. ß 2013 Elsevier Inc. All rights reserved.

JEL classification: E58 F31 F34 Keywords: International reserves Sovereign risk Optimization ARCH Cointegration

1. Introduction Over the last decade, there has been a steep increase in global international reserves from US$2 trillion in December 2000 to US$11 trillion in April 2013 (IMF, 2013). This increase is mainly driven by the massive reserve accumulation by emerging economies, where reserves increased from US$0.75 trillion to US$7.4 trillion in the same period. Since the recent financial crisis, even some of the countries that have traditionally not emphasized the need for reserves have also started accumulating reserves (IMF, 2012). IMF (2012) argues that the excessive reserve accumulation leads to prolonged global economic imbalances due to Triffin’s Dilemma, and jeopardizes the stability of the international monetary system. It is worthwhile to note that the International Monetary and Financial Committee instructed the IMF to help its members to reduce the perceived need for excessive reserve accumulation (IMF, 2009). The prime motivation for the sizable holding of international reserves is precautionary or self-insurance against a sudden stop in capital inflows and the sudden loss of access to the international capital market (Aizenman & Lee, 2007; Mendoza, 2010).1 Countries with high levels of reserves not only reduce the cost of financial crises but also make such crises less likely

* Tel.: +91 40 2301 6013. E-mail addresses: [email protected], [email protected]. 1 An alternative explanation is the mercantilist motive, which states that the reserve accumulation is the by-product of the export and exchange rate policies of the emerging markets (Dooley et al., 2003). However, the empirical evidence for this motive is weak compared to the precautionary motive (Aizenman & Lee, 2007). 1049-0078/$ – see front matter ß 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.asieco.2013.07.001

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Fig. 1. Trends in international reserve holdings in India. Source: RBI.

(Rodrik, 2006). In addition, a high level of reserves also helps to lower the costs of external borrowing and improves credit ratings on sovereign foreign currency debt (Hviding, Nowak, & Ricci, 2004). These benefits, however, come at a cost. Reserves are mainly invested in US treasuries, which earn a modest return that is far lower than a government’s own cost of borrowing either in local or foreign currencies (Aizenman & Marion, 2003).2 Naturally, the question arises as to why one should keep cash in a bank while simultaneously paying high interest on outstanding liabilities. Critics argue that emerging economies require high investment for growth; hence, investing these reserves in productive sectors and infrastructure promises more prospective returns (Afzal, 2010). At the same time, the supporters of high reserve holdings argue that the cost of holding is small compared to the economic contraction of a financial crisis. Given this scenario, the real challenge for the central banks of emerging economies is to maintain reserves at the level at which the benefits are at least equal to the cost of holdings. The present study attempts to determine the optimum level of reserves for India such that the country can optimally control both the benefits of holding precautionary savings and the cost of idle stocks under the risk of economic contraction. India holds more than US$296 billion as international reserves as of the end of April 2013, and this level of reserves accounts for more than 16% of India’s Gross Domestic Product (see Fig. 1). Although the issue of optimality of reserve holdings has been discussed among policy makers, few studies have attempted to estimate the optimum level of reserves for India by following the cost-benefit approach. Ramachandran (2004) and Ramachandran and Srinivasan (2006) derived the optimum level of reserves by following the reserve optimizing model proposed by Frenkel and Jovanovic (1981), and found that India’s reserve level was higher than the optimum level during the periods of 1999–2003 and 2001–2005. However, the major shortcoming of Frenkel and Jovanovic’s optimizing model rests on its assumption that a country’s balance of payment (BoP) disturbance is random. This assumption may not be valid for most developing countries because BoP deficit is a common phenomenon in these countries, and the countries generally borrow from international markets. For such cases, Ben-Bassat and Gottlieb (1992) suggested that the ‘‘sovereign risk’’ of the country should be considered while calculating optimum reserves. Considering India’s sustained current account deficit over the two decades and high external borrowings, it can be argued that sovereign risk is an important factor to be considered while determining optimum reserves for India. The rest of this paper is organized as follows: Sections 2 and 3 address the theoretical model and data sources. Econometric methodology and empirical results are given in Sections 4 and 5, respectively. Section 6 presents the conclusion. 2. Theoretical model In the present study, the optimum level of reserves for India is calculated by following the reserve optimizing model proposed by Ben-Bassat and Gottlieb (1992) (hereafter abbreviated as B-G). This model entails that a central bank optimizes the reserve level by minimizing the total cost associated with reserve holding. The total cost of holding reserves consists of

2

The available estimates suggest that the cost of holding is around 1% of developing countries’ GDP (Rodrik, 2006).

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two components: a cost associated with reserve depletion or zero reserves, and the cost due to positive reserves. The expected cost function is expressed as follows: Minimize EðTCÞ ¼ pC 0 þ ð1  pÞC 1

and

C 1 ¼ rR

(1)

where TC is total cost, E is the expectation operator, C0 refers to the cost due to low reserves, and C1 denotes total opportunity cost or the cost due to positive reserves. Similarly, r and R are the opportunity costs of reserve holdings and total reserve holdings, respectively, and p and (1  p) are the probability of reserve depletion and the probability of positive reserves, respectively. B-G argues that most developing countries borrow from international markets, and therefore hold high levels of reserves in order to maintain creditworthiness. A sudden depletion of reserves may lead to a higher servicing cost of external debt, thus implying a reduction in the supply of foreign credit and further depletion of reserves. That, in turn, may cause a sovereign debt crisis and consequent output decline. Hence, the cost of reserve depletion (C0) can be viewed as the output loss due to default, and p as the probability of default. Eq. (1) implies that the central bank optimizes the level of reserves by trading-off between output and return losses. It is also assumed that reserve holdings and the probability of default are negatively related, which in turn implies that a country with high reserve holdings is less likely to default on its external debt. The probability of default can be expressed as

p ¼ f ðR; ZÞ and

@p ¼ pR < 0 @R

(2)

where Z is a set of economic variables that determine the default risk of a country. pR is expected to be negative because the default risk is likely to decline with an increase in the level of reserves. Differentiating Eq. (1) with respect to R, we arrive the optimum level of reserves:

@EðTCÞ ¼ pR ðC 0  rRÞ þ ð1  pÞr ¼ 0 @R

(3)

which can be expressed as: R ¼

ð1  pÞ

pR

þ

C0 r

(4)

where R*, the optimum level of reserves, depends on the cost of default (C0), opportunity cost (r), and absolute and marginal default probabilities (p and pR). The following subsections explain the measurement of these variables. 2.1. Cost of default (C0) As most developing economies borrow from international capital markets, the cost of reserve depletion, as argued above, can be viewed as the cost of default on external debt. Several studies suggest that default is associated with a decline in output growth ranging from 0.5 to 5%, and contraction of output may last for 10 years (Cohen, 1992; Paoli, Hoggarth, & Saporta, 2009; Sturzenegger, 2002). Thus, GDP foregone due to financial crisis can be a better proxy to measure the cost of default. Hence, for the present study, the cost of default is measured as India’s output contraction during the BoP crisis in 1990–1991.3 2.2. Probability of default (p) B-G assume a logistic probability function for probability of default (p), which is a function of the soundness of macroeconomic variables that reflects external liquidity and solvency. They specify p as follows:

p¼

ef 1þef

(5)

where ef is the exponential function of variables such as reserves to imports, external debt to exports, value of imports and output. p is expected to vary exponentially (e) with respect to the macroeconomic fundamentals because a small deterioration or improvement in the liquidity and solvency condition of a country is expected to have an exponential impact on its default risk. Following Feder and Just (1977), B-G equate the odds of default p/(1  p) to the discounted risk premium in a perfect capital market.

p 1p

¼

i  i 1þi

(6)

3 This crisis was mainly due to low levels of international reserves along with high fiscal deficit and current account deficit. Reserves with the RBI declined from US$3.11 billion in August 1990 to US$896 million in January 1991, which was hardly sufficient to cover three weeks of import (Ministry of Finance, 1992).

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where i is the interest rate offered to the risky borrower, and i* is the risk-free rate. By substituting Eq. (5) in Eq. (6), we obtain

p 1p

¼ ef

(7)

Similarly,  p  ¼ logðe f Þ ¼ f log 1p Therefore,   i  i f ¼ log 1þi

(8)

(9)

or f is equal to the log of discounted risk premium or spread, which can be estimated by regressing it with macroeconomic fundamentals.4 Following Edwards (1986), Nogue´s and Grandes (2001), and Ferrucci (2003) the risk premium equation can be specified for India as       i  i sted fd ¼ a0 þ a1 ln fii lt þ a2 ln þ a3 ln (10) þ et ln res t gd p 1þi t where (i  i*)/(1 + i), fii , sted/res and fd/gdp are risk premium, volatility of foreign institutional investment, short-term external debt to reserves, and fiscal deficit to GDP, respectively. a1, a2 and a3 are the parameters to be estimated, a0 is the intercept, et stands for error term, and t denotes time. A positive relationship is expected between risk premium and volatility of foreign institutional investment. This is because the higher volatility of short-term capital flows increases the financial vulnerability of the country, and, thus, a higher premium may be charged for external borrowings. Similarly, a positive relationship is expected between risk premium and sted/res because a high short-term external debt to reserves indicates high liquidity risk and the inability of a country to meet its short-term external obligations. This may adversely affect the creditworthiness of the country and lead to a higher risk premium. Likewise, a positive relationship is expected between spread and fd/gdp because high fiscal deficit to GDP reduces the ability of the government to retire its external debt and thereby increases the risk premium. 3. Data To estimate the optimum international reserve for India, quarterly data from 1994:02 to 2009:04 were used. Data have been collected from various sources, such as the Handbook of Statistics on Indian Economy of Reserve Bank of India (RBI) and the Status Report on India’s External Debt of the Ministry of Finance of India. All variables are measured in current prices. Because quarterly estimates of India’s GDP are available only from 1996 onwards, the estimates by Virmani and Kapoor (2003)5 have been used for the earlier period. Similarly, the short-term external debt series are not available on a quarterly basis; therefore, the annual series is interpolated into quarterly series. fii is proxied by the conditional variance of net foreign institutional investment (fii) to the Indian stock market. Similarly, the risky interest rate (i) is the average of interest rate paid on India’s external commercial borrowings (ECB) and interest rate offered to non-resident Indian (NRI) deposits.6 The risk free interest rate (i*) is proxied by the London interbank offer rate (LIBOR) drawn from the website of British Banker’s Association, and, finally, the 91 days Treasury bill yield rate is proxied for opportunity cost (r). 4. Econometric methodology The cost of default (C0), i.e., output contraction due to financial crisis, was calculated by employing the H-P filter method, while the ARCH model is used to derive the volatility series of foreign institutional investment (fii). The Autoregressive Distributed Lag (ARDL) cointegration procedure is used for the estimation of the spread Eq. (10). A brief description about these methods is given below. 4.1. H-P filter method Hodrick and Prescott (1997) filter method computes the smoothed series of GDP, gdpT, by minimizing the variance of gdp around gdpT, subject to a penalty that constrains the second difference of gdpT. The H-P filter chooses gdpT to minimize n n1 X X 2 2 ðgd pt  gd pTt Þ þ l ðDgd pTtþ1  Dgd pTt Þ i¼t

4

(11)

t¼2

A similar approach is followed by Ozyildirim and Yaman (2005) to estimate the optimum level of reserves for Turkey. The authors estimated back series of India’s GDP by adopting the methodology developed by the Central Statistical Organization. 6 The share of ECB and NRI deposits to India’s external debt is 27.6% and 25.6%, respectively (Ministry of Finance, 2009). Since these debt components constitute more or less the same share to total external debt (26–28%), a simple average of interest rates of these components is used. 5

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where l is the smoothing parameter and n is the sample size. l takes the value of 1600 for quarterly series (Harvey & Jaeger, 1993). The difference between the actual series (gdpt) and the smoothed series (gd pTt ) is the output gap or the cost of default. 4.2. ARCH model The volatility measure of foreign institutional investment, fii , is generated by applying the Autoregressive Conditional Heteroscedastic (ARCH) model developed by Engle (1982). The ARCH(p) model specification can be written as fiit ¼ m þ et

et  Nð0; ht Þ Vt1 ht ¼ v þ

p X

ai e2ti v > 0;

(12)

a1 ; . . . ; a p  0

(13)

i¼1

Eq. (12) is the conditional mean equation, where m is the mean of fiit. et is the error term, conditional on the information set Vt1, and it is normally distributed with mean zero and variance ht. Eq. (13) is the variance equation, which shows that the conditional variance ht depends on mean v and the information about the volatility from previous periods e2ti . The size and significance of ai indicates the presence of the ARCH process or volatility clustering in the series. 4.3. The ARDL bound testing approach to cointegration To estimate the risk premium equation, the Autoregressive Distributed Lag (ARDL) cointegration procedure, developed by Pesaran, Shin, and Smith (2001), was used. The main advantage of this method is that this test can be applied irrespective of whether variables in the model are purely I(0) or purely I(1). The error correction model of the ARDL model pertaining to Eq. (10) is as follows:           p X i  i i  i sted fd i  i D ln ¼ a0 þ l1 ln þ l2 ln fii lt1 þ l3 ln þ l3 ln þ bi D ln res t1 gd p t1 i¼1 1þi t 1 þ i t1 1 þ i ti     p p p X X X sted fd þ di ln fii lti þ fi D ln þ g i D ln þ ut (14) res gd p ti ti i¼1 i¼1 i¼1 Pesaran et al. (2001) proposed an F-test for the joint significance of all lagged level variables. If they are all jointly significant, then there is cointegration. That is the null hypothesis H0 : l1 = l2 = l3 = l4 = 0, which is tested against an alternate hypothesis H1 : l1 6¼ l2 6¼ l3 6¼ l4 6¼ 0. Pesaran et al. (2001) proposed lower and upper critical values for the Fstatistic, assuming all variables are I(0) for the lower bound and all variables are I(1) for the upper bound. If the computed Fstatistic exceeds the upper critical value, then the null of no cointegration can be rejected irrespective of the order of integration of the variables. Conversely, if the test statistic falls below the lower critical bound, then the null of no cointegration cannot be rejected. However, if the test statistic falls between the lower and upper critical values, then the result is inconclusive. In the present case, the critical values proposed by Narayan (2005) for small sample size is followed. 5. Empirical results 5.1. Estimation of cost of default (C0) The cost of default was measured by calculating the extent of output contraction during the BoP crisis in India in the early 1990s. Table 1 shows the deviation of actual GDP from its potential growth rate for the period 1991–1992 to 1996–1997. The table shows that during the crisis period 1991–1992, the current and constant GDP growth of India contracted by 4.7 and 4.4%, respectively. Similarly, the cumulative output loss due to crisis for the period 1991–1992 to 1993–1994 is found to be 7.5 and 5.2% at the current and constant price, respectively. Therefore, the optimum level of reserves for India was calculated by considering the two maximum ranges of output contraction, i.e., 4.8 and 7.5%. 5.2. Estimation of probability of default (p) 5.2.1. ARCH variance of foreign institutional investment The variable fii is derived by estimating the ARCH (2) model of foreign institutional investment (fii).7 The result in Table 2 shows that the ARCH effect is significant in the conditional variance of foreign institutional investment.8 The model diagnostics do not indicate serial correlation in the standardized squared residuals or ARCH effect on residuals. Therefore, the conditional variance derived from this model was used as the proxy for volatility of foreign institutional investment.

7 8

The variable fii is found to be stationary in level (Phillips–Perron unit root test statistic is found to be 3.12, which is statistically significant at 1%). We also estimated the volatility series using GARCH model. However, the results are not stable.

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Table 1 Actual and potential GDP growth. Year

At current price

At constant price (1993–1994)

Actual

Potential

Deviation

Actual

Potential

Deviation

1991–1992 1992–1993 1993–1994 1994–1995 1995–1996 1996–1997

14.44 15.68 15.78 17.48 17.21 17.66

19.19 17.45 16.78 16.43 15.84 14.81

4.75 1.76 1.00 1.04 1.37 2.85

1.29 5.11 5.90 7.25 7.34 7.83

5.73 5.85 5.98 6.09 6.16 6.18

4.43 0.73 0.07 1.16 1.17 1.65

Source: RBI (actual GDP growth) and author’s estimates (potential GDP growth). Notes: The potential GDP is the trend value of the GDP derived by using H-P filter method, and the annual growth rate is calculated by taking the average growth rates of quarterly GDP corresponding to each period. Annual, rather than quarterly, growth rate is shown to depict aggregate magnitude of the impact of the crisis on output growth.

Table 2 Arch (2) results of foreign institutional investment. +et

fiit

122.48 +0.734 fiit1 [1.90]*** [33.4]* ht 166,923.3 +0.5.89 e2t1 [7.93]* [3.91]* Log-likelihood = 1398, SR LB x2 = 8.49(0.58), SSR LB x2 = 7.70(0.6 + 5), ARCH = 0.82(0.60)

+1.12 e2t2 [6.557]*

Source: Author’s estimates. Notes: SR = standardized residuals, SSR = standardized squared residual, LB = Ljung–Box statistics for serial correlation at 10 lags. ARCH = LM test for ARCH effects in the residuals. Figures in square brackets and parenthesis show t-statistics and level of significance, respectively. * Denote significance at 1% level. *** Denote significance at 10% level.

Table 3 The results of the F-test for cointegration. Lag F-value

1 6.11*

2 6.24*

3 7.23*

4 7.72*

Source: Author’s estimates. Note: The critical bounds of the F statistic with constant at 95% significance are 3.73–4.92 (Narayan, 2005). * Denotes statistically significant at 1% level.

5.2.2. ARDL cointegration test Table 3 reports the results from F-test. Because the F-test is sensitive to the number of lags imposed on each firstdifferenced variable, the F-test is performed for different lag orders, i.e., from 1 to 4, on each first differenced variable in the risk premium equation.9 The results show that calculated F-statistics are greater than the upper bound critical value, rejecting the null of no cointegration. Having established the cointegration relationship, the next step was to estimate the long-run coefficients of the equation using the ARDL specification. After imposing a maximum of 4 lags on each first differenced variable, Schwarz lag selection criteria (SBC) chooses the optimum lag as three. The long-run estimates of equation are given in Table 4. The long-run cointegrating risk premium equation can be written as

i −i* sted fd )t = 43.36 + 2.18ln fii _ volt + 1.89ln( )t + 9.81ln( ) 1+ i res gdp t-value (3.26) (4.87) (2.03) (5.31)

ln(

The long-run coefficients show that all regressors in the risk premium equation exhibit the theoretically expected sign and are statistically significant at the 5% level. The statistical significance ln fii indicates that the rise in the volatility of foreign institutional investment increases the risk premium. This validates the argument that volatile nature of short-term capital flows increases financial vulnerability and thereby sovereign risk. Similarly, the variable short-term external debt to reserves, ln(sted/res), is also found to be statistically significant in the equation. This indicates that India’s ability to meet short-term obligations is an important determinant of its risk premium. It is also interesting to see that the estimated coefficient of fiscal deficit to GDP, ln(fd/gdp), is found to be 9.81, which is higher than that of other explanatory variables in

9 Since the ARDL approach to cointegration does not require pre-testing for unit root, the present study does not address the issues related to the structural break in each variable in the risk premium equation. However, testing for structural breaks and subsequent inclusion of break dummies (if the break is found) in the ARDL model would obtain estimates that are more efficient. The present study leaves this issue for future research.

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82 Table 4 Estimates of the ARDL model. Regressors Long-run coefficients Constant ln fii ln ln

sted res





fd gd p

Short-run coefficients Constant

D ln



 

ii 1þi

D ln

sted

D ln

sted

D ln

sted

t1

res t

res t1

res t2

ecmt1 Adjusted R2

x2AC x2Arch x2Arch

SBC-ARDL(2,0,3,0) 43.36 (3.26)* 2.18 (4.87)* 1.89 (2.03)* 9.81 (5.31)*

6.66 (2.79)* 0.25 (3.18)* 0.37 (2.92)* 0.29 (2.05)** 0.15 (2.84)* 0.53 (4.69)* 0.40 2.34 [0.30] 1.01 [0.60] 1.68 [0.43]

Source: Author’s estimates. Notes: x2AC , x2Arch , x2Normality are LM statistics for serial correlation, for ARCH effect and normality in residuals. Figures in parenthesis and square brackets show t-statistics and level of significance, respectively. * Statistically significantly different from zero at 1% level. ** Statistically significantly different from zero at 5% level.

the model and is statistically significant at the 5% level. This is a clear indication that high and sustained fiscal deficit in India is perhaps a major concern among international lenders when India approaches them for external borrowing. Using Eqs. (7) and (15), it is possible to derive the absolute and marginal probability of default. The estimated marginal probability equation is as follows:

@2 p 1:89 <0 ¼ pR ¼ pð1  pÞ res @res

(16)

Eq. (16) shows that the change in probability of default due to a small increase in reserves is negative, pR < 0,10 indicating that the probability of default diminishes as reserves increase. 5.3. Optimum reserves (R*) After estimating p, pR, C0 and r, the optimum level of reserves can be calculated by substituting these estimates in Eq. (4). The simulated optimum reserves, by considering the impact of 4.8–7.5% of GDP contraction for the period 1995:Q1– 2009:Q4, is shown in Fig. 2. The figure shows that the actual reserve holding is higher than the optimum level predicted by the model, except for the year 1997–1998. During 1997–1998, the actual level of reserves is found to be less than optimum level considering output contraction of 4.8–7.5%. The higher optimum level can be attributed to the risk associated with contagion effects of the East-Asian crisis during this period. This period witnessed an increasing pressure on the Indian Rupee to depreciate due to the expectation of capital outflows. Although the RBI intervened in the foreign exchange market, the effort was met with only limited success (Nayyar, 2002). In the same period, the total inflow of foreign institutional investment declined to US$1.9 billion compared with US$3.3 billion in 1996–1997, and the Rupee depreciated more than 14% against the US dollar (Rangarajan & Prasad, 1999). Furthermore, the higher optimum reserves during this period can also be taken as an outcome of the nuclear test conducted by India in May 1998. The test caused a downgrade in the country’s credit rating due to the economic sanctions imposed by certain industrialized countries along with the suspension of fresh multilateral lending (RBI, 1999).

10 In Eq. (2) pR is defined as the first order differentiation of p with respect to reserves (R). However, in the present context, reserves denoted as res, pR also refer to p with respect to res.

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Fig. 2. Actual and optimum levels of reserves in India. Notes: Optimum reserves at 4.8% GDP and 7.5% GDP are the simulated optimum reserves by considering output contraction 4.8% and 7.5%, respectively. Source: Author’s estimates.

The massive reserve accumulation by the RBI after 2001 could be a reason for the divergence of actual reserves far from optimum levels in the subsequent periods. Even during the recent crisis period of 2008–2010, actual reserves were much higher than the optimum level. The low growth of the optimum level during this period can be attributed to the low risk associated with the contagious effect of crisis. As noted by RBI (2009), ‘‘Indian banks and financial institutions largely escaped the heat of the global contagion because of the strong fundamentals and no direct exposure to the troubled assets and stressed institutions in the advanced countries. The Reserve Bank’s swift and necessary responses ensured orderly functioning of the markets. Thus, the conditions in the financial system did not operate as a constraint to the growth in India, unlike in the advanced countries’’ (p. 30). Conclusively, the Indian financial sector was resilient to the global financial crisis, thus reflecting the soundness of the Reserve Bank’s regulatory and supervisory policies. Fig. 3 shows the optimum versus adequate level of reserves based on import adequacy criteria11 and indicates that the optimum level of reserves was higher than adequate reserves, except during 1995–1996.12

Fig. 3. Actual, adequate and optimum level of reserves. Notes: Optimum reserves are based on 7.5% of GDP contraction. Source: RBI (actual reserves) and author’s estimates (optimum reserves and adequate level).

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Fig. 4. Plot of estimated rolling coefficients of risk premium equation. Notes: The dark line is the estimated rolling coefficients and the standard error bands are indicated by the two upper-lower shaded lines. Panel A: Rolling coefficient of volatility of foreign institutional investment (ln_fii_vol); Panel B: Rolling coefficient of short-term external debt to reserves (ln_sted/res); Panel C: Rolling coefficient of fiscal deficit to GDP (ln_fd/gdp). Source: Author’s estimates.

5.3.1. Rolling regression test results The optimum level of reserves was calculated from a rolling regression analysis to determine whether the calculated optimal reserves vary over time. The regression estimates of Eq. (10) were computed for 20 rolling windows (5 year). The estimated rolling coefficients from least squares regression along with the standard errors are shown in Fig. 4. The figure shows that the estimates of coefficients have undergone certain changes over the sample periods, as reflected in the nonstraight line. Furthermore, using these estimates, the absolute and marginal probabilities of default are derived, and the time varying optimum level of reserves is calculated by inserting these probabilities in Eq. (4). Fig. 5 shows the difference between the time varying optimum level of reserves and the optimum level of reserves based on ARDL estimates (i.e., Eq. (15)). It is observed that deviation between the two optimum series is very low except in the years 2003 and 2006. The significant increase in the time varying reserves in 2003 can be attributed to the surplus in the current account balance, non-debt creating capital inflows and valuation gain (Ministry of Finance, 2003). However, the increase in the time varying reserves in 2006 could be attributed to the strong capital account surplus. During this year, capital inflows to GDP increased to 5.1% from 3% in the previous year (Ministry of Finance, 2007). The Ministry of Finance (2007) stated, ‘‘With active purchase of foreign exchange by RBI of US$ 9.8 billion in the first nine months of 2006–2007, the stock of foreign exchange reserves reached US$180.0 billion on 2 February 2007. The sustained appreciation of other major currencies vis-a`-vis the US dollar in the

11 Import based reserve adequacy criteria suggest that 30% or 4 months of import covering reserves can be considered as a minimum benchmark for reserve adequacy (Triffin, 1947). 12 This is perhaps due to high import bill in 1995–96 and the import growth was 28% compared to previous year (Ministry of Finance, 1997).

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Fig. 5. Deviation of optimum reserves from time varying optimum reserves. Notes: Optimum reserves are based on Eq. (15) (ARDL model and 7.5% of GDP contraction) and time varying optimum reserves are based on rolling regression analysis (20 rolling windows). Source: Author’s estimates.

current year suggests that cumulative accretion to reserves of US$28.4 billion up to 2 February 2007 includes a large element of valuation gain’’ (p. 26). 6. Conclusions This paper has attempted to derive the optimum level of international reserves for India for the period 1994–2010 using quarterly data. The study employed the reserve optimizing approach developed by Ben-Bassat and Gottlieb (1992) for developing countries where sovereign risk estimation has immense significance. Optimum reserves are derived by minimizing a cost function of the central bank, which consists of the costs due to high reserve holdings as well as the costs due to reserve depletion and their associated probabilities. The costs due to high reserve holdings were measured by opportunity cost proxied by domestic interest rate, and the costs due to reserve depletion were measured by taking the percentage contraction in output during the period of BoP crisis in India in the early 1990s. The study found that the cumulative output contraction due to crisis was 4.8–7.5%. The probability of reserve depletion was derived by estimating a risk premium equation that captures the sovereign risk associated with external borrowings. The empirical result shows that the volatility of foreign institutional investment, short-term debt to reserves and the fiscal deficit to GDP significantly explain the variations in risk premium. The estimated optimum reserves show that the actual reserves are higher than the optimum reserves across the sample, except for the period of 1997–1998. The findings also demonstrate that the actual reserve level held by the RBI is much higher than the optimum level during the recent financial crisis of 2008–2010. Accordingly, the present study concludes that international reserves in India are higher than the estimated optimum level of reserves, even after considering the sovereign risk associated with the financial crisis. Furthermore, it suggests that prudent reserve management policies could be used to channel the excess reserves into productive sectors of the Indian economy. Acknowledgements This is a revised version of the paper presented at the 27th International Conference of the American Committee for Asian Economic Studies (ACAES) held at Deakin University, Melbourne, Australia during 26–27th October 2012. The author is thankful to Prof. Tony Makin, Griffith University, Australia, for his valuable comments and suggestions. The author alone is responsible for any omission and errors. References Afzal, M. (2010). Exchange rates and reserves in Asian countries: Causality test. Global Economic Review, 39(2), 215–223. Aizenman, J., & Lee, J. (2007). International reserves: Precautionary versus mercantilist views, theory and evidence. Open Economies Review, 18, 191–214. Aizenman, J., & Marion, N. (2003). The high demand for international reserves in the far East: What’s going on? Journal of the Japanese and International Economies, 17, 370–400. Ben-Bassat, A., & Gottlieb, D. (1992). Optimal international reserves and sovereign risk. Journal of International Economics, 33, 345–362. Cohen, D. (1992). The debt crisis: A post-mortem. NBER Macroeconomics Annual, Vol. 7 (pp. 65–114). Cambridge: National Bureau of Economic Research.

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