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Uruguay: Selected Issues

International Monetary Fund
Published Date:
February 2008
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V. The Optimal Level of Reserves in Financially Dollarized Economies: The Case of Uruguay

By Fernando M. Gonçalves

A. Introduction

1. The recent increase in holdings of foreign reserves in many countries has renewed the interest in assessing the motives and adequacy of reserve accumulation. Because reserves provide protection against external shocks but are costly to carry, a careful assessment of the adequacy of reserve levels is warranted.

2. One frequently cited motive for holding large amounts of foreign reserves is to self-insure against costly crises.1 Reserves can be useful for mitigating the fall in domestic consumption that may result from a sudden stop of external credit and/or a run on banks' foreign currency deposits. Such insurance role of reserves is more pronounced in dollarized economies, where financial account reversals and bank runs typically have larger adverse effects because of currency mismatches in the balance sheets of economic agents.2

3. Foreign reserves played a significant role in mitigating the effects of the 2002 crisis in Uruguay. Following the Argentine crisis in 2001, Uruguay experienced a sudden stop of external credit and a banking crisis.3Figure 1 shows the resulting large financial account reversal and withdrawal of dollar deposits. It also depicts the large amount of reserves—a significant part of which made available through an IMF arrangement—used to offset the outflows. While output dropped significantly, the use of reserves helped offset a potentially much larger fall in economic activity.

Figure 1.Financial Account Reversal, dollar deposits and reserves in Uruguay

(percent of 2001's GDP)

4. This chapter assesses the adequacy of foreign reserves in Uruguay from a prudential perspective. The framework derived by Jeanne and Rancière (2006) (henceforth, JR) is extended to explicitly incorporate the dollarization of bank deposits. The paper illustrates the relevance of this extension by calibrating the model for Uruguay, a highly dollarized country in which higher reserve levels are valuable for prudential reasons, even though short-term foreign currency debt is low.

B. Vulnerabilities and the Role of Reserves in Uruguay

5. Short-term foreign currency debt is now at historically low levels.4 While in 2002 short-term foreign currency indebtedness of public and private sectors was over 40 percent of GDP, by end-2006 it had fallen to less than 3 percent of GDP (Figure 2).

Figure 2.Short-term foreign currency debt and foreign currency deposits in Uruguay

(percent of GDP)

6. Despite significant progress, high deposit dollarization and nonresidents' deposits remain important sources of vulnerability. As illustrated by the 2002 crisis experience, nonresidents' deposits are more susceptible to large withdrawals than residents' (Figure 3). In recent years, nonresidents' foreign currency deposits have decreased sharply, reaching 9 percent of GDP at end-2006, thus representing a significant reduction in banking sector vulnerability. Nonetheless, foreign currency deposits remained at the high level of about 37 percent of GDP in end-2006. Thus, while risks have been reduced considerably since the crisis, dollarization of deposits remains one of the highest in the world and a major vulnerability for the Uruguayan economy.

Figure 3.Withdrawal of foreign currency deposits in 2002

(percent of 2001's GDP)

7. Reserve adequacy measures should take into account the degree of deposit dollarization.5 Traditional measures would suggest that Uruguay holds comfortable reserve levels (Figure 4). Reserves are now well above all short term foreign currency debt (Guidotti-Greenspan rule), in contrast to the years prior to the 2002 crisis. Also, coverage of imports has consistently exceeded 3 months, except in the year of the crisis. The Uruguayan economy was particularly vulnerable to a bank run prior to the 2002 crisis: reserves covered only 18 percent of dollar deposits. Reserve coverage of dollar deposits has increased substantially since then to about 35 percent (more than 100 percent of nonresidents' deposits). However, further analysis is needed to establish whether reserves now provide an appropriate balance between costs and protection against a major withdrawal of dollar deposits.

Figure 4.Benchmark Measures of Reserve Adequacy

Source: International Financial Statistics; Central Bank of Uruguay; and author's calculations.

C. The Optimal Level of Reserves

8. What is the optimal level of foreign reserves for self-insurance purposes in a financially dollarized economy? To address this question, JR's model is extended to explicitly take into account dollar-denominated deposits. The resulting expression for the optimal level of reserves is shown in equation (1) below (a full derivation of the model is in Appendix 1). It includes parameters computed from actual data (Table 1) and also parameters that need to be calibrated and are assumed fixed during the sample period (Table 2).

Table 1.Variable Parameters(In percent)
Public sector short-term foreign currency debt/GDP (λG)8.19.410.222.29.711.311.11.3
Private sector short-term foreign currency debt/GDP (λP)12.513.716.518.
Total foreign currency deposits/GDP (λD)56.363.378.063.769.459.448.545.7
Non-residents' foreign currency deposits/ Total foreign currency deposits (SNR)39.641.645.632.824.420.920.619.8
Residents' foreign currency deposits/ Total foreign currency deposits (SR)60.458.454.467.275.679.179.480.2
Banks' liquid foreign assets as a share of foreign currency deposits—corrected (αc)16.217.313.921.428.941.042.837.3
Table 2.Fixed Parameters
Coverage of non-residents' deposits (CNR)100%
Coverage of residents' deposits (CR)30%
Accumulated output loss (γ)14%
Probability of sudden stop (π)7.5%
Term premium (δ)1.5%
Risk-free rate (r)5%
Risk aversion (σ)2
Real exchange rate depreciation (Δq)30%
Long-run GDP growth rate (g)3%

9. The formula balances the consumption-smoothing benefits with the quasi-fiscal costs of holding reserves. It states that optimal reserves are increasing in the magnitude of deposit withdrawals (φλD), private (λP) and public (λG) short-term foreign currency debt, output cost (γ) and the likelihood of a crisis (π). Intuitively, reserves are more useful as a buffer the larger the drop in consumption (caused by the withdrawal of dollar deposits and sudden stop in foreign currency credit) and the bigger the probability of such drop. A larger coverage of dollar deposits by banks' own reserve holdings (i.e., by banks' liquid foreign assets6αλD) implies less optimal (official) reserves, as such coverage also provides cushion to dollar deposits withdrawals in a crisis. In addition, a real exchange rate depreciation (Δq) increases the burden of foreign currency liabilities, leading to further drops in consumption and, thus, larger optimal reserves. Finally, the optimal level of reserves is decreasing in the cost of holding reserves, which is captured by the interest rate differential between long-term debt issued to finance reserves and the return on reserves (δ).

where λ = (φ−αD + λP + λG,φ = sRCR + sNRCNR, and p=(1π)(δ+π)π(1δπ)(1+Δq).

10. In a crisis, the percentage drop in nonresidents' deposits tend to be larger than the percentage drop in residents' deposits. While the ratio of liquid foreign assets of banks to foreign currency deposits has been relatively stable in Uruguay, the composition of foreign currency deposits has shifted from nonresidents to residents in recent years. Because, in the event of a crisis, the percentage drop in nonresidents' deposits is typically larger than for residents' deposits, the current coverage of deposits by banks' liquid foreign assets can be considered stronger than in 2002. In order to reflect this in the calibration, the ratio of banks' liquid foreign assets to dollar deposits is corrected to control for the change in residents/nonresidents composition of deposits over time.7

11. Many of the parameters are calibrated following standard conventions. The risk aversion parameter is set at 2, a number typically used in the business cycle literature. The risk free short-term dollar interest rate (the return of reserves) is set to 5 percent, about the average U.S. 3-month T-bill rates in the last 10 years. The term premium is assumed to be 1.5 percent, close to the average difference between the yield on 10-year U.S. treasury bonds and the federal fund rate in the last 20 years. The growth of potential output in Uruguay is calibrated at 3 percent. The real exchange rate depreciation following a crisis is calibrated at 30 percent, slightly less than the 33 percent depreciation that took place between March and September of 2002.

12. Coverage of foreign currency deposits by official reserves and banks' liquid foreign assets was set at 100 percent for nonresidents and 30 percent for residents. The full coverage for nonresidents deposits, which broadly matches the current practice by banks in Uruguay, would insulate the domestic economy from sudden withdrawals by nonresidents, that can be large as evidenced by the 2002 crisis. Since residents' deposits are less volatile than nonresidents,' a smaller coverage of 30 percent seems appropriate.

13. The output loss due to a crisis was calibrated at 7 percent of GDP per year during 2 years. The accumulated output loss of the Uruguayan economy as a result of the 2002 crisis was about 18.5 percent, and output took roughly two years to recover to its pre-crisis levels. Given the improved external conditions, compared with 2002 (when the devaluation in Brazil was followed by a severe crisis in Argentina), we assumed a smaller output loss (14 percent). This is also close to estimates found in the literature on currency crisis and sudden stops for a typical emerging market country.8

14. The probability of a crisis was calibrated at 7.5 percent a year, or an average of one crisis every 15 years. JR's estimation, based on a cross-country Probit model, yields a probability of 10 percent for a typical emerging market country. Nonetheless, Uruguay track record of one major crisis every 20 years (1982 and 2002) implies an observed crises frequency of 5 percent. Given the potential specification problems of the Probit estimation and the difficulty of inferring the probability from Uruguay's few crisis episodes, the calibration is set to the intermediate probability of 7.5 percent.

15. As vulnerabilities have diminished since 2002, so has the estimated optimal level of reserves. Because short-term foreign currency indebtedness and deposit dollarization have been decreasing since 2002 and given the exceptionally high banks' liquidity levels, the need for central bank reserves for prudential purposes has diminished (Figure 5). Prior to the crisis, the estimated optimal level of reserves reached almost 80 percent of GDP in 2001 (or US$14.7 billion), highlighting the large vulnerabilities of the economy at the time. In June 2007, with less vulnerabilities, the optimal level of central bank reserves was estimated to be less than 20 percent of GDP (or around US$3.8 billion). That is about 1.7 percent of GDP (or US$300 million) above current levels.9

Figure 5.Optimal versus actual level of reserves in Uruguay

(in percent of GDP)

16. Simulations indicate that reserves are close to adequate levels and would be nearly sufficient to deal with a 2002 like crisis.10 This is a consequence of increased reserves and, more importantly, reduced vulnerabilities. Figure 6 simulates the results of a 2002-like crisis, i.e. drops in nonresidents' and residents' deposits, and short term debt of 63 percent, 36 percent, and 26 percent respectively. While such drops generated a severe reserve gap in 2002 in the absence of external support, a similar scenario in 2006 yields a much smaller gap.

Figure 6.Actual and Implied Reserves

(in percent of GDP)

17. However, further accumulation is still desirable. In particular, the optimal level of central bank reserves is likely to increase in the next few years, as the ongoing credit recovery matures and banks' reduce their currently high holdings of liquid external assets. As an illustration of a relatively extreme scenario, Figure 5 shows that the optimal level of reserves as of June 2007 would increase to 28.9 percent of GDP (or about US$5.7 billion) if banks' coverage of deposits by own foreign liquid assets returned to pre-crisis levels.11 This highlights the importance of proper banking regulation that addresses the vulnerabilities caused by dollar deposits, thereby limiting the need for central bank reserve accumulation.

D. Sensitivity Analysis

18. The optimal level of reserves is very sensitive to calibration choices. Thus, undertaking a sensitivity analysis is important to gain broader perspective on the results under different conditions or parameter values. Figure 7 focuses on those parameters that, if changed, most affect the optimal level of reserves. The following facts emerge: (i) an increase in short-term foreign currency debt to 25 percent of GDP (a level close to 2001's), would result in an optimal level of reserves of over 40 percent of GDP; (ii) coverage of residents' deposits in the range 10-40 percent would imply reserve levels between 15–25 percent of GDP; (iii) an output loss of the magnitude observed in 2002 (about 18.5 percent of GDP) would imply an optimal level of reserves of over 22 percent of GDP; (iv) JR's calibration of a 10 percent probability of a crisis would yield an optimal level of reserves of 21 percent of GDP; (v) an increase in the term premium from 1.5 to 2.5 percent would raise the cost of holding reserves, and would lead to a sharp drop in the optimal level of reserves (more than 4 percent of GDP); and (vi) a real exchange rate depreciation between 0–70 percent results in optimal reserve levels between 10–25 percent of GDP.

Figure 7.Sensitivity Analysis

Source: Author's calculations

19. The current reserve levels would be optimal under certain assumptions. For example, if the parameter on coverage of residents' foreign currency deposits were reduced from 30 percent to 25 percent of deposits, the model would suggest optimal reserves roughly in line with existing levels. An accumulated output loss of 11–12 percent (much smaller than 2002's experience), or a probability of crisis just below 6 percent would yield similar results. Finally, a term premium of 2 percent (significantly higher than historical averages), or a real exchange rate depreciation in a crisis of about 22 percent (much smaller than observed in the last crisis), would also imply that the current reserve level is optimal (Table 3).

Table 3.Implicit Parameters(In percent)
Short-term foreign currency debt/GDP (λGP)0.9
Coverage of residents' deposits (CR)24.8
Accumulated output loss (γ)11.6
Probability of sudden stop (π)5.8
Term premium (δ)2.0
Real exchange rate depreciation (Δq)21.8

E. Conclusions

20. A model calibrated for Uruguay, a financially dollarized economy, suggests that reserves are nearing optimal prudential levels. The model takes into account the risk of financial account reversals typically analyzed in these studies and the possibility of large withdrawals of foreign currency deposits in the event of a crisis. With the substantial decline of nonresidents' deposits and short-term foreign currency debt since the 2002 crisis, and the high holdings of liquid foreign currency assets by banks, the prudential benefit of holding official reserves has diminished. In the model, this is reflected in a significant drop of the optimal level of reserves since 2002 which, together with the accumulation of reserves by the central bank, has nearly closed the gap between the optimal and the actual reserve levels.

21. Nonetheless, there are several reasons that justify further reserve accumulation. In particular, with banks' currently high liquidity levels unlikely to be permanent, the optimal level of official reserves should increase in the years ahead. Also, sensitivity analysis shows that an increase in short-term foreign currency indebtedness, among other possible changes in economic conditions, would lead to a large increase of the optimal level of reserves. In addition, with the model focusing on crisis mitigation (rather than crisis prevention), the calculated optimal level of reserves could be seen as a lower bound. By assuming a crisis probability independent of reserves, the model did not capture a possible preventive role of reserves.12 Adding this role would provide another reason to hold reserves, most likely leading to an increase in the model predictions about optimal reserve levels.


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    Chami, Saade,DonalMcGettigan, and StanleyWatt,2007, “Jordan's International Reserve Position: Justifiably Strong,IMF Working Paper 07/103(Washington: International Monetary Fund).

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    Garcia, Pablo S., and ClaudioSoto,2006, “Large Hoarding of International Reserves: Are They Worth It?” in External Financial Vulnerability and Preventive Policies,ed. byRicardoCaballero,CésarCalderón and LuisCéspedes,Eight Annual Conference of the Central Bank of Chile(Santiago, Chile).

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    Kamil, Herman,2006, “Balance-Sheet Mismatches and Cross-Sectoral Vulnerabilities in a Highly Dollarized Economy: the Case of Uruguay,Uruguay: Selected Issues, IMF Staff Country Report no. 06/427 (Washington: International Monetary Fund).

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Appendix 1. A Model of Optimal Reserve Levels in Financially Dollarized Economies

Consider a small open economy in discrete time which may be hit by a ‘sudden stop’, defined as an exogenous loss of external credit. When a sudden stop hits the economy, (1) short-term external debt is not rolled over; (2) a significant fraction of foreign currency deposits is withdrawn from the banking sector; (3) output falls; (4) a real depreciation occurs. The (non-financial) private sector is subject to the following budget constraint:

where Ct is domestic consumption, Yt is domestic output, qt is the real exchange rate, Bt is the dollar short-term lending by banks to the private sector, Pt is the short-term external debt of the private sector, and Zt is a transfer from the government. The interest rates rB and r are constant. Consumers do not default on short-term external debt, so r is a risk free interest rate. Banks are subject to the following budget constraint:

where RBt is the amount of dollar deposits that banks invest in risk free short-term foreign assets (in dollars) at an interest rate of r, and Dt represent dollar deposits for which banks pay an interest rate of rD. RBt is assumed to be a constant fraction of short-term foreign currency deposits: RBDt = α 0 < α < 1.1 Furthermore, for simplicity, rD = r (introducing a premium in domestic foreign currency deposits would not fundamentally alter our results).

As in JR, the government issues a long-term security that is sold by the price P (assumed constant), and yields one unit of good every period until the sudden stop occurs, after which it stops yielding any income. Therefore, the price of this security before the sudden stop occurs is given by the present discounted value of its expected future returns,

where π is the probability that a sudden stop occurs, r is the interest rate on short-term external debt, and δ is the term premium. Solving the expression above for P yields

The long-term security is issued to finance a stock Rt of official reserves, implying that

where Nt is the number of long-term securities issued by the government in period t.

The government may also issue short-term foreign debt in non-sudden-stop periods. Therefore, before the sudden stop, government's budget constraint is given by:

where Gt is the short-term foreign debt of the government (the government does not default on its short-term external debt, implying that the interest rate on this debt is the risk free interest rate, r).

The subscripts b and d denote the periods before and during a sudden stop. Equations (4) and (5) can be used to substitute out P, Nt and Nt−1 from government's budget constraint, yielding the expression for the government transfer to the private sector before the sudden stop,

The second term in equation (6) corresponds to the cost of carrying reserves, which is proportional to the term premium plus a default risk premium, captured by the sudden stop probability. To pay for this cost, the government taxes the consumer, reducing the government transfer. When a sudden stop occurs, private and public short-term external debt can no longer be issued. In order to smooth the effects on consumption of the sudden stop of external credit, the government transfers its official reserves to consumers, except for the amount (δ + π) Rt−1, which it has to pay on its long-run security for the last time. Therefore, transfers during a sudden stop are given by

Assuming that δ + π < 1, the term (1 − δ − π)Rt−1 will be positive. In the long run output grows at a rate g. When the balance of payments crisis unfolds, a fraction of output γ is lost, and a fraction of dollar deposits φ is withdrawn from banks. Furthermore, the real exchange rate is constant and normalized to 1 before the crisis, and depreciates by Δq during the crisis. With these assumptions and the equations for the transfer in (6) and (7), the expressions for domestic consumption before and during the crisis are, respectively,

The government chooses the amount of reserves to maximize the expected welfare of consumers,

The first order condition to this problem is

From equation (11), it can be shown that the optimal level of reserves before the sudden stop is a constant fraction of output,

where the optimal ratio of reserves to output ρ is given by equation (1) in the text.

Appendix 2. Level Reserves Required to Cover a 2002-like Crisis

The total drop in short-term foreign currency deposits is the sum of the drop in nonresidents' deposits (ΔNR) and residents' deposits (ΔR) and can be written as follows:

The drop in NR and R is calibrated based on 2002 crisis, whereas the composition of deposits in terms of NR and R is obtained from actual data in each year. In other words, the drop in deposits in a particular year y is given by:

Similarly, the drop in short-term foreign currency debt (ΔL) can be written as ΔL = LL / L) and the size of the drop is calibrated based on the 2002 crisis:

The implied level of reserves is simply the level that would result if reserves were used to cover the fall in deposits and debt implied by equations (13) and (14). As a share of GDP, this would be

Countries may accumulate reserves to achieve a range of objectives, not restricted to self-insurance. Other possibilities include: (i) making exchange rate markets more efficient by providing liquidity when needed; (ii) limiting exchange rate volatility (“leaning against the wind”); and (iii) pursuing, even if temporarily, export-led growth supported by a de facto fixed exchange rate (see Becker et al., 2007, and European Central Bank, 2006).

For an analysis of balance sheet mismatches in Uruguay, see Kamil (2006).

See De la Plaza and Sirtaine (2005) for a detailed analysis of the 2002 crisis in Uruguay.

The definition of public and private short-term debt is in a remaining maturity basis. Public sector short-term foreign currency debt includes both domestic and external debt.

See Wijnholds et al. (2001) for a discussion of traditional benchmark measures of reserve adequacy.

Banks' liquid foreign currency assets comprise cash, bonds and deposits with maturity of less than one year in a remaining maturity basis.

In the model, α is defined as the ratio of banks' liquid foreign assets (BLFA) to total dollar deposits (residents - R - and nonresidents - NR), α=BLFAR+NR

. Note that α can be rewritten as follows: α=BLFAR+NR=BLFANR×NRR+NR
. The first term, the coverage of nonresidents' deposits by banks' liquid foreign assets, has increased since the 2002 crisis, while the second term, the share of nonresidents' deposits, has decreased. The reduction of the latter term implies a reduction in the risk of large deposit withdrawals. For comparability purposes, it is sensible to maintain the same “level of risk” in all years of the sample. This is done by assuming that in previous years the composition of residents' /nonresidents' deposits was the same as in 2006, yielding the corrected measure αyC=BLFAR+NR=(BLFANR)y×(NRR+NR)2006
, where y is the year under consideration.

Hutchison and Noy (2006) find that the cumulative output loss of a sudden stop (defined as a simultaneous occurrence of a currency/balance-of-payments crisis with a reversal in capital inflows) is around 13–15 percent of GDP.

The definition of the actual level of reserves excludes an account of the government in the central bank that has liquid foreign assets. While the value of assets in this account can be very large, it is also very volatile (in end-2005 it had US$328 million, then in end-2006 the account had zero assets, and in June 2007 it had US$1.2 billion) and is not included in official reserve figures since it is typically held by the government momentarily and used for debt management purposes, not as precautionary reserves.

See Appendix 2 for an explanation on how simulation results were obtained.

The dashed line in Figure 5 assumes that the corrected ratio of banks' liquid assets to deposits is at pre-crisis level (the later is obtained by the 1999–2001 average of the ratio of banks' liquid assets to deposits).

The model abstracts from moral hazard issues related to the fact that reserve accumulation by the central bank may cause banks to decide to hold less foreign currency assets. Levy-Yeyati (2006) focuses on this issue and obtains an optimal composition of reserves between the banking sector and the central bank.

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