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«Optimal Reserve Management and Sovereign Debt Laura Alfaro Harvard Business School Fabio Kanczuk Universidade de São Paulo May 2007 Working Paper ...»

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FEDERAL RESERVE BANK OF SAN FRANCISCO

WORKING PAPER SERIES

Optimal Reserve Management and Sovereign Debt

Laura Alfaro

Harvard Business School

Fabio Kanczuk

Universidade de São Paulo

May 2007

Working Paper 2007-29

http://www.frbsf.org/publications/economics/papers/2007/wp07-29bk .pdf

The views in this paper are solely the responsibility of the authors and should not be interpreted as reflecting the views of the Federal Reserve Bank of San Francisco or the Board of Governors of the Federal Reserve System. This paper was produced under the auspices of the Center for Pacific Basin Studies within the Economic Research Department of the Federal Reserve Bank of San Francisco.

Optimal Reserve Management and Sovereign Debt* Laura Alfaro Fabio Kanczuk Harvard Business School Universidade de São Paulo May 2007 Abstract Most models currently used to determine optimal foreign reserve holdings take the level of international debt as given. However, given the sovereign’s willingness-to-pay incentive problems, reserve accumulation may reduce sustainable debt levels. In addition, assuming constant debt levels does not allow addressing one of the puzzles behind using reserves as a means to avoid the negative effects of crisis: why do not sovereign countries reduce their sovereign debt instead? To study the joint decision of holding sovereign debt and reserves, we construct a stochastic dynamic equilibrium model calibrated to a sample of emerging markets. We obtain that the optimal policy is not to hold reserves at all. This finding is robust to considering interest rate shocks, sudden stops, contingent reserves and reserve dependent output costs.

JEL classification: JEL classification: F32, F33, F34, F4.

Key words: foreign reserves, sovereign debt, default, sudden stops.

* lalfaro@hbs.edu. Harvard Business School, Boston, MA 02163, Tel: 617-495-7981, Fax: 617-495-5985;

kanczuk@usp.br. Department of Economics, Universidade de São Paulo, Brazil. We thank Joshua Aizenman and conversations with Julio Rotemberg for valuable comments and suggestions.

1 Introduction There is a renewed interest in policy and academic circles about the optimal level of foreign reserves sovereign countries should hold. This recent interest follows the rapid rise in international reserves held by developing countries. In 2005, for example, reserve accumulation amounted to 20% of GDP in lowand middle-income countries; whereas this number was close to 5% in high-income countries. This practice has raised interesting questions in the literature regarding the cost and benefits of reserve accumulation. The cost of holding reserves has been estimated at close to 1% of GDP for all developing countries (Rodrik 2006).1 Against this cost, an explanation commonly advanced is that countries may have accumulated reserves as an insurance mechanism against the risk of an external crisis—self protection through increased liquidity.2 Recently, researchers have undertaken the task of writing analytical models to characterize and quantify the optimal level of reserves and provide policy advice to countries.3 Most of the formal models used in the current analysis tend to take the level of international debt as given and solve for the optimal liquidity-insurance services that reserves can provide. In other words, the literature has set aside the joint decision of holding sovereign debt and reserves. Although this strategy has allowed for a better understanding of the interplay between foreign reserves and a sovereign’s access to international markets, there are several concerns with this approach. First, some of the implications of this assumption may not be generalized once one considers the joint decision by a sovereign to hold foreign debt and reserves. For example, in models a la Eaton and Gersovitz (1981), international debt serves an “insurance” role. That is, the demand for international loans derives from a desire to smooth consumption. Hence, given the sovereign’s willingness-to-pay incentive problems, additional reserves in this type of models tend to reduce sustainable debt levels.4 Second, the strategy of assuming constant debt levels does not address one of the Rodrik (2006) estimates the cost of reserves as the spread between the private sector’s cost of short-term borrowing abroad and the yield the Central Bank earns on its liquid foreign assets.

For policy advice in this direction, see Feldstein (1999) and Caballero (2003). The “Greensan-Guidotti-IMF” rule proposes full coverage of short-term external liabilities to mitigate the risk of currency crises.

See for example Aizenman and Lee (2005), Caballero and Panageas (2004), Jeanne (2007), Jeanne and Ranciere (2006), Lee (2004).

In this type of model, the cost to a sovereign of the denial of foreign credit is that the country must resort to other methods for consumption smoothing (such as building stock piles) or it must accept a greater fluctuation in its consumption. This penalty and hence the sustainable levels of foreign debt are higher the greater the cost to the puzzles behind the current accumulation of reserves. Sovereign countries have an alternative way of reducing the probability and negative effects of external crisis: to reduce the level of sovereign debt. That is, even in the case where reserve accumulation has positive liquidity benefits in terms of reducing the probability of suffering financial crises and the output costs associated with it, a similar net asset position can be obtained by reducing instead the level of foreign debt.5 In this paper, we address these concerns by incorporating debt sustainability issues into the optimal reserve management analysis. Our main objective is to study the implications of the joint decision of holding sovereign debt and reserves. We construct a stochastic dynamic equilibrium model of a small open economy with non contingent debt and reserve assets. Our starting setup is a model a la Eaton-Gersovitz and similar to Arellano (2006) and Aguiar and Gopinath (2006), but where the sovereign has the choice to hold reserves. We assess the quantitative implication of the model by calibrating a sample of emerging markets.





A robust result that emerges from our numerical exercises is that the optimal policy is not to accumulate reserves.

We extend the model in several ways. Most of the recent papers advancing the insurance motive behind reserve accumulation have been motivated by the sudden loss of access to international capital markets and the collapse of domestic production which have characterized the emerging markets crises of the nineties—a phenomenon Calvo (1998) labeled as “sudden stops.”6 In line with the sudden stops literature, most of the formal analysis studying optimal reserve management model reserve accumulation as a cushion against external shocks and capital flows reversals while the level of international debt is taken as given. That is, in these models countries engage in reserve accumulation to seek self-insurance against the potential tightening of international financial constraints rather than income fluctuation per se as in more standard debt models. These models have made important progress in providing an integral framework to analyze quantitatively some of the limitations and risks of the integration of developing countries to borrower of exclusion. This cost in turn is higher the more limited domestically available options for smoothing consumption are and the lower the cost of smoothing via the international capital markets is (i.e. the lower the world interest rate). See Eaton et al. (1986).

Rodrik (2006) mentions that countries could choose instead to reduce short-term debt in order to gain liquidity. More generally, countries can reduce foreign debt.

Additional empirical regularities include the sharp contractions in domestic production and consumption and the collapse of the real exchange rate and asset prices. See Arellano and Mendoza (2003) and Edwards (2004) for overviews of the stylized facts and the literature studying the “sudden stops” phenomena.

international financial markets.7 But by taking the level of debt as given, they have abstracted from willingness-to-pay concerns associated with sovereign debt and the sovereign’s choice over the composition of its assets and liabilities.

In order to analyze the interplay of both effects, we study an economy that is (i) hit by random shocks in the interest rate (which we take to be “contagion shocks”), and (ii) in addition to the interest rate shocks, the economy faces additional output costs associated with abrupt current account reversals (which we take to mean “sudden stops”). However, as mentioned, our model retains willingness-to-pay concerns.

Note that since we focus on debt and reserve management problems, in this paper we do not attempt to advance the understanding of the contagion or sudden stops phenomena.8 Instead we incorporate them into the analysis in a highly stylized form. Our approach, nevertheless, reveals interesting results. Once again the optimal policy does not involve accumulating reserves. Rather, the government reacts by reducing the amount of outstanding debt. Moreover, these results are robust to the possibility of holding contingent reserves, which, as suggested by Caballero and Panageas (2005), are a more efficient device to insulate the country from sudden stops.

We then study the role of output costs. The sovereign debt literature has found output costs to play an important quantitative role even in models where debt should otherwise be sustainable (see Alfaro and Kanczuk (2005)). Although these output losses are well documented, their micro-foundation remains to be understood.9 Nevertheless, some empirical evidence suggests that reserves may reduce the output costs associated with sudden stops (see Frankel and Cavallo (2004)). In order to incorporate these stylized facts in our analysis, we consider a case where foreign reserves reduce output costs exogenously. Interestingly, in this case, if reserves reduce output costs, they reduce sustainability. For this reason, we obtain once again that it is optimal not to hold reserves.

See for example Caballero and Panageas (2004). Estimates by Rodrik (2006) and Jeanne and Ranciere (2006) find reserves holdings to be consistent with a government’s desire to insure against the probability and cost of currency crises. Lee (2004) quantifies the insurance value of reserves.

See Mendoza (2004) for important work on this direction. As the author explains, the economics behind sudden stops remains to be understood. The standard real business cycle models do not seem to account for the main stylized facts of these events. Durdu, Mendoza and Terrones (2007) quantitatively analyze the role of foreign reserves in a model of incomplete asset markets in which precautionary saving affects asset holding via business cycle volatility, financial globalization and sovereign risk.

See Dooley (2000) and Calvo (2000) for theoretical explanations.

The main implication that emerges from our work is that greater attention should be given to the explicit modeling of additional constraints limiting the sovereign’s ability to reduce debt levels (or more generally political economy rationales) as they seem necessary towards the understanding of the observed levels of foreign reserve holdings. To be sure, scholars have considered additional motives for holding reserves. In an earlier literature, reserve holdings were associated with exchange rate management policies.10 More recently, it has been argued that the rapid rise in reserves has little to do with self insurance, but instead with the policymaker’s desire to prevent the appreciation of the currency and maintain the competitiveness of the exporting sector (the mercantilist view by Dooley et al. (2003)).11 Yet, another strand of the literature has considered political economy issues. Aizenman and Marion (2003), for example, analyze the role of interest groups, corruption and opportunistic behavior by future policy makers. In their setup, a policy recommendation to increase international reserve holdings may be welfare reducing as it may increase the chance of a financial crisis. More generally, our work suggests that policy recommendations may differ from the consensus once sovereign debt issues are considered. This, is in line with Rogoff`s (1999) critical remark: “Whereas the debate over why countries repay may seem rather philosophical, it is quite dangerous to think about grand plans to restructure the world financial system without having a concrete view on it.” The rest of the paper is organized as follows. Section 2 presents the benchmark model. Section 3 defines the data and calibration. The results are discussed in section 4, which is complemented by a comment about the role of reserves as collateral. Section 5 concludes.

2 Model Our economy is populated by a sovereign country that borrows funds from a continuum of international risk-neutral investors. The economy faces uncertainty in output. As preferences are concave in consumption, households prefer a smooth consumption profile. In order to smooth consumption, the benevolent government may choose optimally to default on its international commitments. As in Arellano See Frenkel and Jovanovic (1981), Edwards (1983) and Aizenman (2005) and Flood and Marion (2002) for recent reviews of the literature.

See Aizenman and Lee (2005) for a test of the importance of precautionary and mercantilist motives in accounting for the hoarding of international reserves by developing countries.

(2006) and Aguiar and Gopinath (2006), if the government defaults on its debts, it is assumed to be temporarily excluded from borrowing in the international markets. The novelty of our model is that the government has available another device to smooth consumption: in addition to issuing debt, the government can hold international reserves. And even when the government is excluded from borrowing international funds, a reserve buffer can be used to reduce consumption volatility.

In more precise terms, we assume the sovereign’s preferences are given by

–  –  –

where σ 0 measures the curvature of the utility, β ∈ (0, 1) is the discount factor, and ct denotes household consumption.

If the government chooses to repay its debt, the country’s budget constraint is given by

–  –  –



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