metadata: authors: 0: author: Broner, Fernando A.; Lorenzoni, Guido; Schmukler
count: World
docna: 0: docna: Why do emerging economies borrow short term?
docty: Policy Research Working Paper
subtopic: Macro-Fiscal Policy,Taxation & Subsidies,Economic Adjustment and Lending,Public Sector Economics,Capital Markets and Capital Flows,Capital Flows,International Trade and Trade Rules,Public Financial Management,Public Finance Decentralization and
            Poverty Reduction
teratopic: Finance and Financial Sector Development
abstracts: cdata!: The authors argue that emerging
            economies borrow short term due to the high risk premium
            charged by international capital markets on long-term debt.
            They first present a model where the debt maturity structure
            is the outcome of a risk-sharing problem between the
            government and bondholders. By issuing long-term debt, the
            government lowers the probability of a liquidity crisis,
            transferring risk to bondholders. In equilibrium, this risk
            is reflected in a higher risk premium and borrowing cost.
            Therefore, the government faces a tradeoff between safer
            long-term borrowing and cheaper short-term debt. Second, the
            authors construct a new database of sovereign bond prices
            and issuance. They show that emerging economies pay a
            positive term premium (a higher risk premium on long-term
            bonds than on short-term bonds). During crises, the term
            premium increases, with issuance shifting toward shorter
            maturities. This suggests that changes in bondholders'
            risk aversion are important to understand emerging market crises.
repnme: repnme: Why do emerging economies borrow short term?
display_title: Why do emerging economies borrow
            short term
listing_relative_url: /research/2004/09/5119777/emerging-economies-borrow-short-term
topicv3: Public Finance Management m1326316 716,Trade m1326924 698,Capital Markets m1326967 332,Treasury m1327009 1045,Taxation m1327615 1121
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Finance and Financial Sector Development
no_of_pages: 64
model_extractions: # WPS3389

## Why Do Emerging Economies Borrow Short Term?

Fernando A. Broner Guido Lorenzoni Sergio L. Schmukler<sup>∗</sup>

#### Abstract

We argue that emerging economies borrow short term due to the high risk premium charged by international capital markets on long-term debt. First, we present a model where the debt maturity structure is the outcome of a risk-sharing problem between the government and bondholders. By issuing long-term debt, the government lowers the probability of a liquidity crisis, transferring risk to bondholders. In equilibrium, this risk is re fl ected in a higher risk premium and borrowing cost. Therefore, the government faces a trade-off between safer long-term borrowing and cheaper short-term debt. Second, we construct a new database of sovereign bond prices and issuance. We show that emerging economies pay a positive term premium (a higher risk premium on long-term bonds than on short-term bonds). During crises, the term premium increases, with issuance shifting toward shorter maturities. This suggests that changes in bondholders’ risk aversion are important to understand emerging market crises.

### JEL Classi fi cation Codes: E43; F30; F32; F34; F36; G15

Keywords: emerging market debt; maturity structure; sovereign spreads; risk premium; term premium; fi nancial crises

> ∗Affiliations: CREI - Universitat Pompeu Fabra and University of Maryland, Princeton University, World Bank. E-mail addresses: broner@econ.umd.edu, guido@princeton.edu, sschmukler@worldbank.org. We are grateful to Galina Barakova, Tatiana Didier, Lishan Shi, and, particularly, Marina Halac for superb research assistance. For valuable comments, we thank Mark Aguiar, Ricardo Caballero, Eduardo Levy Yeyati, Roberto Rigobon, Jaume Ventura, and participants at presentations held at the AEA Annual Meetings (Washington, DC), the Conference on Sovereign Debt at the Dallas Fed, CREI - Universitat Pompeu Fabra, George Washington University, the Inter-American Development Bank, the International Monetary Fund, the LACEA Annual Meetings (Madrid and Puebla), and the NBER Summer Institute. We thank the World Bank Latin American and Caribbean Research Studies Program and Research Support Budget for fi nancial support.
# 1 Introduction

During the last decade, emerging economies have experienced recurring fi nancial crises. A common factor across many of these crises has been a maturity mismatch between assets and liabilities in the affected countries.<sup>1</sup> There is broad consensus by now that when countries rely excessively on shortterm borrowing they are more vulnerable to sudden reversals of capital fl ows and liquidity crises. The risks associated with heavy reliance on short-term debt have prompted several authors to suggest that countries should decrease their vulnerability to capital in fl ow reversals by lengthening the maturity structure of their liabilities. This view is espoused in Cole and Kehoe (1996), Sachs, Tornell, and Velasco (1996), Furman and Stiglitz (1998), Obstfeld (1998), Radelet and Sachs (1998), Corsetti, Pesenti, and Roubini (1999), Eichengreen and Hausmann (1999), and Feldstein (1999).

Why do emerging economies borrow short term despite its associated risks? In this paper, we argue that countries borrow short term because it is cheaper than borrowing long term. In particular, we show that international capital markets require a high risk premium when emerging economies issue long-term debt, and that the required risk premium is especially high when crises approach.<sup>2</sup> Therefore, countries are forced to balance the cost of a liquidity crisis against the cost of long-term borrowing. In this context, the observed debt maturity could simply be the result of optimal risk sharing between the debtor country and investors holding emerging market bonds. Empirically, we show that the cost of issuing long-term debt is, on average, higher than the cost of issuing short-term debt, and the difference between the two is higher during periods of fi nancial turmoil. Furthermore, we show that there is a negative relation between the relative cost of long versus short-term borrowing and the maturity of new debt issued, i.e. when long-term debt becomes relatively expensive countries issue more short-term debt.

In this paper, we use a simple model to illustrate our argument and present empirical evidence consistent with our explanation. In the model, the optimal debt maturity structure and risk premia

> 1 For example, large amounts of short-term debt had been accumulated by governments prior to the crises of Mexico 1994-95, Russia 1998, and Brazil 1998-99, and by the private sector in Indonesia, South Korea, and Thailand before the 1997 East Asian crisis. According to central bank sources, the average maturity of outstanding government bonds in Brazil was 1.7 years in 1998. In the cases of South Korea and Thailand, short-term debt (maturing at most in fi ve years) was, respectively, 97 and 60 percent of total corporate bonds outstanding in 1997.

> 2 This paper is related to other papers in the international fi nance literature that have stressed the importance of international investors to understand emerging market crises. See, for example, Calvo and Mendoza (2000), Kaminsky and Reinhart (2000), Caballero and Krishnamurthy (2001, 2003), and Chang and Velasco (2001).

1
at different maturities are endogenously determined. The model illustrates the trade-off between cheaper short-term borrowing and safer long-term borrowing. On the one hand, investors are risk averse and have a short horizon, so they may need to liquidate the long-term bonds before maturity. As a result, they require a positive term premium to hold long-term bonds. On the other hand, it is costly for the country to generate large amounts of liquidity (or fi scal revenue) in a short period of time. Therefore, long-term debt is safer for the government because it reduces the expected cost associated with rolling over short-term bonds.

The model has several implications. First, it shows that the risk premium on long-term bonds is higher than the risk premium on short-term bonds, and that this difference increases during crises. Second, the model shows what types of shocks are consistent with the observed pattern of maturity choice and premia at different maturities. A negative shock to government resources leads to an increase in the risk premium on long-term bonds and an increase in the maturity structure of bond issues. This is analogous to a positive demand shock on the market for international loans, leading to higher prices and higher quantities of long-term bonds. A negative shock to investors’ wealth, on the other hand, leads to an increase in the risk premium on long-term bonds and a decrease in the maturity structure of bond issues. This is analogous to a negative supply shock, leading to higher prices and lower quantities of long-term bonds.

Empirically, the paper studies the behavior of bond prices and quantities. To do so, we assemble a new database on bond prices for several emerging economies. We use this database to estimate time series of the term premium for each emerging market. In the process, we also estimate spreads, bond returns, and risk premia at different maturities, relative to Germany and the United States (considered to be “safe” countries). We also study the characteristics of bond issuance by emerging economies to understand the relation between the cost of borrowing at different maturities and the maturity choice.

The main empirical results can be summarized in three stylized facts. First, when compared with Germany and the United States, the excess returns from holding emerging market long-term bonds are, on average, much higher than those from holding emerging market short-term bonds. In other words, there is a high “term premium” of around 4 percentage points per year, when comparing 3-year and 12-year maturities.<sup>3</sup> This high term premium re fl ects the high risk premium required by

> 3 To be precise, the term premium is equal to the difference between the risk premium an emerging economy pays

2
investors to hold long-term debt relative to short-term debt. Second, the term premium is around 30 percentage points higher, on an annual basis, in crisis periods than in non-crisis periods. Third, emerging economies issue relatively more short-term debt during periods of fi nancial turmoil, and wait for tranquil times to issue long-term debt. This suggests not only that the high term premium shortens the average maturity structure, but also that time variations in the term premium lead countries to shorten their maturity structure even more during crises.

In sum, the theoretical and empirical results of this paper suggest that the “investor side” is important to understand the joint behavior of risk premia and maturity structure of emerging market debt. In particular, given our observation that the term premium increases, while the maturity of bonds issued decreases during periods of fi nancial turmoil, we conclude that changes in investors’ risk aversion play an important role in emerging market crises.

Three issues are worth considering when analyzing the results of this paper. First, the term premium is not the same thing as the difference in spreads at different maturities. The reason is that emerging market debtors sometimes default on their debt. Observed spreads can then be decomposed in two parts, a default premium and a risk premium. The default premium simply re fl ects the probability of default at different horizons. The risk premium re fl ects the fact that investors need to be compensated for bearing the risk of default and for the price volatility associated with bonds of different maturity.<sup>4</sup> The yields on long-term bonds may be higher than those on short-term bonds either because the probability of default at longer horizons is higher or because the expected returns required by investors are higher. To study the cost of borrowing at different maturities we need to identify these two components. We do this by estimating excess returns that account for default episodes.

A second and related issue is that estimating the risk premium on defaultable bonds using realized returns can be subject to a “peso problem,” given that defaults are relatively rare events. However, because our primary objective is to study the difference between long and short-term

> on long-term debt (relative to Germany and the U.S.) and the risk premium it pays on short-term debt (again, relative to Germany and the U.S.). This difference can be called excess term premium, due to the comparison with Germany and the U.S. To simplify, however, we will just use the expression term premium throughout the paper, with the understanding that we study the yields that emerging economies pay on top of those charged to Germany and the U.S.

> 4 Chang and Velasco (2000) also make this distinction. They present a model where the term premium is zero (bondholders are risk neutral) even though short-term spreads are lower than long-term spreads. In their model, the probability of default on long-term bonds is higher than the probability of default on short-term bonds.

3
risk premia, we argue that it is very unlikely that our results are affected by a peso problem. The bias affects both elements of the difference. Plus, if anything, the bias should affect the returns on short-term bonds more than those on long-term bonds, tilting the results against fi nding a large term premium.<sup>5</sup> Third, though our evidence points toward the importance of the investor side in understanding short-term debt, other factors are also likely to be relevant in explaining the recurrent use of shortterm debt by emerging economies. In fact, several authors have emphasized the role of debtors, arguing that short-term debt can alleviate moral hazard problems. The early literature, such as Calvo (1988) and Blanchard and Missale (1994), focuses on the government incentive to lower the real value of public debt by creating in fl ation. These papers show that this incentive is higher when the debt is non-indexed, in domestic currency, and of long-term nature. More recent work by Rodrik and Velasco (1999) and Jeanne (2000) show that opportunistic governments have less incentive to default on their debt and more incentive to carry out revenue-raising reforms when they have to meet early debt repayments. In this context, short-term debt serves as a commitment device for the debtor to lower the borrowing cost.<sup>6</sup> The rest of the paper is organized as follows. Section 2 presents a model that highlights the trade-off between issuing short and long-term debt. Section 3 describes the data. Section 4 studies the behavior of the term premium. Section 5 analyzes the pattern of long and short-term debt issuance. Section 6 concludes.

# 2 The model

In this section, we present a model of the joint determination of the debt maturity structure and the risk premium at different maturities. The model describes the government of an emerging economy that borrows from a set of international investors.<sup>7</sup> We assume that it is costly for the

> 5 As discussed below, in Section 4, our argument is that defaults generate larger losses on short-term bonds than on long-term bonds. The reason is that long-term bonds usually trade at larger discounts during times of fi nancial turbulence, while post-default workouts usually involve payments proportional to face value.

> 6 Caballero and Krishnamurthy (2001) discuss the welfare consequences of short-term and long-term debt and show that fi nancial underdevelopment can result in underinsurance from a social point of view and, thus, in too much short-term borrowing.

> 7 In the presentation of the model, we refer to bondholders as international investors, but the results apply more generally to any environment where the government cares about borrowing costs. It is simpler to model bondholders as international investors because in that case their utility does not enter the government’s objective function.

4
government to raise a large amount of revenue in a short period of time. This assumption implies that short-term borrowing may result in a costly liquidity crisis due to rollover difficulties. We also assume that international investors are risk averse and have short horizons. These two assumptions make investors sensitive to the price risk associated with long-term bonds.<sup>8</sup> In this environment, the maturity structure of sovereign debt can be interpreted as the outcome of a risk sharing problem between the government and bondholders. By issuing long-term debt, the country lowers the expected cost of a liquidity crisis arising from rollover difficulties, but, at the same time, it transfers risk to bondholders. In equilibrium, this risk is re fl ected in a higher risk premium and lower bond prices, thereby increasing the cost of borrowing for the country. Thus, the model allows us to analyze the trade-off between safer long-term borrowing and cheaper short-term borrowing.

The model predicts that the term premium (i.e. the difference between the risk premium on long-term bonds and that on short-term bonds) should be positive on average. Moreover, the term premium should be higher during fi nancial crises. The model also predicts that debt issuance should shift toward shorter maturities when crises are due to an increase in bondholders’ risk aversion. On the other hand, debt issuance should move toward longer maturities when crises are due to a decrease in the country’s expected repayment capacity.

# 2.1 Debtor country

There are three periods, dated 0, 1, and 2. In period 0, the government must borrow D0 to fi nance old debt coming to maturity. The government can sell either short-term (one-period) or long-term (two-period) bonds. In period 1, the government pays off the short-term bonds issued in period 0 and issues new short-term bonds. The difference between the two is covered by a short-run fi scal adjustment. In period 2, which represents the long run, the government has access to a stochastic and exogenous amount of fi scal revenue. This revenue is used to pay back maturing long and short-term bonds, to reduce taxation, or for public spending. We abstract from strategic default

> 8 Assuming short horizons is the easiest way of having investors care about short-run returns. Even if investors were long-lived, they would also care about short-run returns if they were subject to liquidity shocks. The qualitative results of the model do not depend on this modelling choice. For a discussion on the type of environment where price risk matters, see Holmström and Tirole (2001).

5
by assuming that the government repays its debt whenever feasible.<sup>9</sup> In period 0, the government’s budget constraint is where DS and DL are the amount of short and long-term bonds issued in period 0, with pS and pL being their respective prices.

In period 1, the government has to roll over the stock DS of short-term bonds. The government’s budget constraint in period 1 is where DS,1 is the amount of short-term bonds issued in period 1, pS,1 is their price, and x is the government’s primary surplus in period 1. Short-term bonds issued in period 1 are junior to existing long-term bonds.

In period 2, the government’s potential revenue equals Y<sup> ̃</sup> , which is a random variable that can take two values, Y in the good state and 0 in the bad state. The extreme case of zero realization in the bad state simpli fi es the analysis because it eliminates the possibility of partial default. As of period 0, the probability of being in the good state is π0. In period 1, there is a shock that affects the probability of being in the good state. The updated probability is denoted by π. As of period 0, π is a random variable distributed on <u>[π, π],</u> with mean π0. As we show below, the volatility of π introduces uncertainty in the government’s ability to borrow in period 1 and, thus, on the required fi scal adjustment. Issuing long-term bonds in period 0 is a way for the government to insure against this uncertainty.

The government’s objective function is where C(x) is a strictly convex function that represents the cost of the short-term fi scal adjustment.

> 9 We are implicitly assuming that default is costly. The costs can be reputational, or involve direct interference by creditors on debtors’ transactions in international goods and capital markets. See Bulow and Rogoff (1989) for a discussion of the latter.

6
We assume that C (0) = 0 and C<sup>�</sup> (0) = 1. Since C is strictly convex, C<sup>�</sup> (x) > 1 for x > 0.<sup>10</sup> This assumption, together with the assumption that in the long run the government’s marginal utility is always equal to 1, results in short-run fi scal adjustments being more costly than long-run fi scal adjustments. This difference can be explained by the fact that, in the long run, the government can spread the adjustment over a longer period of time and thus achieve better tax smoothing, or that by better preparing for the adjustment its associated cost can be reduced.

We assume that government resources satisfy π0Y − D0 > 0, so that, at risk-neutral prices, the government is solvent with no need of fi scal adjustment in period 1. We also assume that the government can carry out a fi scal adjustment large enough and faces a cost of default high enough, such that it never defaults in period 1.<sup>11</sup> When x > 0, the country faces a rollover crisis.

# 2.2 Investors and bond prices

There are two overlapping generations of investors, period 0 and period 1 investors. Period t investors invest in period t and consume in period t + 1. Both generations have mass 1. Period 0 investors have initial wealth w. They invest in three assets: an international risk-less asset, which is offered at price 1 (e.g. U.S. Treasury bills), and short and long-term bonds issued by the government in period 0. Their preferences are represented by the utility function E0 [u(c)], where u(·) is increasing, concave, and displays decreasing absolute risk aversion.<sup>12</sup> Their budget constraint is where b denotes holdings of the international risk-less bond, and dS and dL denote holdings of short and long-term bonds issued by the country. Note that the period 1 budget constraint re fl ects the

> 10 We are implicitly assuming that optimal smoothing of fi scal distortions between periods 1 and 2 is attained at x = 0. It is easy to generalize the model to the case where C<sup>�</sup> (x) = 1 is satis fi ed for x �= 0.

> 11 This is likely the simplest setup in which the trade-off emphasized in this paper can be studied. The fact that default never takes place in period 1 simpli fi es the pricing of bonds in period 0. However, even if default in period 1 was allowed, short-term bonds would remain less risky than long-term bonds from the point of view of investors, since the default would affect both short- and long-term bonds. In addition, the fact that the fi scal adjustment in period 1 does not affect fi scal resources in period 2 rules out multiple equilibria. The possibility of self-ful fi lling “runs” would increase the relative bene fi ts of issuing long-term bonds, but would not affect the results qualitatively.

> 12 This implies that lower levels of wealth are associated with higher levels of investors’ risk aversion. When referring to negative shocks to the supply of funds, we use the two indistinctively.

7
assumption that the government never defaults on short-term bonds issued in period 0.

Period 1 investors can purchase the international risk-less asset, short-term bonds issued in period 1, and long-term bonds issued in period 0, with remaining maturity of one period. We make the simplifying assumption that period 1 investors are risk neutral. As a result, bond prices in period 1 are equal to the probability of the good state which does not depend on the debt maturity structure chosen by the government in period 0. This simpli fi es the government’s problem in period 0.

This setup re fl ects an environment where the market for emerging market debt is segmented and investors are specialists, subject to liquidity shocks. Segmented markets result in bondholders being more affected by movements in the country’s bond prices than would be suggested by the size of this market as a fraction of world assets. Therefore, the cost of borrowing is affected by the wealth and risk aversion of specialized investors.<sup>13</sup> In addition, the existence of short investment horizons makes investors sensitive to the price risk of long-term bonds, since they need to liquidate their portfolios in period 1.<sup>14</sup> Using the market clearing conditions dS = DS, dL = DL, and bond prices in period 1, we can obtain the consumption level of period 0 investors, The period 0 fi rst order conditions are E [u<sup>�</sup> (w + (1 − pS) DS + (π − pL) DL) (π − pL)] = 0 and 1 − pS = 0. These conditions imply that bond prices satisfy E [u<sup>�</sup> (w + (π − pL) DL) (π − pL)] = 0, what de fi nes implicitly the price of long-term bonds as a function of DL, p(DL). This leads us to the following lemma.

Lemma 1. The price of long-term bonds, p(DL), satis fi es p(DL) ≤ π0, where the condition holds as an equality if and only if DL = 0. Furthermore, p(DL) is decreasing in DL.

> 13 Caballero and Krishnamurthy (2003) also model foreign lenders as specialists with limited wealth.

> 14 In a previous version of the paper, we considered a model with long-lived investors subject to liquidity shocks in period 1. The results were very similar to those in this version of the paper.

8
# Proof: See Appendix A.

The lemma implies that the risk premium on long-term bonds, which equals<sup>E0[pL</sup> p<sup><u>,</u></sup> L<sup>1]−pL</sup> =<sup><u>π0</u></sup> p<sup>−</sup> L<sup><u>pL</u></sup> , is generally positive. Since the risk premium on short-term bonds equals zero (they are risk-less), the lemma also implies the existence of a positive term premium. The intuition behind this result is straightforward. Shocks to expected revenues make the price of long-term bonds in period 1 volatile. Since investors care about short-run returns, they require a positive risk premium to hold long-term bonds to compensate for this price risk. Since the degree of exposure to price risk increases with DL, higher levels of DL lead to a higher risk premium and a lower price p(DL).<sup>15</sup> It is useful to discuss the importance of different assumptions for the results. The two assumptions necessary for the existence of a positive term premium are: the period 1 shock to expected revenues and investors’ short horizon. If the shock to expected revenues occurred after period 1, the price of long-term bonds would not change between periods 0 and 1, pL,1 = pL, so investors would not require a positive risk premium to hold them. In addition, if investors did not care about short-run returns, they would require the same risk premium to hold long-term bonds (between periods 0 and 2) as they would to hold short-term bonds (between periods 0 and 1, and then between periods 1 and 2). The reason is that both strategies would pay out the same amount in all states of nature in period 2. On the other hand, the assumptions that no default takes place in period 1 and that investors are risk neutral between periods 1 and 2 substantially simplify the analysis of the model, but are not necessary for the results. In a more general setting in which the country can default in the intermediate period, the risk premium on short-term bonds would also be positive. However, it would still be lower than the risk premium on long-term bonds, since the risk premium on long-term bonds would re fl ect not only the default risk in the intermediate period, but also the price risk.

> 15 The yield on long-term bonds, 1−pLpL<sup>,equalsthesumoftheirriskpremium,π0</sup> p<sup>−</sup> L<sup><u>pL</u></sup> , plus their default premium, 1−π0 pL<sup>.</sup>

9
# 2.3 Optimal maturity and risk sharing

We turn now to the choice of DL by the government. Using the bond prices derived in the previous section, the government problem can be written as,<sup>16</sup> We can solve this problem backward, solving fi rst the optimization problem in period 1. The maximum amount of short-term debt that the government can issue in period 1 is given by Y − DL, which is valued at π (Y − DL). If π (Y − DL) ≥ DS, the government can raise enough funds to repay maturing short-term bonds without any fi scal adjustment. In this case, it sets x = 0 and issues an amount DS,1 = DS/π of short-term bonds in period 1. The value of short-term liabilities is constant over time and the government expected payoff is π (Y − DL) − πDS,1 = π (Y − DL) − DS.

When π (Y − DL) < DS, a fi scal adjustment is needed to avoid default. Since C<sup>�</sup> (x) > 0 for x > 0, it is optimal to set DS,1 to its maximum level to minimize the fi scal adjustment. The government then sets x = DS − π (Y − DL) and the expected payoff is −C(x).

The government’s objective function as of period 1 depends only on the value of its net resources π (Y − DL) − DS. We thus de fi ne the government’s indirect utility function, V (·), as The function V (·) is increasing and concave. Using the fact that D0 = DS + pLDL, we can rewrite

> 16 The constraint on DS,1 is due to the fact that short-term bonds issued in period 1 are junior to long-term bonds. Without this constraint, the government could pledge all period 2 output to short-term bond holders. As a result, in equilibrium the government would not be able to issue any long-term bonds in period 0.

10
the government’s problem in period 0 as Written in this form, the government’s maturity choice in period 0 has the features of a risksharing problem. The problem can be thought as one in which the government has a utility function V (·) over period 1 “consumption,” needs to invest D0 in period 0 to fi nance a risky project that pays πY in period 1, and borrows from risk-averse investors by issuing bonds that pay 1 in every state (i.e. short-term bonds) and bonds that pay π (i.e. long-term bonds). The government’s “consumption” level is given by If the government issued only short-term bonds, it would hold all the risk and CG would be very sensitive to π. Given the concavity of V (·), this volatility of CG would be costly, re fl ecting a higher likelihood and size of fi scal adjustment. Thus, the government has incentives to issue long-term bonds to transfer some of this risk to investors.<sup>17</sup> However, investors require a risk premium to bear the price risk associated with long-term bonds. Since investors’ period 1 consumption equals w + (π − pL)DL, their exposure to π is proportional to DL. The higher DL, the higher the risk premium required by investors and the lower the price pL. This implies that the expected level of government consumption, which equals E[CG] = π0Y − D0 − (π0 − pL)DL, is decreasing in DL. As a result, the government trades-off the insurance bene fi ts associated with long-term bonds against the lower borrowing cost associated with short-term bonds.

# 2.4 Comparative statics: supply and demand factors

We now characterize how the optimal maturity structure and the risk premium on long-term bonds depend on the characteristics of investors and the borrower country. We refer to supply and demand as supply and demand of funds in international capital markets: international investors are on the

> 17 Note that dCG/dπ = Y − DL is decreasing in DL. In particular, when <u>π(Y</u> − DL) − (D0 − pLDL) ≥ 0 the government is fully insured since CG ≥ 0 for all realizations of π.

11
supply side and the debtor country is on the demand side. In particular, we consider the effect of investors’ risk aversion (captured in the model by their wealth w) and the effect of the country’s expected repayment capacity (captured in the model by Y ). We focus on four limit cases.

# Case I: Risk-neutral investors, high expected revenues

Assume that investors are risk neutral and government resources satisfy <u>πY</u> − D0 ≥ 0. Investors’ risk neutrality implies that pL = π0. In addition, the condition on government resources implies that with the last inequality following from π0 ≥ <u>π.</u> As a result, independently of the maturity structure, the risk premium on long-term bonds is zero and the government never needs to carry out a fi scal adjustment in period 1. This case shows that when both investors’ wealth and the government’s expected revenues are high, term premia are low and the maturity structure is undetermined. This result re fl ects the fact that when investors and the government are both risk neutral, it does not matter which one holds the risk.

# Case II: Risk-averse investors, high expected revenues

Assume that investors are risk averse, while government resources still satisfy <u>πY</u> − D0 ≥ 0. This condition guarantees that if the government issued no long-term bonds and fi nanced D0 solely with short-term bonds (DS = D0), it would never face a rollover crisis. Since investors would hold no country risk, the risk premium on long-term bonds would be zero (pL = π0).<sup>18</sup> If the government issued a positive amount of long-term bonds, it would still avoid a rollover crisis in period 1 but it would face a higher borrowing cost. Its payoff would be As a result, any DL > 0 is suboptimal. This case shows that when investors’ wealth is low and the government’s expected resources are high, term premia are low and the maturity structure is

> 18 In this case, pL is the price of long-term bonds in the limit when DL → 0.

12
short. This result re fl ects the fact that when investors are more risk averse than the government, it is optimal for the government to hold the risk by issuing short-term bonds.

# Case III: Risk-neutral investors, low expected revenues

Assume that investors are risk neutral, while government resources are such that <u>πY</u> − D0 < 0. Y Investors’ risk neutrality implies that pL = π0. Let D<sup>ˆ</sup> L =<sup>D</sup> π<sup><u>0</u></sup> 0<sup>−</sup> −<sup><u>π</u></sup> <u>π</u> . If the government issued an amount of long-term bonds DL ≥ D<sup>ˆ</sup> L, then In this case, the government would never face a rollover crisis.<sup>19</sup> Any amount of long-term bonds DL < D<sup>ˆ</sup> L would lead to a positive probability of rollover crisis and would thus be suboptimal. This case shows that when investors’ wealth is high and the government’s expected resources are low, term premia are low and the maturity structure is long. This result re fl ects the fact that when the government is more risk averse than investors, it is optimal for the government to transfer the risk to investors by issuing long-term bonds.

# Case IV: Risk-averse investors, low expected revenues

Finally, assume that investors are risk averse, while government resources are such that πY −D0 < 0. In this case, the government has to trade-off the cost of a rollover crisis associated with short-term borrowing against the high borrowing cost associated with long-term borrowing. This leads us to the following proposition.

Proposition 1. When investors are risk averse and government resources satisfy <u>πY</u> − D0 < 0, there is an optimal amount of long-term borrowing DL ∈ (0, D<sup>ˆ</sup> L), the risk premium on long-term bonds is positive (pL < π0), and the probability of a rollover crisis is positive.

# Proof: See Appendix A.

The proposition states that when investors are risk averse and expected government resources are low, the optimal maturity structure is an interior solution. By setting DL = 0, the government

> 19 Note that Dˆ L ≥ 0 since the government’s expected revenue satis fi es π0Y > D0 and <u>π</u> < π0. In the case in which <u>π</u> = 0, D<sup>ˆ</sup> L =<sup>D</sup> π0<sup><u>0</u>andtheuniqueoptimumistoissuenoshort-termdebt(DS= 0).</sup>

13
would not have to pay the risk premium associated with long-term borrowing, but it would face a high expected fi scal adjustment cost in period 1 (when a large stock of short-term debt is to be rolled over). By setting DL = D<sup>ˆ</sup> L, the government would completely avoid a rollover crisis in period 1, but it would face a high borrowing cost in period 0. It is easy to see why the solution is interior. At low levels of DL, investors are not very exposed to the country risk, so it is not very expensive to increase DL. At high levels of DL, the country is well insured, so the cost of lowering DL in terms of a higher cost from a rollover crisis is low. In addition, since investors are risk averse and DL > 0, the risk premium on long-term bonds must be positive.

# Supply and demand side crises

These four cases are summarized in Figure 1, where they are represented in the (w, Y ) space. This fi gure is useful to discuss the effects of supply and demand side shocks on debt maturity and the term premium.

A shift to the left re fl ects a reduction in investors’ wealth (or an increase in investors’ risk aversion), which represents a deterioration of the supply side. The increase in investors’ risk aversion causes an increase in the term premium and a shift toward shorter maturities, as the government fi nds it optimal to transfer some of the risk from investors to itself. In the case of a shift from region I to region II, this shift does not result in a rollover crisis, since expected repayment capacity is high. In the case of a shift from region III to region IV, this shift does involve an increase in the cost of a rollover crisis, since expected repayment capacity is low. Still, it is optimal for the government to hold this risk because of the savings in borrowing cost associated with short-term debt. Intuitively, a negative supply shock leads to lower quantities (less long-term borrowing) and higher cost of borrowing (higher term premium).

A shift down re fl ects a reduction in the country’s expected repayment capacity, which represents a deterioration of the demand side. The decrease in expected repayment capacity increases the cost of a rollover crisis. As a result, the government fi nds it optimal to transfer some of the increased risk to investors by shifting toward longer debt maturities, which results in a higher term premium. In the case of a shift from region I to region III, investors have low risk aversion and thus are willing to hold the additional risk without demanding a higher premium. In the case of a shift from region 14
II to region IV, the shift toward longer maturities does increase the term premium since investors are risk averse. Intuitively, a positive demand shock leads to higher quantities (more long-term borrowing) and higher cost of borrowing (higher term premium).

# 2.5 Implications of the model

In the remaining of the paper, we empirically study the behavior of the term premium and bond issuance by emerging market sovereigns at different maturities. Due to the stylized nature of the model, we test the main implications that seem likely to hold in any model where investor side factors play an important role. In particular, we focus on whether there exists a positive term premium, whether the term premium increases during crises, and whether the maturity of bond issuance shifts during crises.

The model predicts that the term premium should be positive on average. It also predicts that, during crises, the term premium should increase. This occurs either because of an increase in investors’ exposure to country risk in the case of a demand side shock, or because investors require a higher premium to hold the same amount of risk in the case of a supply side shock. The predictions on the optimal maturity structure depend on the type of shock. While a demand side shock causes the country to issue long-term bonds to shift risk toward investors, a supply side shock causes the country to issue short-term bonds to shift risk away from investors and save on borrowing costs. As a result, even though we cannot identify supply and demand side shocks, the correlation between the term premium and the maturity of bond issuance allows us to establish whether the predominant shocks are on the supply side (shifting the supply curve) or on the demand side (shifting the demand curve).<sup>20</sup>

> 20 In a more general setting, we would expect a demand side shock to affect the wealth of investors through its effect on the price of bonds investors already hold. In this case, a demand shock would have the direct effect highlighted in the model, but also an indirect effect on the supply side. As we show in the empirical section, crises are typically associated with higher term premia and a shift towards shorter maturities. This comovement suggests that either the predominant shocks are on the supply side or that, if they are on the demand side, their direct effects are dominated by their indirect effect on the supply side. In either case, the results support the conclusion that supply side factors play an important role in emerging market crises.

15
# 3 Data

We now turn to the empirical evidence and analyze both price and quantity data. The price data are used to estimate risk premia on short and long-term bonds, and to characterize the behavior of the implied term premium. The quantity data are used to analyze the comovement between the maturity structure of bond issuance and the observed term premium.

We conduct the empirical analysis by collecting data on sovereign bonds from the early 1990s up to 2003 for eight emerging economies. These countries are Argentina, Brazil, Colombia, Mexico, Russia, Turkey, Uruguay, and Venezuela. To calculate the term premium, we also collect data on sovereign bonds for Germany and the U.S., which are assumed to be free of default risk. The choice of emerging markets is constrained by data limitations. To estimate time series of the term premium, we need enough foreign currency denominated bonds of different maturities at each point in time. Therefore, our sample corresponds to those emerging economies that borrowed heavily in foreign currency, generating a rich enough pool of bonds. Furthermore, we restrict the sample to sovereign bonds because they constitute the most liquid debt instrument in most emerging markets, and because private debtors in emerging markets do not issue enough bonds to compute the term premium.

We collect weekly (end-of-week) time series of bond prices, using all available bonds for each country.<sup>21</sup> We also collect other information on these bonds, including currency denomination, coupon structure, and maturity. In addition, we compile time series of bond issuance in foreign currency. For each bond, we collect the amount issued, currency denomination, and maturity date. With this information, we construct weekly time series of amount issued valued in U.S. dollars. We exclude from the sample the bonds with collateral and special guarantees, such as collateralized Brady bonds and those issued by Argentina during the large pre-default swap. We also exclude bonds issued during forced restructurings, like those issued by Argentina and Russia post default and Uruguay post crisis.<sup>22</sup> We collect data from three different sources: Bloomberg, Datastream, and J.P. Morgan.

Regarding the currency choice, we restrict the sample to bonds denominated in foreign currency because it is not possible to construct the term premium by mixing bonds with different risk

> 21 We eliminate the observations where bond prices do not change over time, as this typically re fl ects no trading.

> 22 See Duffie, Pedersen, and Singleton (2003) for more details on the Russian default.

16
characteristics. (Consider that both default risk and currency risk would affect the term premium on domestic currency bonds.) This reduces the sample signi fi cantly, given that many countries, especially Asian and Eastern European ones, mostly issue domestic currency bonds. With respect to the currency selection, we use bonds denominated in U.S. dollars, Deutsche marks, and euros for the estimation of bond spreads. This choice is not very restrictive as most foreign currency bonds are issued in these currencies. As benchmarks of risk-less bonds, we use those issued by Germany in both Deutsche marks and euros and by the U.S. in dollars. We use bonds in all foreign currencies for our estimations of bond issuance.

Table 1 lists the countries in the sample, along with the time periods used for the price and quantity data. The price data start in April 1993 (with a different starting date for each country), ending in May 2003 for all countries. The quantity data cover a longer time span, starting in January 1990 and ending in December 2002. Table 1 also displays the number of bonds available to calculate bond prices and the number of bonds issued during the sample period. For the price data, the table shows the average minimum maturity, maximum maturity, and 75th percentile. Though most bonds have a maturity of less than 15 years, the countries in the sample have been able to issue longer-term bonds with maturity of 20 and 30 years. The bottom panel of Table 1 displays the average amount issued by maturity, showing that issuance is distributed across maturities. Appendix Table 1 lists all the bonds used in the paper, specifying for each bond its characteristics and whether it is used for the price and/or quantity analysis. The number of emerging market bonds used in the paper is 466, while the total number of bonds (including German and U.S. bonds) is 746.

# 4 Term premium

In this section, we show that, consistent with the model predictions, observed term premia on emerging market bonds are positive and increase during crisis times. In the model, the risk premium on short-term debt is set to zero for simplicity, so the risk premium on long-term bonds and the term premium are identical. In reality, the risk premium on short-term bonds is also positive. Thus, to obtain information on the term premium, we fi rst need to estimate the risk premia on bonds of maturities.

17
The risk premium for each maturity is estimated by using ex-post excess returns on emerging market bonds over comparable default-free (German and U.S.) bonds. To calculate the risk premium, we need to obtain fi rst bond yields, spreads, and prices. We begin by estimating time series of German and U.S. yields curves and emerging market spread curves. The maturity-τ spread, st,τ , is de fi ned as the difference between the yield, yt,τ , on an emerging market zero-coupon bond of maturity τ and the yield, yt,τ<sup>∗,onadefault-freezero-couponbondofmaturityτ,st,τ= yt,τ−y</sup> t,τ<sup>∗.</sup> We use this information to obtain bond returns at different maturities and over time for every country. This enables us to make cross-country, cross-maturity, and over-time comparisons. Note that it would be impossible to carry out the analysis using the raw data because each country has a different set of bonds at each point in time, with varying maturity and coupon structure. Appendix B describes the methodology used to estimate yields and spread curves.

Figure 2 displays the estimated spreads over time for each country. The fi gure shows spreads at two maturities to illustrate how short-term (3-year) and long-term (12-year) spreads move over time.<sup>23</sup> The fi gure shows some interesting facts. First, spread curves are, on average, upward sloping. Second, spreads increase during periods of fi nancial crises. For example, during the crises in Argentina, Russia, and Uruguay, spreads jump to more than 25 percent or 2,500 basis points. Third, short-term spreads are more volatile than long-term spreads. In fact, during periods of very high spreads there is an inversion of the spread curve, with short-term spreads becoming higher than long-term ones.

Using the estimated spread curves and U.S. yield curves, we compute the price Pt,τ of a representative emerging market bond of given maturity τ and coupon c. In Figure 3, we plot the price of short and long-term bonds, with a semi-annual coupon of 7.5 percent.<sup>24</sup> To simplify the comparisons, the value at the beginning of the sample is normalized to 100 for each country. The fi gure shows that the prices of long-term emerging market bonds are more volatile than those of short-term bonds. In particular, at the onset of crises the prices of long-term bonds fall much more than those of short-term bonds, while during the recovery, the prices of long-term bonds increase much more than those of short-term bonds. Next, we show how these price changes are re fl ected

> 23 Our methodology allows us to compute spreads at every maturity and, therefore, construct the entire spread curve over time.

> 24 For prices and returns, we choose to use coupon-paying bonds because emerging markets almost never issue zero-coupon bonds. So the pricing errors for coupon-paying bonds are smaller than for zero-coupon bonds.

18
in the risk premium and the term premium.

After having obtained prices, we estimate the risk premium using excess returns or, more precisely, average ex-post excess returns over T periods.<sup>25</sup> The return of holding an emerging market bond, rt+1,t, for one period (one week) is equal to<sup>Pt+1,τ</sup> P<sup>−</sup> t,τ<sup>1−Pt,τ</sup> , in the case of no coupon payment at date t + 1. We compare this return to the return on a German or U.S. bond, rt<sup>∗</sup> +1,t<sup>.</sup> Excess returns, erτ , are then expressed as the returns of holding emerging market bonds of maturity τ and coupon c over the returns of “comparable” risk-less bonds, Positive excess returns mean that emerging market bonds pay positive returns on top of what German or U.S. bonds do. Note that the computation of excess returns does not simply use riskless bonds of the same maturity and coupon structure. In fact, we obtain excess returns by taking into account the payment pro fi le of the emerging market bond, and comparing it to a portfolio of risk-less bonds that replicates its payment structure.<sup>26</sup> The term premium, tpτ 2,τ 1, is given by the difference between the risk premium (average excess returns) on long-term bonds (of maturity τ 2) and that on short-term bonds (of maturity τ 1), Before going to the empirical estimates, two points are worth noting about the term premium. First, a positive slope in the spread curve does not imply that the term premium is positive, since the term premium also depends on the evolution of spreads over time and on how defaults affect bonds of different maturities. Second, the difference in risk premium between long and short-term emerging market bonds would typically re fl ect both the price risk associated with the probability of default and the term premium inherent in default-free bonds. Here we concentrate on the fi rst component, because we de fi ne the term premium on emerging market bonds in excess to the term premium on default-free bonds.<sup>27</sup>

> 25 To calculate the means, we use holding periods of one week. We also experimented with holding periods of one month, obtaining similar results.

> 26 See Appendix B for more details.

> 27 Since the term premium for U.S. and German bonds is positive, the total term premium would be larger if we

19
# 4.1 Unconditional term premium

Table 2 shows average annualized excess returns across all observations in the sample. The table displays values for bonds with maturities of 3, 6, 9, and 12 years and annual coupon payments of 5, 7.5, and 10 percent (paid semi-annually). These “theoretical” bonds are representative of emerging market sovereign bonds both in terms of maturity and coupons. Table 2 shows that, when considering all the countries in the sample, excess returns are positive for all coupon sizes and maturities. More relevant for our analysis, excess returns increase with maturity in all cases, so the term premium is also positive.<sup>28</sup> Not surprisingly, there is heterogeneity in the results at the country level, re fl ecting the different performance of each emerging market. However, the results are not driven by any particular emerging market, since they survive when we exclude from the sample individual countries.

What do the results in Table 2 tell about how much emerging market bonds pay relative to comparable default-free bonds? To answer this question, consider the results for bonds with annual coupons of 7.5 percent (the one closest to actual coupons). The results in Table 2 say that, on average, investors receive an annualized return 3 percent higher when investing in a 3-year emerging market bond than when investing in a German or U.S. 3-year bond, and an annualized return 7 percent higher when investing in a 12-year emerging market bond than when investing in a German or U.S. 12-year bond. In other words, emerging market bonds pay a positive risk premium and a positive term premium.

# 4.2 Term premium during crisis and tranquil times

We now study whether the term premium is different during crisis and tranquil times. To do so, we fi rst need to de fi ne crises. The literature has used different de fi nitions, with no de fi nition being perfect as certain ad-hoc criteria need to be adopted. To partly overcome this problem, we use four different de fi nitions of crises to gauge the robustness of our results. Since we are interested in studying conditional returns, we adopt de fi nitions that use only ex-ante information. In other words, to determine whether there was a crisis at time t, we only use information that was available added the two components.

> 28 Also note that excess returns decrease with coupon size. This is expected given that the term premia are positive and duration is a decreasing function of coupon size.

20
at time t. Crisis de fi nition 1 is our benchmark de fi nition; it sets the beginning of a crisis when 9-year spreads are greater than a threshold, which is de fi ned as the average spread over the previous six months plus 300 basis points.<sup>29</sup> The end of the crisis is at the end of the fi rst four-week period in which spreads have remained below the threshold used to determine the beginning of the crisis. Crisis de fi nition 2 is similar to crisis de fi nition 1, but uses 400 basis points to de fi ne the threshold. Crisis de fi nitions 3 and 4 are similar, but use a one-week period instead of a four-week period to end the crisis.

Table 3 lists the crisis periods obtained with crisis de fi nition 1. All major crises are captured by the crisis de fi nition. For example, the Mexican 94-95 crisis affected Argentina and Brazil. (Note that our sample does not contain spreads for Mexico during that period.) The Russian crisis affected all countries in the sample except Uruguay, which had its own crisis after Argentina defaulted on its debt in early 2002. The Argentine crisis started when the government was forced to change its economic plan and the default became very likely. Brazil and Colombia were also hit by crises in 2002.

Then, we calculate excess returns at different maturities, splitting the sample between tranquil times and crises. The results are reported in Table 4 for all crisis de fi nitions. We report results using bonds with coupons of size 7.5 percent, although the results are similar for bonds with coupons of 5 and 10 percent. The results indicate that both excess returns and the term premium are very large during crises, and close to zero during tranquil times. For example, according to de fi nition 1, the difference between the average 12- and 3-year annualized excess returns (our measure of the term premium) is around 28 percent. Table 5 displays excess returns by country according to crisis de fi nition 1. The table shows that for most countries the risk premium and the term premium are large during crises and low during non-crisis periods. There are two exceptions, excess returns are negative during crises in Uruguay and, for short maturities, in Argentina. This is due to the fact that both countries have experienced actual defaults, namely, crises in which the situation continued to deteriorate rather than improve. In the case of Argentina, this is partly compensated by the Mexican crisis, when excess returns were very high.

In Table 6, we analyze more formally whether excess returns across maturities are predictable,

> 29 To classify the fi rst observations of the sample for each country, we repeat the fi rst price observed during the previous six months.

21
namely whether they change during crisis times. The table presents least squares regressions with the long-short excess return as the dependent variable, de fi ned as the difference for each observation between a long-term (9-year or 12-year) excess return and a short-term (3-year) or medium-term (6-year) excess return. The independent variable is a dummy that takes the value one during crises and zero otherwise. To make sure that the results are robust to our crisis de fi nition, we also try log spreads, de fi ned as log(1+st,τ ), at different maturities as the independent variable. The estimations pool all observations available across countries and over time. Results with and without country and time effects are reported. The regressions use robust estimates of the standard errors. To do so, we de fi ne clusters by the country and crisis indicators, thus, observations are assumed to be independent across clusters, but not necessarily independent within clusters. This allows for a general form of heteroskedasticity across observations and non-zero correlation within clusters.<sup>30</sup> The results in Table 6 show that the crisis variable is positive and statistically signi fi cant at the 1 percent level for all regressions. Since the coefficient on the crisis dummy is an estimate of the term premium, the results imply that the term premium is positive. The estimations also show that the magnitude of the coefficient is very large. For example, the regression for the 12-3 term premium with no country or time dummies shows that the term premium increases by 0.449 percent per week during crisis times, which on an annualized basis corresponds to more than 26 percent. The coefficient of 0.045 on the 6-year spread in the regression of the 12-3 term premium states that when 6-year spreads increase by 1 percent, the annualized long-short excess return increases by 2.4 percent. Con fi rming the evidence presented in the previous tables, these regressions imply that the term premium is time-varying, increasing during periods of crises and high spreads.<sup>31</sup> We have already shown that the term premium increases during crises. To estimate to what degree this increase can be ascribed to an increase in the volatility of returns during crises, we plot in Figure 4 the excess returns against the standard deviation of excess returns for crisis, non-crisis, and all periods. The fi gure shows that during non-crisis periods excess returns are close to zero, with the standard deviation increasing with maturity. During crisis periods, both excess returns

> 30 As further robustness tests, we also estimated regressions with crisis dummies constructed with crisis de fi nitions 2, 3, and 4. Moreover, we rede fi ned clusters using either country or crisis indicators. In all cases, we obtained similar results.

> 31 The fact that investors demand higher risk premia and term premia during crises implies that, at the onset of crises, bond prices need to fall enough such that they become sufficiently attractive to investors. In this sense, bond prices, especially those of long-term bonds, “overreact” during crises.

22
and their standard deviations increase for all maturities. It is important to note that the increase in excess returns cannot be accounted for by the increase in volatility. The reason is that the Sharpe ratio (i.e. the ratio of excess returns over their standard deviation) increases substantially during crisis times. The average Sharpe ratio across maturities is 0.006 during non-crisis periods and larger than 0.06 during crisis periods. Interestingly, the Sharpe ratio is higher for long-term bonds than for short-term bonds during crises.

In sum, the results above are consistent with the model presented in Section 2, which shows that crises can be due to shocks to the country’s repayment capacity or to shocks to investors’ wealth (or other determinants of risk appetite). In both cases, the model predicts that the term premium should increase. In the case of debtor side shocks, or demand shocks, the country demands more long-term funds, driving up the cost of long-term borrowing. In the case of investor side shocks, or supply shocks, bondholders become more sensitive to the price risk of long-term bonds and demand a higher term premium. To complement the price evidence presented so far, the next section studies bond issuance at different maturities, during crisis and tranquil times. This will allow us to shed light on the relative role of debtor and investor side shocks during crises. But before doing so, we discuss three points related to the results presented in this section.

# 4.3 Interpreting the evidence

We end this section with a discussion of three issues that might help clarify the results related to the risk premium and the term premium. First, can our results be due to a peso problem? Second, what is the relation between our results and the literature on the term structure of interest rates in developed countries? Third, does the fact that the risk premium is close to zero during tranquil times imply that our explanation of why countries borrow short term is crisis contingent?

## 4.3.1 Peso problem

It is important to point out that it is very unlikely that our results on the risk premium and, even more, on the term premium are the consequence of defaults being underrepresented in our sample, a phenomenon also known as the peso problem.<sup>32</sup> First of all, our sample does include a number

> 32 To be precise, the name comes from the study of devaluations (of the Mexican peso) rather than defaults, but the same argument applies.

23
of default episodes and it is difficult to claim that the period 1993-2003 was particularly good for emerging markets. Second, as explained below, the behavior of short and long-term bonds during defaults suggests that the results are not driven by a peso problem.

Consider fi rst the results on the term premium. Usually, long-term bonds trade at higher discounts (i.e. lower percentage of face value) than short-term bonds, especially in periods of high spreads (when defaults are likely to take place). In addition, post-default workouts generally involve payments approximately proportional to face value. As a result, episodes of default should lead to larger losses on short-term bonds than on long-term bonds.<sup>33</sup> This suggests that if defaults were underrepresented in our sample, the term premium would be even higher than the one we report, especially during crisis times.

The argument above, that a peso problem is unlikely to drive the results on the term premium, leads one to believe that a peso problem is not driving the positive risk premium either. The argument goes as follows. It is very difficult to think of an environment where long-term bonds have higher returns than short-term bonds, while at the same time either long or short-term bonds have a negative (or zero) risk premium. The reason is that the returns on short and long-term bonds are highly correlated. A negative (zero) risk premium would imply a positive (zero) correlation between bond returns and investors’ stochastic discount factor or marginal utility and, as a result, a negative (zero) price of emerging market risk. But since the returns on long-term bonds are much more volatile than those of short-term bonds, a negative (zero) price of risk would imply a negative (zero) term premium, contradicting our fi ndings. Therefore, it is not likely that the term premium is positive, as we fi nd, without the risk premium being positive as well. In other words, the existence of a positive term premium suggests that the price of emerging market risk is positive and, therefore, the risk premium is also positive.<sup>34</sup>

> 33 This in fact was the case during the Argentine default. We studied the excess returns of buying Argentine bonds of different maturities before the default (which was declared on December 23, 2001) and holding them until after the default. For purchase dates between early November 2001 and one week before the default and selling dates between one week and one year after the default, the losses on short-term bonds were virtually always greater than those on long-term bonds, by around 10 percent.

> 34 The idea that the observed term premia carry information on the underlying risk premium seems to be very useful since estimates of the risk premium are typically very sensitive to the sample under study. For example, Eichengreen and Portes (1988) fi nd that the ex-post excess returns on sovereign bonds issued by foreign countries in the United States and Britain during the interwar years were close to zero. Klingen, Weder, and Zettelmeyer (2003) fi nd that the ex-post excess returns on emerging market sovereign lending were negative during the 1970s and 1980s, but positive during the 1990s. In this paper, although excess returns are positive in the full sample, we fi nd negative excess returns for Argentina and Uruguay.

24
# 4.3.2 Related literature on the term structure of interest rates

There is a vast literature on the term structure of interest rates in developed countries related to our fi ndings on the risk premium and the term premium. Our results can be interpreted as deviations from the “pure expectations hypothesis” and the “expectations hypothesis,” but stated in terms of spreads instead of yields.

Assume fi rst that investors are risk neutral with respect to default episodes in emerging markets. In this case, spreads should only re fl ect the expected losses from default (both the risk premium and the term premium should be zero) and the pure expectation hypothesis in terms of spreads should hold. A second, less restrictive, assumption would be that spreads re fl ect a risk premium that may be different across maturities but is constant over time. In this case, changes in spreads should only re fl ect innovations to the expected default losses, namely, the expectation hypothesis in terms of spreads should hold.<sup>35</sup> In the literature on emerging market borrowing, the idea that spreads mostly re fl ect the market assessment of the probability of default of a given country is still widely held. However, our fi ndings that the risk premium and the term premium are on average positive and that both increase during crises suggest that neither the pure expectation hypothesis nor the expectation hypothesis hold for emerging market spreads. The fi nance literature on the term structure in developed economies has gradually rejected both versions of the expectation hypothesis and has moved toward attempts at modelling and explaining patterns of time-varying risk premia.<sup>36</sup> Our model provides a different simple equilibrium framework that is consistent with the observed patterns of the risk premium and the term premium in emerging market bonds.<sup>37</sup>

# 4.3.3 When is it cheaper to borrow short term?

Our results show that it is cheaper to borrow short-term during both crisis and tranquil times. The fact that it is cheaper to borrow short term during crises is clear from the high term premia during

> 35 For some references on the topic and a de fi nition of the pure expectation hypothesis and the expectation hypothesis, see Cox, Ingersoll, and Ross (1985), Campbell, Lo, and MacKinlay (1997), Bekaert and Hodrick (2001), and Dai and Singleton (2002).

> 36 See references in Cochrane (1999).

> 37 Clearly, to provide a quantitative assessment of these facts more work remains to be done, both in the direction of no-arbitrage models and in the direction of equilibrium models. For no-arbitrage models see Duffie and Singleton (1999) and Duffie, Pedersen, and Singleton (2003).

25
those episodes. In addition, it is also cheaper to borrow short-term during tranquil times because there is a positive transition hazard rate from tranquil to crisis times. As a result, when a country issues long-term bonds during tranquil times, it has to compensate bondholders for the drop in bond prices that would take place if a crisis were to materialize. In other words, the spreads on long-term bonds issued during tranquil times re fl ect not only the expected losses from default, but also the expected risk premia that would need to be paid during the lifetime of the bond. This is true irrespective of whether a crisis actually materializes. All that is needed is a positive transition probability.

A caveat to this reasoning applies. This argument is valid only if emerging economies cannot repurchase outstanding long-term bonds at the beginning of crises by issuing short-term bonds. In other words, we are assuming that by issuing long-term bonds during tranquil times, countries are forcing themselves to go through crises carrying these long-term obligations. The assumption that there is some cost associated with repurchasing long-term bonds during crises is supported by the fact that countries do not repurchase existing long-term bonds during those times, while they very seldom issue new long-term bonds during periods of fi nancial turbulence (as shown in the next section). It is difficult to explain this knife-edge result of zero net new long-term issues in the absence of some cost (signalling or otherwise) associated with retiring existing long-term bonds.<sup>38</sup>

# 5 Bond issuance

The model in Section 2 shows that the comovement between the term premium and the maturity structure of debt can shed light on the type of shocks characterizing the cyclical behavior of emerging market debt. On the one hand, demand side shocks such as an increase in current fi nancing needs or a reduction in future expected government revenues are likely to lead to an increase in the maturity structure of debt and a resulting increase in the term premium, generating a positive comovement. On the other hand, supply side shocks, such as a decrease in investors’ wealth, are likely to lead

> 38 The IMF (1999) reports that in fact there have been some attempts to buyback debt perceived to be “mispriced,” i.e. paying a high risk premium. An example is the buyback of Polish Brady bonds in 1998, which amounted to some 750 million dollars, after a buyback of around 1.7 billion dollars in 1997. Given that these operations, if known, would drive bond prices up, they are usually carefully conducted and not officially con fi rmed until after they have been completed. If successful, a quiet buyback at the discounted price delivers a net reduction in the debt burden. Though these operations exist, the difficulty in completing them successfully makes them rare and small relative to the outstanding debt. Moreover, these operations take place in favorable times.

26
to an increase in the term premium and a resulting decrease in the maturity structure of debt, generating a negative comovement.

In this section, we study whether the behavior of the quantity data are consistent with demand or supply type of shocks. We concentrate on two sets of variables, the amount issued at different maturities and the average bond maturity. We study the time-varying patterns of these variables. In particular, we analyze how their behavior is affected by crises, by different measures of spreads, and by the term premium.

To study the amount issued at different maturities, we run a separate regression of issuance at each maturity as a function of each conditioning variable. We use a Tobit model, estimated by maximum likelihood, pooling all observations. These estimations take into account the fact that observations are left censored at zero. The dependent variable is the amount issued at each maturity in any given week, normalized by the average weekly issues for each country. This normalization takes into consideration that the average amount issued varies across countries. We use four different bond maturities: up to 3-year maturity (short term), more than 3-year maturity and up to 6-year maturity (medium-short term), more than 6-year maturity and up to 9-year maturity (medium-long term), and more than 9-year maturity (long term). As explanatory variables we use, alternatively, the crisis dummy de fi ned above, the 3-year spread, the 9-year spread, the emerging market bond index (EMBI) spread for each country, and the predicted term premium for each country. For spreads, we use log-spreads, de fi ned as log(1+ st,τ ). The EMBI spreads, calculated by J.P. Morgan, are well-known measures of long-term spreads in emerging markets. They not only provide an alternative estimate of long-term spreads, but also extend the sample for Mexico to cover the Mexican crisis (though they exclude Uruguay). We use the predicted term premium because it most directly captures the cost of issuing long-term debt relative to short-term debt. This variable is computed by regressing ex-post excess returns on 3-year and 9-year spreads and then obtaining the predicted value. As before, we compute robust standard errors using the country and crisis indicators as clusters.

The Tobit estimations are reported in Table 7. The estimations show that short-term issues are hardly affected by any of the conditioning variables; only the 3-year spread is statistically signi fi cant at the 10 percent level. However, medium- and long-term issues do show clear cyclical patterns. The conditioning variables become more statistically signi fi cant and the point estimates negative 27
and large in magnitude. In the regressions for long-term issues, all the regressors are signi fi cant, at least at the 5 percent level. The coefficients reported, which are the marginal effects or the effects on the observed (not the latent) variable, also seem large. For example, an increase of 100 basis points in 9-year spreads leads to a decline in the weekly issues of 0.223, where the average value of the normalized weekly issue is 1. In sum, the estimations in Table 7 suggest that during crises and, more generally, in periods of high spreads, countries tend to issue less debt. In addition, the longer the maturity of debt, the larger the effect of crises and spreads on the amount issued. Interestingly, the estimated term premium has a big negative effect on long-term issues, but no statistically signi fi cant effect on shorter-term issues. The result that short-term issues are barely affected by the different variables re fl ects the fact that although countries tend to issue less when spreads are high, they mostly issue short-term bonds (if they issue at all). These two effects cancel out, leading to non-signi fi cant coefficients.<sup>39</sup> To study the average maturity of issues, we estimate a model that takes into account the incidental truncation of the data, since the average maturity is only available when countries issue bonds and, otherwise, there are missing observations. As noted initially by Heckman (1979), ignoring the missing values might lead to a sample selection bias. In our case, one would tend to miss observations when spreads are high and countries do not issue any bonds. To account for this selection, we estimate two equations simultaneously by maximum likelihood. One equation describes the probability of observing the average maturity of issues each week. The second equation estimates how the average maturity is correlated with the conditioning variables. In this type of estimations, it is usually difficult to select the variables that enter in each equation. We choose different speci fi cations to see whether the results are robust to this choice.<sup>40</sup> The regressors included in the selection equation are similar to those used for the Tobit models. These variables help to predict whether countries issue at all. The regressors included are, alternatively, the crisis dummy, the short and long-term spreads, and the country EMBI spread. For the main equation, we use the long-term spread and, alternatively, the estimated term premium, which captures the relative

> 39 Note that the negative sign of the coefficients is not likely the result of reverse causality. If bond issuance had an impact on spreads, an increase in the demand for funds would push down prices and increase spreads, resulting in a positive coefficient. To the extent that reverse causality played a role, it would bias the results against our fi ndings.

> 40 As another robustness check, we also estimated the main equation without taking into account the selection bias and obtained similar results.

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cost of issuing long term. As the variables are not scaled, we include country dummies. Again, we compute robust standard errors using the country and crisis indicators as clusters.

The results of the selection equations, displayed in Table 8, show that countries are less likely to issue bonds during crisis times and, more generally, when spreads are high. In addition, the results of the main equations show that the average maturity of issues shortens when long-term spreads or the predicted term premium increases. These results are consistent with the pattern displayed in Figure 5, which shows the average maturity and spreads over time for each country. The fi gure also shows that issuance is negatively correlated with crises and, more generally, with the level of spreads. Finally, another way to summarize the evidence is that countries try to extend the maturity structure of their debt whenever market conditions permit it, i.e. when markets require a low term premium.

The results presented in this section, when combined with the results in Section 4, provide compelling evidence that supply side factors play an important role during emerging market crises. The results show that crises and, more generally, periods of high spreads, are associated with higher risk and term premia and lower amount and shorter maturity of issues. If crises were mostly the result of debtor side factors (demand shocks), they would be associated with more issues at longer maturities and a higher term premium. The fact that the term premium increases while debtors are curtailing long-term borrowing suggests that investor side factors (supply shocks) play an important role during crises.

# 6 Final remarks

This paper proposes a new explanation to why emerging economies borrow short term, even though this type of debt increases their exposure to liquidity crises. We argue that countries choose to be exposed to crises because investors require a high term premium for holding long-term debt, making short-term borrowing cheaper. The model in the paper shows this trade-off and endogenously derives the maturity structure and the term premium (the relative cost of borrowing long term). The model illustrates the risk-sharing problem between the debtor country and investors. The empirical section of the paper shows that the term premium is, on average, positive and increases signi fi cantly during crises. Therefore, our fi ndings explain not only why countries tend to borrow short term, but 29
also why they rely so heavily on short-term debt during periods of fi nancial turbulence. Finally, the negative correlation between the term premium and the debt maturity strongly suggests an important role of investor side factors in shaping the way that emerging economies borrow.

The distinction between investor and debtor side factors has important implications not only for academic discussions, but also for policy recommendations. One important example is the discussion on how to deal with fi nancial crises. Some papers argue that countries borrow short term as a way to commit to the right policies when moral hazard is a problem. From this perspective, the cost of crises is what makes these episodes a strong disciplining device. Efforts to limit the cost of crises through loans from the international fi nancial community, or other liquidity-providing mechanisms, would exacerbate the moral hazard problem, and could end up reducing welfare.<sup>41</sup> If, on the other hand, countries borrow short term because long-term debt is too expensive, those same crisis prevention mechanisms would improve welfare. The bene fi ts would come not only from fewer and less severe crises, but also from cheaper long-term borrowing as a result of the reduction in the price risk of long-term debt.

The results in this paper lead to several possible directions for future research. First, it would be interesting to extend the coverage of our analysis to contrast the results presented here with results derived from bonds issued by other emerging economies, developed economies, domestic currency debt, and private borrowers. However, data restrictions to construct time series of spread curves will probably limit any future analysis to certain borrowers (likely other developed economies and primarily sovereign debtors). This type of analysis might shed light on whether investors treat the debt from developed countries differently than that from emerging economies. As another extension, the empirical analysis could be carried out in a dynamic framework to study the stochastic properties of spreads at different maturities. Preliminary evidence suggests that long-term spreads “overreact” to movements in short-term spreads. More precisely, long-term spreads seem to react to innovations in short-term spreads as if these innovations were more persistent than what they actually are, leading to excess volatility. It is interesting to note that this type of evidence seems at odds with what other authors have found when studying the dynamic behavior of yield curves in developed countries.<sup>42</sup> Finally, the fact that the Sharpe ratio of long-term bonds is higher than

> 41 See Jeanne (2000) for a discussion of this argument.

> 42 See Campbell and Shiller (1991).

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that of short-term bonds suggests that the risk of long-term bonds is less diversi fi able than the risk of short-term bonds. A possible explanation may lie on a higher sensitivity of long-term bonds to global factors (such as investors’ risk appetite) and a higher sensitivity of short-term bonds to domestic factors (such as default probabilities). This hypothesis could be tested by estimating cross-country correlations at different maturities. A higher correlation at long maturities would not only explain the higher Sharpe ratios on long-term bonds, but also suggest a role for fi nancial linkages as a source of contagion or, more generally, cross-country comovement.

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