Default Risk and Income Fluctuations in Emerging Economies

Countercyclical and volatile country interest rates, consumption more volatile than output, a countercyclical trade balance, and default in the middle of a collapse. “Emerging markets tend to have volatile business cycles and experience economic crises more frequently than developed economies. Recent evidence suggests that this may be related to cyclical changes in the access to international credit. In particular, emerging market economies face volatile and highly countercyclical interest rates, usually attributed to countercyclical default risk.” For Argentina over 1983-2001, the paper reports a spread standard deviation of 5.58 against output volatility of 7.78, consumption volatility of 8.59 (i.e. more volatile than output), a trade balance-output correlation of -0.64, a spread-output correlation of -0.88, a spread-trade balance correlation of 0.70, and a mean spread of 10.25%. In the default quarter itself (2002Q1) spreads stood 28.60 points above trend while output was 14.21% and consumption 16.01% below it. The paper documents the same pattern for two other defaulters: Ecuador (1999Q3: spread +47.58, output -6.46; spread-output correlation -0.63) and Russia (1999Q4: spread +30.43, output -12.6; spread-output correlation -0.70), concluding that “the high volatility of interest rate spreads together with the countercyclicality of interest rates and the trade balance appear to be regularities for recent data in emerging countries.”

A risk-averse benevolent government borrowing from risk-neutral competitive lenders with a single non-contingent bond, free to default, punished by temporary exclusion plus an output loss. Households are identical, risk averse, receive a Markov endowment of a tradable good, and consume their endowment plus lump-sum transfers of the government’s international credit proceeds. The government buys one-period discount bonds at a price q(B′,y) that “is endogenous to the government’s incentives to default and depends on the size of the bond B′ and on the aggregate shock y because default probabilities depend on both.” Default costs have two components: “exclusion from international financial markets and direct output costs.” Specifically, on default “current debts are erased from the government’s budget constraint and… saving or borrowing is not allowed”; the country stays in autarky for a stochastic spell and re-enters with exogenous probability θ; and output while in autarky is a lower, increasing function of the shock. Lenders can borrow or lend freely at a constant world rate r, observe income every period, and price bonds so that expected profit is zero, which pins the price at (1 − δ)/(1 + r) with δ the endogenous default probability. The author is explicit that the resulting risk adjustment is not a risk premium: it “is not due to compensation for risk aversion, as lenders are risk neutral. It reflects the risk neutral compensation for a lower expected payoff.”

Because complete-markets limited-commitment models cannot produce either observed default premia or the observed timing of default. The paper’s contrast is with the optimal-contracting literature (Kehoe-Levine, Kocherlakota, Alvarez-Jermann), which “assume that a complete set of contingent assets is available and search for allocations that are efficient subject to a lack of enforceability.” Two objections: “First, default, defined as a breach of contract, never arises in equilibrium so that default premia are never observed. Second, default incentives in this class of models are typically higher in periods of high output, which is when efficiency dictates loan repayment. These features put these models at odds with the empirical evidence regarding default risk in emerging markets where bond yields are countercyclical and where debt prices largely reflect the risk of default.” The positive case for non-contingent bonds is both realism and mechanism: they “more closely reflect[] the actual terms of international financial markets where foreign debt is largely contracted at non-contingent interest rates,” and they have “the potential to deliver countercyclical default risk, since repayment of non-contingent, non-negotiable loans in low output, low consumption times is more costly than repayment in boom times.”

Policy functions for consumption, government assets, repayment and default sets, and a bond price function, mutually consistent with household budget constraints, government optimisation, and zero expected profit for lenders. The government’s value with the default option is the maximum of the value of staying in the contract and the value of default. The value of default is utility from the reduced autarky output plus a continuation that mixes re-entry at zero debt with probability θ and continued autarky with probability 1 − θ. The value of repayment is the usual Bellman problem in which the government internalises the price schedule when choosing new debt; crucially, “the decision to remain in the credit contract and not default is a period-by-period decision. The expected value from next period onward incorporates the fact that the government could choose to default in the future.” A lower bound on debt “prevents Ponzi schemes but is otherwise not binding in equilibrium.” Default probabilities are the measure of next period’s shocks that fall in the default set, and equilibrium requires bond prices to reflect exactly those probabilities. The author notes the exclusion and output costs are imposed exogenously here while pointing to work deriving each endogenously – reputation-based exclusion (Wright 2002), output damage through non-credit relationships (Cole-Kehoe), and renegotiation (Yue) – and situates the whole exercise relative to the Bulow-Rogoff paradox, “if the government has an enforcement technology of its own such that it can save at the same interest rate after defaulting, no international borrowing can be sustained in equilibrium,” citing Kletzer-Wright’s lack of lender commitment and Amador’s political-economy resolutions.

Default sets shrink in assets: if default is optimal in some state at a higher asset level, it is optimal in that state at any lower level. “The result follows from the property that the value of staying in the contract is increasing in B and that the value of default is independent of B. As assets decrease, the value of the contract monotonically decreases while the value of default is constant. Thus, if default is preferred in a given state y for some level of assets B, the value of the contract is less than the value of default. As assets decrease, the value of the contract will be even lower than before and so default will continue to be preferred.” The author attributes the result to Chatterjee et al. and Eaton-Gersovitz. Because shocks have bounded support, there is an asset level low enough that the default set is the entire endowment set, and – since default can only be attractive with debt outstanding – a non-positive asset level above which the default set is empty. Those two bounds define the region within which default risk is interior.

That default happens only when the country cannot roll its debt over – so default necessarily coincides with a net capital outflow. Formally: if the default set is non-empty at some asset level, then no available contract delivers positive net inflows at that level. The reasoning is a simple arbitrage in the government’s own problem: “Default arises only when the borrower does not have access to a contract that lets him roll over the current debt due. If the borrower could roll over the current debt, then he would simply consume more today and default tomorrow on a higher debt. In particular, given that from tomorrow onward the borrower under the contract has the option to default, if default is chosen today then it must be that today’s period utility is lower under the contract than under default. But given that debt contracts are chosen to maximize the contract value, it must be that today consumption under the contract is less than the endowment for all contracts available.” This is what makes the sign of the cyclical relationship determinate: since default requires paying out, and paying out hurts most when income is low, the timing follows.

Default incentives are stronger the lower the endowment – the opposite of the complete-markets result – because concavity makes a net repayment most painful in a recession. “This result comes from the property that utility is increasing and concave in consumption and that under no default the economy experiences net capital outflows due to proposition 2. The idea is that net repayment is more costly when income is low due to concavity, making default a more likely choice. In low income times, the contracts available are not useful insurance instruments for a highly indebted borrower because none can increase consumption relative to income. Thus, the asset the borrower is giving up is not very valuable and default may be preferable in recessions.” The author is careful that this is a net result of two opposing forces, not a one-sided effect: “When output is high, the value of default is relatively high increasing default incentives. But at the same time, the value of repayment is high which decreases default incentives. With an incomplete set of assets and i.i.d. shocks the latter effect dominates and thus default is more likely the lower the income. This result contrasts with the participation constraint models that have a complete set of contingent assets. These models have the feature that default incentives are higher in times of good shocks and capital outflows in recessions are never part of the contract.” The introduction gives the same intuition dynamically: “after a prolonged recession debt holdings can grow so much that the economy experiences net capital outflows. These capital outflows are more costly for a risk averse borrower in times of low shocks, making default more attractive in recessions.”

Because bond prices fall to zero as debt grows, the cash raised is non-monotone in promised repayment, which creates an endogenous borrowing limit and confines equilibrium risky borrowing to a bounded interval. For assets above the no-default threshold, prices equal the risk-free discount; below the all-default threshold, prices are zero, so “these contracts give zero resources to the borrower”; in between, “bond prices are increasing in the level of assets… but q(B′)B′ is first decreasing and then increasing in B′.” The consequence is a dominance argument: the government “would never choose optimally a bond contract with B < B* because he can find an alternative contract that increases consumption today by the same amount while incurring a smaller liability for next period.” Risky borrowing therefore happens only between the peak of the curve and the no-default threshold, and for that region to be non-empty “the bond price function needs to decrease slow enough such that lower asset levels are associated with larger capital inflows.” The author reports that this is not guaranteed: “for some parameterizations the default boundary and the price function become very steep and this region disappears.” The endogenous limit also does real work in the quantitative model: “in recessions the borrower is often at the constraint,” and borrowing limits are countercyclical, B*(y_High) < B*(y_Low), “because default is preferable mostly during recessions and shocks are persistent.”

No: they deliver countercyclical interest rates but a counterfactually procyclical trade balance. With i.i.d. shocks the price schedule does not depend on the current shock, yet “the model generates a negative relation even with i.i.d. shocks. The reason is that more debt is demanded in recessions as in Huggett (1993), which implies that although the bond price function is independent of the shock, recessions are associated with high interest rates. However this produces a counter-factual feature which is that recessions are correlated with trade deficits.” Persistence is what fixes it: with a persistent process, “the negative relation between output and interest rates remains while the empirically correct negative relation between trade balances and output emerges due to the state dependent debt contracts offered.” The author states the same point later as a robustness fact: “When shocks are i.i.d. the bond price schedule is independent of the shock and the model behaves similar to standard income fluctuations models under incomplete markets delivering lower volatility of consumption relative to income and procyclical trade balance.”

Five parameters fixed a priori, three matched to Argentine moments. Fixed: risk aversion σ = 2, “a common value used in real business cycle studies”; the risk-free rate r = 1.7%, “the average quarterly interest rate of a 5 year U.S. treasury bond during this time period”; and an AR(1) process for log output estimated from Argentine GDP with ρ = 0.945 and η = 0.025, discretised “into a 21 state Markov chain using a quadrature based procedure (Hussey and Tauchen 1991).” Matched: the discount factor β = 0.953, the re-entry probability θ = 0.282, and the output-cost threshold 0.969 E(y), calibrated to “a default probability of 3%, an average debt service to GDP ratio of 5.53%, and the standard deviation of the trade balance.” The 3% comes from Argentina having “defaulted on its foreign debt 3 times in the last 100 years” (1956, 1982, 2001 on the paper’s own accounting). Two of the calibrated values are cross-checked against independent evidence: θ = 0.282 “is consistent with the estimates of Gelos et al. (2002) who find that during the default episodes of the 1990s, economies were excluded from the credit markets only for a short period of time,” and the output cost is “consistent with the empirical observation that Argentina’s output was below trend for 85% of the time while in state of default (December 2001 to March 2004) before the country renegotiated its debt.”

For a mechanical reason the author states outright, with an economic story offered separately. “The quantitative implementation of the model requires a flexible specification for default costs that increase the set of risky loans available so that high default probabilities can be calibrated. Without direct output costs after default, the range of risky borrowing is very small and the equilibrium set of risky loans is limited.” Capping output at a threshold while in autarky means losses are larger for good shocks, and “the asymmetric default output costs make the value of autarky a less sensitive function of the shock which is key for extending sufficiently the range of B′ that carry positive but finite default premium,” which in turn “increases the set of risky loans that can be attractive in equilibrium for borrowers, giving the quantitative model the possibility to deliver the historical default probabilities.” The economic rationalisation runs through private credit: default disrupts the private financial sector and reduces credit, and credit is an essential production input, so “after default, private credit is constrained and thus output cannot be large even under a good shock because an essential input is scarce.” Supporting evidence cited: Borensztein et al. on defaults of the last two decades coming with “substantial decreases in private credit”; for Argentina, “the cumulative private domestic credit during the 13 quarters when Argentina was in default (December 2001 to March 2004) was 454 billion real U.S. Dollars or 53% of that during the 13 quarters prior to default, 855 billion real U.S. Dollars”; and firm-level Ecuadorean evidence where, during a default featuring a 24% fall in private credit, “firms with the largest dependency on credit decrease their output disproportionately and account for a large fraction of the output collapse,” with top-half short-term-debt firms accounting for 80% of a 19% aggregate sales decline. The author frames all of this as justification for a reduced form, not a derivation: “we assume this reduced form specification for default costs that is consistent with empirical observations and use it to calibrate the historical default probability for Argentina. The discipline is then on how the model performs in terms of spread fluctuations and co-movements given an empirical default probability.”

Prices rise with assets and are more generous in booms; borrowing is higher in booms when wealth is low; and the default threshold in assets is higher when output is lower. On prices: “Bond prices are an increasing function of assets making larger levels of debt carry higher interest rates. Importantly, booms are associated with more lenient financial contracts as the interest rate charged for every loan size is lower during booms.” The reason is persistence: “a low shock today predicts that tomorrow the shock will likely be low again and this is when the borrower defaults even for a small amount of debt.” The author names this the key mechanism – “The endogenous countercyclical interest rate schedule due to default is the essential mechanism for the model to match the data in emerging markets.” On savings: “when wealth is large (B > 0.1) the economy saves less in recessions than in booms as in standard models. However when wealth is small and negative, the economy borrows more in booms than in recessions because of the countercyclical interest rate schedules. When wealth is small the borrower would like to borrow heavily during bad shocks, but it cannot because such financial contracts are not available.” On default: with the shock 5% below trend default is chosen for assets below -2% of mean output, and with the shock 5% above trend only below -21%. The author flags the caveat directly: “The particular thresholds are somewhat mechanical given the assumed reduced form of the default value. However if one compares the thresholds of assets for each output realization below which default is chosen, the model delivers defaults for larger assets levels when output is lower.” One further implication is that the default option itself works like insurance: “for a given level of assets, having the option to default reduces the spread in lifetime utility across shocks and completes markets as in Zame (1993). In fact, the asymmetric costs from default amplifies the role of default as a policy for completing markets.”

Well on volatilities and signs, less well on the strength of the correlations and on the depth of the crisis. Simulated moments are computed by taking, from the limiting distribution, the 74 observations preceding each of 100 default events – “to mimic the period length between Q3 1983 to Q4 2001 in Argentina, which constitutes the period between default events” – and treating the series exactly as the data are treated. Model against data: spread volatility 6.36 versus 5.58; consumption volatility 6.38 versus 8.59 and output volatility 5.81 versus 7.78, so consumption remains more volatile than output; trade balance volatility 1.50 versus 1.75; spread-output correlation -0.29 versus -0.88; trade balance-output correlation -0.25 versus -0.64; consumption-output correlation 0.97 versus 0.98; spread-trade balance correlation 0.43 versus 0.70; mean debt 5.95% of output; default probability 3.00%. The economic mechanism behind the joint fit is the state-dependence of contracts: “Consumption in recessions is close to output because borrowing is very expensive and the borrower is constrained. However in booms debt is cheap and is used to tilt the consumption profile, especially when wealth is low. Thus in good times the trade balance is negative, spreads are low and consumption is higher than output, making consumption more volatile than output on average.” In default episodes the model produces a spread 24.32 points above trend with consumption -9.47% and output -9.60%, against data values of 28.60, -16.01 and -14.21: “the model underestimates the massive collapse and misses the reversal in the trade balance observed.” The mean output deviation while in default is -8.13% in the model against -7.3% in Argentina.

Yes, in the right quarter, when fed the actual output series. “We feed into the model the time series of Argentina’s GDP starting in 1993 and the model predicts a default in the fourth quarter of 2001 which is the period when the Argentinean government defaulted.” On the spread path: “The model predicts the higher spreads experienced in Argentina in the periods between 1995-1996 and 2000-2001. The model underestimates the relatively high spreads between 1996 and 1999 because income is very high and the probability of default is close to zero. But overall the model does well at tracing the spread dynamics in Argentina. The dynamics of the trade balance are traced less well by the model, but it predicts the trade balance surpluses during 1995-1996 and during 2001.” A footnote adds a second hit: starting the simulation in 1983 “the model predicts an additional default event in the third quarter of 1989 because GDP in Argentina was 20% below trend in this period. Standard and Poor actually dates 1989 as containing an additional default event in Argentina.”

The level of the average spread, which risk-neutral pricing ties too tightly to the default probability; a risk-averse lender kernel closes the gap. “The main anomaly of the benchmark model is the low average interest rate spread it generates with a default probability calibrated to the historical average. Risk neutral pricing establishes a tight link between default probabilities and spreads which is at odds with the data” – 3.58% in the model against 10.25% in Argentina. Note the diagnosis is careful about which moment fails: “Varying default probabilities seem to be the driving force for the spread volatility, as an average default probability calibrated to 3% is enough to account well for it. However time varying default probabilities alone cannot account for the level of spreads.” The proposed repair replaces the pricing equation with one in which bonds are priced by a lender stochastic discount factor: “If defaults occur when the lender’s stochastic discount factor is high defaultable loans will carry a premium higher than the probability of default.” Specified as an i.i.d. kernel with mean 1/(1+r) whose innovation is correlated with the borrower’s income, and recalibrating β = 0.882 and the kernel sensitivity λ = 24 to hit both the mean spread and the default frequency, “this parametrization breaks the link between the average spread and the default probability bringing the model closer to the data. In terms of business cycles this parametrization delivers similar statistics as the benchmark model but overestimates the volatility of the trade balance and spreads.” The author is careful about what has and has not been shown: “These results show that default risk premium can potentially rationalize the large difference between historical default probabilities and spreads if the lender has a sufficiently high stochastic discount factor in default states. The large sensitivity… required is equivalent to a high degree of risk aversion in the lenders marginal rate of substitution such that the compensation for risk is large,” and a proper microfoundation – lenders as emerging-market specialists whose portfolio returns are hit by particular defaults – is left as future work.

Renegotiation, permanent shocks, and political economy – each with a named alternative. On renegotiation: “this paper assumes that the defaulted debt is never paid back, but most of sovereign defaults are resolved through settlements with creditors,” and Yue’s work shows “the bargaining power of the lender and borrower can affect substantially the terms of contracts and interest rates.” On the output process: Aguiar and Gopinath “take a more serious look at the process for output in emerging countries and find that shocks to the trend are important in these economies. With permanent shocks more debt is demanded in booms because a high output today predicts a high growth rate in the future. Thus in their model trend shocks are the rationale for the positive relation between the trade balance and spreads” – an alternative account of the same facts that the author presents as potentially complementary to her own mechanism rather than nested in it. On politics: Cuadra and Sapriza find “greater political uncertainty increases the frequency of default events in emerging countries.” The closing assessment is deliberately modest: “Even though this paper provides a framework to study sovereign defaults and fluctuations in country spreads, our understanding of international interest rates in emerging markets is still at a very early stage.”