Impact of Disaster Risk on Sovereign Debt and Default

Transcription

1 Impact of Disaster Risk on Sovereign Debt and Default Ming Qiu University College London Abstract This paper assesses the effects of disaster risk on the risk premium of sovereign debt of emerging economies prone to disaster shocks. Countries have strong ex ante incentives to build up assets for insurance by obliging the contracts but are likely to default ex post when a disaster shock strikes. We demonstrates the effects by distinguishing between two types of disaster shock: natural disaster and economic disaster. First, we provide empirical estimates of the likelihoods that countries transit between a boom, a recession and a disaster state. We find that the severe output contractions are largely accounted for by economic disasters. We also find a positive correlation between countries disaster risk and spread on external debt. Second, we develop a small open economy DSGE model that explains the empirical facts. We analyse how the ex ante insurance motive and ex post incentive to default interact in the cases of two disaster shocks. The model predicts that the presence of economic disaster increases a debtor government s average risk premium whereas natural disaster risk reduces it. We also look at measures to improve debtor s ability to insure themselves in the presence of disaster risk. The model is extended to incorporate debt negotiation upon default and debt extension if a natural disaster occurs. The model features endogenous debt recovery rates and they decrease with the level of debt. We find that the option of debt extension improves the debtor s repayment incentives and improves the debtor s welfare. Department of Economics, University College London. Contact: ming.qiu.09@ucl.ac.uk. I especially thank my supervisors Morten Ravn and Wendy Carlin for guidance and support. I also thank Francois Gourio and Almuth Scholl for useful suggestions and participants at Workshop on Quantitative Dynamic Economics (Konstanz) for comments. 1

2 1 Introduction Countries prone to disaster risk are often borrowing constrained in the international credit market, despite their strong ex ante incentive to oblige their debt contracts for insurance in the particularly dire situations when disasters strike. Although countries experiences when disaster shocks strike are similar, e.g. extremely low income levels and debt default, the cause of disaster differs and therefore the output paths preceding the occurrence of a disaster are different. In this paper, we distinguish between two types of income processes: one incorporating a natural disaster shock and the other with an economic disaster shock. A natural disaster occurs independently of previous periods incomes whereas an economic disaster is more likely to occur the lower the current period s income. We firstly find empirically that severe output contractions of emerging countries are largely accounted for by economic disasters and there is a positive correlation between the likelihood of disaster risk and bond spread. Next we model the above empirical finding in a small open economy DSGE model, based on Arellano (2008). The model features endogenous default and default is more likely when the current income is low. The model finds that the presence of a natural disaster increases a country s incentive to repay whereas the presence of an economic disaster reduces it. The keys to generate the model result are non-state-contingent debt contract and persistent income process. Such debt contracts limit a debtor s ability to insure itself in the presence of disaster shocks. We then extend the model to evaluate a measure of insurance for debtors: if a natural disaster strikes, the country can extend its debt until it exists the disaster state. We find that this measure offers effective insurance since the borrowing contract is more lenient for a country facing more severe natural disaster shock (in terms of magnitude, frequency and persistence). We establish our empirical findings by estimating a three-state Markov-switching model of incomes for two panels of emerging economies: Latin America and Southeast Asia. The three states are boom, recession, and disaster. Bayesian estimation results show that the probability of transiting from a recession to a disaster is much larger than that from a boom 2

3 to a disaster. This shows that the severe output contractions in those countries are accounted for by economic disasters. When plotting the disaster probabilities of those countries against the spreads on their external debt, we see a positive relationship suggesting that higher the likelihood a country gets into a disaster state, greater the riskiness of its debt. The model based on Arellano (2008) features one period non-state-contingent debt contract. The lower incentive to default and higher bond price associated with natural disaster risk is generated by debtor countries strong incentive to gain insurance. Facing the potential of being hit by a natural disaster every period, debtor countries have a strong incentive to stay in the contract and build up assets so that they have resources to consume or roll over during disaster episodes. This strong ex ante is reflected in the higher bond price investors offer. We show in the simulation exercise that the economy with natural disaster risk is able to borrow more debt in recession because of a more lenient borrowing contract and would save more next period if the current asset position is positive. The simulated model with natural disaster risk is able to support a higher level of debt than Arellano (2008) s model and it also generates a higher spread, closer to the data. In the case of economic disaster risk, the income process features a higher likelihood of a disaster occurring if the country is currently in a recession. With a persistent income process, a low income shock today means there will be a series of low income shocks in the future and lower the income shocks, higher the likelihood of falling into a disaster state. A disaster state shortens the sequence of low income shocks needed to force a country into default. Once a country is in a recession, it becomes very costly for it to repay its debt. In the simulation exercise, we show that for a income shock of 5% below mean, the higher incentive to default transmits to lower bond price for a significant range of debt and no risky borrowing in the equilibrium because it is too expensive for the government to borrow. We then extend the model to evaluate the measure of debt extension based on Yue (2009) s debt renegotiation model. Under the contract, debt is renegotiated upon default between debtors and creditors. Once a debtor repays the renegotiated debt, it regains 3

4 access to the credit market. The model features endogenous debt recovery rate and it decreases with the level of income. When a natural disaster strikes, debtor is only qualified for postponing debt repayment and extending its debt if it does not have unsolved default (in other words, it has not paid back renegotiated debt following a default). Compared to the original model where a debtor has to default when a disaster strikes, the contract arrangement offers insurance in two ways. Firstly debtors can re-enter the credit market to borrow if renegotiation entails positive surplus following default. This reduces the debtor s loss upon default and enables it to borrow more ex ante. Secondly the contract improves the debtor s welfare during a disaster state by offering conditional debt extension. This arrangement incentivises the debtor to avoid default with unsolved debt and improves creditor s welfare. We show in the simulation exercise that the option of debt extension is more valuable for countries with larger extent of disaster risk, in terms of magnitude of disaster shock, disaster persistence and frequency. This paper is related to two strands of literature: sovereign default and disaster risk. Aguiar & Gopinath (2007) and Arellano (2008) study sovereign debt and endogenous default in an environment of incomplete asset market and exogenous income shocks. They attribute countries default decision as primarily dependent on the income shocks and asset position. We look further on the income process and investigate how the characteristics of an additional low income state representing a disaster state would alter the equilibrium results. We also build additional measures on the debt contract featured in previous papers to look at how the contract can improve a debtor s ability to insure. The literature on disaster risk builds on the notion that incorporating the extreme events improves models estimation of asset price (Barro (2006), Barro et al. (2013) and Gourio (2012, 2013)), but none has looked at the implication of disaster risk on the price of sovereign debt. In this paper, we find incorporating a disaster shock relevant in generating different price schedules for countries sovereign debt. The organisation of the paper is as follows. Section 2 and 3 present the empirical findings. 4

5 Section 2 estimates a Markov Switching income process for two panels of emerging economies, Latin America and Southeast Asia, to see which type of disaster shock dominates their economies output transitions. Section 3 shows the relationship between disaster probability and interest rate spread. Section 4 presents the model economy in which the impacts of two types of disaster shocks are analysed. Section 5 assesses the quantitative studies and demonstrates the bond price, default threshold and borrowing schedules for the disaster shocks. Section 6 presents the model with debt renegotiation and debt extension for natural disasters. Finally section 7 concludes. 2 A Markov Switching Income Process In this section, we investigate the output processes of two panel emerging countries: Latin America vs. Southeast Asia which are historically prone to severe output disruptions. To determine which type of disaster shock is the primary cause of large output drops, we estimate a three-state Markov Switching mean-variance model with Bayesian priors, using Gibbssampling method outlined in Kim and Nelson (1999). Markov switching model is used if the data process is subject to discrete regime shifts (Hamilton, 1989). Countries income process following a disastrous event is typically characterised by very low income levels and high volatility which make a disaster income shock distinctly different from other shocks of smaller magnitude. The three states correspond to boom (state 1), recession (state 2) and disaster (state 3). These three states are characterised by the perspective mean and volatility of income levels. Within each state, income fluctuates in an AR (1) fashion. To see the nature of disaster process of the emerging economies, the parameters of interest are the transitional probabilities of income from normal (boom or recession) to disaster state. We find that despite regional differences, the severe output declines experienced by the two panels display characteristics of economic disasters. Countries are more likely to slip into an extremely low income state if they are currently in a recession. For Southeast Asian countries 5

6 which are particularly vulnerable to natural disasters, what account for large output drops are economic events such as 1997 s financial crisis. 2.1 Data The main difficulty in estimating the model of disaster risk is that there are very few disaster episodes observed. We pooled income data from countries included in Barro and Ursua (2009) s dataset. Before pooling, each country s data series is linearly detrended respectively such that the input to Markov Switching model is the deviation from its own country trend. The Southeastern Asian panel includes Taiwan, Malaysia, Philippines, Sri Lanka, Indonesia, Korea and Japan 1. The Latin American panel includes Argentina, Brazil, Mexico, Peru, Uruguay and Chile. There are in total 678 observations in the Latin American panel and 427 observations in the Southeastern panel. In this way, we not only have more disaster episodes included than in a single country s data series, but also time series data is long enough such that the starting and ending points are not endogenous to the disaster events themselves. We also make sure that there is no gap in countries data series because we are primarily interested in the probability that a country transits from a normal state to a disaster one and it is important that we have continuous information prior to and at the event of disaster. 2.2 An empirical model of income process We model log income as a three-state Markov Switching mean-variance process: y t µ St = φ 1 (y t 1 µ St 1 ) + ɛ t, ɛ t N(0, σ 2 S t ) where y t is the log income at t, φ 1 is the persistence parameter in the AR(1) process and µ St and σ St are state-dependent mean income levels and standard deviation. 1 Japan is included in this panel because we want to maximise the observations of disaster episodes in the panel. 6

7 We model the states as affecting the income in the dimensions of mean income level and volatility. µ St and σ St are modelled as: µ St = µ 1 S 1t + µ 2 S 2t + µ 3 S 3t σ 2 S t = σ 2 1S 1t + σ 2 2S 2t + σ 2 3S 3t, where the indicator variable S jt = 1, if S t = j and S jt = 0 otherwise, j = 1, 2, 3. The transitional probabilities are: P ij = P r[s t = j S t 1 = i], 3 j=1 P ij = 1 To guarantee the identification of the model within the Gibbs-sampling framework, we exert constraints on the mean income µ St such that µ 1 < µ 2 < µ 3. For the variances σ S1, σ S2, and σ S3, we only restrict them to be of positive values. P 21 and P 31 tell us how the economy transits from normal states (S 2 or S 3 ) to the disaster state S 1. If P 21 > P 31, the estimated transitional probabilities indicate that the economy is subject to economic disasters whereas if P 21 P 31, the economy is subject to natural disasters. 2.3 Estimation To carry out the Bayesian estimation, we specify a set of priors on the parameters of the model. Define S T = [S 1, S 2,..., S T ], a vector of states across T periods; σ 2 = [σ 2 1, σ 2 2, σ 2 3] ; p = [p 11, p 12, p 21, p 22, p 31, p 32 ], µ = [µ 1, µ 2, µ 3 ]. In the framework of Gibbs-sampling, we set the conditional prior distribution of µ as: µ σ 2, φ 1 N(a 0, A 0 ) I[µ1 <µ 2 <µ 3 ] Where a 0 is the vector of prior mean income leves in three states and we set it as the 5%, 25% and 75% quantiles of the pooled income series in each panel. We use 5% quantile to reflect the fact that disasters are rare and extreme events. A 0 is a 3 3 diagonal matrix where 7

8 the diagonal elements are the tightness of the joint distribution and we assign a single value of 0.04 to them. The details of Gibbs-sampling are in the Appendix. The key parameters in our model are the probabilities p 21 and p 31 and we set uninformative prior distributions with large standard deviations for them. In this way, we are not putting any prior weight on the likelihood of a recession or a boom transiting to a disaster state. The prior distributions for other parameters are all uninformative. The details are included in the Appendix. An obvious concern regarding the tight priors on µ is that we might mis-identify the disaster states when there are actually only two. We assume that parameters are the same across countries in the same panel. This assumption enables us to pool information on disaster episodes across countries. 2.4 Estimation Results Table 3 presents the Bayesian estimates of the parameters of the above model. For each parameter, we list mean and standard deviation of the posterior distributions and include the 90% confidence bands as well. The estimation results show that disasters unfold over several years (P 11 > 0) and countries have a good chance of recovery after disastrous events. This provides empirical support for the calibration in Section 3.1 that disaster state is only temporary. We find that the disaster state is more persistent in the Latin American panel than in Asian (P LA 11 = 0.61 > P Asia 11 = 0.42), suggesting that a disaster lasts 2.6 periods on average in Latin America and 1.7 periods on average in Southeast Asia. This is inline with the observation that Asian countries are relatively faster exiting their disaster episodes (e.g. Asian financial crisis) than their Latin American counterparts. The posterior standard deviations of income levels in disaster are very large (3.41 in Southeast Asian panel and 2.27 in Latin American panel). This shows that there is a huge amount of uncertainty during disasters. We are mostly interested in two parameters: P 21 (probability that an economy goes from a recession to disaster state) and P 31 (probability that an economy moves from a boom to 8

9 disaster directly). If a country is subject to natural disasters mainly, P 31 should be of non negligible magnitude and not far away from P 21 ; whereas if it is subject to economic disasters, P 21 should be much larger than P 31, indicating that the country slips into the disaster state as the its economic condition worsens. The posterior estimates for both panels P 21 and P 31 show that it is very rare for them to drop from a boom to disaster state directly. For Latin American countries, when the current state is a boom, there is only 0.2% of the time the economies transit to a disaster state and for Southeast Asian countries, it is only 4.6% of the time. This is in contrast to the transtition probability P 21 : once in a recession, Latin American countries transit to a disaster state next period with a probability 19% and Southeast Asian countries with a probability of 24%. This indicates that both panel countries are subject to economic disasters. 3 Disaster Probabilities and Real Interest Rate This section documents the statistical relationship between disaster probabilities and real interest rates for these two panel countries.the positive relationship shown in the plot provides empirical support for the equilibrium implication of the model: the presence of economic disaster shocks increases the sovereign bond s riskiness. The more vulnerable an economy is subject to economic disasters, the higher the risk premium its sovereign bond has. 3.1 Disaster Probabilities To reflect the countries exposure to disasters overtime, we use long time annual series GDP per capita constructed in Barro and Ursua (2010), where the starting and ending points of the series are not endogenous to the disasters. We align the starting dates for countries in the same panel so that disaster probability of each country is calculated across the same duration of time 2. In general, Latin American countries data expands longer than Asian countries 2 We include only data after 1895 for countries in Latin American panel and after 1911 for countries in Asian panel. 9

10 and this makes it important to separate the estimation into two panels. To enrich the sets of countries used for data plots, we add in countries (e.g. Ecuador and Thailand) 3 not included in Barro and Ursua (2010) s data set, using time series constructed in Maddison s (2003) project 4. In total, we have eight countries in the Latin American panel (Argentina, Brazil, Chile, Ecuador, Mexico, Peru, Uruguay, and Venezuela) and another nine in the Asian panel (Japan, Indonesia, Malaysia, Philippines, South Korea, Sri Lanka, Taiwan, Thailand, and Vietnam). We include Japan in the Asian emerging countries panel because we think that its frequent exposure to natural disasters might have impacts on the real interest rate of its debt. The disaster probabilities are calculated following Barro (2006) who uses peak-trough measurement of sizes of macroeconomic contractions. Proportionate decreases in GDP per capita are computed peak to trough over one or more years, and only declines by 10% or greater were considered to be disaster episodes. For example, using the above method we identify eight disaster episodes from 1895 to 2008 in Argentina, three of which are associated with Argentinean sovereign crisis: (-10.1%) 5, (-11.1%) and (-22%). Disaster probabilities are calculated by dividing the number of years a country is in disaster episodes by the normalcy years (subtracting the disaster years from the total number of observations). Details are included in the Appendix. One drawback of identifying disaster episodes this way, as pointed out by various authors, e.g. Gourio (2008) and Barro et al. (2013), is that it assumes that disasters are instantaneous and permanent drops in output. By ignoring the recoveries and periods of high growth after disasters, it may underestimate the length of disaster episodes and hence the disaster probability. Here, since this exercise is mainly for comparison purpose, as long as the same identification method is applied to all countries, the drawback should not matter too much. We find that the average disaster probability calculated for Asian panel is 3.42%, signif- 3 They are: Ecuador, Paraguay, Thailand and Vietnam. 4 Barro and Ursua (2008) constructed their data series based on Maddison s project (2006). We also align the starting dates for the additional countries % is the percentage output drop from 1958 to

11 icantly less than that for Latin American panel (6.46%) 6 which indicates that Asian countries incur significantly fewer events of large output contraction. Given the well documented empirical regularity that emerging economies real interest rates are countercyclical (e.g. Neumeyer and Perri, 2005); frequent exposure to large output declines would be associated with volatile interest rate movements with spikes occurring at times of disasters. Therefore we would expect the real interest rates for Asian panel to be in general lower than their Latin American counterparts. We show this in the section below. 3.2 Real Interest Rate The interest rate measure should reflect the true riskiness of an emerging country s external debt and we have two criterions in mind. Firstly the interest rates should be denominated in US dollars. Given the large swings in inflation rates in many emerging economies, it is difficult to attain a measure of domestic expected inflation to construct the real interest rate. Secondly the interest rate should reflect the true intertemporal cost faced by those economies. As pointed out by Neumeyer and Perrieri (2005), interest rate data on new loans denominated in U.S. dollars is not useful because during the financial crises most of the new borrowing of emerging countries is through official institutions which do not reflect the true borrowing cost over time. Hence we use secondary market prices of emerging economies bond. Based on those two criterions, we measure the expected 3-month expected interest rates as real interest rate = J.P. Morgan s EMBI Global Stripped Spread measure (EMBI SSPRD) 7 + US 90 days T-Bill rate - US GDP deflator inflation rate. For countries not included in EMBI Global Index 8, we use other measures for expected 3-month interest rates. Details are included in the Appendix. 6 This might be as a result of different starting dates: 1895 for LA panel vs for Asian panel, but the 16 years difference should not be the main factor. 7 JP Morgan s EMBI Global family includes two relevant data types: Blended and Stripped Yield Spread (SSPRD). SSPRD differs from the more standard blended spread because the values of any collateralized flows are stripped from the bond. SSPRD reflects the risk premium of emerging economies bond. 8 Japan, Thailand, and Taiwan are not included in EMBI Global Index. 11

12 Figure 1: Real Interest Rate vs. Disaster Probability We plot the real interest rate on emerging countries external debt against their disaster probabilities (Figure 1). The data plot displays a positive relationship with the Asian panel at the low disaster probability and low real interest corner and the Latin American countries distributed further up. Argentina, Uruguay and Ecuador are among the most frequent defaulters in history and their disaster probabilities reflect this empirical fact. The risk premium on their sovereign debt is highest as well, reflecting investors demand for large compensation for risks. The dataplot provides empirical support for the model s equilibrium implication that more likely an economic disaster occurs, the riskier the country s sovereign debt is. Based on the Bayesian estimation of the income processes of Southeast Asian and Latin American countries, the disaster events that have occurred in those two panels are dominated by economic ones. And indeed we find that higher the probability that a country is subject to an economic disaster shock, higher the risk premium its sovereign debt has. 12

13 4 The Model Economy This section lays out the model environment in which we look at the impact of disaster shock on countries incentive to default on their sovereign debt. The model setup is based on Arellano (2008). In this economy, the risk-averse government trades one-period state noncontingent bonds with risk-neutral competitive foreign creditors. The government cannot commit to repaying the bonds and once it defaults, it would be excluded temporarily from the international financial market and incur direct output costs. The price of government bond depends on the government s incentive to default, such that creditors break even in expectation. 4.1 Model Environment Households of the economy are identical and their preferences are given by: E 0 t=0 βt u(c t ) where 0 < β < 1 is the discount factor, c t is the consumption in period t and u : R + R is the period utility function. u(.) is increasing, strictly concave and satisfies the inada condition. Households receive a stochastic stream of exogenous endowment y t which is non-storable. y t is drawn from a compact set Y = [y, y] R +. It is assumed to follow a Markov process with its probability distribution function of y t conditional on the previous realisation y t 1 given by f y (y t y t 1 ). International investors are risk-neutral and have perfect information on the economy s endowment and asset position each period. They borrow or lend at a constant world risk-free interest rate r. Asset market is incomplete. The government in the economy is benevolent and maximises the expected utility of households. The government can buy one-period discount bonds B at price q(b, y). B < 0 means that the government issues new bonds and B > 0 means it purchases bonds. The government cannot commit to repaying the 13

14 bond. When default occurs, it is assumed that creditors forego the current debt. The default punishment for the government is twofold: firstly, the government will remain in financial autarky for a stochastic number of periods: c = y def, and will reenter financial market with an exogenous probability. Secondly, the government also incur direct output costs while it cannot access the financial market: y def = h(y) y, where h(y) is an increasing function. The model s timing is as follows. In each period, the government starts with initial assets B, observes the income shock y, sets of (B, y) determine its resources to roll over the debt. It then decides whether to default or repay its debt. If it decides to repay, the bond price schedule q(b, y) is taken as given, the government chooses B subject to its budget constraint. Creditors then take q as given and choose B. If it decides to default, it is excluded from financial market for a stochastic number of periods. Consumption c takes place. 4.2 Recursive Equilibrium We define a stationary recursive equilibrium in the model economy. Define ν 0 (B, y) as the value function for the government that faces the choice as to default or repay its debt. Given that the government s asset position is negative (otherwise there will not be a default option), ν 0 (B, y) satisfies: ( ν 0 (B, y) = max ν c (B, y), ν d (y) ) (c,d) Where ν c (B, y) is the value function of repaying the debt obligations and ν d (y) is the value function of default. ν d (y) is given as the following: ν d (y) = u(y def ) + β [θν 0 (0, y ) + (1 θ)ν d (y )]f(y, y)dy y The government cannot borrow, lend or save once it decides to default. All the debt from 14

15 previous periods is erased. The length of exclusion from the credit market depends on the value of θ, which is the exogenous probability that the government can re-enter the credit operation market. If the government is allowed to borrow and lend again, it will start with B = 0, and hence ν 0 (0, y ). Otherwise it remains in a financial autarky when its consumption equals its income, the value of which is given by ν d (y). The government s other option value, ν c (B, y), is given by: ν c (B, y) = max u(y + B (B ) q(b, y)b ) + β v 0 (B, y )f(y, y)dy y The second decision the government makes is how much of B to purchase conditional on not defaulting. The government faces a lower bound on debt, B Z, the non-ponzi scheme constraint. It is not binding in equilibrium. The government s first policy function, the default policy, is characterized by default sets. Define D(B) to be the default set for which default is optimal given the asset B. It satisfies: D(B) = y Y : ν c (B, y) ν d (y) Now we can proceed to the definition of the recursive equilibrium. Denote s = (B, y) as the aggregate state variables. The recursive equilibrium for this economy is defined as a set of policy functions for (i) consumption c(s); (ii) government s asset holdings B (s), and default sets D(B); and (iii) the price function for bonds q(b, y) such that: 1. Taking as given the government policies, households consumption c(s) satisfies the resource constraint. 2. Taking as given the bond price function q(b, y), the government s policy functions B (s) and default sets D(B) satisfy the government optimisation problem. 3. Bonds prices q(b, y) reflect the government s default probabilities and are consistent with creditors expected zero profits. 15

16 The bond price q(b, y) satisfies: q(b, y) = (1 δ(b,y)) 1+r Where δ(b, y) is the probability of default that depends on the endowment y and the debt the government purchases B. B tells the creditors the government s indebtedness next period. Government s probability of default is higher, smaller the debt (larger the absolute magnitude of debt). A lower discount price of debt compensates the lender for a possible default. In equilibrium, q(b, y), B represent the set of contracts the borrower can choose from each period. δ(b, y) is linked to the default sets D(B ) by: δ(b, y) = D(B ) f(y, y)dy 5 Quantitative Analysis In this section, we solve the model numerically and illustrate the impact of disaster shocks on the asset price and borrowing schedule for the calibrated model. The model is calibrated to Argentina, the emerging economy that has one of the largest defaults in history. The calibrated model can account for the highly volatile and countercyclical interest rate schedule, as well as other empirical regularities of emerging economies. We use it as model economy to analyse the impact of disaster shocks on emerging economies sovereign debt price. We show that bonds issued by an economy which is subject to natural disasters carry higher equilibrium price on average than an economy without the disaster shocks, indicating that natural disaster shocks are associated with a lower incentive to default. This lower incentive to default is also shown by a lower default threshold. For a given endowment shock, the economy would repay at levels of debt where they would have defaulted if there were no natural disaster shocks. We then show that when an economy is subject to policyinduced sovereign debt crisis, there is a significant range of debt levels associated with higher default risk. In this case, the sovereign debt has become too expensive for the borrower and 16

17 hence no risky borrowing exists in equilibrium. The higher the likelihood that the economy gets into the disaster state, riskier the sovereign debt is. 5.1 Calibration The following utility form is used: u(c) = c1 σ 1 σ Where σ is the coefficient of risk aversion and is set to 2. The risk-free interest rate r is set to 1.7 percent, the average 3-month interest rate of a five-year US treasury bond. The default cost is modelled as: ŷ h(y) = y if y > ŷ if y ŷ Default entails direct output costs and these costs are asymmetric. This specification pushes down the value of default and extends the range of B that carry finite positive default premia, (B, B). A large set (B, B) increases the set of risky loans that can be attractive in equilibrium for borrowers so the high default probabilities can be calibrated. The time preference parameter β, the probability of reentering financial markets after default θ, and the default costs threshold ŷ are calibrated to match the following moments of the Argentinean economy: a default probability of 3%, an average debt service to GDP ratio of 5.53%, and the standard deviation of the trade balance Endowment process The endowment process consists of normal and disaster states. The normal states are calibrated to the Argentine quarterly real GDP for Q to Q from the Ministry of Finance (MECON). It is assumed to follow a log-normal AR(1) process: 17

18 log(y t ) = ρlog(y t 1 ) + ε y t, with E(ε y ) = 0 and E(ε 2 ) = η 2 y We use the Tauchen and Hussy (1991) procedure 9 to compute the endowment grid and Markov chain with 21 states. The impact of disaster shock is modelled as an additional low income state in the endowment grid, representing a disaster state. Modelling the disaster shock this way is because we are primarily interested in equilibrium bond price and by pricing the disaster state, we can see how the additional income state influences the bond price of the normal income states. The original 21 endowment states are percentage deviation from the trend and they are symmetrical around zero. Parameters associated with disaster state are calibrated according to Barro (2006) and Barro et al. (2013). Using data covering 35 (OECD and non-oecd) countries during twentieth century, Barro (2006) recorded events which lead to more than 15 percent declines in real GDP per capita. Those events include natural disasters and economic crises. There are 60 such events for the 35 countries over 100 years. Thus, the probability of entering into a 15 percent or greater event was 1.7 percent per year. To calibrate the size of disaster state, we use the mean of the contraction sizes adjusted for trend growth, 35%. We distinguish between two possible causes of severe output contraction: natural disaster and economic disaster. Natural disasters arrive unexpectedly overtime and the disaster likelihood is unrelated to current income shocks. We model the probability of transiting to the disaster state as independent of previous income shocks: P r(y t = y disaster y t 1 = y i ) = P r(y t = y disaster y t 1 = y j ), i, j = 1, 2,...21, i j where y 21 represents the state with highest income level. We set the value of this probability to the aforementioned 1.7%. For the economic disaster, we calibrate the transitional probabilities to reflect the characteristics of an economic crisis, where lower the income state, higher the likelihood that the economy moves to the disaster state next period: 9 The code is taken from Martin Flodon s teaching page ( 18

19 P r(y t = y disaster y t 1 = y 1 ) > P r(y t = y disaster y t 1 = y 2 ) >... > P r(y t = y disaster y t 1 = y 21 ) This reflects the situation of economic crisis commonly seen in Latin America during the 1980s. Imprudent economic policies led to budget crisis, during which output moved along a downward trajectory. When the government could not rollover on its foreign loans, the budget crisis turned into sovereign debt crisis and output dropped sharply. We are left with the persistence of disaster state. To attribute all the difference in asset pricing implication of two disaster shocks to their respective transition process, we use a single calibration for both shocks persistence parameter. Natural disasters are instantaneous events whereas economic disasters normally span across several periods. Here we are only interested in the output impact of those disaster events and even in the natural disaster case, the output normally takes some time to recover. In this sense, using the same persistence parameter does not exaggerate the extent of natural disaster s impact. Barro (2006) modelled the disasters as instantaneous and permanent events which may overstate the impact of disaster shock to the sovereign bond by failing to take into account the recoveries following the disaster event. We use the empirical estimation obtained by Barro et al. (2013) for disaster persistence. Barro et al. (2013) model both the temporary and permanent effects of disasters on consumption and find strong support for the notion that disasters unfold over several years. Given the strong correlation between consumption and output, we can use the estimates from consumption disasters to infer about output disasters. According to their estimates, a country that is already in a disaster will continue to be in the disaster in the following year with a probability. We set P r(y t = y disaster y t 1 = y disaster ) = and P r(y t = y 1 y t 1 = y disaster ) = , where y 1 is the lowest state of the original income grid, the lowest normal state income. 5.2 Simulation Results This section first analyses policy functions for the calibrated model without disaster shocks to demonstrate the model mechanism. The impact of disaster shocks are then followed. 19

20 (a) Bond price schedule q(b, y) (b) Equilibrium interest rate 1/q(B (B, y), y) Figure 2: Bond Prices and Assets: No Disaster Model without disaster shocks Figure 2 shows the bond price schedule and the equilibrium interest rate faced by the borrower, for two income shocks which are 5 percent above (a boom) and 5 percent below (a recession) trend. The left panel of Figure 1 plots the bond price schedule q(b, y) against B and shows the set of contracts {q(b, y), B } the borrower can choose from every period. Bond prices are an increasing function of assets B, indicating that higher debt levels are associated with higher borrowing cost. Given the same level of debt, bonds in a boom carry a higher price than in a recession which suggests that borrowing conditions are more lenient when the income shock is good. This is because the bond price is dependent on the incentive to default which is lower in a boom than in a recession. The right panel plots the interest rate 1/q(B (B, y), y) the economy pays along the equilibrium path given its choice of borrowing B (B, y). When the asset position B is above -0.02, the borrower chooses to borrow risky in a recession and have to pay a much higher interest rate than in a boom. For large amount of debt, it defaults in a recession while it can still borrow in a boom. This shows again that as the incentive to default decreases with income shock, it is more costly for the borrower to extend their debt contracts in a recession. Two features of the model generate countercyclical interest rate. One is that the asset 20

21 (a) Bond price schedule q(b, y) (b) Default threshold b(y s ) Figure 3: Bond Prices and Assets: Natural Disaster market is incomplete and government s bond is state non-contingent and the other one is that income shocks are persistent. For a highly indebted government, when it receives a bad income shock, it expects the shock to last for a few more periods and this means that it would become increasingly difficult for the government to rollover its debt because the resources available to repay keep declining. Therefore given the same asset position, a government s incentive to default is higher when the income shock is bad Natural Disaster We define default threshold b(y s ) as the debt level such that D(b, y s ) = 1 for b < b, s = 1,..., 21 (the disaster state is excluded for comparison purpose). Figure 3 shows the bond price schedule and default threshold when the no-disaster economy and the economy subject to natural disasters are hit by the same negative income shock (5% below the trend). The bond price is higher with a natural disaster shock, indicating that for the same level of borrowing B, interest rates are lower and borrowers are able to gain more resources from the borrowing contracts {q(b, y), y}. This suggests that the impact of natural disaster is viewed as decreasing the probability of default. The right panel of Figure 2 further demonstrates the lower incentive to default in the 21

22 economy subject to natural disaster risk. The default threshold b is plotted against the level of endowment shock for the two economies. As endowment shocks improve, the debt at which a borrower defaults decreases. Higher endowment shocks give the debtors more resources to repay their debt obligation. For each level of endowment, the threshold in the economy with natural disaster risk is always lower than or equal to the other economy, indicating that the debtor government in this economy would still remain in the debt contract for levels of debt where it would have defaulted had there no natural disaster risk. This impact is further demonstrated in Figure 4. There are two forces from supply and demand sides accountable for generating the government s policy function, B (B, y). On the supply side, the lower default incentive makes the borrowing terms more lenient. This enables the economy with natural disaster shock to borrow more and the additional borrowing available makes the equilibrium interest rate higher, shown in the right panel. This is not to be confused with higher risk premium on sovereign bonds. As we have shown in the left panel of Figure 3, the higher bond price indicates lower interest rate in the economy with natural disaster risk. On the demand side, to avoid defaulting in the disaster state, the debtor government has a strong incentive to build up assets so they are sufficiently wealthy to roll over their debt even in the most dire situation. In the left panel of Figure 4, it is shown that the supply side effect enables the government to borrow more to smooth its consumption in a recession thanks to the more lenient borrowing terms. As the asset position becomes positive, the demand side effect is at work as the bond is risk-free and the higher saving comes purely from the country s incentive to accumulate asset. We conduct simulations of the model economy with 152 periods in each simulation. We then extract 74 observations prior to the default event in the stationary distriubtion to compute the statistics. Table 1 compares the data statistics of two model economies. The direct impact of incorporating a natural disaster shock is that the output series are 10 Measured as mean deviation in default 22

23 (a) Savings Function: B (B, y) (b) Equilibrium interest rate 1/q(B (B, y), y) Figure 4: Bond Prices and Assets: Natural Disaster more volatile (7.0% vs. 5.6%) and the output drop during default episodes is more severe (28.9 vs. 6.27). With lower incentive to default, the model with natural disaster shock supports a level of debt which is 8% higher than the model without disaster risk and is closer to the data statistics. The mean interest spread is also higher and it explains 60.4% of data spread, compared to 55% in the model without disaster risk Economic Disaster Figure 5 shows the bond price schedule for the comparison between the model without disasters and the one subject to economic disasters. There is a significant range of debt (above -0.25) for which bonds with economic disaster risk carry lower price than the one without disasters. This means that for this range of B, economic disasters make the borrower more likely to default. We define the income state representing 5% below trend as a recession and calibrate the probability P (y t = y disaster y t 1 = y recession ) to a value of 0.5. The bond price schedule is generated by such calibration. The average bond price is lower than that of the model without disaster shock. In the Robusness check section, we experiment with other values for P (y t = y disaster y t 1 = y recession ). 23

24 Table 1: Statistics comparison Data No-Disaster Model Model with Natural Disaster Consumption Std. Dev. (%) Corr (Consumption, Output) Consumption Std./Output Std Trade Balance Std. Dev. (%) Corr (Trade Balance, Output) Corr (Trade Balance, Spreads) Output Std. Dev. (%) Corr (Spreads, output) Output drop during default episodes Bond Spreads Std. Dev. (%) Mean debt (percent output) Mean spread (a) Policy function B (B, y) (b) Equilibrium interest rate 1/q(B (B, y), y) Figure 6: Bond Prices and Assets: Economic Disaster The left panel of Figure 5 shows that there is no risky borrowing by the debtor country in the equilibrium, as a result of higher borrowing cost. This suggests that the supply side effect of increased riskiness of the sovereign bond makes the debt too expensive to borrow. The demand side effect as a result of higher incentive to accumulate asset for disaster is much stronger than in the case of natural disaster risk. When the economy is slipping on a downward trajectory, if the government has a favourable asset position (b > 0), it would want to save a lot to prevent itself sliding to default. The right panel shows that along the 24

25 Figure 5: Bond price schedule q(b, y) equilibrium path, the interest rate is at the risk-free level due to no risky borrowing. 5.3 Robustness check In this section, we verify the simulation results in Section that an economy subject to economic disaster risk has a higher incentive to default. We compare the average bond price (units of consumption good) associated with probabilities that a recession state transits to a disaster state: P (y t = y disaster y t 1 = y recession ) (denote it as P rd ). Table 2: Statistics for the Impact of Economic Disaster Risk P rd Average Bond Price The average bond price decreases as the probability P rd, hence riskiness of the bond, increases. Compared to the average bond price in the benchmark model (0.3622), only disaster shocks with probability values of 0.4 and above entail on average higher riskiness of sovereign debt. This shows the simulation result in Section is only robust to output processes which are vulnerable to disaster shock when in a recession. For relatively small probability of transiting from a recesssion to the disaster state, countries still have incentive 25

26 to save itself from sliding to default whereas for higher riskiness, the default is an likely outcome once you are in a recession. Default would indeed be an optimal outcome when P rd is large as it would be too costly for countries to roll over their debt in recession when they know that they are very likely to be in a disaster next period and default with certainty. 6 Debt Renegotiation with debt extension for natural disasters In this section, we develop a small open economy model for emerging economies featuring debt renegotiation upon default and debt extension for natural disasters. In Arellano (2008)s model, given the nature of the state non contingent contract, it is indeed optimal for a debtor country to default in a disaster state but the outcome is associated with welfare loss and inefficiency for both creditors and debtors. Once countries default on their debt, the debt is foregone and debtors are excluded from the credit market for an exogenous period of time. Creditors lose all their debt claims and debtors are in autarky for an uncertain length of time. If a default is led by a disaster shock, the welfare loss on debtor side is particularly severe. We construct an alternative debt contract to improve debtor and creditor s welfare based on the one-period zero-coupon debt contract. It entails two forms of state contingency: debt renegotiation and debt extension. The welfare loss following default is reduced via renegotiation as creditors regain a fraction of the defaulted debt and debtors obtain access to the credit market through renegotiation over debt reduction. Debt extension during a disaster phase allows debtors to postpone their debt repayment until when the economy exits the disaster phase and gives them access to credit market to smooth consumption. This prevents the debtor from defaulting and insures them against the dire situation. The model setup for debt renegotiation is based on Yue (2009) and the debt extension is motivated by the empirical heterogeneity in countries default decision following natural 26

27 disasters. We look at the default history for two regions prone to natural disaster occurrence: South Eastern Asia and the Caribbean. According to the definition of Standard & Poor 11, a default on a debt contract has occurred if a payment is not made within any grace period specified in the contract, or if debts are rescheduled on terms less favourable than those specified in the original debt contract (Beers and Chambers, 2006). Thirteen countries 12 from the above two regions have experienced the defaults of varying lengths in the period Among the thirteen defaults, eight of them were preceded by natural disasters but only two were indeed caused by natural disasters: Grenada was hit by hurricanes in 2004 and 2005 and it was in default from 2004 to Belize was hit by hurricanes in 2005 and 2007 and it defaulted in 2006 and The complete collection of default events is in the Appendix. The debt extension contract we propose offers a possible explanation for the heterogeneity in default decision following natural disaster events. Countries ability to roll over their debt depends on the resources they have at present to pay off their debt claim. The debt extension contract gives countries additional resources. The debt is only postponed and extended to the debtor country if it does not have unsolved default (in other words, it has not defaulted in the previous period). In the two cases (Grenada and Belize) where we find natural disasters as the primary reason for defaults on their foreign debt, after having defaulted in the previous year, they got hit by hurricanes and defaulted again. Because of the insurance provided against the disaster shock, it gives countries additional incentive to stay in the contract. Larger the welfare loss associated with disaster events, lower 11 The most comprehensive and widely used source of data on the dates of defaults on sovereign debts owed to private sector creditors, as well as the dates of settlements of these defaults, is published by the ratings agency Standard and Poors. Here I use two reports for collection of default events: Beers and Chambers (2006) and Chambers and Gurwitz (2012) 12 Southeastern Asian region: Indonesia, Philippines, Vietnam, Pakistan, Myanmar. Caribbean region: Trinidad and Tobago, Jamaica, Grenada, Belize, Antigua, Dominica and Dominican Republic. 13 For each default which is preceded by a natural disaster event, we checked the Google News Archive for the cause of default. We could only find evidence for Grenada and Belize. Defaults in Southeastern Asian countries were mainly caused by financial crisis, regime changes and trade sanctions. No reports could be found for Antigua and Barbuda, Dominica and Dominican Republic which are vulnerable to hurricanes as well. Therefore there are potentially more default events where natural disasters were the primary reason. 27