Heterogeneous borrowers in quantitative models of sovereign default

Transcription

1 Heterogeneous borrowers in quantitative models of sovereign default Juan Carlos Hatchondo Leonardo Martinez Horacio Sapriza PRELIMINARY AND INCOMPLETE Abstract This paper allows policymakers of different type (patience) to alternate in power in the framework used in recent quantitative studies of sovereign default. We show that a default episode may be triggered by the replacement of a patient policymaker by an impatient policymaker. It is also shown that for this to be the case, it is necessary that there is enough political stability in the economy and that the patient policymaker encounters poor economic conditions during his tenure. The latter induces high borrowing levels. When there is high enough political stability, the introduction of government heterogeneity enables the model to generate: (i) a higher and more volatile spread (even when a period without alternation is considered); (ii) lower borrowing levels after a default episode triggered by a change of the type in power; (iii) a weaker correlation between economic conditions and default decisions. These results narrow the gap between the predictions of the model and the data. JEL classification: F34, F41. Keywords: Sovereign Default, Political Risk, Endogenous Borrowing Constraints, Markov Perfect Equilibrium. We thank seminar participants at the 2006 Midwest Theory Meetings, the 2006 Midwest Macroeconomics Meetings, the 2006 SED, the 2006 Federal Reserve System Meeting on International Economics, the 2006 Wegmans Conference, and the Universidad Nacional de Tucumán for helpful comments and suggestions. Remaining mistakes are ours. Any opinions expressed in this paper are those of the authors and do not necessarily reflect those of the Federal Reserve Bank of Richmond or the Federal Reserve System. Federal Reserve Bank of Richmond; juancarlos.hatchondo@rich.frb.org. Federal Reserve Bank of Richmond; leonardo.martinez@rich.frb.org. Rutgers University; hsapriza@andromeda.rutgers.edu. 1

2 1 Introduction Business cycles in small emerging economies differ from those in developed economies. Emerging economies feature interest rates that are higher, more volatile and countercyclical (interest rates are usually acyclical in developed economies), higher output volatility, higher volatility of consumption relative to income, and more countercyclical net exports. 1 Due to the high volatility and countercyclicality of the interest rate, a state-dependent interest rate scheme is a key ingredient in any model designed to explain the cyclical behavior of quantities and prices in emerging economies. Some studies assume an exogenous interest rate scheme. 2 Others provide microfoundations for the interest rate scheme based on the risk of default. 3 This is the approach taken by recent quantitative models of sovereign default, which are based on the framework proposed by Eaton and Gersovitz (1981). 4 The present paper studies the effects of allowing policymakers of different type (patience) to alternate in power in the second class of models. In addition to pure economic variables, political factors are often considered to play a non trivial role as determinants of defaults. Sturzenegger and Zettelmeyer (2006a) conclude that a solvency crisis could be triggered by a shift in the parameters that govern the country s willingness to make sacrifices in order to repay, due to changes in the domestic political economy (a revolution, a coup, an election etc.). Similarly, Van Rijckeghem and Weder (2004) argue that a country s willingness to pay is influenced by politics, i.e., by the distribution of interests and by the institutions and power structures. Santiso (2003) writes, One basic rule of the confidence game [in international financial markets] is then to be very careful when nominating the official government voicer. For investors it is mainly the ministry of economics or finance or the governor of the central bank. In this vein, Moser (2006) finds a significant effect of finance and/or economy minister changes on country interest rate spreads. He argues that such events may reveal important signals about the government s future policy course. The signals may contain information that forms expectations about the future growth potential of a country and at the same time its willingness to service its debt. Figure 1 illustrates the behavior of the sovereign spread in Brazil before and after the election of The movements are often mentioned as an example of the 1 See Aguiar and Gopinath (2004), Neumeyer and Perri (2005) and Uribe and Yue (2006). 2 See, for example, Aguiar and Gopinath (2004), Neumeyer and Perri (2005), Schmitt-Grohé and Uribe (2003), and Uribe and Yue (2006). 3 Tomz and Wright (2006) document 250 defaults by 106 countries between 1820 and Some of the latest episodes are Russia in 1998, Ecuador in 1999, and Argentina in See Aguiar and Gopinath (2006), Arellano (2005), Arellano and Ramanarayanan (2006), Bai and Zhang (2006), Cuadra and Sapriza (2006a,b), Lizarazo (2005, 2006), and Yue (2005). 2

3 importance of political factors as determinants of default decisions. The concerns raised by the left-wing candidate Luis Ignacio Lula Da Silva due to his past declarations in favor of a debt repudiation is the most accepted explanation for the sharp increase in the country spread in the run-up to the Brazilian election (see Goretti (2005)). More recently, the declared intention to restructure the country s debt in order to finance social programs once in power of the elected president of Ecuador, Rafael Correa, were linked to a decline in sovereign bond prices (see, for example, Pimentel and Murphy (2006)). There are other empirical studies that suggest that political factors may be important in understanding sovereign default (see Citron and Nickelsburg (1997), Balkan (1992), Kohlscheen (2003), Reinhart et al. (2003), and Meyersson (2006)). The present paper contributes to the understanding of how the presence political risk may affect borrowing and default decisions. 22 Elections: second round Interest rate spread (in %) Argentinian Default Elections: first round /3/2001 4/26/2002 9/17/2002 2/8/2003 7/2/ Figure 1: Elections and sovereign bond spread in Brazil. Source: JP Morgan (EMBI Global). We introduce a stylized political process into the framework used by recent quantitative studies on sovereign default. We study a small open economy that receives a stochastic endowment stream of a single tradable good. The objective of the policymaker in power is to maximize the expected present value of future utility flows. As in Cole et al. (1995) and Alfaro and Kanczuk (2005), we assume that two types of policymakers that differ in the weights they assign to future utility flows alternate in power. One type of policymaker is more patient than the other type. The policymaker in power has only one financial asset available: one period non-contingent bonds. These assets are priced in a 3

4 competitive market inhabited by a large number of identical, risk neutral lenders. Lenders have perfect information regarding the economy s endowment and the type of policymaker in office. In each period, the policymaker in office makes two decisions. First, he decides whether to refuse to pay previously issued debt or not. Second, he decides how much to borrow or save. The cost of declaring a default is that the endowment is reduced in a fixed percentage in the following period. The model may generate two types of defaults. First, a sufficiently low endowment realization may trigger a default during the spell of a patient or impatient type. The second type of default is triggered when a patient policymaker is replaced by an impatient policymaker. We show that the second type of default may be observed only when there is enough political stability. The intuition behind the role of political stability is the following. The price received by the government for the bonds issued today incorporates a discount that mirrors the probability of a default in the following period (recall that the government can only issue one-period bonds). If a patient type chooses borrowing levels that would lead an impatient type to default in the next period, it has to compensate lenders for this contingency, i.e., for the contingency that an impatient type becomes the decision maker in the following period. If the probability of this contingency is high enough (political stability is low), it is too expensive for the patient type to choose borrowing levels that would lead an impatient type to default. In this scenario, the patient type does not borrow so heavily and therefore, a change in the government s type does not trigger a default. We also find that even in an economy with high political stability, a default does not occur every time a patient policymaker is replaced by an impatient policymaker. This is the case because a patient policymaker chooses high issuance volumes that would lead an impatient policymaker to default only after experiencing a stream of sufficiently low endowment realizations during his tenure. In order to gauge the importance of political factors as determinants of some recent default episodes, we study the behavior of political risk in these episodes. 5 We conclude that the Argentinean default in 2001 is the most likely to have been triggered by a change in political circumstances. 6 Only Argentina and Uruguay exhibit a relatively high degree of political stability that this paper indicates is necessary 5 Bilson et al. (2002) define political risk as the risk that arises from the potential actions of governments and other influential domestic forces, which threaten expected returns on investment. In our environment, default is the government s action that affects the return obtained by lenders, and (for a given debt level) political risk is low (high) when a patient (impatient) policymaker is in power. 6 We look at the composite index of political risk for investors constructed by the International Country Risk Guide for Argentina, Ecuador, Pakistan, Russia, and Uruguay. All of these countries declared a default within the last ten years. We identify higher (lower) values of the index (above the mean or the median) with a good ( bad ) type being power (the index is such that a higher value indicates less political risk). 4

5 for a change in political circumstances to trigger a default. But while the average levels of political risk in Uruguay before and after its default are almost identical, Argentina exhibits the widest difference in the average levels of political risk before and after its default. 7 The model is solved using numerical techniques and a calibration of the endowment process that is based on GDP data from Argentina. We identify the period as a period of low political risk in Argentina (in terms of the model, a period with patient governments in power). We simulate the model and study samples where a patient type is in power and at the end of the sample, a type change occurs and a default is declared by the impatient type once in office. We compare the implications of the model with the Argentinean macroeconomic behavior during the period. We show that introducing government heterogeneity may improve the ability of the model to reproduce the high spreads (margin of extra yield over U.S. Treasuries) paid by Argentina. The average spread observed during this period is 7.3%. The average spread obtained with our benchmark parameterization is 6.2%. The average spread delivered by the model is substantially higher than what is obtained when the alternation in power of different types is shut down. When only the patient type is in office, the spread is 0.3%. When only the impatient type is in office the average spread is 1.5%. Given that the mean spread in the model mirrors the default probability, this implies that an economy in which investor-friendly governments alternate in power with less investor-friendly governments has a higher default probability than an economy where governments are never very friendly to investors. It is the alternation in power of different types that is crucial to generate a higher default probability. We also find that government heterogeneity enables the model to generate higher spread volatility. The standard deviation of the spread is 0.5% in the model with alternation compared to less than 0.03% when there is no alternation in power. In the data, the standard deviation of the spread is 2.8%. Mechanically, government heterogeneity introduces an additional source of uncertainty: the type in power may be replaced in the following period. This smoothes out the bond price scheme faced by the government and therefore, it reduces the marginal cost of the current bond issuance. The bond price function plays a key role in the quantitative performance of the models of sovereign default and it is a challenge for the literature to generate a relatively smooth price function (see, for example, the discussions in Aguiar and Gopinath (2006) and Hatchondo et al. (2006b)). On top of improving the 7 After Argentina s president De La Rua resigned on December 20, 2001, the Congress named Rodriguez Saa as the interim president on December 23, The next day, Argentina announces the suspension of all payments on debt instruments and the default is celebrated in Congress as a victory (see Sturzenegger and Zettelmeyer (2006a)). 5

6 performance of the spread, the model with alternation in power is able to replicate other salient features of the macroeconomic performance of Argentina during the period studied. The model has other testable implications that are consistent with the data. Difficulties in market access seem to be observed after a default (for example, Gelos et al. (2004), and IMF (2002) discuss evidence of a drainage in capital flows into countries that defaulted). The harsher treatment a country receives in international capital markets after defaulting is endogenous in our setup most of the recent work in sovereign default assumes that countries are exogenously excluded from capital markets after a default. In our setup, when the default is triggered by a change of the type in power, investors immediately learn that a new type of policymaker is in power (a bad one). They are still willing to lend to the new government but at different conditions: the bond price scheme offered to the new government shifts. We show that this leads the new government to borrow less and pay lower spreads compared to the pre-default levels. This is consistent with what is observed in Argentina, where the external public debt and the spread after the default episode are below the values observed before the crisis this is not the case, for instance, in Uruguay, where as explained above one could argue that default was not triggered by political factors. Furthermore, and consistent with historical evidence, in our model market access improves after the defaulting government loses power. 8 Finally, the presence of default episodes that are triggered by political factors and not by low endowment realizations enable the model to partially disentangle default decisions from poor economic conditions. Tomz and Wright (2006) report that even though most of the default episodes occur in periods of low output (below the trend), the correlation is much weaker than what is implied by the standard quantitative model of sovereign default (with only one type in power). The present paper confirms their conjecture that introducing government heterogeneity may help to explain the weak correlation between default decisions and economic conditions. 1.1 Related literature This paper is closely related to Cole et al. (1995) and Alfaro and Kanczuk (2005). They also study models of sovereign default with heterogeneous borrowers in which a default occurs if a patient policymaker is replaced by an impatient policymaker. In contrast with the present paper, they assume asymmetric 8 A clear example is discussed by Cole et al. (1995); they explain that the ability of Reconstruction governments in Florida and Mississippi to borrow after the Civil War suggests that the old creditors could not block new loans once the states reputations had been restored by an observable change in regime. 6

7 information about the borrower s type. They focus on equilibria in which patient policymakers always default and impatient policymakers never default. In order to simplify the analysis, Cole et al. (1995) assume that the government can only choose whether to borrow or not the amount offered by lenders, while in Alfaro and Kanczuk (2005) the borrowing level is exogenously given. This enables them to simplify the learning process of lenders and makes the model tractable. The drawback of this approach is that it limits the ability of the model to study the macroeconomic behavior over the business cycle. We consider a similar political process as theirs, but in the setup used in recent quantitative models of sovereign default where the ability of governments to choose the amount they borrow is not restricted. In this scenario, we show that a default is triggered by the replacement of a patient policymaker by an impatient policymaker only if there is enough political stability in the economy and the patient policymaker encounters poor economic conditions during his tenure. Similarly, Chatterjee et al. (2005) study household bankruptcy in a setup with heterogenous borrowers and asymmetric information about the borrower s type. They assume that the borrower s type changes over time. Instead, we assume that borrowers of different types alternate in power. We consider that this is a better representation of a political process that features the interaction of different groups of politicians with different objectives. As Cole et al. (1995) and Alfaro and Kanczuk (2005), they need to restrict the set of savings levels available to borrowers, and they focus on equilibria where, the impatient type always defaults and the patient type never defaults. Amador (2003) studies sovereign default in a setup in which different types alternate in power. The types disagree on the optimal allocation of resources within each period but assign the same weight to future utility flows. This means that the types do not differ in their willingness to repay and are therefore, receive the same treatment from the lenders. Instead, in our setup the two types differ in their willingness to pay. The paper proceeds as follows. Section 2 introduces the model. Section 3 discusses the behavior of a political risk measure in recent default episodes. Section 4 presents the benchmark parameterization of the model (with high political stability). Section 5 discusses the benchmark results. Section 6 studies how the implications of the model change when low political stability is considered. Section 7 concludes and suggests possible extensions. 7

8 2 The model The environment studied in this paper builds on the framework presented by Aguiar and Gopinath (2006), who study the quantitative performance of a model of sovereign default very close to the one in Eaton and Gersovitz (1981). Arellano (2005), Arellano and Ramanarayanan (2006), Bai and Zhang (2006), Cuadra and Sapriza (2006a,b), Lizarazo (2005, 2006), and Yue (2005) study different extensions of this framework. We choose to build on the simplest model because this allows us to discuss the effects of government heterogeneity in a more transparent way. There are three main differences between our framework and the one studied by Aguiar and Gopinath (2006). First, in contrast with Aguiar and Gopinath (2006), we do not assume that countries can be exogenously excluded from capital markets after a default episode. 9 The exogenous exclusion assumption is controversial on several grounds. First, it appears to be at odds with the existence of competitive international capital markets (which is assumed in recent quantitative studies of sovereign default). It is not obvious that after a default episode competitive creditors would be able to coordinate to cut off credit to defaulting countries. This point is also raised by Cole et al. (1995), and Athreya and Janicki (2006). Second, empirical studies suggest that once other variables are used as controls, market access is not significantly influenced by previous default decisions (see, for example, Eichengreen and Portes (2000), Gelos et al. (2004), and Meyersson (2006)). 10 The assumption that countries are excluded from capital markets after a default episode is motivated by evidence of a drainage in capital flows into countries that defaulted (see, for example, Gelos et al. (2004), and IMF (2002)). However, it may very well be that the difficulties in market access observed after a default episode respond to the same factors that triggered the default decision itself. In our model, both default and the difficulties in market access after default may be triggered by a change in the type of policymaker in power. Second, while previous studies assume that after defaulting a country looses a percentage of its 9 Hatchondo et al. (2006b) show that the model delivers a slightly higher equilibrium default probability without exclusion. 10 Sturzenegger and Zettelmeyer (2006b) discusses how holders of defaulted bonds succeeded in interfering with crossborder payments to other creditors who had previously agreed to a debt restructuring. From this, they infer that holders of defaulted bonds may had been able to exclude defaulting economies from international capital markets. On the other hand, they conclude that legal tactics are updated all the time, and new ways are discovered both to extract payment from a defaulting sovereign as well as to avoid attachments. In particular, they expect that the threat of exclusion may be less relevant for some countries or to all countries in the future. For example, they explain that after Argentina defaulted in 2001, attempts to actually attach assets have so far turned out to be fruitless. In any case, other forms of financing are always available to defaulting economies (issuing bonds at home, aid, official credit, multilateral or bilateral financing, etc.). Thus, the discussion in Sturzenegger and Zettelmeyer (2006b) suggests that defaulting economies might face at most a higher borrowing cost, though it is not clear how important this cost differential may be. 8

9 endowment for an stochastic number of periods, we assume that all the output loss is realized in the period after the default. Hatchondo et al. (2006b) explain that assuming that the output loss occur in only one period makes it simpler to lift the exogenous exclusion assumption (it reduces the dimensionality of the problem when countries can choose to default in consecutive periods), and it does not affects the results significantly. The output-loss assumption intends to capture the disruptions in economic activity entailed by a default decision. IMF (2002), Kumhof (2004), and Kumhof and Tanner (2005) discuss how financial crises that lead to severe recessions are triggered by sovereign default. Similarly, Kaminsky and Reinhart (1999) show that debt devaluations in developing countries cause banking problems. Finally and more importantly, we allow for the composition of the government or the distribution of power among government officials to change each period. We study a very stylized political process. Each period, the government determines the consumption level in the economy, c. Its per-period utility is given by: u(c) = c(1 σ) 1 1 σ. As done by Cole, Dow, and English (1995) and Alfaro and Kanczuk (2005), we assume that at the beginning of each period, with a constant exogenous probability π, the incumbent policymaker is replaced by another policymaker who assigns different weights to future utility flows. We assume that patient policymakers discount future utility flows at a rate β h, and impatient policymakers discount future utility flows at a rate β l, where β h > β l. There is a single tradable good. The economy receives a stochastic endowment stream of this good, y, where ρ < 1, and ε t N ( 0,σ 2 ǫ). log(y t ) = ρlog(y t 1 ) + ε t, Each period, the government first decides whether to refuse to pay previously issued debt and later chooses how much to borrow or save for the following period using one period bonds. Let b denote the bond position at the beginning of the period. A negative value of b denotes that the country was an issuer of bonds in the previous period. Each bond delivers one unit of the good next period (if there is no default). There is a continuum of risk neutral lenders with deep pockets. Each lender can borrow or lend at the risk free rate r. Lenders have perfect information regarding the economy s endowment and the 9

10 government s type. 11 The bond price is determined as follows. First, the government announces how many bonds it wants to issue. Then, lenders offer a price for these bonds. Finally, the government sells the bonds to one of the lenders who offered the highest price. Competitive lenders will offer a price q jd (b,y) for each bond if the government decides to issue b bonds, where d denotes the default decision and jǫ{h, l} indicates the government s type. The indicator d is equal to 1 if the government defaulted in the current period, and takes a value of 0 otherwise. Thus, the government s budget constraint is given by ( c + q jd b,y ) b = (1 hλ) y + (1 d) b, where λ denotes the percentage of output lost after default; and h takes a value of 1 when the country defaulted in the previous period, and takes a value of 0 otherwise. When deciding whether to default, the government compares two value functions, V j1 (y,h) and V j0 (b,y,h). The former denotes the value function under default of a government of type j, when the country has a credit history h. The second value function denotes the value function of government j when it did not default, and it has to pay b. Let V j (b,y,h) denote j s value function at the beginning of a period if j is in power, and W j (b,y,h) denote j s value function at the beginning of a period if j is not in power since a government s decisions are influenced by its type, V j and W j do not need to coincide. The optimal borrowing decision of a government that defaulted in the current period solves the following dynamic programming problem: V j1 (y,h) = max b β j u(y (1 hλ) q j1 (b,y) b ) +... π W j (b,y,1)f y (dy y)... + (1 π) V j (b,y,1)f y (dy y). The value function of j when it has decided to pay back the debt is obtained from the following Bellman equation 11 Assuming that the type of the borrower is its private information (as done by Cole et al. (1995), Alfaro and Kanczuk (2005), and Chatterjee et al. (2005)) would complicate the analysis significantly if the ability of the borrower to decide how much he borrows is not restricted (as done by Cole et al. (1995), Alfaro and Kanczuk (2005), and Chatterjee et al. (2005)). 10

11 V j0 (b,y,h) = max b β j u(y (1 hλ) + b q j0 (b,y) b ) +... π W j (b,y,0)f y (dy y)... + (1 π) V j (b,y,0)f y (dy y). The function V j (b,y,h) is computed as follows: V j (b,y,h) = max{v j1 (b,y,h),v j0 (b,y,h)}. Let d j (b,y,h) denote the default decision of government j. In equilibrium 1 if V j1 (y,h) > V j0 (b,y,h) d j (b,y,h) = 0 if V j1 (y,h) V j0 (b,y,h). If d j (b,y,h) = 1, W j (b,y,h) = ) ) u (y (1 hλ) q j1 (b j1 (y,h),y b j1 (y,h) +... π V β j j (b j1 (y,h),y,1)f y (dy y)... + (1 π) W j (b j1 (y,h),y,1)f y (dy y), where b j1 (y,h) denotes the optimal saving behavior of government j after it defaults. If d j (b,y,h) = 0, W j (b,y,h) = ) ) u (y (1 hλ) + b q j0 (b j0 (b,y,h),y b j0 (b,y,h) +... π V β j j (b j0 (b,y,h),y,0)f y (dy y)... + (1 π). W j (b j0 (b,y,h),y,g,0)f y (dy y) where b j0 (b,y,h) denotes the optimal savings of government j when it has decided to pay back its debt. The price of a bond issued by government j if a default decision d was made in the current period satisfies the lenders zero profit condition. Thus, it is given by where ( q jd b,y ) = 1 [ [ 1 πe d j b,y,h ] (1 π) E [ d j 1 + r b,y,h ]], E [ d j b,y,h ] = d j ( b,y,h ) F y ( dy y ) denotes the probability of a policymaker of type j defaulting next period if the current government purchases b bonds, the current endowment is y and h is determined by the current-period default 11

12 decision. The equilibrium price depends on the government type, j, and on its default decision, d. The former is due to the fact that the type conveys information about the probability distribution of future types, and therefore it affects the probability distribution of next period default decisions. The latter is due to the fact that a current default decreases future output and affects future default decisions. 3 A measure of political risk for investors The International Country Risk Guide s index of political risk is the measure of political risk for investors most commonly used in recent empirical studies (see, for example, Reinhart, Rogoff and Savastano 2003, and Meyersson 2006). It tries to evaluate the political risk faced by businesses in different countries. It is made based on subjective analysis of by the International Country Risk Guide s experts. The index ranges from zero to one hundred. A higher value indicates less political risk. Using this index, Figure 2 shows that the December 2001 default episode in Argentina was preceded by an increase in political risk. Moreover, political risk was consistently lower in the 1990s than after the default. Figure 2: Political risk for investors in Argentina (100 minus the International Country Risk Guide s index of political risk). The vertical line marks the month when Argentina defaulted. Figure 3 shows that the behavior of political risk in Argentina is not repeated in other recent default episodes (Ecuador, Pakistan, Russia, and Uruguay). In other countries, political risk is not significantly higher after the default episode, and they seem to exhibit more political instability (i.e., more frequent changes from periods of low risk to periods of high risk). The differences in the behavior of political risk in recent default episodes is also apparent from the 12

13 Figure 3: Political risk for investors in Uruguay, Russia, Ecuador, and Pakistan (100 minus the International Country Risk Guide s index of political risk). The vertical line marks the month of default. statistics presented in Table 1. The table shows that Argentina exhibits the largest difference between the average levels of political risk before and after default. It also shows that among the five countries considered, Argentina is the only one where political risk was consistently low before the default and consistently high after the default. (1) (2) (3) (4) (5) (6) (7) (8) (9) Argentina N/A Ecuador N/A Pakistan Russia Uruguay Table 1: Political risk for investors in recent default episodes (100 minus the International Country Risk Guide s index of political risk). (1) Country. (2) Month of default. (3) Average risk in the sample. For each country except Russia, we consider data starting eight years before the default. Data for Russia starts in April We consider data until June (4) Average risk before the default. (5) Average risk after the default. (6) Percentage of month before the default with risk above the after-default average. (7) Percentage of month after the default with risk below the before-default average. (8) Number of consecutive months before the default with political risk below the after-default average. (8) Number of consecutive months after the default with political risk above the before-default average. N/A indicates that political risk after the default is always above the before-default average. 13

14 Risk aversion σ 2 Interest rate r 1% Autocorrelation coefficient of output ρ 0.9 Standard deviation of innovations σ ǫ 2.7% Loss of output λ 8.3% High discount factor β h 0.9 Low discount factor β l 0.6 Probability that the current government type is replaced π 1.5% Table 2: Benchmark parameter values. 4 Benchmark parameterization Table 2 presents the parameter values for our benchmark parameterization. The coefficient of relative risk aversion of 2 is standard. Each period refers to a quarter with a quarterly risk free interest rate of 1%. The process of output is calibrated to match the process for Argentina from the third quarter of 1993 to the third quarter of We identify this period as a period of low political risk (see Figure 1). We will compare business cycle statistics generated by the model with statistics for Argentina during this period. The calibrated output process (and the business cycle statistics computed from the data) does not change much if we consider a different period (see, for example, Aguiar and Gopinath (2006)). The value of λ is from Hatchondo et al. (2006b). This value gives the model a cost of default which is similar to the cost of default in a model with a stochastic number of periods of output loss when the output loss is 2% per period (as assumed in previous studies). In particular, a one-period output loss of 8.3% generates the same average debt level than the output loss calibrated in Aguiar and Gopinath (2006). As in previous studies, high impatience is necessary to generate default in equilibrium. Aguiar and Gopinath (2006) choose a unique discount factor of 0.8. Here, we choose a higher discount factor for patient governments and a lower discount factor for impatient governments. The 1.5% probability that the current government type is replaced implies an average tenure in office of 16 years. Section 6 presents results obtained with a lower expected tenure. 14

15 5 Results (PRELIMINARY AND INCOMPLETE) The model is solved numerically using value function iteration and interpolation as in Hatchondo et al. (2006a). 12 Figures 4 shows the combination of debt levels and endowment shocks for which each type would choose to default. The grey area is the region for which both types would default, and the black area is the region for which only an impatient government would default. As one would expect, for any combination of debt level and endowment shock such that a patient government would choose to default, and impatient government would also choose to default. Moreover, there are combinations of debt and endowment for which only an impatient government would default. This is reflected in the bond price function faced by the government Endowment shock Assets Figure 4: Default regions. Figures 5 shows the bond price that a patient government faces for the average endowment level. The price function in Figure 4 is close to a step function. With low debt levels, no government would default, and spreads are low (bond prices are high). With intermediate debt levels, only impatient governments would default, and spreads take intermediate values. With high debt levels, both government types would default, and spreads are very high, moving the bond price closer to zero. Figure 7 shows the objective function for this government for the average debt level observed in the simulations. It shows that typically, the objective function is not globally concave we use a global 12 Value functions are approximated using Chebychev polynomials. Fifteen polynomials on the asset space and ten on the endowment shock are used. Results are robust to using more polynomials. 15

16 1 Bond price r 1 π 1+r Two types Only high beta Bonds issued Figure 5: Bond price faced by a patient policymaker when he may be replace by an impatient policymaker and in an economy where all policymakers are patient. search procedure to find an initial guess for the optimal borrowing level and use that guess as a starting point of a nonlinear optimization routine. It increases for debt levels such that the bond price is increasing, and it decreases for debt levels such that the bond price is flat. As in previous studies, when the bond price is decreasing with respect to the borrowing level, it decreases very sharply, and this implies that the objective function is decreasing with respect to the borrowing level at borrowing levels close to the ones for which the price is flat (see, for example, the discussion in Hatchondo et al. (2006b)). For the states used to draw the figure, a patient government would choose an intermediate level of debt and, therefore, it would pay an intermediate spread. On the other hand, we find that a patient government would choose a low level of debt (and therefore, it would pay low spreads) for low initial debts and high endowments. This is described in Figure 6. Figures 5 and 7 also show the bond price function and objective function, respectively, for an economy in which every policymaker is patient. In such an economy, the government always choose to pay low spreads. Figures 7 shows the bond price that a impatient government faces for the average endowment level. As the price function in Figure 5, the price function in Figure 8 is also close to a step function. The intermediate step in Figure 8 is very close to zero because the impatient government is very likely to stay in power. Therefore the default probability is very high for the intermediate debt levels and this is 16

17 z 0.1 b Figure 6: Optimal bond issuance decision of a patient type as a function of the initial asset position (previous issuances) and the endowment shock. When the combination of the endowment shock is high or the initial debt level is sufficiently low, the chosen debt level is low. For intermediate combinations of low endowment or relatively high initial debt, the patient type chooses an intermediate debt level. When the endowment shocks is sufficiently low or the initial debt level is sufficiently high the patient type defaults and chooses a low issuance volume (it does not need to borrow to roll over previously issued debt). reflected in a very low bond price. Thus, the intermediate step in the bond price function introduced by the existence of patient policymakers does not alter the behavior of impatient policymakers. Figure 9 presents the objective function of an impatient government for the average debt level observed in the simulations. The figure shows that impatient governments would choose a low level of debt and therefore, they would pay a low spread. Consequently, with our benchmark parametrization, even though impatient governments assign more weight to current consumption, they may decide to borrow less than patient governments. This is the case because impatient governments are more likely to default and therefore, face higher borrowing costs. 5.1 Simulations The model is simulated for 750,000 periods (500 samples of 1,500 observations each). In the simulations, 77% of the default episodes occur when a patient policymaker is replaced by an impatient policymaker. In their first period in office, impatient policymakers typically find themselves with a debt level that 17

18 9.525 Only high beta b Figure 7: Objective function of a patient policymaker when he may be replaced by an impatient policymaker and in an economy where all policymakers are patient. is higher than the maximum debt level they would choose to pay. Patient governments choose intermediate debt levels when they receive low endowments and stay at these debt levels after that. We find that 95% of the times a patient policymaker is replaced by an impatient policymaker a default occurs the remaining 5% corresponds to situations in which patient policymakers do not encounter a period of low resources during their tenure in office; given their long expected tenure, and the high volatility of output, these situations are infrequent. Out of the default episodes that are not triggered by a change in the policymaker in power, 83% occurs with impatient governments and the remaining 17% with patient governments. Government heterogeneity also implies a weaker correlation between economic conditions and default decisions consistent with the weak correlation found in the data by Tomz and Wright (2006). Using a historical data set with 169 default episodes, Tomz and Wright (2006) report that 62% of these default episodes occurred in years when the output level in the defaulting country was below its trend. They also explain how quantitative models without government heterogeneity cannot generate this weak correlation and suggest that this may be the case in part because government heterogeneity is not considered. If we simulate the economy with only patient governments, only 1% of the default episodes occurs when the shock to the output level is above the mean. With impatient governments only, this is the case in only 7% of the default episodes. When patient and impatient governments alternate in 18

19 Bond price Two types Only high beta Bonds issued Figure 8: Bond price faced by an impatient policymaker when he may be replaced by a patient policymaker. power, the shock to output is above the mean in 38% of the default episodes. We also find that government heterogeneity may explain difficulties to access capital markets after a default. The change in the type of policymaker in power that triggers default also explain why after defaulting the government would have to pay a higher spread for a given level of debt (compare the bond price functions for patient and impatient governments presented above). In the simulations, impatient policymakers are more likely to be in power after default episodes. As explained above, impatient policymakers choose a low borrowing level. This is reflected in a lower debt level after default than before default as illustrated in Figure 10 in the default period, the government borrows even less because its debt level is low. Furthermore, consistently with historical evidence, market access in our model improves after the defaulting government loses power. The decrease in the debt level after a default episode triggered by an impatient policymaker taking office is consistent with the decrease in the debt level of Argentina after the 2001 default. Figure 11 shows that risky governments in Argentina (see Section 3) have chosen low debt levels after the default. 13 Our model also predict that after a default episode triggered by an impatient policymaker taking office, the impatient policymaker chooses to pay a spread lower than the spread paid by patient policymakers before the default. This is consistent with the lower spread paid by Argentina after the 13 The Argentinean debt level decreases sharply in 2005 when the defaulted debt is exchanged. 19

20 With two types b Figure 9: Objective function of an impatient policymaker when he may be replaced by a patient policymaker and in an economy where all policymakers are impatient default. Figure 12 shows that risky governments in Argentina paid lower spreads after the default episode. 14 Summing up, the evolution of the debt level, the evolution of the political risk, the evolution of spreads, and the timing of the default in Argentina are consistent with a typical default episode in our simulations. Uruguay, experienced a crisis similar to the one in Argentina. However, as explain in Section 3, one could argue that the default episode in Uruguay was not triggered by a change in the type of policymaker in power. Figure 13 shows the spread and the debt level in Uruguay after the default episode are not lower than before the crisis (as they are in Argentina) Business cycles We now test the ability of the model with government heterogeneity to replicate the business cycle behavior of Argentina before the 2001 default. As explained above, it can be argued that political risk was low in Argentina since the third quarter of 1993 until the third quarter of 2001 (before the default). We focus on this period. Therefore we take from the simulations 500 samples of 32 quarters such that a patient policymaker replaces an impatient policymaker at the beginning of the sample, and a default occurs at the end of the sample after an impatient policymaker replaces a patient one. 14 The spread is very high between the default episode in 2001 and the debt exchange in 2005 because it is calculated using the price of defaulted bonds. 20

21 Gross issuance Figure 10: Average debt before and after default. Figure 11: Argentina public external debt without arrears. The vertical line marks the month of default. Table 3 reports business cycle moments observed in the data, in the simulation with government heterogeneity, and in simulations with only patient or impatient governments. The moments are chosen so as to evaluate the ability of the models to replicate the distinctive business cycle properties of emerging economies. Emerging economies feature interest rates that are high, volatile, and countercyclical; high volatility of consumption relative to income (typically, higher than one); and countercyclical net exports (see, for example, Aguiar and Gopinath (2004), Neumeyer and Perri (2005), and Uribe and Yue (2006)). Income, consumption, and trade balance data are obtained from the finance ministry of Argentina. Spread data is from Neumeyer and Perri (2005). We apply the natural logarithm to the income and consumption series, the trade balance (TB) is expressed as a fraction of output and the interest rate 21

22 Figure 12: Argentina sovereign spread. Figure 13: Uruguay public external debt and sovereign spread (UBI). spread (R s ) is expressed in annual terms. The log of income and consumption are denoted by y and c respectively. All series are HP filtered with a smoothing parameter of Standard deviations are denoted by σ and are reported in percentage terms; correlations are denoted by ρ. The sample moments for Argentina display the same qualitative features that are observed in other periods and in other emerging markets. The exception is perhaps that the reported volatility of consumption is slightly lower than the reported volatility of income. This is not the case if one considers the same sample period but use a longer period to detrend the series. Table 3 shows that introducing government heterogeneity improves the ability of the model to reproduce the high spreads paid by Argentina during this period (7.3%). The average spread obtained with our benchmark parameterization is 6.2%. These high spreads reflect the compensation to lenders because of the probability of patient governments being replaced by an impatient government that would default. The average spread delivered by the model is substantially higher than what is obtained 22

23 Data Only β h Only β l Periods with β h type type with altern. σ(y) σ(c) σ (T B/Y ) σ (R s ) ρ(c, y) ρ(t B/Y, y) ρ(r s,y) ρ(r s,tb/y ) Mean spread (annual rate %) Table 3: Business cycle statistics. when the alternation in power of different types is shut down. When only the patient type is in office, the spread is 0.3%. When only the impatient type is in office the average spread is 1.5%. Given that the mean spread in the model mirrors the default probability, this implies that an economy in which investor-friendly governments alternate in power with less investor-friendly governments has a higher default probability than an economy where governments are never very friendly to investors. It is the alternation in power of different types that is crucial to generate a higher default probability. Mechanically, a model with government heterogeneity delivers more default in equilibrium than a model without political risk because political risk makes the bond price function smoother and therefore, it makes taking risk more attractive for the borrower. That is, a patient government is willing to pay an intermediate spread with political uncertainty because this allows it to increase its borrowing level by a large amount. Without government heterogeneity, the bond price falls very sharply for debt levels close to the ones that imply a risk free rate. As illustrated in Figure 7, this makes the government s objective function fall sharply for these debt levels. Consequently, in a model without heterogeneity, the government chooses to borrow at debt levels close to the risk-free levels and to pay low spreads (that reflect low default probabilities). The smoother price function enables the model to generate higher spread volatility. The standard deviation of the spread is 0.46% in the model with alternation compared to less than 0.03% when there 23

24 is no alternation in power. In the data, the standard deviation of the spread is 2.8%. The bond price function plays a key role in the quantitative performance of the models of sovereign default and it is a challenge for the literature to generate a relatively smooth price function (see, for example, the discussions in Aguiar and Gopinath (2006) and Hatchondo et al. (2006b)). Table 3 also shows that government heterogeneity does not damage the ability of this framework to replicate other features of business cycles in small emerging economies. As in the benchmark without heterogeneity, the debt levels are much lower than in the data (between 5% and 7% of quarterly output). This is particularly true when it is not assumed that a defaulting economy is excluded from capital markets (see Hatchondo et al. (2006b)). We choose to respect the stylized model and its usual parametrization and therefore, our results also have this limitation. 6 An economy with low political stability (PRELIMINARY AND INCOMPLETE) The mechanism described in the previous section is not operative for every parameterization of the model. If π is high enough, a patient government never chooses the intermediate debt levels that it chooses in our benchmark parametrization. With low political stability, it is very likely that an incumbent patient policymaker is replaced. This implies that the fall to the intermediate step in the price function in Figure 5 is large, and makes a patient government unwilling to pay the spread level that would be required if he chooses intermediate debt levels. In these situations, patient governments do not borrow amounts that would lead impatient governments to default, and there is no default when a government is replaced by another government of different type. 7 Conclusions and extensions This paper introduces a stylized political process into the framework used in recent quantitative studies of sovereign default. We show that in this environment, a default episode may be triggered by the replacement of a patient policymaker by an impatient policymaker only if there is enough political stability in the economy and the patient policymaker encounters sufficiently poor economic conditions during his tenure. Guided by this insight, we look at the behavior of political risk in some recent default episodes, and conclude that the Argentinean default in 2001 is the most likely to have been triggered 24