Why do emerging economies accumulate debt and reserves?

Transcription

1 Why do emerging economies accumulate debt and reserves? Juliana Salomao June, 2013 University of Minnesota Abstract Reserve accumulation has the benet of decreasing external vulnerability but it comes with a high cost. Emerging economies have been accumulating reserves without reducing their levels of debt. This behavior is puzzling because these economies could also decrease their vulnerability by decreasing their debt. In this paper I construct a stochastic dynamic equilibrium model of a small open economy with non contingent debt and reserve assets. Reserves have the benet of smoothing consumption when the country is in autarky, after defaulting. Once we assume the asymmetric default costs of Arellano (2008), the results show that the optimal policy is to accumulate positive levels of debt and reserves in equilibrium. These economies accumulate reserves without decreasing debt because it decreases the cost of autarky after they default. For governments to accumulate reserves and debt simultaneously they need to be patient enough to save but still have positive probability of default, the asymmetric default costs generate that. 1

2 1 Introduction Over the past 20 years, economies have increased their levels of international reserves at a rapid pace. By the end of 2009, reserves had risen to 13 percent of the global GDP, doubling from their 2000 level, and accounting for over 50 percent of total imports of goods and services. This recent trend has renewed the interest in policy and academic circles on the optimal level of foreign reserves countries should hold. Recent research has focused in evaluating the costs and benets of reserve accumulation. Rodrik (2006) estimates the cost of holding reserves at close to 1% of GDP for all developing countries. The common benet of holding reserves proposed by researchers is that countries have accumulated reserves as insurance against the risk of an external crisis, protecting countries by increasing liquidity. Emerging economies are special because of their access to international nancial markets. This advantage, in periods of external turbulence, turns into risk since these countries can be aected when the capital ow becomes scarce. Therefore, emerging economies tend to hoard higher stocks of reserves, as a precaution to a potential international nancial crisis. A common factor across many of the past nancial crises has been the mismatch between assets and liability, which led to rollover problems. Reserves can be used to repay external lines of credit that are not rolled over in a crisis, alleviating the need to reduce domestic absorption and mitigating the decrease in output. However, this is not the only way countries can decrease their vulnerability to capital inow reversals. Countries can also decrease their stock of debt or lengthen the maturity structure of their liabilities. Therefore, when analyzing the level of reserves of a country it is fundamental to consider the joint decision of debt and assets accumulation. However, most of the models used in the literature to analyse the reserve accumulation decision take as given the level of international debt and solve for the optimal level of reserves, not taking into consideration the joint decision of holding debt and reserves. Assuming constant debt levels when evaluating foreign reserve levels does not explains the patterns observed in the data on debt and reserves levels for emerging economies. As one can observe in Figure 1, emerging economies have been accumulating reserves without reducing debt levels (displayed as % GDP). As pointed out above countries have an alternative way of reducing the probability and costs of a crisis, by reducing the level of sovereign debt. In other words, even in the case where reserves have positive liquidity eects by reducing the probability of crisis and output costs associated with it, a similar net position could be obtained by reducing the level of foreign debt. 2

3 Figure 1 Source: IFS, WDI In this paper, we address some of these problems by incorporating debt levels into the analysis of optimal reserve management. We construct a stochastic dynamic equilibrium model of a small open economy with non contingent debt and reserve assets. The model is based on Eaton-Gersovitz (1981), Arellano (2008) and Aguiar and Gopinath (2007), allowing the sovereign the choice of holding reserves. In the set up, debt and assets are not perfect substitutes, as reserves can be used even after a country has defaulted. This means that in the model both defaultable debt and reserves are means to smooth consumption. Default entails an instantaneous reduction in the cost of rolling debt, meaning higher consumption. On the other hand, defaulting implies a lower output and a reduction in the ability to smooth consumption in future periods, since the country loses access to international credit markets. The role reserves play under this circumstance is to allow for consumption smoothing even when the sovereign cannot issue debt. Alfaro and Kanczuk (2009) also tried to answer the same questions with a similar model. The authors however assumed linear default costs, then in order to get the historical default probabilities, they have to calibrate the model with a very low discount factor. Because of that, they get robust results pointing that the optimal policy is not to accumulate reserves. In other words, they suggest that countries should choose reserve levels of zero in equilibrium, an even more puzzling result given that in reality countries hold high positive levels of reserves. We show that if we assume asymmetric default costs as proposed by Arellano (2008), we are able to calibrate default probabilities with a higher discount factor, resulting in positive levels of reserve and debt in equilibrium. This reverses the results of Alfaro and Kanczuk (2009). Interestingly, our results show that the optimal policy is to accumulate positive levels of debt and reserves in equilibrium. Countries accumulate debt and reserves when income is high and reserve is relatively less costly and use reserves to smooth consumption when hit by bad income shocks. In this situation reserve and debt coexist to complete the market. 3

4 This paper is organized as follows. Section 2 presents the model and Section 3 denes the parameters and present the simulation results. The last section concludes. 4

5 2 The Model Dene a small open economy that receives a stochastic stream of income. Preferences are concave in consumption, so households prefer a smooth consumption prole. The government can borrow funds from risk neutral international investors, however, debt contracts are not enforceable so the benevolent government may choose to default on its debt at any time in order to smooth consumption. In case of default, the economy is assumed to be temporarily excluded from international debt markets and to incur on direct output costs. Given that the main goal of this paper is to model assets accumulation, as in Alfaro and Kanczuk (2009), we allow the government to also smooth consumption by holding international reserves. Therefore, when the government is excluded from borrowing from international markets, those assets can be used to reduce consumption volatility. We assume that sovereign preferences given by U = E β t u(c t ) (1) t=0 with u(c) = c1 σ 1 (1 σ) where 0 < β < 1 is the discount factor, c is consumption, and σ > 0 measures the curvature of the utility. Households receive a stochastic stream of the tradable good y. The output shock is assumed to take a nite number of values and evolves according to a Markov process with transition matrix with elements π(y i, y j ). Then the probability that y t+1 = y j given that y t = y i is given by the matrix π element at row i and column j. The government has access to the international nancial markets, where it can buy one-period discount bonds B' at prices q B (B, R, y) which is endogenous to the government incentives to default. The price of the bond depends on the size of the debt (B') and reserves (R'), and on the aggregate shock y, because the default probability tomorrow depends on those. The government may also save by hoarding reserves (R), which are risk free one period bonds at price qt R. Where both B and R are set to be non-negative. Foreign creditors have perfect information regarding the economy's endowment process and observe the level of income every period. They have an opportunity cost equal to the risk free rate r > 0 and price the defaultable bonds in a risk neutral manner such that every bond contract oered breaks even in expected value. This requires that the bond prices satisfy q B = 1 δ 1 + r (2) where δ is the probability of default which is endogenous to the model and depends on the governments incentive to repay the debt. On the other hand since the reserves are invested in risk free bonds we have that their price is q R = r (3) 5

6 If the government decides to repay its debt, the resource constrain is given by c = y B + q B (B, R, y)b + R q R R (4) As in Arellano (2008), we model the costs from default as consisting of two components: exclusion from the international borrowing markets and direct output costs. If the government defaults, current debts are erased from the government budget constrain but smoothing through reserves is still allowed. The government will remain in nancial autarky for a stochastic number of periods. Finally, default entails direct costs such that output is lower during periods the government is in autarky. Moreover, we follow Arellano (2008) in setting asymmetric default costs of the form y def = { ŷ y if y > ŷ if y ŷ } (5) As shown by Arellano (2008) the asymmetric default output costs makes the value of autarky less sensitive to the income shock, extending the range of next period's debt and reserves that carry positive but nite default premia. This feature is fundamental to calibrate high default probabilities with reasonable discount factor and as the results will show later also very important to generate reserve accumulation. Then when the government chooses to default, the resource constrain is c = y def + R q R R (6) The timing of the events is as follows. First the government starts with initial debt and reserve levels B and R, observes the endowment shock, and decides whether to repay its debt obligations or default. If the government decides to repay, then taken as given the bond price q B (B, R, y) and q R the government chooses B' and R' subject to the resource constrain. Finally, consumption takes place. Recursive Equilibrium We focus on the Markov perfect equilibrium for this stochastic dynamic game with no commitment from the government and where the players act sequentially and rationally. The foreign creditors are risk neutral and they lend money to the sovereign as long as the expected return on the bond equals (1 + r). Therefore, for a loan of the size of B with accumulated assets of R and income y, the bond price satises q B (B, R, y) = 1 δ(b, R, y) 1 + r (7) The government observes the income shock y and, given initial foreign assets B and reserve holdings R, decides to repay or default. The choice of default or repayment is made with the objective of maximizing the lifetime utility of the households. If the government chooses to repay the debt and keep the access to international markets, it decides on the next period holdings of debt and reserves (B and R ). When making all those decisions, the government takes into consideration the fact that the price of new borrowing depends on the income state y and on the choice of next periods debt and assets holdings. 6

7 Dene v 0 (B, R, y) as the value function for the government that has the option to default and has current period debt B and reserves R with income y. Given the option to default, v 0 (B, R, y) can be dened as v 0 { (B, R, y) = max v G (B, R, y), v B (R, y) } (8) {G,B} where v G is the value function of the sovereign when it decides to repay its commitments (G for good credit) and v B its value function when it decides to default (B for bad credit). When the government decides to default, the economy is in temporary nancial autarky but can buy/sell reserves. The value of default is given by v B (R, y) = max {R } {u(y def + R q R R ) + β(θev 0 (0, R, y ) + (1 θ)ev B (R, y ))} (9) where θ is the probability that the economy will regain access to international credit markets after default. If the government decides to keep a good credit history, the value conditional on not defaulting is the following v G (B, R, y) = max {B,R } {u(y B + qb (B, R, y)b + R q R R ) + βev 0 (B, R, y )} (10) The government decides on optimal policies B and R to maximize utility. Also, the decision to default is made period by period and the expected value for the future incorporates the fact that the government could decide to default in the future. It is important to highlight that it may not be optimal to payo debt using reserves, by comparing v B (R, y) to v G (B, R, y) one can notice that reserves and debt are not perfect substitutes. Once you default your stock of debt goes to zero, however you are able to keep the reserves accumulated on the previous period and can use it to smooth your consumption in autarky, where debt smoothing is no longer an option. This explains why countries can potentially be interested in accumulating both debt and assets. As usual, it is useful to dene a default set and a repayment sets. Let A(B,R) be the set of y's for which repayment is optimal when debt is B and assets R, such that A(B, R) = {y Y : v G (B, R, y) v B (R, y)} and D(B, R) = Ã(B, R) be the set for which default is the optimal policy for a level of assets B: D(B, R) = {y Y : v G (B, R, y) < v B (R, y)} Now it is time to dene the equilibrium, let s = {B, R, y} be the states of the economy. Denition: The equilibrium for this economy is dened as the set of policy function for (1) consumption c(s), (2) government debt holding B (s) and (3) government reserve holdings R (s), a price function for bonds q B (B, R, y),and repayment A(B, R) and default sets D(B, R) such that 7

8 1. Taking as given the government policies, consumption c(s) satises the resource constraint. 2. Taking as given the bond price function q B (B, R, y), the government's policy functions B (s) and R (s), repayment sets A(B, R) and default sets D(B, R) satisfy the optimization problem, 3. Bond prices q B (B, R, y) reect the government's default probabilities and are consistent with risk neutral pricing. 3 Quantitative Analysis 3.1 Parametrization The model is solved numerically to evaluate its predictions regarding occurrence of default events, accumulation of debt and reserves, and business cycle properties of interest rates. As pointed out before, the implementation of the model requires a exible specication for default costs that increase the set of risky loans available, so that it is possible to calibrate high historical default probabilities with reasonable discount factors. Default costs can be broken into two components: exclusion from the international borrowing markets and direct output costs. The output costs assume an asymmetric form as specied by equation 5, which make the value of autarky less sensitive to the income shock. The inspiration behind this type of default cost function comes from the evidence that sovereign default disrupts the functioning of the nancial private sector and decreases the aggregate credit available in the economy. Borensztein, Levy-Yeyati and Panizza (2007) document that the sovereign default events of the last two decades have been accompanied by substantial decreases in private credit. This asymmetric default cost function captures the idea that without default, if the credit markets function well, output covaries closely with the productivity shock because credit can be adjusted according to shocks. In the case of default, credit markets are disrupted and output can not be large even in the case of a large technology shock. In this paper, we assume this reduced form specication for direct output costs and use it to calibrate the historical default probability for Brazil. Table 1: Parameters Risk-free interest rate r = 4% Risk Aversion σ = 2 Stochastic structure ρ = 0.9,η = Discount Factor β = Probability of reentry θ = 0.17 Output costs ŷ = 0.9E(y) The risk aversion coecient σ is set to two, its standard value in the real business cycle literature. The risk free interest rate is calibrated to 4 percent which corresponds to the U.S. interest rate. The stochastic 8

9 process for output is a log-normal AR(1) process, log(y t+1 ) = ρlog(y t ) + ε t+1 with E(ε 2 ) = η 2. We discretize the state space of debt and reserves, assuming they could take values between zero and 50% of GDP. We assume the grids are large and ne enough not to aect the decision rules. We also discretize the shocks into a ve-state Markov chain using equally spaced grids of the original processes steady state distribution. We then integrate the underlying normal density over each interval to compute the values of the Markov transition matrix. We set the autocorrelation coecient for the output process of 0.9, which is in line with the standard estimations for emergent economies, then we use the data for GDP growth for from World Development Indicators to calibrate the volatility of output 1. Finally we choose the probability of reentering nancial markets, θ, so that the average length of time in exclusion is 6 years, as is suggested by the results of Benjamin and Wright (2009). A summary of the calibration parameters can be found in Table Simulation Results 2 Since the main innovation of the model presented is the addition of asymmetric costs of default, we will rst present the results of the simulation of the model without asymmetric default costs and then compare to the simulation that incorporate asymmetric default costs No Asymmetric Default Costs If we exclude asymmetric costs of default and assume that default entails linear output costs ( equation 5 becomes y def = λy) we fall into the model presented in Alfaro and Kanczuk (2009). In Table 3 we will present the results of the Alfaro and Kanczuk 3 (2009) benchmark calibration of the linear costs model (Model 1), their calibration with a high discount factor β (Model 2) and our calibration of the model but excluding the asymmetric default costs (Model 3). In this table, we present the means of the simulation results. In Table 1A in the appendix the parameters of the three calibrations can be found. Table 2: Results with No Asymmetric Costs Default Exclusion Debt Debt if not Ex Reserves if not excluded Reserves if excluded Model (per 500) (%) (% GDP) (% GDP) (% GDP) (% GDP) Model Model Model From the results presented in Table 3, one can conclude that in a model without asymmetric default costs it is not possible to get reserve accumulation with default occurring in equilibrium. In model 1, as one can 1 The GDP growth sample is too short to properly estimate the both parameters, so we follow Arellano and Ramanarayanan (2010). 2 For the results in Table 3 and 4, we simulate the path for 1000 periods, and average the moments over the last There is an additional dierence from our model and the Alfaro and Kanczuk(2009) model, they have three states for production shocks and we have ve. In model 1 and 2, we then calibrate with three states and in model 3 we calibrate with ve states. 9

10 check in the appendix, in order to get default in equilibrium it is necessary to have a very low discount factor (β = 0.5). As noted by Arellano (2008) and Aguiar and Gopinath (2006) in this type of model debt is used to front load consumption and thus high impatience is necessary for generating high debt levels and reasonable default in equilibrium. However, this makes reserve accumulation very costly, as the sovereign impatience is much higher than the reserves remuneration. In other words, in order to accumulate reserves in this model, the economy needs to consume less and save. The more impatient it is, the harder and more costly is to save. As we make the discount factor higher and the government less impatient (models 2 and 3), debt and default no longer occur in equilibrium. With this calibration we also do not get signicant reserve accumulation because we no longer need reserves to smooth consumption during periods when the economy is excluded from the market since exclusion never happens in equilibrium Asymmetric Default Costs Now we calibrate the model adding the asymmetric cost of reserves as specied in equation 5 and using the parameters specied in Table 2. The results of the simulation can be found in Table 3 below. Table 3: Results with Asymmetric Costs Default Exclusion Debt Debt if not Ex Reserves if not excluded Reserves if excluded (per T=500) (% Time) (% GDP) (% GDP) (% GDP) (% GDP) Model Brazil Once we add the asymmetric default costs, it is possible to get simultaneous historical default probability with debt and reserves accumulation. As shown by Arellano (2008) the asymmetric default costs make the value of autarky less sensitive to the income shock and increases the set of risky loans available, so that it is possible to calibrate high historical default probabilities with reasonable discount factors. This relatively higher discount factor (β = 0.948) make reserve accumulation less costly, generating in equilibrium a higher level of reserves. The model is able to generate the historical default probabilities and reasonable debt and reserve levels. However, the debt levels generated by the model overshoot the average for (33.44% in model vs % actual), but it is also important to notice that the data only considers external debt and Brazil in the past years has been exchanging external debt for domestic debt as its domestic market is developing. Also, the levels of reserve generated by the model undershoot the average level of reserves accumulated in the past years (4% in model vs. 5.29% actual). Nonetheless, the model shows promise in evaluating joint decision of debt and reserve accumulation, since after assuming asymmetric default costs we are able to reverse the result of zero optimal reserves. More interesting is to check when do countries decide to hoard reserves. In order to properly analyze this question it is helpful to look at the policy functions for debt and reserve accumulation 4, presented in 4 These policy functions are given the decision of not defaulting this period. 10

11 Appendix B. It is also very interesting to look at the plot of a simulated path for interest rate, GDP, debt and reserves. Figure 6 In the simulated path shown in the gure above one can observe that countries default after a sequence of bad productivity shocks, when they have no other option to smooth consumption but defaulting 5. Also countries accumulate reserves when they have high income, after high productivity shocks, when the reserves are not very costly relative to debt and countries are able to save. Then one can observe periods when countries accumulate debt and reserves at the same time, as it happens in the data. This can also be observed by looking at the debt and reserve policy functions in the appendix, specially for high income levels (Z=4 and Z=5). Once the productivity shock declines, countries lower reserve and debt level, as both become more expensive, because of the higher probability of default tomorrow. They use the reserves accumulated the previous period to compensate for the lower income, using the reserves to smooth consumption even in periods of no default. It is important to notice that reserve and debt are both one period bonds, so they mature every period, making the decisions on level to be period by period. When countries have low productivity shocks it is very costly to issue debt, as it becomes more expensive given the high probability of default tomorrow. Also the lower the productivity shock, the more costly it becomes to buy reserves. This happens for two reasons, rst it is necessary to reduce consumption in order to save which is more costly when you have a bad shock, second lower productivity shock means higher probability of default tomorrow and therefore higher relative cost of reserves. This patterns of lower reserve and debt levels for lower income can be observed in the policy functions for debt and reserves in the appendix,specially for low income levels (Z=1 and Z=2). Since default only happens after a sequence of bad income shocks and reserve accumulation happens when we have high income shock, it is no surprise that when countries default they have low reserve levels. However it is interesting that the model is able generate positive reserve levels with default events happening in equilibrium, reversing the results of Alfaro and Kanczuk (2009) and of the model without asymmetric costs, where zero reserve levels is the optimal policy. 5 Miller, Tomz and Wright (2006) document that in the last century default generally occur during periods of low output. 11

12 4 Conclusion Over the past 20 years emergent economies have been increasing their levels of international reserves while keeping high levels of external debt. In this paper we propose a model that evaluates the joint decision of debt and reserve accumulation. In our model debt and reserves are not perfect substitutes as reserves can be used even after a country has defaulted. We show that if we assume the asymmetric default costs proposed by Arellano (2008) the model is able to generate debt and reserve accumulation at the same time, as it occurs in the data. Countries accumulate reserves when they have positive income shocks and use it to smooth consumption after bad shocks. The results show that reserve and debt coexist to complete the market. This model seems promising to jointly evaluate the optimal reserve and debt management. 12

13 References 13

14 Appendix A Parameters No Asymmetric Model 1 Model 2 Model 3 Risk-free interest rate r = 4% r = 4% r = 4% Risk Aversion σ = 2 σ = 2 σ = 2 Stochastic structure ρ = 0.85,η = ρ = 0.85,η = ρ = 0.9,η = Discount Factor β = 0.5 β = β = Probability of reentry θ = 0.5 θ = 0.5 θ = 0.17 Output costs y def = 0.9y y def = 0.9y y def = 0.9y 14

15 Appendix B 15

16 16

17 Appendix C The following algorithm is used to solve the model: 1. Start with a guess for the value function given no default and the value function given default. 2. Start with a guess for the bond price schedule such as q 0 (B, y) = 1 (1+r) for all B, R and y. 3. Given the bond price schedule, solve the optimal policy functions for consumption c(b, R, y), debt holdings B (B, R, y), repayment sets A(B, R), and default sets D(B, R) via value function iteration. For each iteration of the value function, we compute the value of default which is endogenous because it depends on the value of contract at B = 0. At each iteration we update the bond price schedule, using the default and repayment sets, such that lenders break even in expectation. 4. We iterate the value function until convergence. 17