Nominal Exchange Rate Volatility, Default Risk and Reserve Accumulation

Transcription

1 Nominal Exchange Rate Volatility, Default Risk and Reserve Accumulation Siqiang Yang Feb 2017 Abstract The paper investigates how the nominal exchange rate volatility affects a sovereign s default risk and the incentive to accumulate reserves. The model considers an environment where the sovereign faces a currency mismatch problem. That is, the sovereign has income in domestic currency, but can only borrow in foreign currency. Moreover, the sovereign is subject to volatile exchange rate fluctuations. Whenever the exchange rate depreciates, the debt burden in terms of domestic currency increases, leading to a higher default risk and borrowing cost. To insure the risk, the sovereign optimally accumulates foreign reserves to smooth consumption, to hedge against the depreciation of the exchange rate, and to stabilize the fluctuations of the exchange rate. Quantitatively the model can generate more than half of the reserve holdings.. Keywords: Sovereign Default, Foreign Reserves, Nominal Exchange Rates Volatility JEL Codes: F32, F34, H63 University of Pittsburgh, Department of Economics, siy10@pitt.edu. I am grateful to Dani Coen-Pirani and Sewon Hur for advising me on this paper. I would also like to thank Marla Ripoll, Douglas Hanley and seminar participants at the University of Pittsburgh for useful comments. 1

2 1 Introduction During the last thirty years, with rapid financial integration, emerging countries have borrowed extensively from international financial markets. However, most of emerging countries external debt are denominated in foreign currency 1, while most of their income are denominated in domestic currency. This gives rise to a currency mismatch problem. The problem can make a country vulnerable to volatile exchange rate fluctuations. That is, whenever its nominal exchange rate depreciates, the foreign debt burden in terms of domestic currency increases, making the country harder to repay the debt and rising the default risk. The potential vulnerability resulting from foreign currency debt and exchange rate volatility creates the need for precautionary measures. On the other hand, since the 21th century, emerging countries have accumulated foreign reserves fasterly. The paper argues that the large reserve accumulation is the natural response to the precautionary demand to insure the risk resulting from foreign currency debt and exchange rate volatility. Moreover, the paper aims to investigate how the interaction between foreign currency debt and exchange rate volatility affects a sovereign s default risk, interest spread and debt dynamics, and whether it can generate large reserve accumulation observed in the data. To explore the logic, the paper extends the classic Eaton and Gersovitz (1981) sovereign default model to study an environment where the sovereign can borrow long-term foreign currency debt, save in short-term liquid foreign reserves. Moreover, the sovereign faces exogenous output shock and nominal exchange rate shock. In this context, whether increasing reserve holdings is a tradeoff between the insurance benefit of reserves and the larger gross debt positions as in Bianchi et al. (2016). Particularly, the paper provides three channels through which large reserve holdings can be rationalized. The first is the consumption smoothing channel. Because of the different maturity of debt and reserve, the sovereign can borrow long-term debt and save in short-term reserves to insure the bad states where borrowing is very costly. The second is the currency hedging channel. Since both debts and reserves are denominated in foreign currency, whenever exchange rate depreciates, debt 1 The situations where countries are not able to borrow in their domestic currency is described as the Original Sin by Eichengreen et al. (2007). 2

3 payments in domestic currency increases, but at the same time reserves in domestic currency also increases which alleviates the effect of depreciation. Thirdly if reserves can be used to stabilize the exchange rate fluctuations, then larger reserve holdings will reduce the volatility of exchange rate and lead to a lower default risk and spread. To test the mechanisms, the paper calibrates the model for quantitative exercises. The first exercise looks at how exchange rate volatilities affect the default risk, borrowing and reserve accumulation decisions. The result shows that with more volatile exchange rate, the default risk is higher, and the sovereign optimally reduces the debt exposures and increases the reserve holdings. The second exercise aims to investigate whether the incentive for reserve accumulation is stronger if larger reserve holdings can reduce the exchange rate volatility. The result confirms that the exchange rate stabilization role of reserves is quantitatively important. The reserve holdings increases from baseline 4 percent to 5.5 percent, where the data counterpart is 9 percent. Related Literature. The paper is related to two different literatures. The first is the sovereign default literature. The main theoretical background is established by Eaton and Gersovitz (1981). The later quantitative exercises are developed by Arellano (2008). Hatchondo and Martinez (2009) and Chatterjee and Eyigungor (2013) extend the Arellano (2008) to incorporate different durations of long-term sovereign bond instead of only one period short-term bond. The model setup in this paper is based on the long-term bond sovereign default model. The novel difference is that the paper considers the foreign currency denominated nominal bond instead of commonly used real bond. By incorporating the foreign currency nominal bond, the paper contributes to the literature by pointing out the exchange rate volatility could be an important channel that affect emerging countries default risk and borrowing decisions. The paper also quantitatively investigate how different exchange rate volatilities will affect their borrowing decisions and the bond spread. The paper is also closely linked to the reserve accumulation literature. This literature tries to explain why emerging countries hold large amount of foreign reserves. There are two popular views in this literature. The first is the mercantilism view, which suggests that reserve accumulation can promote export growth by preventing appreciation (Dooley et al. (2004)). The second is the precautionary view, which argues that reserves can act 3

4 as a self-insurance against future sudden stop events (Alfaro and Kanczuk (2009), Bianchi et al. (2016), Hur and Kondo (2016) and Jeanne and Rancière (2011)). The sudden stop events is known as the quick and sharp reversal of private capital flows in emerging market economies. It is usually modeled as an exogenous event that happens with certain probability. For instance, in Bianchi et al. (2016), the sudden stop is modeled as an exogenous situation where countries are not able to borrow external debts. This paper also illustrates the precautionary motives for reserve accumulation, but in the presence of currency mismatch and volatile exchange rate fluctuations. This two features with defaultable debts can endogenously generate tight borrowing constraint, which provides a micro foundation for the exogenous sudden stop events. Moreover, the paper contributes to the literature by arguing that the exchange rate volatility is an essential factor that increasing the precautionary demand for reserve holdings, and the paper proposes three channels through which large reserve holdings can be rationalized. The rest of the paper proceeds as follows. Section 2 illustrates the empirical motivation, section 3 presents the model and section 4 shows the quantitative results. Section 5 concludes. 2 Empirical Motivation This section aims to establish that foreign currency debt exposure and exchange rate volatility are associated with severe default risk, which naturally incentives precautionary reserve accumulation. To illustrate the point, I collect relevant information 2 on 19 emerging countries from various sources of data 3. The reason for focusing on emerging countries is that most of their external debt is in foreign currency and they also experience volatile exchange rate movements, which is consistent with the key features that this paper emphasize on. The final data I used consist constitutes an unbalanced panel which includes 19 countries and spans from the fourth quarter of 1993 to the last quarter of The nominal exchange rate and foreign reserves data are from International Financial Statistics. The external debt information is from World Development Indicators, and the sovereign bond spread is from JPMorgan Emerging Market Bond Index (EMBI). 3 The emerging countries in our sample include: Argentina, Brazil, China, Colombia, Egypt, Indonesia, Lebanon, Malaysia, Mexico, Morocco, Pakistan, Peru, Philippines, Russia, South Africa, Thailand, Turkey, Ukraine, Venezuela. 4

5 Average FC Composition of External Public Debt Average Interest Rate Spread Fitted Values Averge Exchange Rate Volatility Average Interest Rate Spread Fitted Values Figure 1: Spread, FC Debt Ratio and ExRate Volatility Before going to the analysis, I first explain the measure I used for the important variables. The exchange rate volatility is defined as the standard deviation of quarterly changes of the natural logarithm of the nominal exchange rate within a year, which captures how volatile the depreciation or appreciation is in a given year. Since I am interested in how short-run sudden changes of exchange rate affects default risk, a shorter time window is preferred, and later I will also show that my results are robust to 1.5 years and 2 years window of calculating exchange rate volatility. For the measure of foreign currency debt exposure, in Figure 1, I use the foreign currency composition of external public long-term debt, which directly links to the currency mismatch problem and indicates how much external debt is borrowed in foreign currency. In the regressions shown in Table 1 and 2, I use the ratio of foreign currency external public long-term debt on GDP, which emphasizes on whether the foreign currency debt exposure is large in terms of GDP. For the measure of default risk, I use the EMBI interest spread, which is common in the sovereign default literature. Figure 1 shows the long-run pattern between average spread 4, exchange rate volatility and foreign currency share of external public long-term debt for each country 5. It also provides descriptive statistics about the key variables for each countries. Note that during the time interval 1993Q4 to 2014Q4, most countries borrow over 90% of their long-term public debt 4 In Figure 1, I scale the spread basis point and divide each by 10 4, so that it is comparable to the other two measures. In later regressions, I use the basis point measure. 5 The World Development Indicators only provides the currency composition of external long-term public debt. There is no currency composition information for private and short-term debt 5

6 in foreign currency, and this value is positively related to the interest rate spread. the other graph, we can see that there is also a strong association between exchange rate volatility and interest spread. These two positive relationships are consistent with the idea that higher foreign currency debt ratio and more volatile exchange movements can lead to larger foreign currency debt burden in domestic currency when exchange rate depreciates, which increases the default risk. On However, the associations between the variables might be driven by other common factors that affect spread, exchange rate volatility and foreign currency debt ratio. Moreover, I am more interested in how the interaction between foreign currency debt and exchange rate volatility increases the default risk 6. Therefore, I turn to linear regression analysis to control for potential common factors and explicitly consider the interaction between foreign currency debt and exchange rate volatility. Table 1 shows the coefficients obtained by regressing the interest spread on foreign currency long-term public debt-to-gdp ratio, exchange rate volatility, their interaction term and other controls. All the variables are calculated in a one year rolling window centered at current time period. Except for the exchange rate volatility measures, all other variables indicates the average value in the rolling window. Since both exchange rate volatility and foreign currency public debt-to-gdp ratio are continuos variables instead of dummy variables, the coefficient on the interaction term is not easy to interpret. To help interpret the coefficient, I calculate the difference to the mean value for the variables related to foreign currency debt and exchange rate volatility for each country, which have additional (DM) notations in Table 1 and 2. In this way, it is much easier to interpret the coefficient especially when one of the variables is at the mean level. On all the specifications, I control for all other components of external debt, so that the coefficient on the foreign currency public long-term debt ratio is not interpreted as how total external debt affects spread. On the first two specifications (1), (2), without controlling for country fixed effect, all the variables are significant. Specifically, the interaction between foreign currency debt and exchange rate volatility is significantly positive correlated with the spread. On the other hand, the reserves to short-term debt ratio, which captures whether reserves is enough 6 For instance, if there is no foreign currency debt, then volatile exchange rate movement will not increase the default risk through the currency mismatch channel. Similarly, when the exchange rate is fixed, foreign currency debt will be similar to local currency debt. 6

7 (1) (2) (3) (4) (5) (6) Spread Spread Spread Spread Spread Spread Variables 1 Year RW 1 Year RW 1 Year RW 1 Year RW 1.5 Yrs RW 2 Yrs RW FC Public Debt-to-GDP(DM) 1,988*** 2,022*** 2,606** 3,576** 3,358** 3,129** (348.0) (347.8) (1,223) (1,434) (1,348) (1,223) ExRateVolatility(DM) 811.5* 798.1* 1,687*** 1,563** 1,621** 1,812*** (434.3) (424.9) (576.8) (585.9) (584.0) (572.1) FC Public Debt-to-GDP(DM) 29,454*** 29,332*** 19,161*** 15,626*** 17,165*** 18,857*** ExRateVolatility(DM) (2,789) (2,745) (4,765) (4,738) (4,504) (4,092) Res-to-STDebt *** (4.124) (5.240) (3.781) (4.478) (4.970) RGDP Growth ,947 1,775 (2,283) (3,911) (4,739) CA-to-GDP (985.9) (1,035) (1,107) Inflation ** *** *** (0.0961) (0.112) (0.125) Trade Openness (2.319) (2.282) (2.168) Financial Openness *** *** *** (149.3) (146.1) (145.7) LC Public Debt-to-GDP -3,449*** -3,039*** -1,576-2,553-2,408-2,257 (374.8) (352.4) (2,063) (2,513) (2,419) (2,292) Private Debt-to-GDP (177.4) (177.9) (643.3) (550.5) (556.8) (568.0) Short Term Debt-to-GDP 936.8*** ,601 1,612 1,603 1,627 (328.2) (331.0) (1,539) (1,297) (1,259) (1,219) Constant ** (145.1) (140.1) (237.3) (268.8) (272.6) (254.9) Observations 1,328 1,328 1,328 1,313 1,313 1,313 R-squared Country FE NO NO YES YES YES YES Year FE YES YES YES YES YES YES Number of Countries Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Table 1: Spread, FC Debt Exposure and ExRate Volatility 7

8 to cover the recent debt payment, is significantly negative correlated with the spread. If the country fixed effect is included in specification (3), the coefficient of reserves to short-term debt ratio is still negative but less significant. If we look at the interaction between foreign currency debt and exchange rate volatility, it can still significantly increases the spread. Its significantly positive association with the spread is preserved even if I control for other fundamentals 7 as in (4) or run the regressions in longer rolling windows as in (5) and (6). The take-way from the above regression analysis is that there is a strong and robust positive relationship between the sovereign spread, and the interaction of foreign currency debt and exchange rate volatility. The finding is consistent with the currency mismatch problem that when exchange rate volatility is higher, a more likely larger currency depreciation increases the domestic debt burden, and makes the sovereign harder to repay the debt. If the international financial markets cannot help the sovereign perfectly insure the risk, the sovereign could self-insure by precautionary saving through accumulating reserves 8. Note that the precautionary demand for reserves could correlate exchange rate volatility with different signs. On the one hand, a higher exchange rate volatility can lead to higher precautionary saving to help repay foreign currency debt when output is low or exchange rate depreciates, which gives a positive association. On the other hand, a higher reserves holding can reduce the likelihood of currency crises, sudden stop or exchange rate volatility, which gives a negative sign 9. Or a higher reserves can signal a stronger commitment to smooth the exchange rate volatility through foreign exchange intervention, which also gives a negative sign 10. Which sign is observed in the data not only implies which precautionary motive dominates, but also provides guide on which precautionary channels should be in the structural model. Specifically, since the buffer stock precautionary motive is usually present in the incomplete market model with uninsurable shocks, if the sign observed in the data is negative, which suggests that the channel of having more reserves to reduce the exchange 7 The financial openness is taken from the Chinn-Ito index. The rest control variables are taken from World Development Indicators. 8 Similarly, Fogli and Perri (2015) shows how output volatility increases net foreign assets position through precautionary motives. Bianchi et al. (2016) shows with long-term debt setting, sovereign optimally accumulate large reserves to insure the output fluctuations. 9 Hur and Kondo (2016) shows how higher reserves can reduce the sudden stop probability. 10 Hviding et al. (2004) documents how the signalling effect of higher reserves can reduce the exchange rate volatility. 8

9 Averge Reserve-to-GDP Fitted Values 45 Degree Line Average FC Public Long-Term Debt-to-GDP Average Exchange Rate Volatility Averge Reserve-to-GDP Fitted Values Figure 2: Reserves, FC Debt-to-GDP and ExRate Volatility rate volatility is stronger, then this additional channel should be in the model. Figure 2 shows the descriptive statistics and long-run pattern between reserves-to-gdp, foreign currency long-term public external debt-to-gdp and exchange rate volatility. On the first graph, we can see that all the countries borrow external foreign currency debt and save in reserves at the same time, and most of countries borrow more than they saved. On the second graph, there is a negative association between reserves and exchange rate volatility, which suggests that the channel of using reserves to reduce exchange rate dominates. However, a more robust implication should control for confounding factors. So I turn to the linear regression reported in Table 2. Table 2 reports the coefficients obtained by regressing the reserves-to-gdp ratio on foreign currency long-term public debt-to-gdp ratio, exchange rate volatility, their interaction term and other controls. On specifications (1), (5) and (6), we can see that without controlling for country fixed effect, given the external debt structure, there is a robust negative correlation between reserves and exchange rate volatility on different rolling windows. It is consistent with the argument that for certain countries, the negative relationship of using reserves to reduce exchange rate volatility is stronger than the positive relationship of using reserves as a buffer for uncertain exchange rate realizations. On specifications (2) and (3), with country fixed effect and same fundamental control variables, we can see that the coefficient on the exchange rate volatility alone is still negative, but less significant, which is consistent with previous argument. However, the coefficient on the interaction term becomes positive with 9

10 (1) ResGDP (2) ResGDP (3) ResGDP (4) ResGDP (5) ResGDP (6) ResGDP Variables 1 Year RW 1 Year RW 1 Year RW 1 Year RW 1.5 Yrs RW 2 Yrs RW FC Public Debt-to-GDP(DM) 0.260*** 0.162* *** 0.277*** (0.0502) (0.0898) (0.123) (0.133) (0.0506) (0.0512) ExRateVolatility(DM) ** * *** *** *** (0.0383) (0.0701) (0.0786) (0.0386) (0.0383) FC Public Debt-to-GDP(DM) *** *** *** ExRateVolatility(DM) (0.259) (0.268) (0.439) (0.265) (0.292) Lagged ExRateVolatility(DM) * (0.0724) FC Public Debt-to-GDP(DM) Lagged ExRateVolatility(DM) (0.423) RGDP Growth * (0.341) (0.365) CA-to-GDP 0.344** 0.354** (0.132) (0.136) Inflation 1.02e e-06 (1.25e-05) (1.13e-05) Trade Openness ** ** ( ) ( ) Financial Openness (0.0345) (0.0376) LC Public Debt-to-GDP 0.416*** *** 0.408*** (0.123) (0.434) (0.335) (0.317) (0.123) (0.124) Private Debt-to-GDP *** *** *** (0.0615) (0.128) (0.146) (0.150) (0.0614) (0.0615) Short Term Debt-to-GDP 1.136*** * 0.309* 1.135*** 1.132*** (0.0811) (0.180) (0.172) (0.178) (0.0810) (0.0810) Constant ** *** ** ** (0.0126) (0.0207) (0.0495) (0.0526) (0.0125) (0.0124) Observations 1,760 1,760 1,706 1,664 1,760 1,760 R-squared Country FE NO YES YES YES NO NO Year FE YES YES YES YES YES YES Number of Countries Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Table 2: Reserves, FC Debt Exposure and ExRate Volatility 10

11 less significance. The positive association is consistent with the positive precautionary motive that when country borrows in foreign currency, higher exchange rate volatility can lead to more reserve holdings as a buffers for higher domestic debt repayment with depreciated exchange rate. On specification (4), I change the regressors of exchange rate volatility to 1 year lagged exchange rate volatility. The idea is that if higher reserves can reduce the current exchange rate volatility, it is less likely that it can affect exchange rate volatility 1 year before, so that the link between lagged volatility and reserves reflects more of the positive precautionary motive. I use 1 year lag so that there is no intersection between lagged volatility and current reserves in the 1 year rolling window. The finding is similar that lagged exchange rate along is still significantly negative correlated with reserves, but the interaction term has a positive association with reserves. The main message from Table 2 is that there is a significant and robust negative relationship between reserves and exchange rate volatility along (without the interaction term), which motives the need to consider this channel in a quantitative structural model. Combing the information from Table 1, the empirical evidence is consistent with the argument that the interaction between foreign currency debt and exchange rate volatility can increase the sovereign s default risk and borrowing cost, which incentives the precautionary demand for reserve accumulation. Next I will build a sovereign default model to discuss how the interaction between foreign currency debt and exchange rate volatility can give rise to a severe default risk, and through which channels reserve accumulation can help the sovereign insures this risk. 3 Model 3.1 Framework The empirical section shows that emerging countries borrow extensively in foreign currency, which expose them to the risk of large exchange rate depreciation. Whenever exchange rate depreciates, the foreign debt burden in terms of domestic currency increases, making them harder to repay the debt. This potential vulnerability can provide precautionary demand for 11

12 reserve accumulation. To capture the currency mismatch problem and its link to the reserve accumulation, I construct a sovereign default model with following three novel features. Firstly I introduce nominal foreign currency assets. That is, the sovereign can only borrow long-term foreign currency bonds, and save in one-period liquid foreign currency reserves. Since the sovereign s endowment is in domestic currency, and its domestic price level is assumed to remain unchanged over time, the sovereign is exposed to the currency mismatch problem. Secondly, I add an exogenous nominal exchange rate shock to the model in addition to the standard output shock, which stochastically moves the sovereign s domestic currency value of its foreign currency debt and creates a currency risk to the sovereign through the currency mismatch problem. Thirdly I introduce an exogenously estimated link between reserves and exchange rate volatility, which captures the negative association between them in the data, and also allows the sovereign accumulating more reserves to reduce the exchange rate volatility and mitigate the currency mismatch problem. Next, I will present the detailed description of the model. 3.2 Environment Endowment Time is discrete and indexed by t = 0, 1, 2,... The endowment of representative agent is stochastic, which follows the standard AR(1) process as in quantitative sovereign default models: log y t = (1 ρ)µ + ρ log y t 1 + ε t, ρ < 1, ε t N(0, σ 2 ε). Here the endowment is in real value Preference Preference of the representative agent or the sovereign is given by: E t j=t β j t u(c j ), 12

13 where E is the expectation operator, β is the subjective discount factor, and c is the sovereign s real consumption. The utility function is strictly increasing and concave. The interpretation here is that the benevolent sovereign can borrow and lend from international financial markets, and then make transfer to its domestic hand-to-mouth agents to help them smooth consumption Nominal Exchange Rate Shock To make the balance sheet effect work through the currency mismatch problem, the exogenous nominal exchange rate shock ξ is introduced. The shock ξ aims to capture the short-run unanticipated movements of nominal exchange rate, which can increase or decrease domestic value of foreign currency debt. The exchange rate process is assumed to be exogenously determined, the reason is that since the dynamics of nominal exchange rate is disconnected from the fundamentals in the short-run 11, it is hard to endogenize the short-run exchange rate based only on the output shock. Instead of adding other shocks to determine the exchange rate, I choose to directly estimated the process of nominal exchange rate from the data. Moreover, since the empirical section documents a robust negative relationship between reserves and nominal exchange rate volatility. The volatility of nominal exchange rate is assumed to be determined by the foreign reserves level, which is time-varying. The time-varying feature of the nominal exchange rate volatility is consistent with the empirical estimation and forecasting of nominal exchange rate 12. The nominal exchange rate shock ξ t is defined as the net percentage depreciation of current nominal exchange rate compared with last period nominal exchange rate. Mathematically ξ t = e t e t 1 1, where e t denotes the nominal exchange rate, which is domestic currency value of 1 unit of foreign currency. If the exchange rate depreicates at time t, that is e t > e t 1 and ξ t > 0. Then 1 unit of foreign currency becomes more valuable in terms of domestic currency and 11 Gabaix and Maggiori (2015) summarizes the literature related to the exchange rate disconnect. 12 Erdemlioglu et al. (2012) provides a comprehensive summary of recent 30 years of different econometric specifications for estimating exchange rate process. Almost every specifications allow the volatility of exchange rate to be time-varying. 13

14 vice versa. Therefore the exchange rate shock ξ t can randomly fluctuate domestic value of foreign currency assets. The shock ξ t will be estimated as a AR(1) process with time-varying volatility. ξ t = ρ ξ ξ t 1 + υ t, ρ ξ < 1, υ t N(0, σ 2 t ), σ 2 t = exp(α 1 + α 2 ResPerGDP t ), where ResPerGDP t denotes the ratio between foreign reserves and GDP at the beginning of period t. In my calibration later, each period corresponds to a quarter, so 4 periods correspond to a year. Based on my estimation which is reported in the calibration section, the parameter α 2 is negative, which means that larger reserves can reduce the exchange rate volatility International Financial Markets The sovereign can issue long-term bonds from foreign investors, but only in foreign currency. To model the long-term bonds in a tractable way, I follow Aguiar et al. (2016), Hatchondo and Martinez (2009), and Chatterjee and Eyigungor (2013). Specifically, each long-term bond will pay a coupon every period up to and including the period of maturity. Without loss of generality, the coupon payment is normalized to the risk-free nominal interest rate r per unit of face value as in Aguiar et al. (2016). The benefit is that with this normalization, a unit of risk-free long-term bond will have a price of one. The long-term bond is assumed to mature randomly at probability δ [0, 1]. That is, for an outstanding long-term bond of measure b, a δ fraction b will mature this period and the associated debt repayment is (r + δ)b. The continuation face value of the long-term bond is (1 δ)b. If the sovereign changes its outstanding debt level at the end of this period to b. Then the net issuance this period is b (1 δ)b. With this setup, the expected maturity of the long-term bond is 1. The sovereign also has access to a one-period risk-free foreign δ currency reserves, that pays 1 + r each period. 14

15 3.2.5 Budget Constraints Firstly let me discuss the assumption on the domestic price level. Define the foreign price level p as the numeraire, therefore p t = 1 for all t. To model the currency mismatch problem, I assume that in the short run, domestic price is predetermined, that is, they are set a period in advance but can be adjusted fully after one period. Mathematically, it means that at the beginning of the period t, p t = p t 1. Only at the end of the period t, p t = p t e t according to the purchasing power parity. Under the setting, when the nominal exchange rate changes, the domestic currency value of foreign currency assets will change. Since domestic price level is fixed, the nominal change of foreign assets in domestic value will result in real change of foreign assets in terms of goods, which exactly replicates the currency mismatch. However, by setting a sticky domestic price, the purchasing power parity p t = p t e t does not always hold. There are two reasons for not imposing the purchasing power parity here. Firstly the model studies how short-run unanticipated exchange rate movements affect the sovereign s default risk, however, the purchasing power parity only approximately holds in the long-run instead of short-run, so it is reasonable to deviate from the purchasing power parity. Secondly since financial markets clear faster than good markets as in Dornbusch (1976), the short-run movements of nominal exchange rate can result in immediate change of foreign currency assets, however, the domestic price level can be sticky for a longer time. Next, I will present the budget constraints in both nominal and real term. Denote b t 0 as the measure of outstanding foreign currency long-term bond, ã t 0 as the measure of foreign currency reserves. Then without default, the nominal budget constraint is p t c t = p t y t (r + δ) b t e t + q t e t ( b t+1 (1 δ) b t ) + ã t e t ãt+1e t 1 + r, where q t is the foreign currency nominal price of the bond issued by the sovereign, (r + δ) b t is the foreign currency coupon payments and debt payments due, and all the terms are in nominal domestic currency. Now define b t+1 = b t+1 e t p t, a t+1 = ãt+1e t p t as the real value of foreign currency debt and reserves in terms of goods value at period t, when they are issued. The associated real 15

16 budget constraint is c t = y t (r + δ) b t e t 1 p t 1 Since ξ t = p t 1 e t + q t b t+1 e t q t(1 δ) b t e t 1 p t 1 e t + ãte t 1 p t 1 e t p t e t 1 p t p t 1 p t e t 1 p t 1 p t e t 1 et e t 1 1 and domestic price level is constant p t = p t 1, we have c t = y t (1 + ξ t )(r + δ)b t + q t (b t+1 (1 + ξ t )(1 δ)b t ) + (1 + ξ t )a t a t r, ãt+1e t (1 + r)p t. where all the terms are in real value now, and we can see that nominal exchange rate depreciation ξ t > 0 can result in real increase in foreign currency outstanding debt b t and also foreign currency reserves a t. Next, I will present the real budget constraint when the sovereign defaults. When the sovereign defaults, it does so on all current and future debt obligations. A default triggers exclusion from borrowing in credit markets for a stochastic number of periods. The sovereign will regain access to credit markets with a constant probability θ [0, 1]. In every period where the sovereign is excluded from credit markets, there is a real output loss of φ(y), which is important to help the model match the statistics on debt ratio and interest spread. In addition, I assume that during the default periods, there is no effect of using reserves to reduce exchange rate volatility α 2 = 0, and the exchange rate volatility will remain the highest value exp(α 1 ) until it regains access to credit markets. This assumption is consistent with the fact that during financial crisis, the exchange rate volatility shoots high, and the emerging countries does not primarily rely on reserves and foreign exchange interventions to absorb the shock (see Aizenman and Hutchison (2012)) 13. In case of default, the sovereign will still retain the control of their foreign reserves. Therefore the real budget constraint can be derived similarly c t = y t φ(y) + (1 + ξ t )a t a t r, where the sovereign can only save in reserves to smooth consumption. 13 Aizenman and Hutchison (2012) documents the fact and denotes the behavior as Fear of reserve loss. 16

17 3.2.6 Timing The timing within each period is as follows: First, the output shock and exchange rate shock are realized, where the variance of the exchange rate shock depends on the reserves at the beginning of the period. After observing these shocks, the sovereign chooses whether to default on its debt and then makes its borrowing and saving decisions. 3.3 Recursive Formulation The recursive formulation of the sovereign s problem is described here. The sovereign cannot commit to repay the debt. So in each period, the sovereign will compare the value of repayment and the value of default to make its repayment decision. Let V indicate the value function of a sovereign that is not in default. For any bond price function q, the function V satisfies the following functional equation: V (b, a, y, ξ) = max{v R (b, a, y, ξ), V D (a, y, ξ)}, (1) where the sovereign s value of repayment is given by subject to V R (b, a, y, ξ) = max {u(c) + βe a 0,b (y 0,c,ξ ) (y,ξ)v (b, a, y, ξ )}, (2) c = y (1 + ξ)(r + δ)b + q(b (1 + ξ)(1 δ)b) + (1 + ξ)a a 1 + r. The value of defaulting is given by: subject to V D (a, y, ξ) = max a 0,c u(c) + βe (y,ξ ) (y,ξ)[(1 θ)v D (a, y, ξ ) + θv (0, a, y, ξ )], (3) c = y φ(y) + (1 + ξ)a a 1 + r. The solution to the sovereign s problem gives the decision rules for default ˆd(b, a, y, ξ), debt 17

18 ˆb(b, a, y, ξ), reserves in default â D (a, y, ξ), reserves when not in default â R (b, a, y, ξ), consumption in default ĉ D (a, y, ξ), and consumption when not in default ĉ R (b, a, y, ξ). The default rule ˆd is equal to 1 if the sovereign defaults, and is equal to 0 otherwise. 3.4 Bond Prices Sovereign bonds and reserves are priced in a competitive market inhabited by a large number of identical risk-neutral international investors. Investors discount future payoffs at the riskfree rate 1 + r. This implies that in equilibrium the bond-price function solves the following functional equation: q(b, a, y, ξ)(1 + r) = E (y,ξ ) (y,ξ)[(1 ˆd(b, a, y, ξ ))(r + δ + (1 δ)q(b, a, y, ξ ))], (4) where b = ˆb(b, a, y, ξ ) a = â R (b, a, y, ξ ). This means that, in equilibrium, a risk-neutral investor is indifferent between selling a bond today, and keeping the bond to the next period. If the investor keeps the bond and the sovereign does not default in the next period, he will receive the coupon and the debt repayments (r + δ). In addition, his continuation value of bond worth (1 δ) times the price of a bond issued in the next period. 3.5 Recursive Equilibrium I emphasis on the Markov Perfect Equilibrium. That is, in each period the sovereign s equilibrium default, borrowing, and saving decisions depend only on the payoff-relevant state variables. Then a Markov Perfect Equilibrium is defined by a set of value functions V, V R and V D, rules for default ˆd, borrowing ˆb, reserves {â R, â D }, and consumption {ĉ R, ĉ D }, and a bond price function q, such that: (i) given a bond price function q, the policy functions ˆd, ˆb, â R, â D, ĉ R, ĉ D, and the value functions V, V R, V D solve the Bellman equations (1), (2), 18

19 and (3). (ii) given the sovereign s policies, the bond price function q satisfies condition (4). 4 Quantitative Results 4.1 Calibration and Function Form For the function form, the utility function displays a constant coefficient of relative risk aversion, u(c) = c1 γ 1, with γ 1. 1 γ The endowment shock follows the standard AR(1) process : log y t = (1 ρ)µ + ρ log y t 1 + ε t, ρ < 1, ε t N(0, σ 2 ε). At current stage, I let the nominal exchange rate shock follow another independent AR(1) process with constant variance σ 2 υ. ξ t = ρ ξ ξ t 1 + υ t, ρ ξ < 1, υ t N(0, σ 2 υ). For the default cost function, I follow Chatterjee and Eyigungor (2013). That is φ(y) = max{0, d 0 y + d 1 y 2 }, so that it is asymmetrically more costly to default in good times. For the calibration, the paper targets Mexico as the benchmark economy, since Mexico is a common reference for studies on emerging economics. The data for Mexico is mainly taken from International Financial Statistics and EMBI spread dataset from 1993Q4 to 2014Q4. Since the calibration uses quarterly data, a period in the model will correspond to a quarter in the data. There are total twelve parameters that need to be determined. The first three parameters discount factor β,default cost d 0, d 1 will be jointly calibrated to match three moments. These are the mean external debt-to-gdp ratio, the mean interest spread and the standard deviation of consumption over the standard deviation of output. 19

20 Four parameter values will be set directly. The risk aversion γ will be set to 2 as in the sovereign default literature. The risk-free rate r will be set to 1% to match the three-month US treasury bill real return. The probability of reentry θ will be set to to reflect that on average it takes three years for countries to regain access to credit markets after default. The debt duration δ will be set to 0.05 to match the 5 years average bond duration in Mexico as in Broner et al. (2013) The remaining five parameters µ, ρ, σ 2 ε, ρ ɛ, σ 2 υ for output shock and nominal exchange rate shock will be estimated based on the HP-filtered Mexico real output and the raw nominal exchange rate data from 1993Q4 to 2014Q4. The benchmark calibration result is shown in Table 3. Table 3: Parameter Values Discount factor β Output cost of defaulting d Output cost of defaulting d Risk aversion γ 2 Risk-free rate r 1% Probability of reentry after default θ Debt duration δ 0.05 Output autocorrelation coefficient ρ 0.94 Depreciation autocorrelation coefficient ρ υ 0.21 Standard deviation of innovations for output σ 1.5% Standard deviation of innovations for depreciation σ υ 8.18% Mean log output µ (1/2)σ 2 ε The interest spread can be calculated as follows. Firstly the yield i is calculated, which is defined as the return an investor would earn if he holds the bond to maturity and no default is declared. This yield satisfies i = r + δ q (1 δ) The sovereign spread is then computed as the difference between the yield i and the risk-free rate r. The annualized spread is used here: r s t = ( 1 + i 1 + r )4 1 20

21 4.2 Simulation Results Matching Moments In this section, the paper will firstly show how the model s calibration result matches the targeted and non-targeted moments. illustrate the mechanisms of the model. Then there will be three quantitative exercises to Table 4 shows that the model exactly matches the three targeted moments. For the nontargeted moments, the model also closely matches the standard deviation of trade balance, the correlation of consumption and output and the correlation of interest spread and output. Moreover, the model also generate reasonable 4% of reserve holdings. For the remaining nontargeted moments, the model is able to give the correct sign as in the data. Table 4: Simulation Statistics Model Data Mean Debt-to-GDP Mean r s σ(c)/σ(y) σ(r s ) σ(tb) ρ(c, y) ρ(r s, y) Mean Reserve-to-GDP ρ( a, y) ρ( a, r s ) The Role of Reserve Accumulation This section will illustrate the role of reserve accumulation. The tradeoff of reserve holdings is whether using the reserves to run down the debt exposures or increasing both debt and reserve level to capture the insurance benefit of reserves. The budget constraint can help understand the tradeoff. c = y (1 + ξ)(r + δ)b + q(b (1 + ξ)(1 δ)b) + (1 + ξ)a a 1 + r 21

22 With no new debt issuing, the future debt payment is b = (1 + ξ)(1 δ)b. Therefore, the exchange rate shock not only affect current debt and reserve level (1 + ξ)b, (1 + ξ)a, but also affect future debt payment (1 + ξ)(1 δ)b. A large depreciation will also push up future debt payment, resulting in higher future default probability, which results in a higher current borrowing cost. Therefore, with no reserve holdings, when borrowing is costly, the sovereign has to choose either repaying the debt and suffering large drop in consumption, or defaulting. Since the debt is long-term, the sovereign can increase the total debt exposures without increasing debt payments due in each period much, and save part of the borrowing as reserves. In this case, reserves can help smooth consumption when facing tight borrowing constraint. Another important role of reserve holdings is the currency hedging. Since both debt and reserves are denominated in foreign currency, even if large depreciation happens, the increase in reserve (1 + ξ)a can help increase the consumption. The last role of reserves to stabilize exchange rate volatility will be discussed in later quantitative exercise The Effects of Exchange Rate Volatility Table 5: The Effects of Exchange Rate Volatility Std(ɛ t ) Mean Debt-to-GDP Mean Reserve-to-GDP Mean r s Default Rate per 100 Years Table 5 illustrates how different exchange rate volatility will affect sovereign s borrowing and reserve accumulation decisions. Here the exchange rate shocks take the calibrated persistent value of 0.21, but vary with different standard deviations: ξ t = 0.21ξ t 1 + υ t, υ t N(0, σ 2 υ). The result shows a clear pattern that more volatile exchange rate process will lead to less 22

23 borrowing, more reserve accumulation, higher spread and higher default probability. The intuition is that as the exchange rate becomes more volatile, a shock with larger depreciation becomes more likely, increasing the current and future debt burden in terms of domestic currency. Moreover, a larger future debt payments suggest higher chance of default in the future, which reflects as a higher borrowing cost today. If it is expensive to borrow today to rollover the debt, the sovereign will suffer the large drop in consumption or the default output cost. To get less exposure to the shock, the sovereign optimally choose to reduce borrowing. The quantitative exercises also generate large reserve holdings and it increases with exchange rate volatility. The idea is that since sovereign issues long-term debt, large reserves accumulation will increase the total debt payment, but not much increase in the debt payments due in each period. Therefore, the sovereign can accumulate reserves to smooth consumption against bad shocks and tighter borrowing conditions, and also hedge against depreciation in exchange rate. As the exchange rate becomes more volatile, the demand for precautionary safe assets increases Reserve Accumulation for Less Exchange Rate Volatility Here I allow the reserves to reduce the exchange rate volatility. simple way, the paper uses the following exchange rate process: To implement this in a ξ t = 0.21ξ t 1 + υ t, std(ξ t ) = if Res < 0.09 std(ξ t ) = 0.04 if Res > 0.09 where Res indicates the Res-to-GDP ratio. The 9% cutoff value reflects the mean Res-to- GDP ratio observed in the Mexico s data. The two different exchange rate standard deviation value are calculated separately for the period when the Res is above and below the cutoff. The result in Table 6 shows that if larger reserve holdings can reduce the exchange rate volatility, there will be stronger incentive to accumulate the reserves. In addition, the associated exchange rate volatility will also be lower. This is consistent with the empirical pattern 23

24 Table 6: Simulation Results Mean Debt-to-GDP Mean Reserve-to-GDP 5.5 4,0 Mean r s ρ(exvol,reserve) ρ(exvol,spread) ExVol that there is a robust negative association between reserves and exchange rate volatility. 5 Conclusion The paper investigates how the exchange rate volatility affects the sovereign s default risk and the incentive to accumulate reserves. The benchmark model considers an environment where the sovereign can only borrow external debt in foreign currency and subject to volatile exchange rate fluctuations. Whenever the exchange rate depreciates, the debt burden in terms of domestic currency increases, leading to a higher default risk and borrowing cost. The paper proposes three channels through which reserve accumulation can insure against volatile exchange rates. Specifically, it can help smooth consumption when rollover debts becomes costly, hedge against depreciation in exchange rate, and stabilize the fluctuations in exchange rate. Moreover, in the quantitative exercises, the baseline model can generate half of the reserve holdings. If reserves can reduce the volatility of exchange rate, the model can generate 60 percent of actual reserve holdings. 24

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