A Tale of Two Countries: Sovereign Default, Trade, and Terms of Trade

Transcription

1 MACROECON & INT'L FINANCE WORKSHOP presented by Grace Gu FRIDAY, Oct. 30, :30 pm 5:00 pm, Room: HOH-706 A Tale of Two Countries: Sovereign Default, Trade, and Terms of Trade Grace W. Gu August 3, 2015 (click here for the latest version) Abstract Sovereign defaults are associated with income and trade reductions and termsof-trade deterioration. This paper develops a two-country model to study the interactions between foreign-debt default risk, income, trade, and terms of trade. Debt crises are costly because they adversely affect the vertical integration of production between the creditor and the borrower. Consequently, trade flows change due to income losses and home bias in consumption. The defaulter s terms of trade also deteriorate endogenously, which accelerates its income and trade losses. The model produces procyclical imports, exports, and terms of trade, and other empirical features of Mexicos business cycles and default episodes. Keywords: sovereign default, terms of trade, real exchange rate, trade, DSGE. JEL code: F34 - F41 - F44 Gu: Department of Economics, UC Santa Cruz, Engineering 2 Building, Room 463, Santa Cruz, CA 95060, grace.gu@ucsc.edu. I thank Laura Alfaro, Yan Bai, Paul Bergin, George Bulman, Michael Dooley, Fabio Ghironi, Michael Hutchinson, Ken Kasa, Ken Kletzer, Huiyu Li, Eswar Prasad, Katheryn Russ, Ina Simonovska, Alan Spearot, Viktor Tsyrennikov, Carl Walsh, Beiling Yan, Vivian Yue, as well as many others, for their incredibly helpful discussions. This paper has also benefited from comments from conference/seminar participants at Cornell, AEA-Boston, UC Davis, UC Riverside, UC Santa Barbara, UC Santa Cruz, Santa Clara Univ, Atlanta Fed, Peking Univ, Tsinghua Univ, San Francisco Fed, and NBER Summer Institute.

2 1 Introduction Sovereign debt default events are associated with three empirical regularities: (a) deep recessions, (b) a decline in international goods trade, and (c) deteriorating terms of trade and real exchange rates. Recent evidence shows that, across countries, default episodes have on average been accompanied by a GDP drop of 5 percent below trend, a bilateral trade value decline of 8 percent, and real depreciation of percent. 1 However, these three phenomena have not been addressed simultaneously by existing sovereign default models. This paper fills the gap by studying how foreign-debt default risk and occurrences endogenously interact with income, terms-of-trade, and international goods trade through production vertical integration in a two-country DSGE model. 2 The model features four key elements. First, the model has default risk and occurrences (as in Eaton and Gersovitz, 1981; Aguiar and Gopinath, 2006; Arellano, 2008; and Mendoza and Yue, 2012). The second key element is consumption home bias in both countries. In the model, I show that as the borrower country s default risk increases with debt, its budget constraint tightens and its terms of trade deteriorate due to home bias and reduced world relative demand for its final good. Deterioration in the terms of trade prevents the borrower country from real appreciation that could have eased the debt burden denominated in the creditor country s final good. Thus, the default risk increases further. In this way, the default risk interacts with the terms of trade and the real exchange rate prior to a sovereign default. The third key element of the model is vertical integration of production, where some firms in the creditor country import an intermediate good from the borrower country to produce a final good. 3 The last key element of the model is a default penalty through the vertical integration. When a large adverse productivity shock causes the borrower country to default, the event triggers an efficiency loss in the creditor-country firms operations regarding the intermediate good input from the defaulting country, which causes the demand for the intermediate good to decline. Empirical analyses indicate such efficiency loss exists. Specifically, this paper finds that Canadian output was negatively affected by Mexican default events and the size of 1 See Rose (2005), Cuadra and Sapriza (2006), Reinhart and Rogoff (2011), and Mendoza and Yue (2012). 2 As illustrated in the model and result sections of this paper, the two-country model differs from a small open economy model in offering unique insights about bond market equilibrium pricing and the impact of a sovereign default on a creditor country s income. 3 Here the vertical integration is narrowly defined. It does not include activities where creditor country firms export an intermediate good to borrower country. Mendoza and Yue (2012) use this latter channel for a default penalty. 1

3 the impact increases with an industry s dependency on Mexican inputs. Moreover, the efficiency loss in vertical integration is also consistent with other papers empirical findings that foreign firms activities (e.g., FDI, offshoring, and other global sourcing) are more severely damaged than domestic firms in a crisis country, possibly due to crisis-elevated trade costs, information asymmetry, and risk aversion (e.g., Brennan and Cao, 1997; Tille and van Wincoop, 2008; Milesi-Ferretti and Tille, 2010; and Broner, Didier, Erce, and Schmukler, 2013). 4 The decline in foreign demand for the intermediate good upon default in the model generates an income loss additional to that from the initial adverse productivity shock in the defaulting country. Its wealth declines relative to the creditor country s because its overall income loss exceeds the gain from not repaying the debt. This reduces the world relative demand of the defaulting country s final good, due to home bias in consumption. Therefore, its terms of trade and real exchange rate deteriorate, taking a third toll on income and trade. In this way, the model builds an endogenous terms-of-trade mechanism by which a sovereign default amplifies the effects of adverse productivity shocks on the borrower country s income and trade. 5 This paper contributes to the literature by examining the role of vertical integration for both creditor and borrower countries during sovereign debt crises. In particular, it incorporates the impact of sovereign default on creditor-country firms vertically integrated production activities with the defaulting country. This produces a sovereign-default cost to both the creditor and the borrower countries, which affects their debt contract. The second contribution of this paper is that it studies the endogenous consequences of a sovereign default to income, trade, terms of trade, and real exchange rate, and thus how they affect the incentives to default. For one thing, the model captures reductions in trade flows during default episodes, which have been well studied in the empirical literature (e.g., Rose, 2005), but not in the theoretical literature. Modeling this stylized fact helps us understand how a country s consumer preferences regarding home goods and imports affect its propensity to default (Rose and Spiegel, 2004; Rose, 2005). 6 For another, this paper endogenizes terms of trade and real exchange rate in a sovereign 4 Moreover, Fuentes and Saravia (2010) find that a default event can reduce FDI inflows by 72 percent. Aizenman and Marion (2004) also document that greater supply uncertainty reduces the expected income from vertical FDI. 5 It is worth emphasizing that, as in previous sovereign default models, this paper s default also arises in equilibrium as an optimal decision of a benevolent government. 6 Past empirical research suggests that less outward-oriented sovereigns are more willing to default. Therefore, if a sovereign government internalizes its citizens desire for imported goods, we can begin to consider how a country s reduced desire for foreign goods can spur defaults, or how we can motivate the country to service its debt on time. 2

4 default model. It captures their two-way interaction with default risk prior to sovereign default occurrences. During sovereign default events, it also captures the terms of trade and real exchange rate deteriorations as they contribute to a defaulting country s income and trade losses. For instance, for 45 sovereign default episodes in 27 developing countries over the period , on average at least half of the defaulting countries losses of output and export value came from real depreciation. 7 Therefore, the terms of trade and real exchange rate in my model results in an endogenous penalty on income and trade upon default. That is, unlike many previous sovereign default models, this model does not rely on an exogenous endowment loss. 8 In a quantitative exercise, I apply the model to the Mexican debt crises in the 1980s and the country s business cycles for the period of 1981Q1-2012Q4. 9 This model generates three empirical features of emerging markets business cycles and their sovereign default episodes. First, it delivers countercyclical trade balances and procyclical trade flows. Second, the model supports high bond spreads that are also countercyclical. Third, the model accounts for terms-of-trade deterioration, real depreciation, and trade flow and GDP declines during and right after a sovereign default. To further study the role of terms of trade in affecting income, I examine the model results where GDP and trade losses are partially due to terms-of-trade deterioration and partially due to volume changes, as in the data. I also evaluate the welfare of both countries, as the welfare of the creditor country is often left out of existing sovereign default models. This reveals that upon default, both countries welfare declines, but higher vertical integration and maintaining healthy foreign business environment reduce their post-default welfare losses. In explaining the cyclical movements of trade balances and terms of trade, this paper is related to other studies in the international business cycle literature. 10 But many of them ruled out actual default events in equilibrium, unlike this model. Thus this paper is closely related to sovereign debt literature (e.g., Grossman and Van Huyck, 1988; Kletzer and Wright, 2000; Alfaro and Kanczuk, 2005), especially to previous quantitative small- 7 The relevant figure is not included in this version of the paper due to space limitation, but is available upon request. All data are real, logged, and HP-filtered. Raw data sources are detailed in the Appendix. 8 It is similar to Mendoza and Yue (2012), where their model endogenizes output losses by a production efficiency loss due to a default-triggered decline of trade credit to import inputs. 9 I chose Mexico for this two-country model because Mexico has a relatively large open economy among the countries that have recently defaulted, as well as relatively large vertically integrated sectors involved in foreign production, including its maquiladora sector (Zlate, 2012). 10 These include but are not limited to works by Backus, Kehoe, and Kydland (1992, 1994), Mendoza (1995), Stockman and Tesar (1995), Heathcote and Perri (2002), Kehoe and Perri (2002), Kose (2002), Broda (2004), Iacoviello and Minetti (2006), Bodenstein (2008), and Raffo (2008). 3

5 open-economy sovereign default models, such as those by Aguiar and Gopinath (2006), Arellano (2008), and Mendoza and Yue (2012), based on Eaton and Gersovitz (1981). They have made significant contributions to endogenizing default risk (and income), as well as to accounting for key empirical patterns of developing countries business cycles and default episodes. However, those models do not focus on default-triggered changes to trade flows and the terms of trade. A few recent sovereign default papers (Cuadra and Sapriza, 2006; and Bleaney, 2008; Popov and Wiczer, 2014) have examined the roles of exogenous terms-of-trade shocks and exogenous terms-of-trade default penalty in small open economy models. The inclusion of endogenous terms of trade and real exchange rate distinguishes this paper from them. Na, Schomitt-Grohe, Uribe, and Yue (2014) also include endogenous exchange rate but focus on optimal exchange rate policy. Like the model in this paper, their model achieves concurrent default and depreciation. However, their depreciation is driven by wage rigidity and the government s intention to reduce unemployment, whereas this model s depreciation is associated with consumption home bias and changes to trade flows. Most recently, Asonuma (2014) has also endogenized the real exchange rate in a two-country sovereign default model, but through a different mechanism in endowment economies. 11 paper, I use production economies to incorporate richer business cycle fluctuations. In this In addition, this paper complements the vast literature about international trade and financial crises with incomplete markets, especially for emerging economies (e.g., Mendoza 2002, 2003, 2010). More specifically, it fits in the existing strand that focuses on the connection between international trade and sovereign defaults, and the strand on the connection between trade and exchange rate. In the former strand, which consists largely of empirical studies, Rose (2005) documents that a default can reduce real bilateral trade value (in USD) by 8 percent for an extended period after the event. However, it remains unclear why trade declines. The four hypotheses trade sanctions, trade credit collapse, asset seizures, and reputation are commonly mentioned, but the empirical evidence supporting them remains ambiguous (Martinez and Sandleris, 2011; Tomz and Wright, 2013). One exceptional theoretical model is proposed by Bulow and Rogoff (1989), who apply creditors seizures of a defaulting country s exports. This paper instead incorporates vertical integration and terms of trade to examine the interaction between trade and sovereign defaults. In the latter strand of literature on trade and exchange rate, this paper is related to works by Baldwin and Krugman (1989), Alessandria, Kaboski, and Midrigan (2010), Engel and Wang 11 Asonuma (2014) uses traded and non-traded goods to generate real depreciation in his model, similar to the idea proposed by Arellano and Kocherlakota (2014). 4

6 (2011), Drozd and Nosal (2012), and Alessandria, Pratap, and Yue (2014). My model differs by endogenizing default risk in interest rates. The remainder of this paper is organized as follows. Section 2 describes the model environment, equilibrium, and mechanisms. Section 3 provides the model calibration and quantitative results. Section 4 concludes. 2 Model 2.1 Environment In this section, I describe a dynamic model of two countries with endogenous sovereign default, terms of trade, real exchange rate, and risk averse agents. In the model, the two countries (i = 1, 2) trade one-period discount bonds, produce two unique final goods (j = 1, 2), respectively, and consume both through trade. The two final goods are imperfect substitutes with constant elasticity, and c ij stands for country i s consumption of final good j. p j stands for the final good j s price, and country 1 s final good price p 1 is normalized to 1. I assume that the nominal exchange rate between the two countries is 1, and thus the real exchange rate is the ratio of country 2 s over country 1 s aggregate price index. When the ratio decreases, country 2 experiences real depreciation. I set country 1 to be the creditor who never defaults and has constant productivity e 1 ; country 2 is the borrower who has an option to default on its sovereign bonds and faces stochastic productivity e 2 that follows a Markov chain. 12 Creditor country 1 has a fixed amount of capital, k 1, which can be paired either with a fixed amount of domestic labor n 1 to produce the final good 1, or with an imported intermediate good produced by borrower country 2 s labor to produce the same final good 1. I use k 1 to denote capital used with domestic labor, k m to denote that used with imported intermediate inputs, and k 1 + k m = k Borrower country 2 has a fixed amount of labor, n 2. It is divided into n m who produce intermediate inputs for creditor country 1, and n 2 = n 2 n m who produce final good 2 with domestic capital k One way to interpret the creditor country s constant productivity is that it always can smooth its production through other financial channels that are not in this model, regardless of the situation in the bond market with the borrower country. Moreover, since the creditor country never defaults, it is not of interest in this paper to complicate the model results by including its productivity shocks. It would be of future research interest, however, to study the spillover effects when a creditor country s productivity shocks trigger a borrower country s sovereign default. 13 Another setup is creditor country 1 s imported intermediate good and domestic labor directly substitute each other imperfectly as inputs, and produce final good 1 with capital. Similar results are expected, but it emphasizes the role of labor substitution in the creditor country, whereas the current setup emphasizes the role of capital allocation and has the flexibility to alternatively interpret k m as FDI. 5

7 Three reasons stand out for this asymmetric model setup, where creditor country 1 allocates capital and borrower country 2 allocates labor and produces the intermediate good for exporting. First, many of the countries that have recently defaulted are developing or emerging economies, where labor tends to be abundant and is used to produce intermediate goods for export, through vertical FDI, offshoring, and other global sourcing activities. Second, even though creditor country 1 does not produce intermediate goods, its domestic labor input is an imperfect substitute for the imported intermediate good and can be considered as creditor country 1 s own implicit intermediate inputs. Third, the impact of a sovereign default on the demand for borrower country 2 s intermediate good exports serves as one of the default penalties in the model. Even though the data show defaulting countries intermediate good imports are also usually damaged, I extract it from this paper because the inclusion makes it difficult to single out the impact of the intermediate good export reduction upon default as a penalty, which is the focus of this paper. The current setup keeps the model tractable, yet retains a connection to reality. integration in future research. 14 However, it is interesting to include more channels of global It is also worth noting that borrower country 2 produces the intermediate good only for export, not for domestic use. It is to distinguish the globally integrated production activities from purely domestic activities in the borrower country. Because the two types of activities are affected differently by crises, according to empirical studies mentioned in the introduction. Meanwhile, we can consider those intermediate goods for domestic use to be embedded in the value of borrower country 2 s final good 2. In the bond market, a non-state-contingent one-period bond denominated in the creditor country s final good 1 is traded between the two countries. The bond is denoted as b i for country i s asset holdings. The borrower country s default can be triggered by negative productivity shocks and can happen along the equilibrium. The two countries hold their own beliefs/concerns about borrower country 2 s default probabilities, while the actual default probabilities are endogenous to debt holding and fundamental. Risk-averse creditors in country 1 are willing to offer debt contracts that in some states may result in a default by charging a high interest rate. Hence, equilibrium interest rates reflect the two countries concerns about the default probabilities, as well as the creditor s consumption changes and risk aversion (Lizarazo, 2013). The timing of this model is as follows. Both countries start off with initial sovereign bond assets. After they observe the current productivity shock, borrower country 2 decides 14 Mendoza and Yue (2012) use a default-triggered intermediate good import reduction as the default penalty and reach a similar output-loss result as this paper does. 6

8 whether to repay its debt. If it does not default, bond market equilibrium determines the bond price and the next period s quantity. If it defaults, both countries enter financial autarky and return with a certain probability, and creditor country 1 firms operations with the intermediate good from borrower country 2 suffer from an efficiency loss. Then accordingly, both countries reallocate their capital and labor. And last, production, trade, and consumption take place. The following sections describe the model specifications. 2.2 Country 1: Creditor Creditor country 1 has two types of agents: representative firms, and households Firms Firms hire domestic workers n 1, rent capital from households, choose capital allocation {k 1, k m }, and decide how many intermediate good inputs to import from borrower country Firms goal is to maximize their profits, taking wage w 1, capital rent r 1, and intermediate good price p m as given: Π 1 = { max e1 n α 1 1 k 1 α 1 1 w 1 n 1 r 1 k 1 + e 1 (εq m ) α 3 } k 1 α 3 m p m q m r 1 k m n 1,q m,k 1,k m (1) The first three terms are the profit the firms gain from using domestic labor n 1 to produce final good 1. The last three terms are the profit the firms gain from using intermediate inputs εq m to produce final good 1, after deducting intermediate good costs and capital rents. ε symbolizes the firms efficiency of operating with the intermediate good from borrower country 2. When the borrower country is not in default, ε = 1. When the borrower country is in default, a small portion of its intermediate good used by country 1 s firms is lost in operation. More specifically, during default episodes ε = min(ɛ ē2 e 2, 1), where 0 < ɛ < 1 and ē 2 is borrower country 2 s average productivity. This formulation has four indications. First, creditor country 1 firms production using the foreign intermediate good suffer from an additional efficiency loss on top of the defaulting country s negative aggregate productivity shock that lowers its intermediate good production in the first place. 16 This 15 The model results would not be different if country 1 s firms internalize the production decision of the intermediate good sector in borrower country 2. The arrangement would be similar to that used in the global sourcing literature (Antras and Helpman, 2004). But the current setup helps the model clarify that the default-triggered efficiency loss is on the creditor country firms operations, not directly on the defaulting country firms and their intermediate good production and exports. 16 Unless the aggregate productivity in defaulting country 2 is already lower than ɛē 2. The model calibration ensures that min(e 2 ) > ɛē 2. 7

9 setup reflects the empirical findings that foreign firms activities (e.g., FDI, offshoring, and other global sourcing) are more severely damaged than domestic firms activities in a crisis country, as evidenced by but not limited to Brennan and Cao (1997), Tille and van Wincoop (2008), Milesi-Ferretti and Tille (2010), and Broner, Didier, Erce, and Schmukler (2013). Second, the default-triggered efficiency loss lies only in the foreign operations of country 1 s firms, not in defaulting country 2 s firms, given that the latter are already subject to the negative aggregate productivity shocks that trigger sovereign defaults. Hence, the model assumes that default events and efficiency losses in ε do not directly affect the supply of the intermediate good. It is country 1 firms demand of the intermediate good that is directly affected, possibly due to defaulting country 2 s worsened foreign business environment and/or crisis-elevated trade costs and information asymmetry that cause country 1 firms marginal cost of operating with the imported intermediate good to rise. Third, the efficiency loss is applied only to country 1 firms production using imported inputs from the defaulting country, not to their production using domestic inputs, for which this paper provides empirical support. In the regression analysis, Mexico is used for the defaulting country and Canada for the creditor country, as in the model calibration. I collect Canadian monthly output data on 13 manufacturing industries for the period from January 1981 to October After controlling for crisis-impacts from the U.S., Canadian business cycles, and industry-specific trends and other factors, I find negative impacts of Mexican sovereign default episodes on Canadian manufacturing outputs. Moreover, a Canadian industry that uses more Mexican inputs is more negatively affected by those default episodes than an industry that uses less Mexican inputs. See the Appendix for more details. Last, the formulation of ε generates efficiency losses and default penalties that increase with defaulting country 2 s productivity state, such that, all else being equal, the borrower country has a larger incentive to default at a lower productivity state. This is consistent with previous sovereign default models (Arellano, 2008) Households Households in creditor country 1 supply fixed amounts of capital k 1 and labor n 1 to the firms. They use the proceeds from firms for consumption to maximize a standard timeseparable utility function E[ t=0 βt 1U(c 11t, c 12t )], where 0 < β 1 < 1 is the discount factor and U(.) is a one-period utility function that is continuous, homothetic, strictly increasing and concave, and satisfies the Inada conditions. More specifically, based on Krugman 8

10 (1980), I use an additive separable utility function U(c 11t, c 12t ) = ρ 1 c θ 1 11t + (1 ρ 1 )c θ 1 12t, 1 where 0 < ρ 1, θ 1 < 1. The elasticity of substitution is constant at This utility 1 θ 1. function assumes independence between the domestic final good and the imported final good in marginal utility, and brings tractability and computability to this model. Households also choose how many of the one-period non-state-contingent bonds issued by borrower country 2 to purchase, given the bond price q. Hence, their expected lifetime utility depends on borrower country 2 s default decisions. When the borrower country does not default in the current period, the creditor country households optimization problem can be written recursively as: V 1c (s, b 1 ) = max b 1,c 11,c 12 U(c 11, c 12 ) + β 1 [ V 1c(s, b 1)dF 1 (s s) + V 1d(s )df 1 (s s)] s / D 1 (b 2 ) s D 1 (b 2 ) where b i is country i tomorrow s bond asset holding, and s is the aggregate state of the two economies. F 1 and D 1 are creditor country 1 households beliefs about borrower country 2 s productivity process and default set, respectively, which I explain in the next section. The household problem is subject to: s / D 1 (b 2 ) V w 1 n 1 + r 1 k1 + b 1 = c 11 + p 2 c 12 + qb 1. (3) where q = β 1 λ 1, and λ 1 is the multiplier of the budget. When a default happens, bond assets are set to zero, both countries undergo financial 1c / b 1 df 1(s s) autarky, and only with a certain probability 0 < φ < 1 can they resume bond trading. Some may argue that it is not realistic to also exclude the creditor from the international financial market. But since the creditor country has no productivity shock, its consumption losses from the bond market exclusion are reduced. The creditor country s constrained maximization problem becomes: V 1d (s) = max c 11,c 12 {U(c 11, c 12 ) + β 1 E 1 [φv 1x (s, 0) + (1 φ)v 1d (s )]} (4) where V 1x = [V 1d (s) or V 1c,b1 (s) borrower country 2 defaults or not]. The problem is subject to (2) w 1 n 1 + r 1 k1 = c 11 + p 2 c 12. (5) Given the above setup, I calculate creditor country 1 s GDP as the gross production 9

11 of final good 1 minus the cost of the imported intermediate good, i.e., e 1 n α 1 1 k 1 α 1 e 1 (εq m ) α 3 k 1 α 3 m p m q m. Note that its GDP value and volume are the same in the model because its final good price is p 1 = Country 2: Borrower/Defaulter Country 2 has four types of agents: intermediate good firms, final good firms, households, and a government Intermediate Good Firms Intermediate good firms produce intermediate good inputs for creditor country 1 firms final good 1 production. They decide how many domestic workers to hire, n m, and labor is the only input needed for the intermediate good production. I assume the production to be linear in n m and associated with the country s aggregate productivity e 2. The firms maximize the following profit: max n m {p m e 2 n m p 2 w m n m } (6) Note that the supply of the intermediate good is not directly affected by ε, even though the equilibrium quantity is. From the first order condition, we have p m = p 2w m e Final Good Firms Country 2 s final good firms rent capital k 2, hire domestic workers n 2 to produce final good 2. They maximize the following profit: where w 2 is domestic sector wage. max{p 2 e 2 n α 2 2 k 1 α 2 2 p 2 w 2 n 2 p 2 r 2 k 2 } (7) n 2,k Households Households in borrower country 2 supply labor n 2 and capital k 2. They derive income from two sources: wages from producing the intermediate good for creditor country 1, and wages and capital rent from domestic final good firms. Their utility is a standard timeseparable homothetic function of a consumption bundle E[ t=0 βt 2U(c 21t, c 22t )], where 0 < β 2 < 1 is the discount factor. Similar to creditor country 1, the one-period utility function is specified as U(c 21t, c 22t ) = (1 ρ 2 )c θ 2 21t + ρ 2 c θ 2 22t, where 0 < ρ 2, θ 2 < 1. The 10

12 elasticity of substitution is constant at 1 1 θ 2. As in Mendoza and Yue (2012), households do not borrow directly from abroad, but the government chooses a debt policy internalizing the utility of households, taking as given the wages and the capital rent Government Country 2 s sovereign government issues one-period non-state-contingent discount bonds, so the asset market is incomplete. It cannot commit to repaying its debt, it compares the value of repaying debt V 2c and that of default V 2d and chooses the option that provides the greater value, that is: V 2x (s, b 2 ) = max {V 2c (s, b 2 ), V 2d (s)} (8) The nondefault value is given by the choice of (b 2, c 21, c 22 ) that maximizes the following problem, taking wages, capital rent, p 2, and bond price q as given: V 2c (s, b 2 ) = max b 2,c 21,c 22 U(c 21, c 22 ) + β 2 [ V 2c(s, b 2)dF 2 (s s) + V 2d(s )df 2 (s s)] s / D 2 (b 2 ) s D 2 (b 2 ) (9) subject to p 2 w 2 n 2 + p 2 r 2 k2 + p 2 w m n m + b 2 = c 21 + p 2 c 22 + qb 2. (10) where F 2 and D 2 are the government s beliefs about its country s productivity process s / D 2 (b 2 ) V and default set, respectively. q = β 2 λ 2, and λ 2 is the multiplier of the budget constraint. It is worth noting that here the government takes q as given, which 2c / b 2 df (s s) differs from previous small open economy sovereign default models, where the borrower follows a bond price schedule set by the creditor and understands its debt choice can affect the bond price accordingly. In the event of a default triggered by an adverse productivity shock to the borrower country, the foreign demand for the defaulting country s intermediate good declines due to an efficiency loss in foreign firms operations with those inputs. Meanwhile, both countries enter financial autarky as their bond assets are set to zero, and return to bond trading with probability 0 < φ < 1. There is no other direct penalty, such as exogenous endowment loss or trade sanctions. 17 However, in equilibrium the defaulting country does suffer other 17 There lacks empirical evidence in the literature that other countries impose trade sanctions on defaulting countries (Martinez and Sandleris, 2011; Tomz and Wright, 2013). 11

13 endogenous losses, as discussed in the mechanism section. Taking into account all the consequences of a sovereign default, the borrower country s default value is as follows: V 2d (s) = max c 21,c 22 {U(c 21, c 22 ) + β 2 E 2 [φv 2x (s, 0) + (1 φ)v 2d (s )]} (11) subject to p 2 w 2 n 2 + p 2 r 2 k2 + p 2 w m n m = c 21 + p 2 c 22 (12) The definitions of the actual default set D and the actual probability of default are standard from Eaton-Gersovitz type models (also see Arellano, 2008). Default set D at each current debt level b 2 is a collection of exogenous states when borrower country 2 s government strategically chooses to default to maximize its value: D(b 2 ) = {s S : V 2c (s, b 2 ) < V 2d (s)} (13) Because no one can be certain about the aggregate state tomorrow, the actual default probability π is the sum of all the probabilities of tomorrow s states where the borrower country will choose to default, given the debt level: π(s, b 2) = f(s, s )ds (14) s D(b 2 ) This default probability exists whether or not the borrower or the creditor country considers the default risk when issuing or purchasing bonds. It is possible for two countries to have different beliefs/concerns about the actual default set or the actual default probability. That is, π 1 (s, b 2) = s D 1 (b 2 ) f 1(s, s )ds, π 2 (s, b 2) = s D 2 (b 2 ) f 2(s, s )ds, and {D, D 1, D 2 } and {π, π 1, π 2 } are not necessarily equal to each other, respectively. More discussion about the two countries beliefs about the default probability is in the equilibrium bond price section. Given the above setup, I calculate borrower country 2 s GDP value as the gross production of final good 2 plus the intermediate good exports, p 2 e 2 n α 2 2 k 1 α p m e 2 n m, and its GDP volume as e 2 n α 2 2 k 1 α e 2 n m. 2.4 Equilibrium Finally, in equilibrium all goods, capital, labor, and bond markets clear for both countries in default and nondefault regimes. Also, in the borrower country, the intermediate good sector per-worker wage is equal to the wage paid in its domestic production sector, so 12

14 that there is no labor flowing between the two sectors. The equilibrium conditions are formulated and defined as follows: b 1 (s, b 1 ) + b 2 (s, b 2 ) = 0 in nondefault regime, (15) or b 1 (s, b 1 = 0) = 0 & b 2 (s, b 2 = 0) = 0 in default regime (16) and n 1 = n 1, k 1 + k m = k 1, n 2 + n m = n 2, k 2 = k 2, w m = w 2, (17) e 1 n α 1 1 k 1 α e 1 (εq m ) α 3 k 1 α 3 m = c 11 + c 21, e 2 n α 2 2 k 1 α 2 2 = c 12 + c 22, e 2 n m = q m. (18) Definition 1 A recursive competitive equilibrium is defined as a set of functions for (a) creditor country 1 s capital allocation and borrower country 2 s labor allocation; (b) both countries household consumption policy c and saving policy b ; (c) welfare value V at default and nondefault regimes; and (d) the law of motion for the aggregate state s, such that: (i) the borrowing and lending policies satisfy the problem s first-order conditions; (ii) the two countries value functions satisfy Bellman Equations; (iii) r 1, r 2, p m, p 2 and q clear the capital, goods, and bond markets; (iv) w m and w 2 stabilize labor flows between the two sectors in borrower country 2; and (v) the law of motion is consistent with the stochastic processes of e 2. Borrower country 2 s terms of trade are calculated using unit value index, as in the World Bank data; and its real exchange rate is two countries CPI ratio using Laspeyres price index. 18 More specifically, they are calculated as follows: T OT 2t = (p t 2 ct 12 +pt m qt m )/(ct 12 +qt m ) (p 0 2 c0 12 +p0 m q0 m )/(c0 12 +q0 m ) p t 1 ct 21 /ct 21 p 0 1 c0 21 /c0 21 REXR 2t = NEXR (pt 2c p t 1c 0 21)/(p 0 2c p 0 1c 0 21) (p t 2c p t 1c 0 11)/(p 0 2c p 0 1c 0 11) (19) (20) Mechanism This section summarizes the important mechanisms in this model. First of all, prior to a default, how is default risk linked with trade and the terms of trade? As the borrower country accumulates debt, its default risk and the equilibrium bond interest rate rise. The higher cost of debt reduces the borrower country s available funds for consumption relative to the creditor country s; thus, owing to home bias in both countries, the world 18 The qualitative results do not change if using Paasche price index. 13

15 relative demand of final good 2-to-1 decreases. 19 Decreasing relative demand of final good 2-to-1 puts downward pressure on the relative price p 2, preventing the borrower country from improving terms of trade to ease its budget constraint and debt burden. Hence, when the terms of trade deteriorate because of higher default risk, in turn, the deterioration increases the borrower country s default risk. Once a large enough adverse productivity shock causes borrower country 2 to default, the mechanism affecting income, trade, and terms of trade works as follows. The default triggers an efficiency loss to the creditor country firms operations using the defaulting country s intermediate good, which has several effects. First, the demand of the intermediate good declines, resulting in a lower p m. Second, creditor country 1 s firms have to reallocate capital away from combining with the imported intermediate good, and towards its domestic labor to produce final good 1. This decreases creditor country 1 s marginal product of capital, as well as its capital rents. Third, in the defaulting country 2, fewer workers are hired in the intermediate good sector, so some workers have to shift to domestic production of final good 2, since this model has no unemployment. 20 The labor shifting enables the defaulting country to produce and export more of its own final good 2 despite the initial adverse productivity shocks than the country would be able to without such labor shifting. In addition, the lower demand for labor and the overflow of workers into the domestic good sector lowers the defaulting country s wage in both sectors. 21 The reduced labor income contributes to the sovereign default costs. Overall, owing to the initial adverse productivity shock and the additional wage reduction, the defaulting country s income declines even though it does not repay the debt. When its available funds for consumption declines relative to the creditor country s, the world relative demand of final good 2-to-1 decreases, again because of two countries home bias preferences in consumption. Therefore, the defaulting country s terms of trade and real exchange rate deteriorate, which in turn induces more losses to its income, purchasing power, and trade values. In particular, from both countries households first order conditions (Eq. 21) and budget constraints, we can see how the defaulting country s wealth share in the world 19 As proven in the Appendix, consumption home bias in both countries is a sufficient condition to reduce the world relative demand of final good 2 when the country s world wealth share declines. The more home biased the two countries are, the more the relative demand decreases. 20 Usually high unemployment occurs during default episodes, but for my calibrating country Mexico, the unemployment rate has been relatively low in comparison with international standards, because of its informal sectors. 21 In general, emerging markets wage fluctuations are more volatile than developed countries, while their employment fluctuations are less volatile, as documented by Li (2011). 14

16 affects the world relative demand of final good 2-to-1 (RD, Eq. 22): p 2 = ρ 2 1 ρ 2 ( c 21 c 22 ) 1 θ 2, p 2 = 1 ρ 1 ρ 1 ( c 11 c 12 ) 1 θ 1 (21) RD c 12 + c 22 = S 2( 1 g 2 1 g 1 ) + 1 g 1 c 11 + c 21 1 p 2 g 1 + S 2 ( p 2 g 1 p 2 g 2 ) (22) where S 2 = GDP 2+b 2 qb 2 GDP 1 +GDP 2 is the wealth share of borrower country 2 in the world, g 1 = ( p 2ρ 1 1 ρ 1 ) 1 1 θ 1 + p 2, and g 2 = [ p 1 2(1 ρ 2 ) 1 θ ρ 2 ] 2 + p 2. If the two countries households have exactly the same preferences towards the two final goods, i.e., g 1 = g 2, then the world wealth share has no effect on the world relative demand. In this model, because there is home bias in both countries making g 1 > g 2, all else being equal, the world demand of final good 2 (i.e., c 12 + c 22 ) is positively related to S 2, while that of final good 1 (i.e., c 11 + c 21 ) is negatively related to S 2. Therefore, the world relative demand of final good 2-to-1, RD, increases with borrower country 2 s wealth share in the world S 2. The above is generalized in the following proposition. Proposition 1 (1.1) If g 1 > g 2, then all else being equal the world relative demand of final good 2-to-1, RD, is positively related to borrower country 2 s wealth share in the > 0. (1.2) In other words, if the sum of the two countries home goods world S 2, i.e. RD S 2 expenditure shares is strictly larger than 1, i.e., else being equal RD S 2 > 0. Proof. See Appendix. c 11 GDP 1 +b 1 qb 1 + c 22 p 2 GDP 2 +b 2 qb 2 > 1, then all As default risk increases or during default episodes, borrower country 2 s wealth share in the world declines, which causes the world relative demand of final good 2-to-1 to decrease. This reduces the relative price of final good 2, p 2, and borrower country 2 s real exchange rate. 22 Together with lower p m, its terms of trade also deteriorate. This mechanism becomes stronger as g 1 increases, or g 2 decreases, i.e., as either country becomes more home biased in consumption. Proposition 2 When g 1 > g 2, RD S 2 increases with g 1 and decreases with g 2. Proof. See Appendix. From Eq. 21, we can also see that as p 2 decreases when default risk increases or during default episodes, borrower country 2 s consumption shifts towards the home good (i.e., 22 In equilibrium, the world relative quantity of final good 2-to-1 declines, as shown by the first panel in Appendix Figure 9. 15

17 c 21 c 22 declines), while creditor country 1 s shifts towards the foreign good (i.e., c 11 c 12 Hence, trade flows change. declines). To summarize, the main costs to the creditor when the borrower defaults are the missed debt repayment, and the production loss caused by an efficiency loss in using imported intermediate inputs from the defaulting country. These constrain the creditor country s budget. However, the creditor gains from more favorable terms of trade and real appreciation that allow it to import more of the borrower country s final good. For the borrower country, the main costs upon default are wage losses, lower purchasing power, and no access to the international bond market for consumption smoothing. It gains by forgoing the debt repayment Equilibrium Bond Price This section illustrates how bond prices are determined in the model. Figure 1 plots bond price q against creditor country 1 s asset level tomorrow b 1 (i.e., borrower country 2 s borrowing tomorrow) for a given productivity state s and current asset level of the creditor country, b 1 (i.e., the borrower country s current borrowing). In a simpler case without default risk, the bond price is determined by the following equation in equilibrium: q (b, b, s) = β 1 E 1 U c 11 U c 21 E 2 = β 2 (23) λ 1 λ 2 where λ 1 = U c 11 and λ 2 = U c 21. The first equation is creditor country 1 s bond demand function, and the second equation is borrower country 2 s bond supply function. As shown in the left panel of Figure 1, the bond demand curve and bond supply curve (dashed lines) are close to linear and intersect at point E1. 23 Point E1 pins down the market equilibrium bond price and tomorrow s bond quantity. If the current bond holding b 1 is at a higher level, as in the right panel of Figure 1, then bond demand curve will shift up (to the thicker dashed line) because of a lower current marginal utility of domestic consumption (i.e., λ 1 ), according to Equation 23. Meanwhile, bond supply curve will shift down because of a higher current marginal utility of imported consumption (i.e., λ 2 ). The resulting new intersect point E1 provides a larger equilibrium bond quantity and a slightly lower price, depending on the two countries risk aversion. Now let s consider default risk. In equilibrium, bond demand and supply curves take into account the borrower s and the creditor s perspectives on default probability, respec- 23 Even in this risk-free bond case, the bond supply and demand curves are not exactly linear, because of the agents risk aversion. 16

18 Figure 1: Bond Price (given aggregate productivity state s) Note: Dashed lines indicate that neither country considers default risk; solid lines indicate that both countries consider default risk but borrower country 2 is more optimistic about its repayment probability. The x-axis in the above plots is b 1. As b 1 is positive (right hand side) and becomes larger, borrower country 2 accumulates more and more debt. tively, as in the following equations: q (b, b, s) = β 1 s / D 1 (b 2 ) U c 11 df U 1 (s s) = β 2 c 11 s / D 2 (b 2 ) U c 21 U c 21 df 2 (s s) (24) When the two countries believe that default probability increases significantly, both the demand and supply curves imply lower bond prices. It is reflected by the solid lines in the left panel of Figure 1, given current b 1, both curves bend downward as tomorrow s b 1 (i.e., country 2 tomorrow s borrowing) becomes larger. In particular, for borrower country 2, the intuition is that, taking default probability into account, the government knows it has to lower the bond price in order to issue more bonds. But, as proven by Arellano (2008), there is a lower bound for bond price q, up to which a borrower country is willing to take on debt. That is, for any bond price q below a certain threshold, a borrower country is able to issue less bond with a higher price q to finance the same amount of consumption (of final good 1). Hence, the bond supply curve terminates at the lower bound for q. The result is a different equilibrium point from the no-default-risk case, at E2: both the equilibrium bond quantity and price are lower than those at E1. Again, if the current bond holding is at a higher level, as indicated by the solid lines in the right panel of Figure 1, then creditor country 1 s bond demand curve will shift upward and borrower country 2 s bond supply curve will shift downward. The new intersect point E2, again, provides a larger equilibrium bond quantity and a lower price. However, owing to the default risk, the increase in the bond quantity is much smaller and the decrease in 17

19 Figure 2: Default Probability Beliefs and Bond Price Note: Here I assume that the creditor country always has the correct belief/concern about the default set and probability, i.e., D 1 = D and π 1 = π. Case (1) depicts the bond supply curve if borrower country 2 does not consider default probability when issuing bonds, used as baseline. Case (2) depicts the bond supply curve if the borrower country does consider default probability and is more optimistic about its repayment probability, or less concerned about default risk, than the creditor country is. Case (3) depicts the bond supply curve if the borrower country considers default probability and has the same belief or is more pessimistic about its repayment probability than the creditor country is. the bond price is much larger than in the no-default-risk case. However, Figure 1 only shows one special case of the two countries beliefs/concerns about default probabilities, i.e., the bond supply curve starts to bend downward at a higher bond quantity (b 1) than the bond demand curve does. It implies that when the bond is initially issued, the borrowing government is more optimistic about making repayments, or less concerned about default risk, than the creditor country is. The level of b 1 at which the supply and demand curves start to bend down may differ depending on the countries beliefs or concerns about the default probability. This issue does not arise in small open economy sovereign default models because the borrowing government chooses bond according to a price schedule following the creditor country s bond demand curve. Figure 2 shows three possible relations between the bond supply and demand curves, assuming that the creditor country always has the correct belief about default risk and default probability, i.e., D 1 = D and π 1 = π. The thick solid line (1) depicts the bond supply curve when borrower country 2 s government does not consider default probability when issuing bonds, i.e., D 2 = or π 2 = 0. It can be interpreted as follows: even though the government aims to maximize the households utility in the long run, it is myopic on debt repayments. Here I emphasize the timing of when issuing bonds, not after the issuance. In reality, whether and when a borrower country s government is not concerned about sovereign default risk is difficult to verify. But given many countries serial default events, it is possible that their governments learned little about their own default risk 18

20 from the past or were not concerned about the risk when issuing new bonds. A unique equilibrium is guaranteed in case (1). The thin solid line (2) depicts the bond supply curve when the borrower country does consider default probability but is more optimistic about its repayment probability, or less concerned about the default risk, than the creditor country is. This case also yields at least one equilibrium. 24 The dashed line (3) depicts the bond supply curve when the borrower country considers default probability and has the same belief or is more pessimistic about its repayment probability than the creditor country is, i.e., π = π 1 π 2 for each (s, b 2). That is, the bond supply curve starts to bend down at the same time or earlier than the bond demand curve does. This case, however, does not guarantee an equilibrium as in the graph; the borrowing government may ration the supply of bonds. It is of future research interest to investigate this case and look for the zone of such bond rationing. This paper focuses on case (1) and (2), since they provide at least one equilibrium in the bond market. I first solve case (1) as the baseline, then the optimistic borrower model in case (2). In particular, for case (2) I specify that the borrowing government believes its country has a higher steady-state productivity than the actual level that the firms and the creditor country know. That is, all the agents in the model share the same default sets D 1 = D 2 = D, but have different beliefs about default probabilities π = π 1 > π 2, since the borrowing government is more optimistic about productivity on average. In reality, this situation may stem from a developing country government s overly optimistic perspective on the country s growth. Other scenarios can generate case (2) as well; I use the above specification for its simplicity. 25 I expect case (1) and case (2) to generate similar results. 3 Quantitative Results 3.1 Baseline Calibration In this section, I study the quantitative implications of the model by conducting numerical simulations at the quarterly frequency and using a baseline calibration based on the data, largely from Mexico and Canada. Table 1 shows the calibrated parameter values The equilibrium is unique as long as line (2) does not bend down to cross the bond demand curve again. It depends on the slope of both curves. When both countries hold the same beliefs about the standard deviation and the transition probabilities of the borrower s productivity shocks, the equilibrium is unique. 25 For example, the borrowing government may not be concerned about default risk until its debt level reaches a certain level. 26 U.S. is Mexico s number 1 trade partner and creditor, while Canada is also among the top 6 since 1980s. 19