Consumption Baskets and Currency Choice in International Borrowing

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1 Public Disclosure Authorized Policy Research Working Paper 587 WPS587 Public Disclosure Authorized Public Disclosure Authorized Consumption Baskets and Currency Choice in International Borrowing Julien Bengui Ha Nguyen Public Disclosure Authorized The World Bank Development Research Group Macroeconomics and Growth Team November 211

2 Policy Research Working Paper 587 Abstract Most emerging markets do not borrow much internationally in their own currencies (e.g. pesos), although doing that is an attractive insurance mechanism. This paper provides a new insight for that phenomenon: domestic borrowers demand for peso loans can be met by domestic lenders, who can afford a lower premium than foreign lenders. This is because a large part of domestic lenders consumption basket is denominated in pesos, whereas all of foreign lenders is in dollars. If peso prices are sticky, in bad times, the dollar value of domestic lenders consumption expenditure declines. This partially offsets the negative impact of a lower peso bond return. In our model, the small prevalence of external borrowing in pesos can arise as an equilibrium outcome, despite the absence of exogenous frictions or limits on market participation. This paper is a product of the Macroeconomics and Growth Team, Development Research Group. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at The author may be contacted at The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent. Produced by the Research Support Team

3 Consumption Baskets and Currency Choice in International Borrowing Julien Bengui and Ha Nguyen January 23, 215 Abstract Most emerging markets do not borrow much internationally in their own currencies (e.g. pesos), although doing that is an attractive insurance mechanism. This paper provides a new insight for that phenomenon: domestic borrowers demand for peso loans can be met by domestic lenders, who can afford a lower premium than foreign lenders. This is because a large part of domestic lenders consumption basket is denominated in pesos, whereas all of foreign lenders is in dollars. If peso prices are sticky, in bad times, the dollar value of domestic lenders consumption expenditure declines. This partially offsets the negative impact of a lower peso bond return. In our model, the small prevalence of external borrowing in pesos can arise as an equilibrium outcome, despite the absence of exogenous frictions or limits on market participation. Keywords: Dollarization, External Debt, Original Sin, Portfolio Choice. JEL Classifications: F32, F34, G11, C68 The authors are at the University of Montreal and the World Bank, respectively. We thank Aart Kraay, Anton Korinek, Norman Loayza, Luis Servén, Carlos Végh and Liang Choon Wang for helpful comments and discussions. This paper reflects the author s views and not necessarily those of the World Bank, its Executive Directors or the countries they represent. All errors are our own. Contact address: Ha Nguyen, Development Research Group, The World Bank, 1818 H Street NW, Washington D.C. 2433; 1

4 1 Introduction Most developing countries do not borrow much internationally in their local currencies (Lane and Shambaugh 21). This may seem puzzling because local currency borrowing is generally seen as a good hedging strategy for a small open economy. In bad times, local currencies usually depreciate, which benefits issuers of local currency bonds who pay back less in real terms. As local currency bonds pay less in bad times and pay more in good times, local currency debt provides insurance against domestic income risk to borrowers. In practice however, we observe very little international borrowing in local currencies 1. This lack of external local currency borrowing is a longstanding puzzle in international finance and has mostly been interpreted as evidence of developing and emerging countries inability to borrow internationally in their own currency (Eichengreen and Panizza 25). This is referred to as the original sin hypothesis. The argument is that markets for emerging market local currency debt do not exist because lenders are afraid that the borrowing countries will manipulate the exchange rates. This paper contributes to the literature by offering a new insight for this phenomenon. It argues that domestic borrowers need for loans in domestic currency (for brevity, referred to as pesos ) can be met by domestic lenders. More precisely, local households might be able to lend to domestic firms in pesos at a lower premium than foreigners can. Local households can accept a lower currency premium on peso bonds because a large part of their consumption basket is denominated in pesos. In an economic downturn, the peso depreciates and the real return of peso bonds falls. If peso prices are sticky, the dollar value of local households consumption expenditure declines, which partially offsets the negative impact of the peso bond lower return. On the other hand, since foreigners have a consumption basket consisting of dollar-denominated goods only, their dollar consumption expenditure is little changed. Therefore, the impact of the peso bond s lower return on foreigners is not mitigated. In other words, the correlation between real consumption expenditure and the peso bond s real return is higher for domestic households than for foreign lenders: when peso bonds real return is low, domestic households real consumption expenditure is also low. This so-called consumption basket effect can effectively reduce the premium demanded by local savers on peso debt, and can bring this premium down to a level where foreign 1 Although a few countries are starting to borrow more in their currencies in recent years, the overall phenomenon of liability dollarization largely holds. 2

5 investors might be pushed out of the peso-bond market. On the other hand, domestic lenders may have a disadvantage compared to foreign lenders: their income is potentially more correlated to domestic borrowers income than foreign lenders income is. If foreign lenders income from other sources is orthogonal to the developing country s business cycle, foreign lenders do not require a high premium for holding peso-bonds, thereby pushing local savers, whose income co-varies with the domestic business cycle, out of the market. Foreign lenders in this case, by lending in pesos, effectively act as an insurer to the small country. This is precisely the rationale of the existing literature on why small countries should borrow in their domestic currencies. Our model hence predicts that the relative willingness of local vs. foreign lenders to hold peso-bonds depends on the relative strength of the consumption basket effect versus the income correlation effect. When foreign lenders income is more positively correlated to the small economy s country risk, foreign lenders incentive to hold pesobonds declines. If the consumption basket effect is large enough, domestic lenders are more willing to hold peso bonds than foreign lenders. The strength of the consumption basket effect depends on the degree of nominal price rigidity. If prices are perfectly flexible, in bad times, the peso prices also increase and that reduces that advantage of domestic households compared to foreign lenders. In the calibration exercise, we will illustrate the bond holdings with and without nominal rigidities. We find that with only some level of nominal rigidity, consumption basket effect is much stronger than the business cycle effect, which, not surprisingly, implies that domestic households do most of the peso lending. It is important to stress that our paper does not refute the original sin hypothesis. Rather, it provides an additional insight to help explain better the stylized fact that countries borrow very little in their domestic currencies. Our view is that the original sin hypothesis is valid: foreign lenders are concerned about potential exchange rate manipulations, and require a risk premium for their loans. We add a new insight to complete the argument: if foreign lenders required risk premium is high enough, domestic lenders can accept a lower risk premium and push them out of the peso debt market. In other words, the concern about exchange rate manipulations, combined with the consumption basket effect can generate such a stark outcome that we see in the data: the vast majority of countries do not borrow much internationally in their domestic currencies. 3

6 The literature offers three main explanations why countries borrow in dollars. The first is the moral hazard hypothesis. Krugman (1998) and Schneider and Tornell (24) show that private agents take on risky forms of finance such as dollar debt to take advantage of bailout guarantees. However, Eichengreen and Hausmann (1999) argue that this cannot satisfactorily explain the high level of dollar debt that could be observed in firms that were unlikely to be bailed out. The second line of explanation is the original sin hypothesis, by Eichengreen and Hausmann (1999) and their subsequent papers. They argue that markets for emerging market local currency debt do not exist because lenders are afraid that the borrowers will manipulate the exchange rate. Hence any ex-ante risk premium is potentially insufficient if the exchange rate depreciation is large enough. Related to this, Jeanne (23) suggests that the original sin is the result of the lack of credibility in domestic monetary policy that makes borrowers unsure about the real value of their domestic currency debt and decide to dollarize their liabilities instead. The third line of explanation is due to Korinek (29), who argues that financial accelerator effects create an externality that induces individual borrowers to undervalue the social risks of dollar debt and take on too much of it. In relation to the literature, our explanation does not rely on any particular friction. It rests on the insight that domestic agents consumption basket is more favorable than foreign lenders s in terms of peso risk. Hence, domestic lenders can afford a lower risk premium of peso bonds. Unlike the existing literature that tends to treat a developing country as a single borrowing agent, we examine separately the problem of domestic borrowers (usually firms) and that of domestic lenders. Doing this helps us identify differential consumption baskets as another factor that works toward explaining heavy dollarization in international debt markets. The intuition of our paper is related to the work of Engel and Matsumoto (29) and Coeurdacier and Gourinchas (211). We share the idea that bonds are used to hedge against real exchange rate fluctuations. However, the focuses are different. Engel and Matsumoto (29) and Coeurdacier and Gourinchas (211) focus on explaining the equity home bias puzzle. In symmetric two-country setups, they show that not much equity diversification is required when agents can hedge their foreign exchange risk sufficiently, using a forward position in foreign exchange (Engel and Matsumoto 29), or bonds Coeurdacier and Gourinchas (211). Our focus is different. We use a small open economy setup to explain international debt dollarization. We argue that international debt dollarization might be optimal, because domestic lenders may 4

7 satisfy all the peso needs of domestic entrepreneurs and push foreign lenders out of the market. By opening up the small open economy to a set of entrepreneurs and a set of households, we can identify different peso needs of agents within the same country. In the equilibrium, we show that domestic agents hold opposite peso positions. Domestic entrepreneurs borrow in pesos and domestic households lend in pesos, a characteristic not found in Engel and Matsumoto (29) and Coeurdacier and Gourinchas (211). We describe in detail the mechanism in a framework of a DSGE model. The model features three agents (domestic households, entrepreneurs, foreign lenders), two sectors (tradable and non-tradable goods) with sticky non-tradable price and wage and endogenous debt currency choices. All agents can borrow and lend in the domestic currency (i.e. the peso) or in a foreign currency (i.e. the dollar). We extend the new solution method developed by Devereux and Sutherland (21) and Tille and van Wincoop (21) to solve for the long run currency choice of households, entrepreneurs and foreign lenders in a three-agent, two-asset DSGE setup with incomplete markets. The paper is organized as follows: section 2 describes the model. Section 3 presents the solution of the model. Section 4 analyzes a special case when international borrowing is entirely in dollars. Section 5 analyzes the full-fledged model. And finally section 6 concludes. 2 The model 2.1 The framework In this section we describe a model with a small economy and a set of foreign lenders. Foreign lenders are small and risk averse. This is a crucial deviation from the literature, a point to which we will return later. Foreign lenders can choose between a dollar bond and a peso bond. The small economy is populated by a continuum of households and a continuum of entrepreneurs. Both types of agents consume two goods: a good that can be exchanged with the rest of the world (a tradable good) and a good consumed by domestic agents only (a non-tradable good). The non-tradable sector employs labor supplied by households and makes use of a non-traded fixed factor (i.e. capital or land) owned by entrepreneurs. The tradable good, for simplicity, follows a stochastic endowment. Agents can transfer wealth across periods using money, a domestic currency bond (i.e. peso bond) and a foreign currency bond (i.e. dollar bond). The environment features price and wage nominal rigidities in the non-tradable good 5

8 market while the tradable good s nominal price is flexible. We assume that the law of one price holds, thus the real price (i.e. dollar price) 2 of the tradable good is driven by its international price. The tradable good s nominal price can be interpreted as the nominal exchange rate, which is flexible. The role of non-tradable price s nominal rigidity is important. If the non-tradable price is flexible, it can fully adjust and the consumption basket effect does not play a big role 3. The role of wage nominal rigidity is not important. In fact, if we remove wage nominal rigidity, the consumption basket effect will be stronger. We will come back to this point in subsequent sections. The reason we keep wage nominal rigidity in the model is because empirically, wage and price nominal rigidities tend to go together. As a standard convention in New Keynesian models, nominal rigidities in the nontradable sector are modeled by dividing the sector into monopolistic intermediate good producers and competitive retailers. We would like to analyze a situation in which households lend to the entrepreneur sector of the economy, yet we refrain from modeling capital accumulation for tractability reasons. Thus we essentially assume capital is fixed. In order to induce the desired pattern of credit in the economy, we assume that entrepreneurs discount the future more strongly than households. As a result, relatively impatient entrepreneurs borrow from relatively patient households in equilibrium. 2.2 Households Households expected life-time utility is given by: E t= [ 1 ψ Ht 1 σ ) 1 σ (c Ht Φ L1+ν t + χ ln 1 + ν ( MHt Households utility comprise of consumption (c Ht ), real money holdings ( M Ht P t, where P t is the aggregate price level) and employment (L t ). The utility takes the form of GHH utility function to remove wealth effect and hence generate a decline of employment in bad times. c Ht ( c T Ht) γ ( c N Ht ) 1 γ is a consumption bundle of tradable and nontradable goods, and ψt H β t Π t k= c µ Hk is an unternalized endogenous discount factor that depends on the aggregate (economy-wide) level of households consumption. As in Schmitt-Grohe and Uribe (23), this is a simple technical device to induce uniqueness 2 Throughout this paper, nominal prices refer to prices in pesos, and real prices refer to prices in dollars. 3 Engel and Matsumoto (29) also find that price rigidity has a large impact on international equity choice 6 P t ) ]

9 of the deterministic steady state and stationary responses to temporary shocks. Specifically, the endogenous discount factor decreases with the aggregate consumption, which the representative entrepreneur takes as given. In addition, µ is set very small so that in the short run, the deviations of the endogenous discount factor from the standard discount factor β are negligible. Households face a sequence of budget constraints P T t c T Ht+Pt N c N Ht+B Ht +Pt T f Ht +M Ht = R t B Ht 1 +R Pt T f Ht 1 +M Ht 1 +W t L t +Pt T yht, T (1) where Pt T and Pt N are the nominal prices of the tradable and non-tradable goods, W t is the nominal wage, R is the return of the dollar bond and R t is the nominal return of the peso bond (which are determined in the previous period). B Ht is the nominal peso bond holdings of households (i.e. positive B Ht implies lending). f Ht is the real dollar bond holding of households. Each period, a household receives bond repayments, their wage payment and a tradable endowment. holding and bond holdings for the next period. They choose their consumption, money To model wage rigidity, we separate the labor supply into households and a labor aggregator. Households supply labor to competitive aggregator who combine their labor to produce final labor using a constant elasticity of substitution (CES) production function [ 1 Yt N = ] L N ω H 1 ω H ω H 1 ω H it, where ω H is the elasticity of substitution between any two households labor, and is household s wage markup. ω H 1 ω H We model nominal wage rigidities with Calvo pricing. In each period, only a fraction 1 θ H of households can adjust wage. This means that for each household, at the beginning of each period, there is a constant probability of 1 θ H that they can change their price if they want to. If the household had fully flexible price (θ H = ), they would set the hypothetical flexible wage (W t ) as a mark-up of the marginal rate of substitution between labor disutility and consumption: W t P T t = ω H ω H 1 MRS t = ω H ω H 1 ΦLν Ht As in standard in New-Keynesian models, at the first order approximation the 7

10 nominal wage is governed by the following equation: logw t logw t 1 = c µ Ht βh t(logw t+1 logw t )+λ H ( log( MRS t w t ) log( MRS ) ss ) w ss where λ H = (1 θ H)(1 c µ Ht βθ H) θ H, c µ Hit β is the discount factor of households. MRS t w t is the ratio between the the marginal rate of substitution and the real (sticky) wage, and MRS ss w ss is its steady state value. Note that MRSss w ss = ω H 1 ω H. The first-order conditions of the households problem are: (c Ht Φ L1+ν t 1 + ν (c Ht Φ L1+ν t 1 + ν Pt N = 1 γ Pt T γ ) σ c T γ 1 Ht c N1 γ Ht = βc µ ) σ c T γ 1 Ht c N1 γ Ht = βc µ (2) c T Ht, (3) c N Ht ( Ht R E t c Ht+1 Φ L1+ν t ν Ht R Pt T t+1e t P T t+1 (c Ht+1 Φ L1+ν t ν ) σ c T γ 1 Ht+1 cn1 γ Ht+1, (4) ) σ c T γ 1 Ht+1 cn1 γ Ht+1, (5) ) σ (c Ht Φ L1+ν t γc T γ 1 Ht c N1 γ Ht = χ P t + βc µ 1 + ν M Ht Ht E t P T t P T t+1 ) σ (c Ht+1 Φ L1+ν t+1 γc T γ 1 Ht ν cn1 γ Ht+1 (6) Equation (3) is a static optimality condition describing the optimal composition of the household s tradable and non-tradable consumption. Equations (4), (5) and (6) are Euler equations for dollar bond, peso bond and money holdings. 2.3 Entrepreneurs Entrepreneurs expected life-time utility is given by E ψt E t= [ c 1 σ Et 1 σ + χ ln ( MEt P t )]. Entrepreneurs maximize their expected discounted lifetime utility function, which includes aggregate consumption c Et and real cash holdings M Et P t. Aggregate consumption c Et ( cet) T γ ( ) c N 1 γ Et is a CES consumption bundle of tradable and non-tradable goods, ψt E (φβ) t Π t k= c µ Ek is an uninternalized endogenous discount factor that depends on the aggregate (economy-wide) level of entrepreneurs consumption. φ < 1 reflects that the entrepreneurs are more impatient than households. This is to generate lending 8

11 from households to entrepreneurs. Entrepreneurs face a sequence of budget constraints P T t c T Et + Pt N c N Et + B Et + Pt T f Et + M Et = R t B Et 1 + R Pt T f Et 1 + M Et 1 +P N t A N L N t + P T t y T Et W t L t, where f Et and B Et are dollar and peso bond holdings of the entrepreneurs (a positive number implies lending, a negative number implies borrowing). Each period, entrepreneurs receive their tradable endowment, collect their non-tradable output and pay wages. They pay back their bond borrowings and issue new bonds for the next period. Entrepreneurs receive their tradable endowment and carry out production in nontradable sectors. We assume the tradable price is flexible, to allow for movements in the nominal exchange rate. To model nominal rigidities in the non-tradable market, we separate the sector into intermediate good producers and retailers. Intermediate producer j produces a differentiated intermediate good y jt using labor L jt according to a linear production function y N jt = A N L jt, The producers sell their output to competitive retailers who combine these intermediate goods to produce a final good using a constant elasticity of substitution (CES) production function [ 1 Yt N = ] y N ω E 1 ω E ω E 1 ω E jt, where ω is the elasticity of substitution between any two differentiated intermediate non-tradable goods, and price. ω E 1 ω E is the firm s markup. In each period, only a fraction 1 θ E of the intermediate producers can adjust This means that for each firm, at the beginning of each period, there is a constant probability of 1 θ E that they can change their price if they want to. If the firm had fully flexible price (θ E = ), it would set the hypothetical flexible price (P N t ) as a mark-up of the marginal cost: Pt N = ω E ω E 1 MCN t = ω E ω E 1 As in standard in New-Keynesian models, the aggregate non-tradable price is gov- W t A N t 9

12 erned by the following equation: logp N t logp N t 1 = c µ Et φβe t(logp N t+1 logp N t ) + λ E (log(mc t ) log(mc ss )) (7) where λ E = (1 θ E)(1 c µ Et φβθ E) θ E, c µ Et φβ is the discount factor of the entrepreneurs, and mc t is the real marginal cost. Note that the steady state vale MC ss = ω E 1 ω E. (7) is the New-Keynesian Phillips Curve. It says that entrepreneurs set the nominal price of non-tradable goods as a combination of the expected inflation and the marginal cost. When the price is very flexible (i.e. θ E is approaching ), λ E becomes very large. What this means is that when entrepreneurs can flexibly change the price, they care very little about how future prices might be, and care much more about the changes in the marginal cost. When the price is fully sticky (i.e. θ E = 1, λ E = ) firms can not change the price in response to the change in the marginal cost. They set the price in expectation of future prices, which end up being constant. The first-order conditions of the entrepreneurs problem are c σ Et c σ Et c σ Et ct γ 1 Et P N t P T t c N1 γ = 1 γ γ Et = φβc µ c T Et, c N Et (8) Et R E t (c σ γ 1 ct ), (9) Et+1 Et+1 cn1 γ Et+1 ( γ 1 ct Et c N1 γ Et = φβc µ Et R t+1e t c σ γ 1 Et+1cT γ 1 γct Et c N1 γ Et = χ P t T + φβc µ Et M E tc σ Et Et+1 cn1 γ Et+1 P T t γ 1 Et+1cT Et+1 cn1 γ Et+1 P T t+1 P T t ), (1) P T t+1, (11) Equation (8) is a static optimality condition describing the composition of the entrepreneur s consumption basket between tradable and non-tradable goods. Equations (9), (1) and (11) are the Euler equations for dollar bonds, peso bonds and money holdings. 2.4 Fundamentals We consider two distinct sources of uncertainty in the economy: real shocks and nominal shocks. A real shock z t is assumed to cause random fluctuations in the tradable endowment, while monetary shocks cause fluctuations in the money supply. We assume away the fluctuations in the non-tradable productivity because it is not empirically rel- 1

13 evant. The real and monetary shocks follow the following processes: ln(z t ) = ρ T ln(z t 1 ) + ɛ T t, (12) yht T = Y H z t (13) yet T = Y E z t (14) ln(m t ) = ρ M ln(m t 1 ) + ɛ Mt. (15) where ɛ T t N(, σ D ), ρ T and ρ M are autoregressive coefficients, and ɛ T t and ɛ Mt are i.i.d. random variables with variance σ 2 T and σ2 M, respectively. 2.5 Foreign lenders Foreign lenders are assumed to be small and risk-averse. This is a crucial deviation from the literature. This assumption reflects the fact that due to information barriers and other reasons, foreign investors can only invest in a few foreign markets, and therefore are affected by the investment s performance in those markets. This assumption is consistent with the empirics. For example, Didier, Rigobon, and Schmukler (21) finds that U.S. equity mutual funds that operate globally only invest in a surprisingly limited number of stocks, around 1. Foreign lenders have a stochastic endowment of the tradable good in every period. They have access to dollar and peso bond markets. In addition to the loan market of the small country, foreign lenders can also borrow or lend in dollars to the rest of the world at the exogenous rate R. Foreign lenders face a sequence of budget constraints Pt 1 T c F t + b F t + f F t + d F t = R t b F t 1 + R f Pt T F t 1 + R d F t 1 + y F t, (16) where y t is endowment that follows an exogenous process: ln(y F t ) = ρ F ln(y F t 1 ) + ɛ F t, where ɛ F t N(, σ F ) and f F t and b F t B F t P t are dollar and real peso loans from the foreign lenders to the domestic country, d F t is the dollar loan to the rest of the world. A foreign investor s expected life-time utility is given by E ψt F t= c 1 σ F t 1 σ, 11

14 ( ) µ where ψt F β t Π t c F t k= c F t is an endogenous discount factor that depends on the aggregate level of foreign lenders consumption, and the steady state consumption c F t. µ will be set very small so that the endogenous discount factor do not significantly affect the model s dynamics. The first-order conditions for foreign lenders are as follows: c σ F t = β c σ F t = β 2.6 Market clearing ( cf t c F t ( cf t c F t ) µ R E t c σ ) µ R t+1p T t E t c σ F t+1 (17) F t+1 1 P T t+1 First, there is a market for the final non-tradable good, where demand from households and entrepreneurs equates supply from retailers: (18) c N Ht + c N Et = A N L N t, Second, the net peso bond demand from local savers and entrepreneurs and foreign investors is zero: b Ht + b Et + b F t =. In other words, the demand for peso bonds (i.e. peso lending) stemming from domestic and international lenders has to equal the supply of peso bonds (i.e. peso borrowing) of the entrepreneurial sector. Finally, demand for tradable consumption by households and entrepreneurs has to match domestic tradable good production and imports from abroad (financed via current account imbalances). Define the entrepreneurs and households net worth as a Et f Et + b Et and a Ht f Ht + b Ht, the tradable market good clearing implies: ( ) c T Et + c T Ht + a Et + a Ht = Rt P t 1 (f Et 1 + f Ht 1 ) + R t (b Et 1 + b Ht 1 ) + yht T + yet T (19) P t 12

15 2.7 Basic intuition To see the basic intuition of the model more clearly, let s rewrite the households and the foreigners budget constraint (money holdings are removed for brevity): c T Ht + P t N Pt T t 1 Pt T c N Ht + b Ht + f Ht = R t P T t 1 Pt T c F t + b F t + f F t + d F t = R t P T b Ht 1 + R f Ht 1 + w t L t + y T Ht (2) b F t 1 + R f F t 1 + R d F t 1 + y F t, (21) When peso depreciates, the real return of households and foreigners bond holdings Pt 1 decline (i.e. R T t ). This hurts both households and foreigners. However, if peso Pt T prices are sticky (i.e. Pt N is unchanged), the real consumption expenditure on the nontradable good goes down for households ( P t N ). This is the consumption basket Pt T advantage that households have over foreigners. 3 Numerical solution of the model 3.1 Solving for the long-run currency choice It is well-known that up to the first-order approximation, the values of the portfolio choices are indeterminate, because at this level of approximation, the two assets are perfect substitutes. Previous literature usually relies on perfect market structures that make portfolio choice irrelevant. We extend the method of Devereux and Sutherland (21) and Tille and van Wincoop (21) to solve for the long run currency choices of households, entrepreneurs and foreign lenders. Details are presented in Appendix B. In essence, households, entrepreneurs and foreign lenders choose optimal levels of peso loans to cross-insure, that is, the covariance between the difference in their marginal utility and the peso-dollar bond return differential is zero. In the secondorder approximation, the conditions are the following: E t [(ˆr B t+1 ˆR )(co cht ĉ T Ht+1 + co chn ĉ T Ht+1 + co lˆl cocet ĉ T Et+1 co cen ĉ N Et+1] =, (22) E t [(ˆr B t+1 ˆR )(σĉ F t+1 + (γ 1 σγ)ĉ T Et+1 + (1 γ)(1 σ)ĉ N Et+1)] =, (23) where r B t+1 R t+1 σγ c H c H Φ L1+ν 1+ν P t P t+1 co cen = (1 γ)(1 σ). is the real return of the peso bond next period. co cht = γ 1, co chn = 1 γ σ(1 γ) c H c H Φ L1+ν 1+ν 13, co l = σφ L1+ν c H Φ L1+ν 1+ν, co cet = γ 1 σγ,

16 (22) and (23) are derived from the second order approximations of Households, Entrepreneurs and Foreigners portfolio choice Euler equations. 3.2 Calibrations The values of the discount factor is set for annual data: β =.97. The share of tradable consumption is a third of total consumption: γ = 1. χ is set equal.5, 3 and the impatience coefficience φ =.999. The elasticities of substitution ω H and ω E are from Chugh (26). We set the endogenous discount factor coefficient very small µ =.1, so that it does not have a significant impact on the model s dynamics. Following GHH, we set Φ = 1 and ν =.6 for the labor disutility function. We use Peru and U.S. data to calibrate the parameters. Peru is a stable small open economy in South America, which reasonably takes the U.S. as the main rest of the world investor. From Peru s money stock data we obtain ρ M =.84 and σ M =.3. From Peru s HP-filtered GDP per capita data, we obtain ρ D =.8 and σ D =.3. From U.S. s HP-filtered GDP per capita data, we obtain ρ F =.75 and σ F =.12. Note that the nominal shock s standard deviation is much larger than that of the real shock. We set A N = 4 to obtain a reasonable employment in the non-tradable sector in the steady state. Then we choose Y H and Y E to generate the levels of domestic lending and external debt to match those of Peru (the average percentages of private credit to GDP and of external debt to GDP for Peru in the last two decades are both about 49%, according to the World Development Indicators). For the foreign lenders, we choose y F = 3, about three times the total output of the borrowing country. 4. The full set of parameters is in Table Steady state For the calibrated parameters above, the steady state values of the non-portfolio choice variables are in Table 2. In the steady state, total output of the country (in terms of the tradable good) is 1.14 (units), from which.345 is the sum of the tradable endowment. Total lending from domestic households to entrepreneurs in terms of the tradable good is.4568, about 45.7% of total output. The net asset of the country is then -.54, about 54% of output. These figures aprroximately match the averages of Peru. 4 The relative size of output is not important to our results 14

17 β Discount factor.97 φ Entrepreneurs relative impatience coefficient.999 R Dollar-bond interest rate 1 β µ Endogenous discount factor coefficient.1 1 γ Consumption component (utility) 3 χ Coefficient of the Utility from Money.5 ν Coefficient of the Utility from Leisure.6 ω E Elasticity of input substitution for non-tradable production 1 ω H Elasticity of labor substitution 21 A N TFP of the non-tradable production 4 Y H Household s tradable endowment.115 Y E Entrepreneur s tradable endowment.23 ρ T Persistence of the domestic tradable endowment.4 σ T Standard deviation of the domestic tradable endowment.3 M Long run money supply 1 ρ M Persistence of the monetary shocks.5 σ M Standard deviation of the monetary shocks.3 y F Mean of foreigners other income 3 ρ F Persistence of foreign income shocks.31 σ F Standard deviation of foreign income shocks.12 Table 1: Values of benchmark parameters L N Labor in the Non-tradable production.698 Y N Non-tradable Output (units) Y T Tradable Output (units).345 p Price of Non-tradable relative to Tradable.2351 Y T + p Y N Total Output in terms of tradable 1.14 a E Net asset position of Entrepreneurs a H Net asset position of Households.4568 a H Net asset position of the country Table 2: Steady State Values 4 A special case: All domestic and international borrowing is in dollars This section considers a special case of the model, in which we do not allow for peso lending and borrowing, both domestically and internationally. This is to completely isolate the impacts of bond returns on income. We will examine the impacts of monetary and real shocks on agents consumption, with a focus on households. From that, we will assess how nominal rigidities play to households advantage. Note that foreigners consumption is not shown here because it is not changed, since the return of the dollar bond is fixed, and foreigners endowment stays constant. 15

18 First we consider the monetary shock. We consider a 1% increase in the money supply and pay particular attention to changes in aggregate consumption. Figure 1a shows the impulse responses to the shock when price and wage are very flexible (θ H = θ E =.1, which means that 99% of firms and households can adjust price and wage in a period). For all the variables, the y-axes represent percentage deviations from the steady state values. The first reaction is that since prices and wages are flexible, monetary shocks have no impact on output or consumption. Only nominal prices jump, and the peso depreciates. Note that the nominal price of the tradable good is the peso s nominal exchange rate Non tradable price Tradable price Nominal wage Entrepreneur Consumption 4 x Household Consumption 1 x Labor 15 x (a) Flexible price and wage 4 x x 1 4 Non tradable price Tradable price Nominal wage Entrepreneur Consumption Household Consumption Labor (b) Sticky price and wage Figure 1: Impulse Responses to a 1% increase in the money supply 16

19 In Figure 1b, we consider a 1% increase in the money supply when non-tradable price and wage are sticky (θ H = θ E =.99). In this case, a positive monetary shock has positive real effects. Labor and non-tradable output increase. Household s consumption goes up for potentially two reasons (1) employment is higher and (2) since the peso depreciates in value and the non-tradable price is sticky, the dollar value of their non-tradable expenditure goes down. However the first channel is less important, because the increase in employment is offset by a similar decrease in the real wage (since the peso depreciates). Therefore the increase in households consumption is due largely to the non-tradable price s nominal rigidity. This is the key channel to play to households advantage compared to foreigners. The higher the volatility of the monetary shocks, the more important this advantage is. Note that wage rigidity is not important. If we remove wage rigidity and only keep non-tradable price rigidity, the consumption basket channel even gets stronger. To see the point, let s go back to Figure 1b. If wage is flexible, the nominal wage now will go up following the increase in the money supply, which increases the real wage. This further helps households consumption. However, note that this comes at a cost to entreprneurs because now they have to pay a higher real wage to households. This will have an implication to entrepreneurs peso demand. Entrepreneurs would like to borrow more in pesos to hedge against their larger exposure to shocks. In section 5, we will come back to this point. Second we consider the real shock. We consider a 1% decrease in the domestic tradable endowment when price and wage are flexible (Figure 2a). Since the supply of the tradable good now shrinks, the demand for non-tradable good also drops, which results in lower non-tradable employment and lower non-tradable output. The real shock affects households negatively in three ways: (1) their tradable endowment shrinks, (2) their real wage falls (their nominal wage is up but the peso depreciates more), (3) lower employment. The negative real shock helps households in one way: the dollar value of their non-tradable consumption drops slightly, because the tradable price (i.e. the exchange rate) increases more than the non-tradable price. All in all, the first three channels dominate the last one. Households are worse off after the shock. Their aggregate consumption declines. Next we consider a 1% decrease in the tradable endowment when non-tradable price and wage are sticky (Figure 2b). Non-tradable price and wage now remain the same after the shock. Since the money supply is unchanged, this implies higher non-tradable 17

20 Non tradable price Tradable price Nominal wage Entrepreneur Consumption Household Consumption Labor (a) Flexible price and wage 4 x Non tradable price Tradable price Nominal wage Entrepreneur Consumption Household Consumption 1 x Labor (b) Sticky price and wage Figure 2: Impulse Responses to a 1% decrease in tradable endowment output. The shock affects households negatively in two ways: (1) their tradable endowment shrinks, (2) their total real wage bill is down, because the higher employment is outweighed by a disproportionately lower real wage. However, the shock helps the households in one way: the dollar value of their non-tradable consumption drops significantly, because the non-tradable good s peso price remains unchanged, while the peso depreciates sharply. Compared to the case where price and wage are flexible, the effect from the third channel becomes a lot stronger and almost offsets the first two channels. Households aggregate consumption drops very little as a result. Again, we see that nominal price rigidity in non-tradable good reduces the impact of the negative 18

21 real shock on households (relative to foreigners). In addition, if wage is flexible, households consumption drops even less, because their wage now is higher. This comes at a cost of entrepreneurs. 5 Full-fledged model In this section we consider the currency choice of Households, Entrepreneurs and Foreigners in a full-fledged model, where all agents can borrow or lend in both pesos and dollars. Figure 3 shows the peso lending of foreigners (represented by the thick straight lines) and local households (the thin dashed lines). The horizontal axis shows the correlation between the tradable endowment s and foreign output s stochastic processes. The vertical axis shows the long run value of peso lending (in terms of the tradable good) Peso lending to Entrepreneurs most flexible more sticky most sticky Correlation between domestic tradable endowment and foreign endowment Figure 3: Peso lending to Entrepreneurs. Note households peso lending is shown by the thin dashed lines, foreigners lending thick straight lines. First of all, note that the correlation between the domestic tradable endowment and the foreign endowment matters in the allocation of peso holdings. When the correlation is low, foreigner can provide insurance to the country against their income shocks, hence they lend more in pesos. However, when the correlation is going toward 19

22 one, foreigners incentive to lend in pesos gradually drops. The blue lines show the peso lending when non-tradable price and wage are most flexible (θ E = θ H =.1). In this case foreigners do all of the lending in pesos to entrepreneurs (the thick blue line), local households do not lend in pesos at all (the dashed blue line). They actually borrow in pesos, since their peso lending is negative. Foreigners dominate in peso lending because the consumption basket effect is nulled by the flexible price and wage. The green and red lines show peso lending when the non-tradable price and wage are more sticky (θ E = θ H =.75) and most sticky (θ E = θ H =.99). In these cases, the consumption basket effect kicks in. Nominal rigidity in the non-tradable price helps households mitigate the impacts of real and monetary shocks, when foreigners have to bear the full impact of peso bond return s fluctuations, because their consumption basket is entirely in dollars. The peso bond composition goes to the other extreme: foreigners are pushed out completely from peso lending at all levels of the correlation. All the of peso lending is done by households (the green and red dashed lines) Foreign peso lending Household peso lending Peso lending to Entrepreneurs The degree of nominal rigidities Figure 4: Peso lending to Entrepreneurs, corr=.3 In a different angle, we anchor the correlation between domestic and foreign endowment at.3, and vary the degree of price and wage stickiness in the horizontal axis. The horizontal axis shows the value of θ, while the vertical axis shows the amount 2

23 of long run peso lendings by households and foreigners. The straight line shows the peso lending from domestic households, while the dahsed line shows the peso lending from foreigners. We purposely choose a low value of the correlation and would like to examine at what degree of nominal rigidities foreigners are pushed out of the peso lending market. Figure 4 shows that they are pushed out when θ is at about.25, a relatively low number. This suggests that households do not need a high level of nominal rigidities to push foreigners out of the peso debt market. The result is striking given that we do not consider any other types of market frictions, or political economy of exchange rate manipulations (in our model, money supply fluctuations are random). We simply rely on some level of nominal rigidities to suggest that international debt dollarization emerges because domestic households, with the help of the consumption basket effect, has an advantage over foreign lenders in the peso debt market. As a robustness check, we examine if the role of nominal wage stickiness is important. Figure 5 helps us to show that it is not. Figure 5 repeats what we do in Figure 3, except now wage is always flexible (θ H =.1), and we only vary the nominal rigidity level of the non-tradable price. Similar to Figure 3, the thick straight lines show foreigners peso lending, and the thin dashed lines show domestic households peso lending. The blue lines show the peso lending when non-tradable price is most flexible (θ E =.1), the green and red lines show peso lending when the non-tradable price is more sticky (θ E =.75) and most sticky (θ E =.99). The overall picture does not change: as the non-tradable price becomes more sticky, foreigners increasingly lend less in pesos, and households increasingly lend more in pesos. At θ E =.75 and θ E =.99, foreigners are also completely pushed out of the peso lending market at all levels of correlation. However, there is one notable difference. When the non-tradable price is sticky, households peso lending is a lot more in Figure 5 (where wage is flexible) compared to Figure 3 (where wage is sticky). The reason is that domestic entrepreneurs need to borrow more in pesos to hedge against their income shocks, and households provide that insurance. Recall that in the impulse response exercises, we learn that a flexible wage mitigates the impact of a shock on households, at the cost of entrepreneurs. In other words, in a flexible wage environment, entrepreneurs become more exposed to shocks and households become less exposed to shocks. As a result, households provide larger insurance (by lending more in pesos) to entrepreneurs. 21

24 1 Peso lending to Entrepreneurs most flexible more sticky most sticky Correlation between domestic tradable endowment and foreign endowment Figure 5: Peso lending to Entrepreneurs when wage is always flexible. Note households peso lending is shown by the thin dashed lines, foreigners lending is shown by the thick straight lines. 6 Conclusion This paper provides a new explanation of why developing countries may appear to be unable to borrow much internationally in their domestic currency. We argue that countries might not need to, as entrepreneurs can borrow in the domestic currency from domestic households at a lower premium than they could from foreign lenders. Local lenders might accept a lower risk premium than foreign lenders on local currency bonds because a large part of their consumption basket consists of non-tradable goods whose nominal prices typically adjust slowly to shocks. Therefore in downturn, a peso depreciation is less damaging to domestic peso bond holders than to foreign ones, whose consumption baskets are entirely in dollars. We developed a simple DSGE model to provide a quantitative evaluation of the mechanism. With reasonable parameters, our results indicate that differential consumption baskets can go a long way to explain international debt dollarization, without having to resort to market frictions and exchange rate manipulations. The results from the model suggest a testable hypothesis: holding everything else constant, the higher the correlation between local and global shocks, the more dollar 22

25 lending from foreigners we should expect to see. While not a trivial exercise, as one needs to to control for other factors such as investors fear of depreciation, it can be an interesting piece of future research. References Chugh, S. K. (26, October). Optimal fiscal and monetary policy with sticky wages and sticky prices. Review of Economic Dynamics 9 (4), Coeurdacier, N. and P.-O. Gourinchas (211, November). When Bonds Matter: Home Bias in Goods and Assets. NBER Working Papers 1756, National Bureau of Economic Research, Inc. Devereux, M. B. and A. Sutherland (21, July). Country portfolio dynamics. Journal of Economic Dynamics and Control 34 (7), Didier, T., R. Rigobon, and S. L. Schmukler (21, December). Unexploited gains from international diversification: Patterns of portfolio holdings around the world. NBER Working Papers Eichengreen, B. and R. Hausmann (1999, November). Exchange rates and financial fragility. NBER Working Papers 7418, National Bureau of Economic Research, Inc. Eichengreen, B., R. H. and H. Panizza (25). The pain of original sin. In B. Eichengreen and R. Hausmann (Eds.), Other people s money: debt denomination and financial instability in emerging market economies. The University of Chicago Press. Engel, C. and A. Matsumoto (29, July). The International Diversification Puzzle When Goods Prices Are Sticky: It s Really about Exchange-Rate Hedging, Not Equity Portfolios. American Economic Journal: Macroeconomics 1 (2), Jeanne, O. (23, August). Why do emerging economies borrow in foreign currency? CEPR Discussion Papers 43, C.E.P.R. Discussion Papers. Korinek, A. (29). Excessive dollar borrowing in emerging markets balance sheet effects and macroeconomic externalities. University of Maryland, mimeo. Krugman, P. (1998). Analytical afterthoughts on the asian crisis. Lane, P. R. and J. C. Shambaugh (21, March). Financial exchange rates and international currency exposures. American Economic Review 1 (1),

26 Schmitt-Grohe, S. and M. Uribe (23). Closing small open economy models. Journal of International Economics 61 (1), Schneider, M. and A. Tornell (24, 7). Balance sheet effects, bailout guarantees and financial crises. Review of Economic Studies 71, Tille, C. and E. van Wincoop (21, March). International capital flows. Journal of International Economics 8 (2), A Appendix A: Solving for portfolio choices of entrepreneurs, households and foreign lenders This appendix presents the solution for the zero-order portfolio choices in the case where households and entrepreneurs trade both dollar bonds and peso bonds with foreign investors, and where we make the assumption that the foreign lenders are small and risk averse. Define the entrepreneurs and households real holdings of peso bonds as b Et B Et /Pt T, b Ht B Ht /Pt T and b F t B F t /Pt T and their net worth as a Et f Et + b Et, a Ht f Ht + b Ht and a F t f F t + b F t. The only equilibrium conditions of the model where these peso bond and net worth positions show up are the entrepreneurs budget constraint, the foreign lenders budget constraint and and the economy s resource constraint 5. We rewrite the equations: c T Et + p N t c N Et + a Et = Rt Pt 1 T a Et 1 + (R t R Pt T t )b Et 1 + p N t A N L N t +yet T w t (L N t + L T t ). (A.1) and c F t + a F t + d F t = R Pt 1 T a F t 1 + (R t R Pt T t )b F t 1 + R d F t 1 + y F t (A.2) and ) c T Et + c T Ht + a Et + a Ht = R Pt 1 (a Et 1 + a Ht 1 ) + (R T t R Pt T t (b Et 1 + b Ht 1 ) + yet T + yht T (A.3) Denote the first-order components of the excess return of the portfolio of entrepreneurs and households as ɛ E t b E R( ˆP T t 1 ˆP T t + ˆR t ˆR ) and ɛ H t b H R( ˆP T t 1 5 The households budget constraint can be obtained by combining these constraints. 24

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