Foreign Asset Accumulation among Emerging Market Economies: a Case for Coordination

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1 Foreign Asset Accumulation among Emerging Market Economies: a Case for Coordination Hao Jin Xiamen University Hewei Shen Indiana University ABSTRACT We develop a two-sector, core-periphery country general equilibrium framework with endogenous financial crises and argue for coordination on foreign asset accumulations among emerging market economies (EMEs). We show that a national planner in each peripheral country prefers a higher foreign asset position than the decentralized agents. This is consistent with the policy prescription derived in Bianchi (211). However, a coordinator for all peripheral countries, who internalizes the effect of aggregate peripheral savings on the world interest rate, prefers a lower foreign asset position relative to the national planner. We find that uncoordinated foreign asset accumulations may even be inferior to decentralized equilibrium once we allow for a variable world interest rate. Our quantitative analysis shows that the coordinated level of net foreign assets for the peripheral countries is only 56% that of the uncoordinated level. Keywords: Foreign Asset Accumulation; World Interest Rate; Policy Coordination; Credit Constraints; Financial Crises. JEL Classification: D62; E43; F32; F42; G1 We are indebted to Juan Carlos Hatchondo and Amanda Michaud for many thoughtful comments. We thank Yongquan Cao, Siming Liu and Jaeger Nelson for helpful discussions. We thank seminar and conference participants at Indiana University, 215 Fall Midwest Macroeconomics Meeting, and the 1th Annual Washington University of St.Louis Economic Graduate Student Conference. All errors are our own. Corresponding author: Wang Yanan Institute for Studies in Economics and Department of International Economics and Trade, School of Economics, Xiamen University. haojin.econ@gmail.com Department of Economics, Indiana University, Bloomington. heshen@indiana.edu 1

2 1 INTRODUCTION There have been many macro-prudential policy proposals that suggest individual emerging market economies (EMEs) with less developed financial markets accumulate foreign assets to insure against financial crises, especially in emerging Asian economies. For instance, the 1997 Asian financial crisis had a profound impact on the economic performance of emerging Asian economies. Before the crisis, the Asian emerging economies experienced constant capital inflows and high economic growth. This trend was suddenly reversed in Table 1 and 2 report the real GDP growth and current account balance of selected Asian countries 1 from 1994 to 2. We can see that in 1998, capital flowed out dramatically and total production dropped by more than 5% on average in these economies. More importantly, the crisis seemed to waken the desire for emerging Asian economies to maintain positive net foreign asset positions. Figure 1 plots the average net foreign asset position as a share of GDP for these emerging Asian economies over the past three decades. It is clear that, after the crisis, emerging Asian economies accumulated net foreign assets (NFAs) at an unprecedented pace. Table 1: Real GDP Growth (%) Country Indonesia Malaysia Philippines Thailand Vietnam Republic of Korea Table 2: Current Account Balance (%GDP) Country Indonesia Malaysia Philippines Thailand Vietnam Republic of Korea Prevailing theory suggests that the buildup of NFAs by emerging Asian economies, 1 The selected countries include Indonesia, Malaysia, Philippines, Thailand, Vietnam, and Republic of Korea. 2

3 NFA/Tradable GDP(%) Change of NFA/Tradable GDP(%) Selected Emerging Asia's Net Foreign Assets/Tradable GDP Year Selected Emerging Asia's Change of Net Foreign Assets/Tradable GDP Year Figure 1: Selected Emerging Asia s Net Foreign Assets/Tradable GDP Data Source: World Bank s World Development Indicators. The data is in annual frequency from 198 to 212. The selected emerging Asian countries include Indonesia, Malaysia, Philippines, Thailand, Vietnam, and Republic of Korea. with underdeveloped financial systems, was done to self-insure against volatile capital flows. 1 Empirical evidence also lends itself favorably to the importance of holding foreign assets to avoid international financial crisis, not only in the 1997 Asian crisis but also in the 28 global financial crisis 2. The rise of NFA positions is consistent with the policy prescriptions in Bianchi (211), Korinek (21) and Korinek (211). These studies characterize the optimal macro-prudential policies in the context of a single small open economy. We revisit this issue in the context of multiple small open economies, which raises the issue of coordination among macro-prudential policies. We argue in this paper that EMEs should collectively, through coordination, accumulate less NFAs relative to the policy proposed in Bianchi (211), Korinek (21) and Korinek (211). This is because that while savings from individual EMEs are relatively small, and are therefore unlikely to impact the world interest rate, the aggregate savings from all EMEs are of considerable size and are likely to push up the prices on foreign assets. Bernanke (25) famously links the global saving glut to the low 1 See for example, Aizenman and Marion (23) and Gourinchas and Obstfeld (212) for a review. 2 Flood and Marion (1999), Dominguez et al. (212), Frankel and Saravelos (212), Catão and Milesi- Ferretti (214) and Bussière et al. (215) provide detailed evidence. 3

4 global interest rates observed in the 2s. Follow-up empirical papers strongly support this hypothesis: the aggregate capital flows to reserve assets have a significant effect on the rate of returns of those assets 1. We develop a two-sector, core-periphery country model to study the optimal foreign asset accumulation for EMEs quantitatively. The periphery consists of a continuum of small open economies (SOEs), each facing a financial friction in which borrowing is constrained by the value of collateral. The borrowing is denominated in the international unit of account, i.e. tradable goods. The collateral is in the form of current endowment income from both the tradable and nontradable sectors, as in Mendoza (22) and Bianchi (211). The core country is financially developed, and does not face any credit constraints. Two externalites arise in this model: a relative price externality and an interest rate externality. A relative price externality emerges as decentralized agents fail to internalize the effect of their saving/borrowing decisions on the market value of their collateral. As a result, they tend to overborrow/undersave and are vulnerable to sudden stop crises 2. Building off of the existing literature, our framework also features an interest rate externality. The interest rate externality results from individual national planners failing to take into consideration the general equilibrium effects of their saving/borrowing decisions on the world interest rate. To analyze the welfare and regulatory implications of the externalities, we compare three equilibria in our model: the decentralized equilibrium, the SOE planner equilibrium, and the periphery coordinator equilibrium. In the decentralized equilibrium, private agents in each SOE make saving/borrowing decisions competitively, taking both the collateral value and the world interest rate as given. As a consequence, the private agents fail to internalize both the relative price and the interest rate externalities. Following the current literature on designing optimal macroprudential policies, we assume there exists a national planner for each SOE who internalizes the relative price externality since this externality arises at the national level. On the other hand, each SOE planner fails to internalize the interest rate externality. Finally, we assume there exists a periphery coordinator who coordinates saving/borrowing decisions on behalf of all SOEs and therefore takes into consideration both externalities. Table 3 summarizes the three equilibria we consider in the model and the externalities each of them internalizes. We find that the SOE planner prefers an allocation with a higher NFA position 1 For example, Warnock and Warnock (29) finds international purchases of U.S. Treasuries to significantly lower U.S. long-term interest rates. 2 Bianchi (211), Korinek (21) and Korinek (211) provide detailed explanations on this relative price externality and propose corresponding policy perscriptions. 4

5 than the one preferred by the private agents, resulting from the internalization of the relative price externality. Private agents facing an occasionally binding credit constraint tend to undervalue the liquidity of their asset holdings, as highlighted in Lorenzoni (28), Bianchi (211), Korinek (21) and Korinek (211). The SOE planner therefore should encourage saving to reduce systemic risks and avoid financial crises. Critically, the SOE planner takes the world interest rate as given. On the other hand a periphery coordinator, that takes into account the general equilibrium effect of SOEs saving decisions on the world interest rate, prefers an allocation with a lower NFA position than the one preferred by the SOE planner. This lower NFA position in turn leads to a higher rate of return on savings 1. After calibrating our model to a group of emerging Asian economies, our quantitative analysis shows the coordinated NFA level for each peripheral country is only 56% of the uncoordinated level, and is 58% of the decentralized equilibrium level. More strikingly, in the absence of policy coordination, country-level foreign asset accumulations may reduce welfare once we take into account the variable world interest rate. This means instead of undersaving, the peripheral countries may oversave during normal times. Our result suggests that macro-prudential policy proposals that fail to consider the general equilibrium effect on the world interest rate may be misguided. Notice that we do not pursue a global welfare objective in this paper. When a group of countries exerts market power to manipulate the world interest rate, the other group of countries are worse off. In total, this monopolistic behavior reduces global welfare as suggested by Korinek (213) and Korinek (216). Therefore, the coordination policy we consider in this paper is desirable from the joint perspective of periphery countries, but not desirable from a global perspective. Our contribution is to highlight how coordination within the groups of economies to manipulate the world interest rate through monopoly power may overturn the direction of a desirable national macro-prudential policy intervention and quantify its effects. The rest of the paper is structured as follows. We start with a discussion of the related literature in section 2. In section 3 we use a three period model to demonstrate analytically the key externalities and their effects on saving decisions. In section 4 and 5 we extend the three-period model into an infinite horizon model to quantitatively analyze the macroeconomic and welfare implications of foreign asset accumulation 1 We restrict our attention to the case that periphery countries are net savers. We think this case is of clear relevance in the current economic environment since a lot of emerging market economies have engaged in large amounts of foreign asset accumulation. If periphery countries are net borrowers, then the coordinator should keep the world interest rate lower by borrowing less. 5

6 Decentralized Agents Small Open Economy Planner Periphery Coordinator Table 3: Comparison of Three Equilibria Internalize the Internalize the Relative Price Externality Interest Rate Externality coordination. Specifically we compare the decision rules and the welfare outcomes between the decentralized agents, SOE planner, and the periphery coordinator equilibria. Finally, section 6 offers some concluding remarks. 2 RELATED LITERATURE This paper is related to a series of recent papers 1 that proposes the use of exante macro-prudential policies to prevent financial crises and improve social welfare in SOEs. The existing literature adopts a specific form of financial frictions, an occasionally binding collateral constraint, following the work by Mendoza (22) and Mendoza (21) to generate an endogenous financial crisis. The argument for macroprudential policies of this sort is that ex-ante restrictions on external liabilities can improve welfare. This is because the additional liquidity private agents carried over relaxes future financial constraints and reduces the likelihood of a crisis. However, private agents do not take into account the social value of liquidity. The economy exhibits excessive borrowing (insufficient saving) during normal times, and as a result, a national planner should discourage borrowing (encourage saving). Our model extends their framework to a general equilibrium setting. This allows us to endogenize the world interest rate and to capture another pecuniary externality, i.e. the interest rate externality, that is absent from the existing literature. We show the SOEs may be oversaving instead of undersaving during normal times 2, and coordination on savings improves welfare for the SOEs. Another branch of literature examines how a national planner in a large economy may use capital controls to take advantage of its monopoly power of manipulating intertemporal prices. Some notable contributions include Hamada (1966), Rogoff and 1 Some pioneering works include Bianchi (211), Korinek (21) and Korinek (211). 2 Benigno et al. (213) concludes the same result, but for a different reason. Their argument is that when ex-post policy instruments are available to mitigate financial crises, ex-ante prudential measures are inefficient. 6

7 Obstfeld (1996) and Costinot et al. (214). In our framework, many SOEs, by coordinating on their foreign asset accumulations, are also capable of influencing the intertemporal prices, i.e. the world interest rate. We complement the existing analysis by incorporating financial instability into the framework, and study how the considerations of financial stability and intertemporal price management interact and shape optimal policies. Notice that distorting intertemporal prices in the global economy has a beggar-thy-neighbor effect. It improves national welfare at the cost of reducing global welfare; however, in this paper we do not examine globally optimal policies. It is also important to discuss the macro-prudential policy coordination literature. Korinek (213) and Korinek (216) show room for global coordination if capital controls are designed to exert market power to manipulate international prices. In this direction, Bengui (213) and Rabe (216) investigate macro-prudential policy in a multi-country model and find a role for coordination. Both papers provide specific externalities that benefit individual nations but reduce global welfare. The policy coordination we consider in this paper is not globally Pareto efficient. The welfare of periphery countries is improved if they exert market power. However, the core country is worse off more than the periphery countries gain. 3 A THREE-PERIOD MODEL We highlight how the relative price and interest rate externality affect the decision rules using a three-period model. This model is stylized but provides clear analytic results from which we can derive intuition on how the two externalities interact and affect the optimal foreign asset accumulation. Our analytic framework draws from Korinek (211). In that paper, he develops a three-period, small open economy model featuring endogenous financial crises due to the presence of an occasionally binding collateral constraint. We extend Korinek (211) s model to a core-periphery country setting in order to emphasize the general equilibrium effect on the world interest rate, which is a key ingredient in our analysis. In our model, the world economy consists of two categories of countries, core and periphery. The countries are of equal size 1. We model the periphery as a continuum of small open economies (SOEs) and the core as one large country. We also assume that periphery countries are completely identical in the sense that they share the same preferences, market structure and endowments. Each country is populated by a representative agent who lives for three periods and receives an endowment in 1 We normalize the size of each category of countries to 1. We relax this assumption in the infinite horizon model. 7

8 tradable goods, nontradable goods or a combination of both in every period. International borrowing and lending in the unit of tradable goods is only possible between the core and periphery. Moreover, the peripheral countries are financially underdeveloped such that the borrowing contracts are not perfectly enforceable. As a result, they face a collateral constraint and can only borrow up to a certain fraction of their income in each period. In contrast, the core country is financially developed so that it does not face such a collateral constraint. We write out the three-period model in more details and then solve for the peripheral countries decision rules for three equilibria: decentralized equilibrium, SOE planner equilibrium, and periphery coordinator equilibrium. 3.1 PERIPHERAL COUNTRIES A representative agent in each of the peripheral countries, denoted by a country identifier i, consumes tradable goods in period and 2 and a composite of tradable and nontradable goods in period 1. The composite good is in Cobb-Douglas form and σ is the share of the tradable good. We assume the utility function takes the form of log in the first two periods, and is linear in terminal wealth in the last period. The agent s discount factor is β. As all peripheral countries are identical, without loss of generality we drop the country specific identifier i and write the peripheral country s problem as maximizing: U = log(c σ T, ) + βlogc 1 + β 2 c T,2, where c 1 = c σ T,1 c1 σ N,1 (3.1) subject to period-by-period budget constraints. We assume the tradable endowment follows y T, = σ, y T,1 = and y T,2 = σ. This assumption resembles a large fall of tradable output in period 1, so that the private agents have an incentive to save in period and borrow in period 1 in order to smooth consumption intertemporally. The peripheral countries receive a nontradable endowment of the amount y N,1 = 1 σ in period 1 only. The international asset market is incomplete, and the core and peripheral countries can only trade one-period risk-free bonds, the only mechanism through which countries can allocate resources intertemporally. The peripheral countries budget constraints are written as: c T, + a = y T,, (3.2) c T,1 + pc N,1 + a 1 = y T,1 + py N,1 + r a, (3.3) c T,2 = y T,2 + r 1 a 1. (3.4) Equations (3.2), (3.3), and (3.4) are the budget constraints for period,1 and 2 re- 8

9 spectively. They are denominated in terms of tradable goods. Peripheral countries savings in period and 1 are denoted by a and a 1 respectively where p is the relative price of nontradable goods in terms of tradable goods. The interest rates are denoted by r and r 1. Since the peripheral countries have tradable endowment in period 1, they want to borrow from the core country in period 1 in order to smooth consumption. This implies a is positive and a 1 is negative in equilibrium. In addition to the budget constraints, the peripheral countries are subject to a collateral constraint when they borrow in period 1. The collateral constraint reads as: a 1 κ(y T,1 + py N,1 ). (3.5) This borrowing constraint is in the same spirit as the one used in Mendoza (21), Bianchi (211) and Korinek (211). This financial friction restricts the borrowing capacity of peripheral countries up to a fraction κ of the market value of their income in period 1. Therefore, κ can be interpreted as the tightness of the international financial market. 3.2 CORE COUNTRY The core country is financially developed in the sense that it does not face any financial frictions. For tractability, we assume the core country consumes only tradable goods. The main result does not change qualitatively if we relax this assumption and allow the core country to consume both tradable and nontradable goods. A representative agent in the core country maximizes life-time utility: U = logc T, + βc T,1 + β2 c T,2, (3.6) subject to period-by-period budget constraints. The representative agent in the core country is risk averse between period and 1 and risk neutral between period 1 and 2. We specify the utility function in this way to guarantee a constant world interest rate between the latter two periods, but a variable rate between the first two periods. This specification allows us to disentangle the two externalities that emerge in this model. We will see later that the relative price externality arises only between the latter two periods and the interest rate externality shows up only between the first two periods. We denote all core country variables with a superscript asterisk. 9

10 The budget constraints are given by: c T, + a = y T,, (3.7) c T,1 + a 1 = y T,1 + r a, (3.8) c T,1 = r 1a1 + y T,2. (3.9) We assume the core country discounts utility at the same rate, β, as the periphery countries. Let a t denotes the saving/borrowing decisions made by the core country in period t, and y T,t represents the tradable endowment that core country receives in period t. The first order conditions from the core country s problem imply that: r = 1 1 β y T,, (3.1) a r 1 = 1 β. (3.11) The required rate of return between period 1 and 2 equals the inverse of the discount factor β since the core country is risk neutral between these two periods and only requires to be compensated by a return that makes agents indifferent between consuming in either period. The required rate of return between the first two periods, r, is decreasing with initial wealth y T, and increasing with first period asset position a. This suggests when the interest rate is low, the core country borrows more and vice versa. 3.3 MARKET CLEARING CONDITIONS This section summarizes the market clearing conditions. Since the savings and borrowing must take place between the peripheral countries and the core country, the net asset position in the world must equal zero in each period: where i is the peripheral country index. a i di + a =, (3.12) a1 i di + a 1 =, (3.13) In addition, the tradable good market clears each period globally, and nontradable 1

11 good market clears for each peripheral country in period 1: c i T,t di + c T,t = y i T,t di + y T,t, t =, 1, 2 (3.14) c i N,1 = yi N,1, i (3.15) Using the asset market clearing conditions in the interest rate schedule (3.1), we demonstrate how the interest rate externality arises in this model. Interest rate schedule (3.1) becomes: r = 1 1 β y T, + a i (3.16) di. When the peripheral countries make saving decisions in period, (3.16) implies that interest rate goes down when they save more. However, individual country in the periphery takes the world interest rate as given, and does not internalize the general equilibrium effect on the world interest rate. A periphery coordinator who coordinates saving/borrowing decisions on behalf of all the peripheral countries, on the other hand, internalizes the interest rate externality. By managing the aggregate capital flows the periphery coordinator can achieve a more favorable world interest rate. In section 3.4 and 3.5, we solve the equilibria for the decentralized agents, the SOE planner, and the periphery coordinator in turn. We then compare the equilibria to show how the relative price externality and interest rate externality affect the market clearing allocations. 3.4 SOLUTION TO THE DECENTRALIZED EQUILIBRIUM We first solve for the decentralized equilibrium. The private agents take both the relative price of nontradable goods and the world interest rate as given when making consumption and savings decisions PERIOD 1 PROBLEM We solve the decentralized equilibrium by backward induction. Consider the representative agents problem in each peripheral country at period 1. Define m = y T,1 + r a as the starting tradable wealth at period 1 and treat it as the state variable, and r a is the the savings from period. This problem can be written as follows: V de (m) = max [log(c 1 ) + β(y T,2 + r 1 a 1 )], c T,1,c N,1,a 1 where c 1 = c σ T,1 c1 σ N,1 (3.17) 11

12 subject to the period 1 budget constraint and financial constraint, c T,1 + pc N,1 + a 1 = m + py N,1, (3.18) a 1 κ(y T,1 + py N,1 ), (3.19) where V de (m) is the value function at period 1 and is a function of starting tradable wealth m. The first order conditions with respect to c T,1, c N,1 and a 1 are: σ = µ, c T,1 (3.2) 1 σ = pµ, c N,1 (3.21) βr 1 µ + λ =, (3.22) where µ and λ are the Lagrangian multipliers associated with constraints (3.18) and (3.19) respectively. Combining first order conditions (3.2) and (3.21) yields the relative price as a function of tradable and non-tradable consumption: p = 1 σ σ c T,1 c N,1. (3.23) Given the assumption y N,1 = 1 σ and that the non-tradable goods market clears, c N,1 = y N,1, the relative price between tradable and non-tradable becomes, p = c T,1 σ, (3.24) which shows that the relative price of tradable goods in period 1 is increasing in tradable consumption. Equation (3.24) helps us illustrate the relative price externality in this model. Assume the borrowing constraint is binding in period 1, one extra unit of assets carried over to period 1 (i.e., save more in period to increase m by one), increases consumption c T,1 by one unit. Moreover, from (3.24), we can see such an increase in c T,1 pushes up the relative price of nontradable goods, and relaxes the borrowing constraint as in (3.19). As a result, private agents are able to borrow more and to further increase the period 1 consumption c T,1. This feeds back into the financial constraint and generates a financial amplification effect. However, when the private agents make their 12

13 consumption decisions in period 1, they take the relative price of the nontradable goods as given. This generates a relative price externality as private agents fail to internalize the effect of their consumption decisions on the relative price, which in turn affects their borrowing capacity. In contrast, both the SOE planner and the periphery coordinator internalize this relative price externality. We proceed to solve the period 1 problem for two cases. In one case the borrowing limit is reached, and in the second case the borrowing constraint is slack. We also show the conditions under which the borrowing constraint will be binding. Loose Financial Constraint The borrowing constraint being slack in period 1 implies λ =. We plug this into (3.22) and obtain: µ = βr 1. (3.25) Substituting µ from the expression above into the optimality conditions (3.2) and (3.21), we can write the tradable consumption, c T,1, and relative price, p, in period 1 as: c T,1 = σ, βr 1 (3.26) p = 1. βr 1 (3.27) Finally plugging these two expressions into the budget constraint (3.18) yields the asset position in period 1: a 1 = m σ βr 1. (3.28) Substitute the values of c T,1 and a 1 into the objective function to obtain the period 1 value function as a function of starting tradable wealth m: V de,slack (m) = v de,slack + βr 1 m, (3.29) where v de,slack = σlog (σ/(βr 1 )) + (1 σ)log(1 σ) + βy T,2 σ is a constant and does not depend on the starting tradable wealth m. As shown in (3.29), the value function is linear in starting tradable wealth m. Therefore, the derivative of (3.29) with respect to m is given by: V de,slack m = βr 1. (3.3) 13

14 The derivative of the value function measures the marginal value of carrying one extra unit of liquid tradable goods from period to 1. Given that the interest rate r 1 = 1/β from the core country s optimization condition, the marginal value of liquidity Vm de,slack = 1 when the borrowing capacity is ample. Intuitively, when the financial constraint is non-binding, the private agents are able to borrow freely at the interest rate r 1. As a result, the private agents are indifferent between carrying one unit liquidity m into period 1 and borrowing one unit of liquidity in period 1. Binding Financial Constraint Now we consider the more interesting case where the borrowing constraint is binding in period 1. When the borrowing constraint is binding, the total borrowing equals the collateral value of the endowment income in period 1: a 1 = κ(y T,1 + py N,1 ), (3.31) Substitute the binding constraint (3.31) into the budget constraint (3.18), we can back out the tradable consumption in period 1: c T,1 = m a 1. (3.32) Plug c T,1 from (3.32) into the objective function to obtain the value function as a function of starting tradable wealth m and asset position a 1. The value function V de,bin is given by: V de,bin (m) = v de,bin + σlog(m a 1 ) + βr 1 a 1, (3.33) where v de,bin = (1 σ)log(1 σ) + βy T,2 is a constant and does not depend on m. Analogous to the case when the borrowing constraint is slack, the derivative of (3.33) with respect to m measures the marginal value of liquidity when the borrowing constraint is binding: V de,bin m = σ c T,1. (3.34) As we will show later, c T,1 < σ when the private agents borrow up to the limit. Therefore, a comparison between (3.34) and (3.3) implies Vm de,bin > Vm de,slack. The private agents value liquidity more when the financial constraint binds than the case when the constraint is slack. This is because the private agents can borrow no more to achieve the desired consumption level σ when the financial constraint binds. As a consequence, each unit of consumption becomes more valuable. To solve for the explicit asset allocation a 1 and consumption c T,1 when the bor- 14

15 rowing constraint is binding, we combine equations (3.31) and (3.32) to obtain: a 1 = κ σy T,1 + my N,1 σ κy N,1, (3.35) c T,1 = σ κy T,1 + m σ κy N,1. (3.36) We then solve for the explicit marginal liquidity value Vm de,bin. Since the private agents do not internalize how tradable consumption depends on the starting tradable wealth, the marginal value of liquidity can be calculated by plugging (3.36) into (3.34): V de,bin m = σ κy N,1 m + κy T,1. (3.37) So far we have solved for the period 1 decision rules when the financial constraint is either slack or binding. We have also shown that the private agents value liquidity more when the financial constraint is binding as extra liquidity relaxes the borrowing constraint. Next we investigate the necessary and sufficient conditions for the borrowing constraints to bind. From the collateral constraint (3.19), the financial constraint is binding as long as: a 1 > κ(y T,1 + py N,1 ). (3.38) Using the asset position derived under the loose financial constraint (3.28) to substitute out a 1, we can see the financial constraint is binding at period 1 if and only if: a < 1 [ (κ + 1)y T,1 + κy N,1 σ ]. (3.39) r βr 1 βr 1 This condition says if the private agents save less than the threshold illustrated above at period, he/she will borrow up to the collateral limit at period 1 in order to have a consumption level that is as close as possible to the optimal level. The binding threshold depends on the income at period 1, the interest rate, and the tightness of the financial constraint PERIOD PROBLEM Now we use the decision rules derived from the period 1 problem to solve for the decision rules in period. Given the value function from the period 1 problem, we can rewrite the period objective as: max a [log(y T, a ) σ + βv de (m)] (3.4) 15

16 where V de {V de,slack, V de,bin }, depending on whether (3.39) is satisfied. The first order condition with respect to a is, σ c T, = βr V de m, (3.41) where Vm de = Vm de,slack if a does not satisfy (3.39) and Vm de = Vm de,bin if (3.39) is satisfied. This equation characterizes the decentralized consumption/savings decision in period. 3.5 SMALL OPEN ECONOMY PLANNER AND PERIPHERY COORDINATOR In this section, we characterize equilibria for the SOE planner and the periphery coordinator. We then compare them with the decentralized equilibrium. A SOE planner maximizes the representative agent s utility subject to the same set of constraints, but internalizes the effect of individual saving and consumption decisions on the relative price of the nontradable goods. On the other hand, this SOE planner still takes the world interest rate as given. This is because the savings from each SOE are small and unlikely to affect the world interest rate. However, the aggregate savings from all peripheral countries are of considerable size, and are likely to influence the world interest rate. This generates an interest rate externality that is absent from single SOE analysis. A coordinator for all the peripheral countries who takes into consideration this interest rate externality in addition to the relative price externality, chooses a different asset position compared to the SOE planner and the decentralized agents in period. By coordinating on the saving behaviors, the periphery coordinator is able to internalize both externalities and improve welfare PERIOD 1 PROBLEM The set-up of the problems of the SOE planner and the periphery coordinator are identical to the problem of the private agents. We will solve their problems by backward induction. Notice that the decision rules of the SOE planner and the periphery coordinator are identical except in period since the interest rate externality only arises between period and period 1. Therefore, we denote the variables from both the SOE planner and the coordinator s problem as sp (social planner) and make no distinction between them when we solve the period 1 problem. When the borrowing constraint is slack in period 1, the social planner s allocations collapse to those of the private agents. As a result, we only discuss the case where the borrowing constraint is binding in period 1. The difference between the period 1 problems of the decentralized agents and the 16

17 social planner is that social planner internalizes the the effect of a binding constraint on the saving and consumption decisions. Therefore, we plug in (3.35) and (3.36) and write the social planner value function in period 1 as: V sp,bin (m) = v sp,bin + σlog(m + κy T,1 ) βr 1 κmy N,1 σ κy N,1, (3.42) where v sp,bin = σlog(σ/(σ κy N,1 )) + (1 σ)log(1 σ) + βy T,2 βr 1 κσy T,1 /(σ κy N,1 ) is a constant and unrelated to m. Taking the derivative with respect to m in (3.42) yields the marginal value of liquidity to the social planner when the borrowing constraint is binding: V sp,bin m = σ m + κy T,1 βr 1 κy N,1 σ κy N,1, (3.43) Lemma 1 summarizes the liquidity value for the SOE planner and periphery coordinator in period 1 when the borrowing constraint is either slack or tight. Lemma 1. When the financial constraint is slack in period 1, the decentralized agents, SOE planner, and periphery coordinator value liquidity identically on the margin, V de,slack V sp,slack m m = = 1. When the financial constraint is binding, the SOE planner and periphery coordinator value liquidity the same, but more than the decentralized agents, Vm de,bin < Vm sp,bin. Proof. The case when the financial constraint is slack is easy to show. From (3.3) we can see that the decentralized marginal value of liquidity is 1. The social planner values liquidity the same as private agents because when the financial constraint is not binding, the borrowing in period 1 does not depend on collateral value. If the financial constraint is binding, the difference between the two marginal values of liquidity is: V sp,bin m V de,bin m = σ m + κy T,1 βr 1 κy N,1 σ κy N,1 σ κy N,1 m + κy T,1 = κy N,1 m + κy T,1 βr 1 κy N,1 σ κy N,1, (3.44) where the two marginal liquidity values are given by (3.37) and (3.43) respectively. We plug in βr 1 = 1 from the core country s problem to show: κy T,1 + m σ + κy N,1 = κy T,1 + y T,1 + r a σ + κy N,1 = r a σ + κ(1 σ) <. (3.45) 17

18 The last equality holds when we plug in the tradable and nontradable endowments y T,1 = and y N,1 = 1 σ. The last inequality in (3.45) holds as long as (3.39) is satisfied, which must be true when the financial constraint is binding in period 1. As a result, (3.45) implies Vm sp,bin Vm de,bin > and hence the social planner values liquidity more than decentralized agents when the borrowing constraint is binding. Lemma 1 proves that if the borrowing constraint is binding in period 1, the SOE planner and the periphery coordinator value liquidity more than decentralized agents, on the margin. The SOE planner and periphery coordinator know that the marginal benefit of extra savings in period will be amplified when the borrowing constraint is binding in period 1. As a result, the presence of the relative price externality induces the SOE planner and the periphery coordinator to save more relative to the private agents in period PERIOD PROBLEM We proceed to solve the social planner s problem at period. Notice that due to the existence of an interest rate externality, the decision rules of the SOE planner and the periphery coordinator differ in period. The first order condition with respect to a for the SOE planner is, and with respect to a for the periphery coordinator is, σ c T, = βr V sp m, (3.46) σ c T, = β r a a V sp m, (3.47) where Vm sp {Vm sp,slack, Vm sp,bin }, depending on if (3.39) is satisfied. r is determined in general equilibrium and depends on the choice of a which is internalized by the periphery coordinator but not the SOE planner. We combine the optimality conditions and impose market clearing conditions to obtain equilibria for the private agents, SOE planner, and periphery coordinator. Proposition 1 summarizes and compares the allocations under each equilibrium. Proposition 1. If the financial constraint is slack in period 1, the decentralized agents and the SOE planner save the same amount in period, but more than the periphery coordinator. If the financial constraint is binding, the SOE planner saves more than the decentralized agents and the periphery coordinator in period. Proof. We outline the proof of proposition 1 in this section, and put the details in 18

19 appendix A. We plug the interest rates equation (3.11) and financial market clearing condition (3.13) into the period Euler equations, (3.41), (3.46), and (3.47), of the private agents, SOE planner and periphery coordinator respectively: Decentralized Agents: SOE Planner: PC: σ y T, a de σ y T, a soep σ y T, a pc = = 1 y T, + ade }{{} asset returns 1 = y T, + asoep }{{} asset returns 1 y T, + apc }{{} asset returns V de m }{{} private liquidity value V sp m }{{} social liquidity value a pc (y T, + apc }{{ )2 } return externality V sp m }{{} (3.48) (3.49) social liquidity value (3.5) The left hand sides of those three equations represent the marginal costs of saving one extra unit of tradable goods in period. The right hand sides represent the marginal benefits of carrying the additional savings to period 1, where Vm de and Vm sp denote the marginal value of liquidity from the perspective of the decentralized agent and the social planner, respectively. Financial constraint is slack in period 1 the private value as shown in Lemma 1. This implies V de m The social value of liquidity coincides with = Vm sp = 1. It is obvious from (3.48) and (3.49) that a de = asoep in this case. Thus, private agents and the SOE planner save the same amount in period. On the other hand, the periphery coordinator understands higher savings lowers the rate of return. This is reflected by the return externality term in equation (3.5), which is absent in the private agents and SOE planner s Euler equations. Therefore, the periphery coordinator saves less than the private agents and the SOE planner in period. Financial constraint is binding in period 1 The SOE planner values liquidity more than the private agents, i.e. Vm sp,bin > Vm de,bin, as proved in Lemma 1. Consequently, the desire to relax future financial constraints induces the SOE planner to save more in period relative to the private agents. Next we compare the period savings decisions between the SOE planner and the 19

20 periphery coordinator. They differ because the periphery coordinator internalizes the general equilibrium effect of savings on the world interest rate. This effect is captured by the return externality term, a pc /(y T, + apc )2, in the periphery coordinator s Euler equation (3.5). As a result, the periphery coordinator saves less than the SOE planner in period in order to better manage the world interest rate. When the financial constraint is binding, the extra unit of savings carried over has two competing effects from the point of view of the periphery coordinator. On the one hand, it relaxes the future financial constraints and on the other hand, it puts downward pressure on the rate of return on savings. These two forces move in opposite directions. The relative strength of these two effects determines the difference in savings between private agents and the periphery coordinator. A closed-form solution to compare these two effects is difficult to obtain, however, we rely on numerical methods to analyze how these two effects play out. 4 AN INFINITE HORIZON MODEL In this section, we extend the three-period model to an infinite horizon model in order to evaluate the nation-level macro-prudential policies analogous to the SOE planner, and to quantitatively analyze the optimal level of NFAs and any welfare gain associated with policy coordination. We introduce two sources of uncertainties into the peripheral countries, one in the income process and the other in the financial market. We also use more general utility and technology functions. There is no uncertainty in the core country. As in the three-period model, we study three equilibria: the decentralized equilibrium (DE), the small open economy planner (SOE Planner) equilibrium and the periphery coordinator (PC) equilibrium. In order to simplify the analysis and ease the computational burden, we model the agents in the core country as overlapping generations. 4.1 PERIPHERAL COUNTRIES The set-up of the peripheral countries problem is similar to the one in the three-period model but the time horizon is now infinite. There is a continuum of identical peripheral countries. In each peripheral country, there is a representative agent. The representative agent maximizes life-time utility: U t = E t= β t c1 γ t 1 γ, (4.1) 2

21 subject to a flow budget constraint: c T,t + p t c N,t + a t+1 = y T,t + p t y N,t + r t a t, t (4.2) where c t = [ω(c T,t ) η + (1 ω)(c N,t ) η ] 1/η is a composite good and is produced using CES combination technology from tradable and nontradable goods. The relative price of nontradable goods in terms of tradable goods is denoted as p t. We let γ denotes the relative risk aversion, η and ω measure the elasticity of substitution between tradable and nontradable goods and agents relative preference for tradable goods respectively. At the beginning of each period, the stochastic endowments y T,t and y N,t are realized. The agent then make decisions on tradable consumption c T,t, nontradable consumption c N,t and next period s asset position a t+1. The peripheral countries also face a collateral constraint: (4.3), a t+1 κ t (y T,t + p t y N,t ), (4.3) where their borrowing capacity is limited to a fraction κ t of the market value of their current period income. κ t is stochastic and measures the tightness of this borrowing constraint in period t. The first order conditions with respect to tradable and nontradable goods imply a relative price function: p t = 1 ω ω ( ct,t c N,t ) 1+η. (4.4) The price function (4.4) indicates that the relative price of nontradable goods is increasing in the tradable consumption. Therefore, the relative price externality is preserved in the infinite horizon model. The first order condition with respect to asset holdings implies an Euler equation: U de T,t = βe tr t+1 U de T,t+1 + λde t, (4.5) where UT,t de = ωc1 γ t c η 1 T,t /(ωc η T,t + (1 ω)c η N,t ) is the first derivative of the utility function with respect to tradable consumption, and λ de t is the Lagrangian multiplier associated with the borrowing constraint (4.3). When the borrowing constraint is not binding, the Lagrange multiplier λ de t =. In this case, (4.5) collapses to a standard Euler equation that equalizes the marginal utility of current period consumption and expected discounted value of marginal utility from next period consumption. However, when the constraint (4.3) binds, λ de t >, which creates a wedge between the 21

22 current and next period s marginal utility as in (4.5). 4.2 CORE COUNTRY The core country is populated by a continuum of overlapping generation agents who live for two periods and consume only tradable goods. We denote all core country variables with a superscript asterisk. The agents in the core country do not face a collateral constraint when they participate in the international capital market. A representative agent who is born in period t maximizes lifetime utility: subject to the flow budget constraints, U t = (c T,t (t))1 γ 1 γ + β (c T,t+1 (t))1 γ 1 γ, (4.6) c T,t (t) + a t+1 (t) = y T,t (t), (4.7) c T,t+1 (t) = y T,t+1 (t) + r t+1a t+1 (t). (4.8) where the t in the bracket means that the agent is born in period t and a t+1 (t) is the representative agent s savings carried over into his last period of life. y T,t (t) and y T,t+1 (t) are the tradable endowments that core country agents who are born in period t receive in each period of their life. The representative agent s Euler equation is given by: β r t+1 (y T,t (t) a t+1 (t))γ = (y T,t+1 (t) + r t+1a t+1 (t))γ. (4.9) By comparing (4.5) and (4.9) we can see that the core and peripheral countries engage in risk sharing which in turn determines the world interest rate r t+1. When the interest rate is low, the agents in the core country are willing to borrow from peripheral countries. This implies that in equilibrium, higher savings from the peripheral countries will be associated with a lower world interest rate. Analogously, if the peripheral countries borrow more from the core country, this is associated with a higher world interest rate. Starting in section 4.5, we assume that the core country agents have deterministic endowments in their first and second period of life, so we drop the time script and denote them as y1 and y MARKET CLEARING In equilibrium, the asset market, tradable goods market and nontradable goods market all clear. The asset market clearing condition at period t is: 22

23 a i t+1 di = a t+1 (t), (4.1) where i is the peripheral country index. The nontradable goods market clears within each peripheral country i: c i N,t = yi N,t i, (4.11) and the tradable goods market clears by: c i T,t di + c T,t (t) + c T,t (t 1) = y i T,t di + y T,t (t) + y T,t (t 1). (4.12) Discussion of Assumptions Before solving the model, we would like to discuss some of our assumptions. First, we assume the populations in the core country are overlapping-generation agents. This OLG structure is mainly for computation convenience since it enables us to calculate the world interest rate period-by-period without keeping track of the entire sequence of interest rates. While the elasticity of the world interest rate is typically higher in an OLG structure compared to in an infinitely lived structure, the core country s endowment process in our calibration gives an elasticity that is consistent with the empirical regularity. Second, we assume all periphery countries are affected by identical endowment and financial shocks. Historical observations suggest emerging market economies in the same regions are often times subject to the similar external financial condition and experience economic downturn together due to financial integration. We abstract from explicitly modeling the underlying causes of the contagion but assume that the endowment processes of the peripheral countries are synchronized and those countries face the same external financial market. While periphery countries are subject to idiosyncratic shocks as well, and we agree that the analyses of policy coordination with idiosyncratic shocks are important, but it is beyond the scope of this paper. 4.4 OPTIMALITY CONDITIONS In this section we derive the optimality conditions for the decentralized agents, the SOE planner, and the periphery coordinator. The decentralized agents maximize their life-time utility (4.1), subject to the budget constraints (4.2) and borrowing constraints (4.3). Their optimality conditions are characterized by the Euler equations (4.5). Following the definition of constrained efficiency, as in Kehoe and Levine (1993), we assume the SOE planner is constrained by the same pricing rule (4.4) as the decen- 23

24 tralized agents. Specifically, the SOE planner maximizes the representative agent s lifetime utility (4.1), subject to the budget constraints (4.2) and the borrowing constraints (4.3). However, the SOE planner internalizes the relative price effect (4.4), so that the borrowing constraint becomes: [ a t+1 κ t y T,t + 1 ω ( ) 1+η ct,t y N,t]. (4.13) ω c N,t The first order conditions of the SOE planner s problem are: µ soep t µ soep t = U soep T,t + λ soep t Ψ t (4.14) = βe t r t+1 µ soep t+1 + λsoep t (4.15) where µ soep t, λ soep t are the Lagrangian multipliers attached to the budget constraint (4.2) and collateral constraint (4.13), and Ψ t = κ t p t (1 + η)(c N,t /c T,t ). Combining the first order conditions from the SOE planner s problem, we obtain the Euler equation for the SOE planner: U soep T,t = βe t r t+1 [U soep T,t+1 + λsoep t+1 Ψsoep t+1 ] + λsoep t (1 Ψ soep t ) (4.16) A comparison between the Euler equations (4.5) and (4.16) shows how the decision rules from the decentralized agents and SOE planner differ. When the borrowing constraint is not binding, the decentralized Euler equation (4.5) becomes: and the SOE planner Euler equation (4.16) becomes, U de T,t = βe tr t+1 U de T,t+1, (4.17) U soep T,t = βe t r t+1 [U soep T,t+1 + λsoep t+1 Ψsoep t+1 ]. (4.18) By comparing (4.17) and (4.18), we see that the SOE planner values next period marginal utility more than the decentralized agents. This difference is captured by the term λ soep t+1 Ψ t+1. If there is a positive probability of a binding collateral constraint in the next period, i.e. λ soep t+1 >, the SOE planner will borrow less (or save more) relative to the decentralized agents. This is a result of the SOE planner internalizing the benefit of carrying over more liquidity into the next period in order to reduce the probability of decreased borrowing capacity. The SOE planner in our framework behaves exactly the same as the constrained social planner in Bianchi (211). Crucially, 24