WPS6462 Policy Research Working Paper 6462 International Liquidity Rents Maya Eden The World Bank Development Research Group Macroeconomics and Growth Team May 2013 Policy Research Working Paper 6462 Abstract This paper presents a model of global liquidity shortages. that unrestricted liquidity flows are (a) welfare reducing Liquid claims are enforceable promises that play a for emerging economies and (b) Pareto inefficient. The transaction role. Since developed economies have a inefficiency results both from excessive investment for the comparative advantage in creating liquidity, they export purpose of creating collateral-backed liquid claims, and liquid claims to emerging economies, resulting in a from excessive global fragility with respect to collateral permanent current account deficit. This model suggests shocks. 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 http://econ.worldbank.org. The author may be contacted at meden@worldbank.org. 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 International Liquidity Rents Maya Eden ∗ World Bank, DECMG May 23, 2013 Abstract This paper presents a model of global liquidity shortages. Liquid claims are enforceable promises that play a transaction role. Since de- veloped economies have a comparative advantage in creating liquidity, they export liquid claims to emerging economies, resulting in a per- manent current account deï¬?cit. This model suggests that unrestricted liquidity flows are (a) welfare reducing for emerging economies and (b) Pareto inefficient. The inefficiency results both from excessive invest- ment for the purpose of creating collateral-backed liquid claims, and from excessive global fragility with respect to collateral shocks. JEL Classiï¬?cation: E44, F30, G15 Keywords: Liquidity shortage, the welfare effects of ï¬?nancial integration, international liquidity flows, liquidity creation Sector board: Economic Policy (EPOL) ∗ I thank Alessandro Barattieri, Ricardo Caballero, Arnaud Costinot, John Duca, Ben Eden, Anton Korinek, Ha Nguyen, Vincenzo Quadrini, Luis Serven and Christoph Steffen for helpful comments. I have also beneï¬?ted from comments made by seminar partici- pants at MIT’s international breakfast and the World Bank and conference participants at IGIDR, INFINITI and the NBER summer institute, IFM workshop. This paper reflects my own views and not necessarily those of the World Bank, its Executive Directors or the countries they represent. Please send comments to meden@worldbank.org. 1 1 Introduction The behavior of international capital flows is puzzling from a neoclassi- cal perspective: while standard considerations would suggest that capital should flow from steady-state developed economies to converging emerging economies, there are large net capital flows in the opposite direction (com- monly referred to as “global imbalancesâ€?). The persistent decline in interest rates in the US is also a puzzling trend, as, given the high returns to capital in emerging economies, the neoclassical model would predict that ï¬?nancial integration should increase the returns to savings in global markets. In their seminal work, Caballero et al. [2008] present a highly stylized model of global asset shortages that can help explain these puzzles. Their model features overlapping generations with an inelastic demand for saving. Developed economies have a comparative advantage in creating assets, and, in equilibrium, export assets to emerging economies. In this paper, I attempt to embed this stylized intuition in a standard neoclassical growth model, generating a demand for assets from a need for liquidity. This focus is in line with the ï¬?ndings in Gourinchas and Rey [2007] who show that US external liabilities are predominantly composed of liquid claims which carry a signiï¬?cant liquidity premium. I then use the model to revisit the welfare implications of ï¬?nancial integration, as well as the implica- tions for consumption, investment and volatility. The model illustrates that, despite a growing consumption path and high returns to capital, emerging economies may be net lenders in equilibrium; in this case, ï¬?nancial inte- gration is welfare-reducing for emerging economies. In contrast, developed economies are made better off by ï¬?nancial integration as they enjoy rents from liquidity supply. Even though developed economies gain from ï¬?nan- cial integration, it is possible to show that ï¬?nancial integration is Pareto inefficient, and, in some cases, welfare inferior to autarky. The inefficiency is a result of excessive capital accumulation in the developed economy and unnecessary fragility with respect to collateral shocks. 2 The starting point of the model is the assumption that, compared to emerging economies, developed economies have a comparative advantage in creating liquid claims. This assumption is consistent with ï¬?gure 1, that shows that the average level of broad money (M3) as a fraction of nominal GDP is positively correlated with income. To generate a need for liquidity, I assume a transaction role for liquid claims. In the spirit of Neumeyer and Perri [2005], this transaction role is modeled as a “working capitalâ€? constraint in the labor market: labor is unable to enforce payment ex-post, and must be paid in advance with liquid claims (which are easily enforceable). In emerging economies, there is not enough liquidity to ï¬?nance the un- constrained wage bill. Consequently, the autarkic wage is depressed relative to the marginal product of labor. In the integrated equilibrium, this wedge creates an incentive to buy liquid claims issued by foreigners. However, the purchase of foreign-issued liquid claims is associated with a pecuniary exter- nality, as “importedâ€? liquidity bids up wages.1 Since liquidity is expensive, the increase in labor income is not enough to offset the fall in ï¬?rms’ proï¬?ts.2 Aggregate domestic income is lower than in the autarkic counterfactual, as payments for liquidity services are sent abroad. These “liquidity rentsâ€? incentivize agents in developed economies to ex- plore innovative ways to create more liquidity. A high liquidity premium increases the private return to physical capital, as it can be used as collat- eral to back liquid claims. This is Pareto inefficient for two reasons: ï¬?rst, it leads to excessive capital accumulation in the developed economy. Second, equilibrium reliance on collateral-backed liquid claims exposes the economy to unnecessary fragility, as collateral shocks change the incentives to accu- mulate physical capital. 1 This result is broadly consistent with the empirical ï¬?ndings in Chari et al. [2012], who show that ï¬?nancial integration in emerging economies is associated with an increase in wages. 2 The way that ï¬?nancial integration changes domestic income shares is in the spirit of Antras and Caballero [2009]: the returns to liquidity decline, as liquidity can be imported more cheaply from abroad, allowing labor to absorb a higher share of output. 3 M3 as a percent of GDP (log) 6 5 4 3 2 1 4 5 6 7 8 9 10 11 GDP per capita (log) Source: World Development Indicators, 2013: Liquid liabilities (M3) as % of GDP, and GDP per capita (constant 2000 US$). Figure 1: A positive cross-country correlation between the ratio of M3 and M3 nominal GDP ( P Y ) and income per capita (in the year 2000). A 1% increase in income per capita is associated with a 0.3% increase in real balances. The general principle underlying the welfare analysis in this paper is that agents are willing to undertake costly measures to relax binding constraints, even when doing so is socially inefficient. For emerging economies, this takes the form of buying liquid claims issued by foreigners. Privately, each ï¬?rm thinks it can increase its proï¬?ts by importing liquidity and increasing its labor inputs. In general equilibrium, foreign-issued liquidity merely bids up the wage rate, leaving ï¬?rms worse off as they face higher wages and must make payments to foreign liquidity suppliers. For developed economies, the inefficiency takes the form of accumulating collateral. Privately, each agent stands to proï¬?t from creating collateral-backed liquid claims; however, in general equilibrium, this merely reduces the liquidity premium and wastes valuable resources. 4 2 Related literature The global equilibrium view expressed in this paper is closely related to the “asset shortageâ€? view, summarized in Caballero [2006] and Caballero et al. [2008]. Subsequent work such as Caballero and Krishnamurthy [2009] and Maggiori [2008] observe that the surplus of emerging economies is composed primarily of treasuries and other safe assets, and relate the demand for assets to a demand for safety. In this paper, safety is de-emphasized and replaced with liquidity. Of course, the views are not mutually inconsistent as safety and liquidity often go together (see Krishnamurthy and Vissing-Jorgensen [2012] for the case of treasuries). However, the focus on liquidity is key for the welfare implications explored here. The welfare implications are conceptually related to the idea of inter- national seigniorage, as in Matsuyama et al. [1993] and Eden [2009]. In the monetary literature, the fact that foreigners use dollars allows the US central bank to collect seigniorage payments from abroad. An implication of this is that the foreigners would be better off if using dollars were illegal, as the only seigniorage payments would be collected by the domestic government and consumed domestically. The results here are of similar flavor: in the autarkic emerging economy, there are rents to liquidity supply, but they are consumed domestically. Under ï¬?nancial integration, the developed economy extracts some liquidity rents, which reduces aggregate domestic income in emerging economies. This paper is related to others that emphasize inefficient pecuniary ex- ternalities in constrained environments, including Korinek [2011], Lorenzoni [2008] and Eden [2012]. Most closely related is Eden [2012], in which I con- sider a closed economy with pledgeability constraints in which the price of production inputs is determined in equilibrium. Producers are willing to pay an “intermediation costâ€? to relax their pledgeability constraint, but in equilibrium this only raises the price of inputs and generates an inefficiency. This pecuniary externality is the key ingredient in both models. The main 5 difference between the papers is in their focus. Here, I focus on the welfare implications of international liquidity flows and on the distribution of sur- plus between emerging and developed economies, as well as the implications of collateral shocks in this context. In Eden [2012] I focus on the general equilibrium costs of ï¬?nancial intermediation in a closed economy context. The idea that in liquidity-scarce environments collateral shocks can trans- late into liquidity shocks appears also in Midrigan and Philippon [2011]. Midrigan and Philippon [2011] consider a general equilibrium monetary model, in which the Friedman rule is not implemented and “cash in advanceâ€? con- straints bind in equilibrium. The ability to borrow against housing wealth in order to relax the “cash in advanceâ€? constraint increases the private return to housing. Thus, shocks to the collateral value of housing reduce the incen- tives to invest in new houses. The mechanism here is similar: the economy can issue liquid claims against the “collateralizableâ€? part of its capital stock. Shocks to the collateral value of capital reduce the incentives for capital ac- cumulation. While the mechanism is similar, the suggested interpretation is somewhat different: capital-backed liquid claims are interpreted not only as mortgage loans, but also as securities with favorable liquidity properties (for example, MBS or ABS that can be used as collateral in the repo market). This paper contributes to the theoretical literature on the welfare im- plications of ï¬?nancial integration in emerging economies, including (among others) Gourinchas and Jeanne [2006] and Levine [2001]. Mendoza et al. [2007] similarly consider the welfare implications of ï¬?nancial integration for a ï¬?nancially underdeveloped economy. Similarly, the conclusion is that ï¬?- nancial integration is welfare reducing. However, the mechanism is very different.3 3 In Mendoza et al. [2007], the welfare effects operate through the domestic distribu- tional implications. Relatively poor households are equilibrium borrowers that are made worse off by higher equilibrium interest rates. In this model, there is no household hetero- geneity and all emerging market households are net lenders in equilibrium. The welfare effects operate through the pecuniary externality on wages, which makes it more difficult for domestic producers to ï¬?nance production. 6 3 Setup I consider a discrete time inï¬?nite horizon model, where time periods are indexed by t = 0, 1, 2.... Technology. There is a unit measure of identical ï¬?rms indexed i ∈ [0, 1]. The production technology is time invariant and given by: α 1−α Fi (ki,t , li,t ) = Ai ki,t li,t (1) Where Ai is the ï¬?rm’s productivity, li,t is the labor employed by ï¬?rm i and ki,t is ï¬?rm i’s physical capital. Physical capital. Physical capital is owned by ï¬?rms. The ï¬?nal good can be invested and turned into physical capital, to be used in the next period. Capital depreciates at the rate δ . This implies the standard capital accumu- lation equation (where ii,t is investment): ki,t+1 = (1 − δ )ki,t + ii,t (2) Paying labor. To generate a role for liquidity, I assume that ï¬?rms need to pay labor with enforceable promises on post-production output, prior to production. Enforceable promises are transferable “IOU notesâ€? which I will refer to as liquid claims.4 There are two types of liquid claims: publicly-backed liquid claims and collateral-backed liquid claims (which will also be referred to as privately- backed liquid claims). 4 This simpliï¬?ed modeling of liquid claims captures two important aspects of liquidity. First, it can easily be used for transaction purposes (here, purchasing labor). Second, liquid claims can be enforced without any expertise or enforcement power, a property that is necessary for liquid claims to be widely acceptable. See Holmstrom and Tirole [2011], Holmstrom [2008] and Kurlat [2010] for a more rigorous discussion of the necessary attributes of liquid claims. 7 Publicly backed liquid claims. The government can guarantee a ï¬?rm’s promises up to m units of output. Publicly guaranteed claims are tradable IOU notes that are issued by the ï¬?rm, and enforced by the government.5 I assume for simplicity that the limit on publicly backed claims is proportional to output: 1 mt = θ Fi (ki,t , li,t )di (3) 0 The proportion coefficient θ captures the economy’s aptitude for creating publicly backed liquid claims. Publicly backed liquid claims should be inter- preted as traditional forms of liquidity, such as government bonds or money. A government bond is a claim on domestic output, backed by the govern- ment’s ability to collect tax revenues; similarly, money is a claim on output, its purchasing power guaranteed by the the commitment of the central bank not to inflate the currency. The parameter θ captures attributes such as the government’s ability to commit future tax revenues and the central bank’s commitment to low inflation. Collateral backed liquid claims. In addition, ï¬?rms can privately back their promises against a fraction γ of their capital stock.6 These privately backed liquid claims should be interpreted as less traditional forms of liquid- ity, such as MBS or ABS. There are two important differences between publicly backed claims and collateral backed claims. First, publicly backed claims are undistortive, in the sense that the ï¬?rm does not internalize the effect of its capital accumulation decisions on the amount of publicly backed claims that it can issue; rather, ï¬?rms take the amounts mt as exogenous. In contrast, the ability to use capital to issue collateral backed claims is internalized by the ï¬?rm in its investment 5 These claims are in the spirit of “moneyâ€? in Caballero and Krishnamurthy [2005]. 6 The distinction between “publicly backedâ€? and “privately backedâ€? liquid claims is in the spirit of Farhi and Tirole [2011], who similarly distinguish between “insideâ€? and “outsideâ€? liquidity. 8 Firms enter with xt Labor market Production; Liquidity ~ ,~ i t, Bi,t ki,t i t, bi,t i t, Bi,t i t bi,t it revealed ( (wt) ): li,t it ppaid p consumption market; ; rt, ~ rt, with bi,t (ci,t) and Bi,t+1, bi,t+1, and xtb ~ investment (ki,t+1); ~ ,~ i,t B i,t+1 bi,t+1 ~ firms repay Bi,t and xtBi,t Figure 2: The within-period timing of the model. decisions. Second, unlike publicly backed claims, collateral backed claims are (po- tentially) risky: there is a random variable xt ∈ [0, 1] that determines the fraction of collateral backed claims can be enforced. The use of collateral backed claims therefore may expose the economy to aggregate “enforceabil- ityâ€? risk. Denote by S T the history of the realizations of xt up to time T (S T = (x1 , x2 , ..., xT )). To simplify, this is the only source of uncertainty that I will consider. Realistically, there is a sense that collateral-backed claims are less liquid than publicly-backed claims. To capture this, I will assume that collateral backed claims are specialized, in the sense that they are not enforceable across borders. While, in principle, wage bills in one country can be paid with publicly backed claims issued in another country, collateral backed claims are only enforceable domestically. This captures the idea that collateral backed claims are more specialized, and, in some sense, serve as “inside moneyâ€? within a domestic ï¬?nancial system. This assumption will not be essential for any of the theoretical results, but will play a role in the numerical simulation.7 To summarize, let Bi,t denote the total amount of publicly backed liquid Ëœi,t denote the total amount of privately claims that ï¬?rm i can issue, and let B 7 In the numerical simulation, this assumption affects the wage dynamics associated with an enforceability shock. Speciï¬?cally, if emerging markets hold privately-backed liquid claims issued by developed economies, part of the instantaneous adjustment in wages would take place in emerging economies. 9 backed liquid claims that ï¬?rm i can issue. These amounts are bounded by: Bi,t ≤ mt (4) Ëœi,t ≤ γki,t B (5) Liquidity markets. After production takes place and investment decisions are made, ï¬?rms issue liquidity that can be used in period t + 1 (the choices of Bt+1 and B Ëœi,t+1 are made at the end of period t). There is a liquidity market, in which ï¬?rms can buy and sell liquid claims. The price of publicly backed 1 liquid claims in terms of goods is 1+ rt : one good can purchase 1 + rt publicly backed liquid claims, that can be used to hire labor for production in period 1 t + 1. Similarly, the price of collateral backed liquid claims is 1+Ëœ rt . Denote by bi,t the amount of publicly backed liquid claims that ï¬?rm i holds at the beginning of period t, and let Ëœ bi,t denote the amount of collateral backed liquid claims that ï¬?rm i holds at the beginning of period t (these quantities are determined in the liquidity market at the end of period t − 1). The amount of labor that ï¬?rm i can hire is bounded by these quantities, and the aggregate state x that determines the extent to which collateral-backed claims are enforceable: wt li,t ≤ bi,t + xtËœbi,t (6) This constraint, which resembles a “cash in advanceâ€? constraint on labor purchases, will be referred to as the liquidity constraint. Households. There is a unit measure of households indexed i ∈ [0, 1]. For simplicity, I assume that each household owns one ï¬?rm (but cannot supply its own labor to its ï¬?rm). Household i’s preferences over state-contingent consumption sequences {ci,t (S t )}t,S t are represented by: ∞ t U ({ci,t (S )} t,S t ) = E( β t u(ci,t (S t ))) (7) t=0 10 Where u(·) satisï¬?es the standard assumptions: u (c) > 0, u (c) < 0. Households supply li,t = l units of labor inelastically. As I will focus primarily on steady state analysis, l should be interpreted as the long-run level of labor supply; the assumption is consistent with the widely-held view that long-run labor supply is inelastic.8 Household i (that owns ï¬?rm i) faces the following optimization problem: ∞ max E( β t u(ci,t (S t ))) {ci,t (S t ),ki,t+1 (S t ),li,t (S t ),bi,t+1 (S t ),Bi,t+1 (S t ),Ëœ Ëœi,t+1 (S t )} t bi,t+1 (S t ),B t,S t=0 (8) s.t. (for any S t ): bi,t+1 Ëœ bi,t+1 ci,t + ki,t+1 + + = Fi (ki,t , li,t ) − wt li,t (9) 1 + rt 1 + r Ëœt Ëœ +(1 − δ )ki,t + bi,t − Bi,t + xt (Ëœ Ëœi,t ) + wt l + Bi,t+1 + Bi,t+1 bi,t − B 1 + rt 1 + r Ëœt ki,t+1 ≥ 0 (10) And the inequalities in equations 4, 5 and 6. The productivity parameters Ai and the initial conditions ki,0 , Bi,0 , bi,0 , Bi,0 , Ëœ Ëœ bi,0 are identical across ï¬?rms within a country. As households are identi- cal (and subject to the same aggregate risk), it follows that consumption and capital accumulation are the same across households and ï¬?rms in all periods. At time t, households have seven choice variables: household consumption (ci,t ), labor demand (li,t ), next-period capital levels (ki,t+1 ), demand for next- period’s publicly backed claims (bi,t+1 ), demand for next-period’s privately backed claims (Ëœ bi,t+1 ), supply of next-period’s publicly backed claims (Bi,t+1 ) and supply of next-period’s privately backed claims (B Ëœi,t+1 ). Equation 9 is the household’s budget constraint. The household’s income 8 Long run labor supply is typically thought of as being inelastic, as permanent changes in the wage rate have both an income and substitution effect that roughly cancel out. See, for example, Basu and Kimball [2002]. 11 is composed of dividend income, labor income, and revenue from selling liquid claims (issued against next period’s output). This income is divided between consumption, the accumulation of physical capital, and the purchase of liquid claims. Equation 10 states that capital cannot be negative (this will not be binding). Wage setting. For simplicity, I assume that wt is set at time t so that the labor market clears (there is no wage stickiness and no unemployment). Timing. Figure 2 summarizes the timing of the model. The within-period timing of the model is as follows: 1. Firms enter period t with ki,t units of physical capital, bi,t units of publicly backed liquid claims and Ëœ bi,t units of collateral backed liquid claims. They also enter with Bi,t publicly backed outstanding obliga- tions and BËœi,t collateral backed outstanding obligations, that they are to repay at the end of the period. 2. The aggregate enforceability state, xt , is revealed. 3. Firms use their enforceable liquid claims to hire labor (li,t ). The wage (wt ) is set so that the labor market clears. 4. After production takes place, ï¬?rms repay their enforceable outstanding Ëœi,t ). Households (who are shareholders) decide obligations (Bi,t + xt B how much to invest in next period’s physical capital (ki,t+1 ), and how much to consume. 5. Firms issue liquid claims against next period’s output and capital (Bi,t+1 and BËœi,t+1 ) and sell them in the liquidity market. Firms buy liquid claims to be used in the next period (bi,t+1 and Ëœbi,t+1 ). 12 3.1 Global environment There are two countries: an emerging economy (em) and a developed econ- omy (d). The size of the emerging economy relative to the developed econ- omy is Ï? (in the emerging economy, there is a measure Ï? of households-ï¬?rms, and in the developed economy there is a measure 1 of households-ï¬?rms). As household-ï¬?rms are identical within a country, with a slight abuse of notation I will use the subscript i to denote country variables (i = d, em). The countries differ both in their ability to create publicly backed liquid claims and in their ability to create collateral backed liquid claims. The emerging economy is assumed to be unable to create collateral backed liquid claims: γ em = 0 (11) The emerging economy is also not particularly good at creating pub- licly backed liquid claims: the fraction of output that the government can guarantee, θ, is such that the liquidity constraint is binding in equilibrium. Recall that given the Cobb-Douglas production technology, the wage bill in an unconstrained economy is a fraction 1 − α of output. Thus, the following restriction guarantees that in the autarkic emerging economy, the liquidity constraint is binding in equilibrium: θem < 1 − α (12) The developed economy is superior to the emerging economy both in its ability to create publicly backed liquid claims and in its ability to create privately backed liquid claims. I assume that in the developed economy, a positive fraction of capital can be used as collateral: γd = γ > 0 (13) In addition, the government is able to back enough claims to ï¬?nance the 13 autarkic wage bill: θd ≥ 1 − α (14) I also allow for cross country differences in productivity levels and in Ëœi,0 , bi,0 and Ëœ initial conditions (Ai , ki,0 , Bi,0 , B bi,0 for i = d, em). 4 Efficient allocations It is useful to consider the social planner’s problem. Consider a social planner, facing the following problem: maxt U ({cd,t (S t )}) + ΨU ({cem,t (S t )}) (15) {ci,t (S t ),k i,t+1 (S )}i∈{d,em} s.t.: cd,t (S t ) + Ï?cem,t (S t ) + kd,t+1 (S t ) + Ï?kem,t+1 (S t ) = (16) Ï?Fem (kem,t (S t−1 ), l) + Fd (kd,t (S t−1 ), l) + (1 − δ )(Ï?kem,t (S t−1 ) + kd,t (S t−1 )) Where kem,0 and kd,0 are given. The social planner chooses consumption and investment to maximize a weighted sum of developed and emerging market utilities, given the aggregate budget constraint. The parameter Ψ is the Pareto weight that the planner puts on emerging economies. Note that the standard equivalence applies here: any Pareto efficient allocation corresponds to the solution to the planner’s problem, for some value of Ψ. In other words, if an allocation does not correspond to the planner’s solution for some value of Ψ, both emerging and developed economies can be made better off by switching to an allocation that does. While the planner’s problem allows for state-contingent consumption and investment sequences, it is easy to see that the solution is deterministic. This is because the shock xt only affects the ability to issue collateral-backed liquid claims against capital; as the planner is not subject to any liquidity 14 constraint, this shock is irrelevant. The planner’s solution corresponds to the efficient allocation in a standard open economy neoclassical growth model. Lemma 1 The solution to the planner’s problem satisï¬?es the following equa- tions: ∂Fem (kem,t+1 , l) ∂Fd (kd,t+1 , l) = (17) ∂kem ∂kd u (cd,t ) = Ψu (cem,t ) (18) ∂F (kd,t+1 , l) u (cd,t ) = βu (cd,t+1 )( + 1 − δ) (19) ∂k cd,t + kd,t+1 + Ï?(cem,t + kem,t+1 ) = (20) Fd (kd,t , l) + (1 − δ )kd,t + Ï?(Fem (kem,t , l) + (1 − δ )kem,t ) The planner’s solution converges to a steady state in which: ss ss 1 ∂Fd (kd , l) ∂Fem (kem , l) = +1−δ = +1−δ (21) β ∂k ∂k css ss ss ss ss ss d + Ï?cem = Fd (kd , l ) − δkd + Ï?(Fem (kem , l ) − δkem ) (22) The proof of this lemma, together with other omitted proofs, is in the ap- pendix. 5 Closed economy equilibrium This section characterizes the autarkic equilibrium. In this economy, the autarkic equilibrium is deï¬?ned as follows: Deï¬?nition 1 An equilibrium of the closed economy is a sequence of inter- est rates {rt (S t ), r Ëœt (S t )}t,S t , a sequence of wages {wt (S t )}t,S t , a sequence of labor demands {{li,t (S t )}t,S t }i∈[0,1] , a sequence of physical capital stocks {{ki,t+1 (S t )}t,S t }i∈[0,1] , a sequence of liquidity demands {{bi,t+1 (S t ), Ëœ bi,t+1 (S t )}t,S t }i∈[0,1] , a sequence of liquidity supplies {{Bi,t+1 (S t ), B Ëœi,t+1 (S t )}t,S t }i∈[0,1] and a set of 15 consumption paths {{ci,t (S t )}t,S t }i∈[0,1] that jointly satisfy the following con- ditions: 1. Given the sequence of interest rates and the wage sequence, the con- sumption sequences, the labor demand sequences, the sequences of liq- uidity demands and liquidity supplies, and the capital sequences solve the optimization problem of household i (owner of ï¬?rm i). 2. Given the wage wt (S t ), the labor market clears: li,t (S t ) = l (23) Ëœt (S t ), the liquidity market clears: 3. Given the interest rates rt (S t ) and r bi,t+1 (S t ) = Bi,t+1 (S t ) (24) Ëœ Ëœi,t+1 (S t ) bi,t+1 (S t ) = B (25) The last condition states that the liquidity market clears domestically; there is no international trade in publicly backed liquid claims, so the do- mestic r may be different across countries. This implies that in an autarkic equilibrium, the entire wage bill is ï¬?nanced by domestically issued claims. Assume that initial conditions satisfy b0 = B0 = m0 and Ëœ Ëœ0 = γk0 . b0 = B The following lemma characterizes the closed economy equilibrium: Lemma 2 1. The equilibrium is characterized by the following equations. The consumption and capital sequences are given by: ∂Fi (ki,t+1 , l) u (ci,t ) = βu (ci,t+1 )( + 1 − δ) (26) ∂k ci,t + ki,t+1 = Fi (ki,t , l) + (1 − δ )ki,t (27) For i = em, d. 16 Equilibrium wages are given by: ∂Fd (kd,t , l) wd,t = (28) ∂l θem Fem (kem,t , l) wem,t = (29) l Equilibrium ri,t are given by: u (cd,t ) = β (1 + rd,t )u (cd,t+1 ) (30) ∂F (kem,t+1 ,l) ∂l u (cem,t ) = β (1 + rem,t ) u (cem,t+1 ) (31) wem,t+1 Equilibrium r Ëœem,t = −1 and: Ëœi,t are given by r Ëœd,t )Et (xt+1 )u (cd,t+1 ) u (cd,t ) = β (1 + r (32) 2. The autarkic equilibrium converges to a steady state, in which r, k , w and c are constant. Steady state consumption and capital are pinned down by: ss 1 ∂Fi (ki , l) = +1−δ (33) β ∂k css ss ss i = Fi (k , l ) − δki (34) For i = em, d. Steady state wages are: ss ∂Fd (kd , l) ss = wd (35) ∂l ss ss θem Fem (kem , l) wem = (36) l 17 Steady state ri are: ss 1 1 + rd = (37) β ss ss wem 1+ rem = ss (38) (kem ,l) β ∂Fem∂l ss As for r Ëœem Ëœi , r Ëœd,t may depend on S t and need not converge = −1 and r to a steady state. The developed economy has enough publicly backed claims so that the liquidity constraint is never binding, and there is no liquidity premium. Con- sequently, the return to investment is unaffected by liquidity motives, and unchanged by the shock xt . Equilibrium capital accumulation is given by equation 26, which is the standard Euler equation. Enforceability shocks have no effect on the equilibrium path. Equation 28 states that, in the autarkic developed economy, the wage is equated with the marginal product of labor. This standard equilibrium condition implies that producers are indifferent with respect to hiring an ad- ditional unit of labor: the marginal productivity of labor exactly offsets its cost. This indifference is evidence that the liquidity constraint is not bind- ing: a producer endowed with another unit of liquidity would be indifferent between using it or not. The closed economy equilibrium of the emerging economy is different in nature. In the autarkic emerging economy, there are not enough liquid claims to ï¬?nance the unconstrained wage bill, and the liquidity constraint is binding. The wage bill is constrained by the aggregate amount of liquidity, and thus given by wl = θem F (kem,t , l). At this equilibrium wage, the ï¬?rm’s liquidity 1 constraint is binding: an additional liquid claim could purchase w units of ∂F (kem,t ,l) labor, which, at the margin, produce ∂l > w units of output each. The return to liquidity is positive, reflected in a liquidity premium in r. Importantly, while the liquidity constraint is binding from the ï¬?rm’s per- spective, it is not binding from an aggregate perspective: since labor is sup- 18 plied inelastically, even though each ï¬?rm would like to hire more workers at the equilibrium wage, from an aggregate perspective, all labor is already employed in its most efficient use.9 The shortage in liquidity changes the distribution of surplus between labor and the ï¬?rm’s proï¬?ts, but does not change aggregate income. Consequently, similar to the unconstrained developed economy, equations 26 and 27 fully characterize the consumption and capital sequences in the emerging economy. The assumption that γ em = 0 implies that, even though there is a liquidity premium, the binding liquidity constraint does not affect the incentive to accumulate physical capital; capital accumulation is undis- torted and follows the same path as in the unconstrained equilibrium. Corollary 1 When initial capital levels are given by their steady state values ss (ki,0 = ki, 0 for i = d, em), the closed economy equilibrium is Pareto efficient. To see this, note that in this case, the autarkic equilibrium corresponds u (css d ) to the solution to the planner’s problem with Ψ = u (css . em ) ss Of course, under the more realistic assumption of kem,0 < kem and kd,0 = ss kd , the autarkic equilibrium is not Pareto efficient, as there are gains from intertemporal trade between the two countries. In particular, it is optimal for the emerging economy to borrow from the developed economy in order to smooth consumption and speed up capital accumulation. 6 Integrated equilibrium In the open economy, it is no longer required that the market for liquidity clears domestically: foreigners and domestic ï¬?rms can trade publicly-backed 9 The assumption that labor is supplied inelastically is important for the efficiency result: absent this assumption, the depressed wage would affect labor supply and generate an inefficiency. The assumption that ï¬?rms are identical is not important: in the presence of domestic liquidity markets, the wedge between the marginal product of labor and the wage would be equated across ï¬?rms. Thus, the marginal product of labor would be equated across ï¬?rms and labor would be allocated efficiently. 19 liquid claims in a global liquidity market. The deï¬?nition of an equilibrium in the integrated economy is analogous to the deï¬?nition of the autarkic equilibrium, with a single departure: rather than requiring that the market for publicly backed liquid claims clears do- mestically, it requires that the rate of return on publicly backed claims is equated across countries. Formally, the equilibrium condition in equation 24 is replaced with: Ï?bem,t (S t ) + bd,t (S t ) = Ï?Bem,t (S t ) + Bd,t (S t ) (39) The other equilibrium conditions remain unchanged. The following parametric restriction guarantees that in the autarkic steady state, the aggregate amount of liquidity is insufficient to ï¬?nance the uncon- strained wage bill in the integrated economy: ss Assumption 1 Let ki denote the autarkic steady state capital level in coun- try i, and assume the following parametric restriction: d ss θi Fd (kd ss , l)+ Ï?θem Fem (kem ss , l)+ γkd ss < (1 − α)(Fd (kd ss , l)+ Ï?Fem (kem , l)) (40) The left hand side is the aggregate amount of liquidity in the autarkic steady state, given xt = 1. The right hand side is the aggregate unconstrained wage bill at the autarkic steady state (which is a fraction 1 − α of steady state output in each country). Characterizing the integrated equilibrium is less straightforward than characterizing the autarkic equilibrium, because there may be occasionally binding constraints. However, it is possible to prove the following key result: Proposition 1 The integrated equilibrium is Pareto inefficient. There are two sources of inefficiency in the integrated equilibrium. First, there is excessive capital accumulation in the developed economy, driven by 20 an incentive to create collateral backed liquid claims. To see this, note that the household’s ï¬?rst order condition with respect to the accumulation of physical capital (the Euler equation) is given by: ∂F (kd,t+1 , l) u (cd,t ) = βEt (u (cd,t+1 )( + 1 − δ )) + γλt+1,B Ëœ (41) ∂k Where λt,B Ëœ is the Lagrange multiplier on equation 5 (the constraint on issuing collateral-backed liquid claims, B Ëœ ). Under autarky, the incentive to create private liquidity is muted, since there are enough publicly backed liquid claims to insure that the liquidity constraint never binds. Thus, λt+1,B Ëœ = 0 and the above condition amounts to the standard Euler equation. In the in- tegrated equilibrium, there is a global liquidity shortage driven by the excess demand for liquidity in emerging economies. This results in a liquidity pre- mium on internationally traded publicly backed liquid claims; consequently, there is also a liquidity premium on privately-backed liquid claims, that can be used to substitute for publicly-backed claims domestically. Thus, in the in- tegrated equilibrium, λt+1,B Ëœ > 0, and the incentive to create privately backed liquid claims enters into the developed economy’s capital accumulation deci- sion. From the planner’s perspective, this is inefficient. The second source of inefficiency is that reliance on collateral-backed liq- uid claims creates vulnerability with respect to enforceability shocks. In the autarkic equilibrium, enforceability shocks have no effect on the incen- tive to accumulate capital: when λt+1,B Ëœ = 0, expectations regarding xt+1 do not enter the condition in equation 41. However, when λt+1,B Ëœ > 0, expected changes in enforceability can affect the incentives to accumulate capital. The value of λt+1,BËœ depends on the expected transformation of physical capital into enforceable collateral-backed claims. Thus, changes in the expectation of xt+1 will change the incentives to accumulate physical capital, which results in inefficient volatility in capital accumulation. Of course, the fact that the integrated equilibrium is Pareto inefficient 21 does not necessarily imply that it is welfare inferior to autarky, as given real- ss ss istic initial conditions (for example, kem,0 < kem and kd,0 = kd ), the autarkic equilibrium is Pareto inefficient as well. Standard considerations would sug- gest that ï¬?nancial integration can be associated with welfare gains: emerging markets can borrow from developed economies to implement a smoother con- sumption path and faster capital accumulation. A natural question is: in the presence of liquidity motives for borrowing and lending, are these gains from ï¬?nancial integration still relevant? It turns out that these standard considerations are relevant only when kem is sufficiently small. At this range, the emerging economy borrows from the developed economy in order to increase investment and implement a smoother consumption path. Given these efficiency gains, ï¬?nancial integra- tion may be welfare superior to autarky, and beneï¬?t both emerging and developed economies. However, when capital levels are close to their autarkic steady state lev- els, this is no longer the case: in this range, the emerging economy starts to ss ss lend to the developed economy, even if kem < kem and kd ≥ kd . The reason for lending has nothing to do with differential returns to capital or consump- tion smoothing, but rather with liquidity shortages. Recall that, faced with binding liquidity constraints, producers in emerging economies stand to make strictly positive proï¬?ts from additional units of liquidity: with an additional 1 liquid claim, producers can purchase w units of labor, which, at the mar- ∂F (kem,t ,l) gin, produce a return of ∂l > w. Anticipating their constraint in the next period, producers in emerging economies ï¬?nd it optimal to buy liquid claims in global liquidity markets. Importantly, when producers decide to buy foreign issued liquid claims, they do not internalize the pecuniary exter- nality on wages. At the aggregate level, since labor is supplied inelastically, “importedâ€? liquidity does not increase employment but translates entirely into higher wages. At this range, the emerging economy is made worse off by ï¬?nancial integration, as the economy must spend resources on importing 22 foreign liquidity. Proposition 2 Assume that there is no enforceability risk (xt = 1 for all t). 1. There exists a unique integrated equilibrium steady state in which: (a) The capital level in the emerging economy is equal to its autarkic steady state level; (b) The capital level in the developed economy is higher than its au- tarkic steady state level; (c) The emerging economy lends to the developed economy (bss em − ss Bem > 0). 2. For kem,0 and kd,0 sufficiently close to their autarkic steady state levels, ï¬?nancial integration reduces equilibrium welfare for emerging economies. Developed economies are made better off by ï¬?nancial integration (re- gardless of initial conditions). The ï¬?rst part of the proposition describes the steady state of the inte- grated equilibrium. The capital level in the emerging economy is the same as its autarkic level; however, the incentive to create privately-backed liquid claims implies a higher steady state capital level in the developed economy. At the steady state, the emerging economy lends to the developed econ- omy in every period. This is because the steady state wage bill in emerging economies is too high to be ï¬?nanced with domestically issued liquid claims; effectively, emerging economies “importâ€? liquidity in order to ï¬?nance inflated production expenses. The second part of the proposition summarizes the discussion above: when initial conditions in emerging economies are very different from ini- tial conditions in developed economies, emerging economies may gain from ï¬?nancial integration through standard channels. However, when initial con- ditions are sufficiently close, ï¬?nancial integration reduces welfare for emerg- ing economies, as it creates inefficient dependence on foreign liquidity. The 23 numerical example in the next section illustrates that, in this context, “suf- ï¬?ciently closeâ€? need not be very close: even when the initial capital stock of the emerging economy is 15% of its steady state level (and kd,0 is at its autarkic steady state), it is a net lender in every period and made worse off by ï¬?nancial integration. Interestingly, regardless of initial conditions, developed economies are al- ways made weakly better off by ï¬?nancial integration. In this model, this conclusion holds true even in the presence of enforceability risk. For agents in developed economies, the autarkic consumption sequence is always feasible under ï¬?nancial integration, as they always have enough publicly backed liquid claims to ï¬?nance the autarkic level of employment. For emerging economies this is not the case, because given equilibrium wages, domestically issued liquidity is insufficient to ï¬?nance autarkic production. 7 Numerical example This section presents two quantitative exercises. First, abstracting away from enforceability shocks, I compare the autarkic equilibrium with the integrated equilibrium. Second, I consider the implications of a permanent enforceabil- ity shock. I assume that the intertemporal elasticity of substitution is 1, or u(c) = ln(c). The choice of parameters is summarized in table 1. The ï¬?rst three parameters, β , δ , and α, are standard. The choice of l = 1 and Ad = 1 are convenient normalizations. The productivity of the emerging market is calibrated based on Hsieh and Klenow [2009], who estimate manufacturing productivity in the US to be about 150% higher than in India and China.10 The value of θd was chosen to match the value of M3 over GDP in the US. The value of θem was calibrated to roughly match M3 over GDP in emerging 10 I chose to calibrate TFP differences based on the differences in manufacturing pro- ductivity, which are relatively small compared to current differences in TFP levels. This reflects some expected convergence in TFP in the long run. 24 Table 1: Calibration parameters Notation Variable Value β Discount factor 0.97 δ Depreciation rate 0.1 α Capital share in production 0.33 Ad Productivity: developed economies 1 Aem Productivity: emerging economies 0.4 Ï? Size of emerging market (relative to developed) 10 l Labor supply 1 θd Public backing as a share of output: developed economies 0.7 θem Public backing as a share of output: emerging economies 0.35 γ Private liquidity as a share of capital: developed economies 0.078 kd,0 Initial capital level: developed economies 3.97 kem,0 Initial capital level: emerging economies 0.15 economies, in particular China and India.11 The value of Ï? was chosen to roughly match the population of BRIC countries (Brazil, Russia, India and China) relative to the US. I use the following procedure to calibrate γ . According to Gorton et al. [2012], privately backed claims (including MBS, ABS, corporate bonds and loans) accounted for about 25% of the supply of liquid claims in the US in 2006. I choose γ to match this proportion in the integrated steady state. Importantly, this proportion approaches its steady state level quite quickly: at t = 4 (the timing of the calibrated “shockâ€?), this share is already 23%. Thus, the calibration of γ would be roughly the same if I were to choose γ to match this proportion at t = 4. 11 For the US, the average value of M3 as a percent of nominal GDP is about 70% M3 between 1960-2011. It is worth noting that P Y in the US is essentially trend-less in this period, despite the fact that the US has experienced high GDP growth. This feature of the data is consistent with the assumption that θ is a time invariant parameter that does not change with GDP. Unfortunately, data for China is available only for the years 1977-1982. For these years, M3 was 30% of nominal GDP on average. More data is available for India. Between 1977 and 1992, the average M3 over nominal GDP in India was 38%. Source: World Development Indicators. 25 The initial capital level in the developed economy is chosen as the autarkic steady state level. In the emerging economy, the initial capital level is chosen to match a 10% growth rate (under autarky). The other initial conditions are given by the autarkic equilibrium levels, Bi,0 = bi,0 = θi Fi (ki,0 , l) and BËœi,0 = Ëœ bi,0 = γ i ki,0 . 7.1 Financial integration To illustrate the workings of the model, I present a quantitative comparison between the autarkic equilibrium and the integrated equilibrium, abstracting away from any enforceability risk (xt = 1 for all t). Given the chosen parameters, the model suggests that, in developed economies, ï¬?nancial integration is associated with welfare gains equivalent to a 12% permanent increase in consumption, while, in emerging economies, ï¬?nancial integration is associated with a welfare loss equivalent to a 6.5% permanent reduction in consumption. Steady state analysis. The steady state values of the autakic and open equilibria, given the calibrated parameters in table 1, are summarized in the ï¬?rst two columns of table 2 (the third column presents steady state values for a permanent enforceability shock studied in the next section). In this numerical example, steady state consumption in emerging economies is about 5.3% lower in the ï¬?nancially integrated equilibrium, while steady state consumption in developed economies is about 16.1% higher. The last two rows are net exports as a fraction of GDP. Notice that, in this model, the trade balance is equal to the current account. These parameters suggest that, in the steady state, the emerging market exports roughly 4.2% of its GDP to the developed economy, as payment for liquidity services. At the same time, the developed economy enjoys a steady state flow of imports equal to 9.7% of its GDP. 26 Table 2: Steady state comparison Open Shock Variable Autarky Open Shock Autarky No shock cem 0.3 0.284 0.283 0.947 0.996 cd 1.179 1.369 1.357 1.161 0.991 kem 1.012 1.012 1.012 1 1 kd 3.974 5.188 3.974 1.305 0.766 wem 0.141 0.211 0.18 1.496 0.853 wd 1.056 0.905 0.707 0.857 0.781 rem -0.461 -0.191 -0.31 1.623 rd 0.031 -0.191 -0.31 1.623 nx ( y )em 0.042 0.044 1.048 ( nx ) y d -0.097 -0.113 1.165 Transitional dynamics. I solve for the equilibrium using Dynare. Figures 3 and 4 describe the transitional dynamics of the integrated equilibrium compared to the autarkic counterfactual. Upon ï¬?nancial integration, the developed economy starts accumulating capital, until it converges to its new steady state. The incentive to accu- mulate additional capital stems from the ability to create collateral-backed liquid claims. This trend is broadly consistent with the pre-crisis boom in the US, and especially with the view that the housing boom was driven by the incentive to create MBS (which had favorable liquidity properties). On impact, ï¬?nancial integration leads to a 6% increase in consumption in the developed economy, reflecting a higher permanent income due to inter- national liquidity rents. Faced with higher private returns to capital, house- holds in the developed economy initially sacriï¬?ce some consumption growth in favor of investment. However, consumption growth quickly recovers as it converges to its new steady state. Interestingly, the wage rate in the developed economy falls, despite the fact that it is accumulating capital. Capital accumulation raises the “un- constrainedâ€? wage bill, as the marginal product of labor increases; however, 27 1.5 0.4 1.4 Integration Autarky 0.3 Integration 1.3 0.2 1.2 Autarky 0.1 1.1 1 0 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 (a) Consumption: developed econ-(b) Consumption: emerging econ- omy omy 6 1.2 Integration 5 1 Integration 4 0.8 Autarky Autarky 3 0.6 2 0.4 1 0.2 0 0 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 (c) Capital: developed economy (d) Capital: emerging economy 1 0.12 0.1 0.8 Integration 0.08 0.6 Autarky Integration 0.06 0.4 Autarky 0.04 0.2 0.02 0 0 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 (e) Investment: developed economy (f) Investment: emerging economy 1.1 0.3 Autarky Integration 1 0.2 Integration Autarky 0.9 0.1 0.8 0 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 (g) Wage: developed economy (h) Wage: emerging economy Figure 3: A comparison of the integrated and autarkic equilibria: consump- tion, capital, investment and wages. 28 0.1 Autarky: d 0.2 0 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 0.1 -0.1 nx: em 0 -0.2 Integration 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 -0.1 -0.3 nx: d -0.4 -0.2 Autarky: em -0.5 -0.3 (a) Interest rate (r) (b) Net exports (as a fraction of out- put) Figure 4: A comparison of the integrated and autarkic equilibria: the interest rate on publicly backed claims and net exports (in the closed economy, net exports are 0). at the same time, the return to liquidity increases, and the option of selling liquid claims abroad becomes more attractive relative to paying for domestic labor. The widening gap between the marginal product of labor and the wage is consistent with recent trends in the US.12 The interest rate (r) is declining over time. From the perspective of developed economies, ï¬?nancial integration is associated with an initial drop in r from its autarkic steady state level of 3% to around 0. During the transition, the interest rate declines until reaching its steady state value of -19%. In principle, there are two competing forces affecting the interest rate trend: on the one hand, capital accumulation in both the emerging and the developed economies decreases the marginal return to capital, thus putting downward pressure on r. In addition, as the emerging economy grows, its excess demand for liquidity increases. This channel further contributes to the decline in r and to the increase in liquidity premiums. On the other hand, 12 Calibrating the marginal product of labor as M P L = (1−lα)Y with α = 0.33, the “labor wedgeâ€? Mw PL has been increasing steadily in the US, from around 1.2 in 1990 to 1.3 in 2010. The calculations are based on the following data from the OECD, 2013. For Y : B1 GA: Gross domestic product (output approach) National Currency, current prices. For l: Annual Labor Force Statistics, Total Employment. For w: Average annual wages, current prices in NCU. 29 capital accumulation in the developed economy increases the supply of both public and private liquid claims, somewhat countering the increased demand for liquidity; this channel puts some upward pressure on r. In equilibrium, the ï¬?rst channels dominate and the path of r is steadily decreasing. Though not detectable in the ï¬?gures, ï¬?nancial integration actually slows down capital accumulation in the emerging economy. For example, after one period, capital is 0.89 of what it would have been under autarky; by the ï¬?fth period, capital is 0.96 of its autarkic counterfactual level, and by the tenth period, it is 0.99 of its autarkic counterfactual level. This ï¬?nding suggests that (contrary to popular beleifs in policy circles) high foreign savings does not accelerate growth, but rather slows down growth. In this model, growth is driven by standard convergence considerations, and, while a high saving rate emerges in equilibrium, equilibrium output growth is slower compared to the autarkic counterfactual. Similarly, consumption in emerging economies initially drops by almost 13% (compared to the autarkic counterfactual). The gap gradually declines until it converges to its steady state level of 5.6%. Both consumption and investment are disproportionately affected in the ï¬?rst periods. In later pe- riods, the increase in liquidity supply in the developed economy somewhat mitigates the strain on the budget constraint, as liquidity imports become relatively cheaper. On impact, net exports in the emerging economy increase to roughly 20% of GDP, mirrored by net imports of around 25% of GDP in the developed economy. This initial surge is due to the fact that, in the ï¬?rst period, the emerging economy is buying foreign bonds but not redeeming foreign bonds; in subsequent periods, the trade balances are more modest, as the emerging economy is both buying and redeeming bonds. 30 7.2 A permanent enforceability shock The second quantitative exercise illustrates the effects of a permanent and unexpected enforceability shock. In the benchmark economy, there are no enforceability problems and xt = 1 for all t. At some t ¯, enforceability breaks down unexpectedly and xt = 0 for every t ≥ t ¯. Notice that this shock is equivalent to a shock to γ in the developed economy, that brings the value of γ d permanently to γ = 0. This extreme scenario is meant to illustrate how, in a global environment characterized by liquidity shortages, a shock to enforceability - or, alternatively, a shock to the ability to use capital to create collateral-backed liquid claims - can lead to a surge in liquidity premiums and a reduction in investment. Before presenting the results, it is useful to clarify how this type of “en- forceability shockâ€? is related to other models of the recent crisis. Broadly, theories attempting to explain the recent crisis fall into one of two categories: the “credit shockâ€? view (e.g., Jermann and Quadrini [2012]) and the “demand shockâ€? view (e.g., Mian and Suï¬? [2012]). The key difference between the two views is the implication for the investment wedge. According to the “credit shockâ€? view, the tightening of a ï¬?nancial constraint creates an investment wedge that prevents agents from taking advantage of high-return investment opportunities. In contrast, according to the “demand shockâ€? view, the con- traction in investment is voluntary, as low demand lowers the expected return to capital. This model falls somewhere in between. Mechanically, the shock is similar to a credit shock, or a fall in the underlying collateral value of physical capital. However, similar to the demand shock view, the contraction in investment is voluntary: the incentive to accumulate physical capital is lower, as it can no longer be used as collateral to back liquid claims.13 13 This feature of the model is similar to Midrigan and Philippon [2011]. 31 Steady state analysis. The steady state variables associated with the permanent enforceability shock are given by the third column of table 2. In both economies, steady state capital is equal to its autarkic steady state level. Compared to the no-shock trajectory, consumption is lower in both economies. In the emerging economy, this reflects higher liquidity rents. In the developed economy this reflects lower steady state capital and output. The steady state interest rate is substantially lower compared to the no- shock scenario, at -31%. With a higher liquidity premium, steady-state trade balances become slightly more extreme: the emerging economy exports an additional 0.2% of its GDP, and the ratio of imports to GDP in the developed economy increases by 0.6%. Transitional dynamics. Figures 5 and 6 present the transitional dynam- ics associated with the enforceability shock, compared to the uninterrupted equilibrium path. The timing of the shock was chosen as t ¯ = 4, to match an 8% growth rate in the emerging market at t = 3 (in 2006, the average growth rate of the BRIC economies was 8.55%14 ). The dynamics of the model can qualitatively account for three interesting features of the recent crisis. First, in the model, the shock is associated with a sharp and permanent decline in interest rates and a surge in liquidity premiums. This reflects a shock to liquidity supply, as collateral-backed claims cease to be liquid. This is qualitatively consistent with the decline in the treasury rate following the 2007-2008 crisis. Second, the model generates a decline in investment in the developed economy, and an increase in investment in the emerging economy. The decline in investment in the developed economy reflects the lower private return to capital. The increase in investment in the emerging economy is a result of the developed economy running down its capital stock: in part, this is achieved through saving in emerging economies, to smooth the declining consumption 14 Source: World Development Indicators. 32 1.45 0.3 1.4 0.25 No shock Shock 1.35 Shock 0.2 No shock 1.3 0.15 1.25 0.1 1.2 0.05 1.15 0 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 (a) Consumption: d (b) Consumption: em 6 1.2 No shock 5 1 No shock 4 0.8 Shock Shock 3 0.6 2 0.4 1 0.2 0 0 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 (c) Capital: d (d) Capital: em 0.8 0.14 Shock 0.12 0.6 No shock 0.1 0.08 No shock 0.4 Shock 0.06 0.04 0.2 0.02 0 0 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 (e) Investment: d (f) Investment: em 1.2 0.25 No shock 1 No shock 0.2 0.8 Shock 0.15 Shock 0.6 0.1 0.4 0.05 0.2 0 0 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 (g) Wage: d (h) Wage: em Figure 5: The equilibrium dynamics with and without the shock: consump- tion, capital, investment and wages. 33 0.1 0.25 0.05 Shock 0 0.2 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 0 No shock -0.05 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 0.15 -0.1 -0.1 0.1 -0.15 No shock -0.2 0.05 -0.2 No shock -0.25 Shock 0 Shock -0.3 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 -0.3 -0.05 -0.35 NX NX (a) Y : d (b) Y : em (c) Interest rate (r) Figure 6: The equilibrium dynamics with and without the shock: net exports and the interest rate. path. These predictions are roughly consistent with the observed changes in investment around the 2008-2009 crisis. The model predicts that the invest- ment share of output in the developed economy should drop by 6.4% in the period following the shock. In the US, the investment share dropped by 5.1% between 2007-2009. The subsequent recovery is also of a similar magnitude: the model predicts that after two (additional) periods, the investment share in the developed economy should increase by 0.96%, which is roughly consis- tent with the 0.8% increase in the investment share in the US between 2009 and 2011. For the emerging economy, the model predicts an increase in the investment share of 3.7%, which is somewhat smaller that the increase in the investment share in China between 2007-2009 of 6.5%.15 Third, the model predicts a temporary current account reversal: in the period of the shock, the developed economy becomes a net exporter, and the emerging economy becomes a net importer. While the magnitudes in the model are large compared to the data, this result is qualitatively in line with current account movements during the crisis: the current account surplus in China dropped form 8.5% of GDP in 2006 to 4% of GDP in 2010, and the current account deï¬?cit in the US dropped from 6% of GDP in 2006 to 3.3% of GDP in 2010.16 15 Source: World Development Indicators, Gross Capital Formation (% of GDP). 16 Source: World Development Indicators, 2013: Current account balance (% of GDP). 34 In the model, this temporary reversal is driven by standard neoclassical channels: as the developed economy runs down its capital stock, it ï¬?nds it optimal to smooth consumption by lending to emerging economies. It is worth emphasizing that, in this model, the current account reversal is temporary: the steady state current account balances are even larger than in the “no-shockâ€? trajectory. While the model qualitatively accounts for some aspects of the crisis, it misses the mark on others. Most notably, in the model, consumption in the developed economy increases following the shock. Part of this is due to mechanical aspects of the model: in a simple neoclassical framework, the only way to reduce global investment is to increase global consumption. Given that wages adjust instantaneously, the shock has no contemporaneous effect on output or employment. Standard “ï¬?xesâ€? such as sticky wages would imply a contemporaneous effect on output, which would perhaps also translate into lower consumption. Part of the increase in consumption reflects an increase in equilibrium welfare which is potentially worth noting. Since the developed economy re- mains a net exporter of liquid claims, the surge in liquidity premiums implies a permanent increase in liquidity rents. Welfare calculations reveal that the developed economy is made better off by the shock.17 The intuition for the welfare gain is one of standard “terms of tradeâ€? manipulation: as an exporter of liquid claims, developed economies are made better off by restricting the supply of liquid claims and enjoying higher liquidity premiums. This mo- nopolistic argument reveals a coordination failure among agents in developed economies. Privately, each agent ï¬?nds it proï¬?table to create collateral-backed claims, not internalizing the effect that this will have on the equilibrium r. From an aggregate perspective, developed economies are made better off if they refrain from creating and using privately backed liquid claims, as limited 17 The welfare improvement for the developed economy is equivalent to a permanent increase in consumption of 1.75%, compared to the “uninterruptedâ€? integrated equilibrium. 35 supply hikes up the liquidity premium. With the permanent enforceability shock, the steady state equilibrium is Pareto efficient, as the incentive to create privately-backed liquid claims is once again muted. However, the emerging market is made worse off by the shock: steady state consumption drops by about 0.38%, and, compared to the no-shock counterfactual, consumption is lower in every period. Emerging economies, who import liquid claims, are made worse off by the permanent increase in liquidity premiums. Their welfare loss is equivalent to a perma- nent 1.23% reduction in consumption. 8 Concluding remarks The presence of binding liquidity constraints implies a transfer of surplus to liquidity suppliers. In the closed economy, liquidity is supplied domes- tically so the “liquidity rentsâ€? (if any) are consumed domestically. In the integrated equilibrium, “liquidity rentsâ€? are consumed disproportionately by those who have a comparative advantage in creating liquidity. Under the assumption that developed economies are better at creating liquidity than emerging economies, this implies a transfer of surplus from emerging to de- veloped economies. Even in the presence of neoclassical motives for intertemporal trade, ï¬?- nancial integration may be welfare reducing for emerging economies when capital flows are primarily driven by liquidity motives. From the producer’s perspective, the liquidity constraint is binding, and there are strictly posi- tive proï¬?ts to be made from getting hold of additional liquidity. However, from a macro perspective, as the economy is in full employment, the binding constraint is not the liquidity constraint but rather the resource constraint. Importing liquidity is similar to importing money: in equilibrium, this does not change output but merely inflates domestic prices. Similarly, investing in capital for the purpose of creating privately backed liquid claims is similar 36 to investing in private money-printing machines, in that it merely inflates nominal prices but does not contribute to economic efficiency. The monetary analogy is useful, also for pointing out potential avenues for further analysis. Naturally, this paper emphasizes some aspects of liquid claims, abstracting away from others. In this framework, a shortage in liq- uid claims does not create any inefficiency (as long as it does not increase the incentives to accumulate capital or import liquidity from abroad). Of course, there is a rich monetary literature suggesting various inefficiencies associated with the shortage of liquid claims (see, for example, Friedman [1969] with respect to transaction costs). The welfare analysis in this pa- per, by abstracting away from these channels, is of course incomplete. In particular, international trade in liquid claims may have some beneï¬?ts if the shortage in liquid claims in emerging economies generates large inefficiencies. I hope that in light of the relevance of liquidity motives in international cap- ital flows, the stark welfare conclusions suggested by this paper will refocus attention towards this important question. References Pol Antras and Ricardo J. Caballero. Trade and capital flows: A ï¬?nan- cial frictions perspective. Journal of Political Economy, 117(4):701–744, August 2009. Susanto Basu and Miles Kimball. Long-run labor supply and the elasticity of intertemporal substitution for consumption. Working Paper, University of Michigan, 2002. Ricardo Caballero and Arvind Krishnamurthy. Global imbalances and ï¬?nan- cial fragility. American Economic Review: Papers and Proceedings, 99(2): 584–588, 2009. Ricardo J. Caballero. On the macroeconomics of asset shortages. In An- 37 dreas Beyer and Lucrezia Reichlin, editors, The Role of Money: Money and Monetary Policy in the Twenty-First Century. The Fourth European Central Banking Conference, 2006. Ricardo J. Caballero and Arvind Krishnamurthy. Exchange rate volatility and the credit channel in emerging markets: A vertical perspective. Inter- national Journal of Central Banking, 1(1):207–245, 2005. Ricardo J. Caballero, Emmanuel Farhi, and Pierre-Olivier Gourinchas. An equilibrium model of ‘global imbalances’ and low interest rates. American Economic Review, 98(1):358–393, 2008. Anusha Chari, Peter Blair Henry, and Diego Sasson. Capital market inte- gration and wages. American Economic Journal: Macroeconomics, 4(2): 102–132, April 2012. Benjamin Eden. Liquidity premium and international seigniorage payments. Working Papers 0901, Department of Economics, Vanderbilt University., 2009. Maya Eden. Should wall-street be occupied? an overlooked price externality of ï¬?nancial intermediation. 2012. Emmanuel Farhi and Jean Tirole. Bubbly liquidity. Review of Economic Studies, 2011. Forthcoming. Milton Friedman. The optimum quantity of money. In The Optimum Quan- tity of Money and Other Essays, pages 1–50. Chicago: Aldine, 1969. Gary Gorton, Stefan Lewellen, and Andrew Metrick. The safe-asset share. American Economic Review, 102(3):101–106, May 2012. Pierre-Olivier Gourinchas and Olivier Jeanne. The elusive gains from inter- national ï¬?nancial integration. Review of Economic Studies, 73(3):715–741, July 2006. 38 Pierre-Olivier Gourinchas and Helene Rey. From world banker to world ven- ture capitalist: The us external adjustment and the exorbitant privilege. In Richard Clarida, editor, G7 Current Account Imbalances: Sustainability and Adjustment, pages 11–55. The University of Chicago Presse, 2007. Bengt Holmstrom. Comment on: ‘the panic of 2007’, by gary gorton. In Maintaining Stability in a Changing Financial System. Symposium spon- sored by The Federal Reserve of Kansas City at Jackson Hole, Wyoming, 2008. Bengt Holmstrom and Jean Tirole. Inside and Outside Liquidity. MIT Press, Cambridge, MA, 2011. Chang-Tai Hsieh and Peter J. Klenow. Misallocation and manufacturing tfp in china and india. The Quarterly Journal of Economics, 124(4):1403– 1448, November 2009. Urban Jermann and Vincenzo Quadrini. Macroeconomic effects of ï¬?nancial shocks. American Economic Review, 102(1):238–71, 2012. Anton Korinek. The new economics of prudential capital controls. IMF Economic Review, 59(3):523–561, August 2011. Arvind Krishnamurthy and Annette Vissing-Jorgensen. The aggregate de- mand for treasury debt. Journal of Political Economy, 120(2):233–267, April 2012. Pablo Kurlat. Lemons, market shutdowns and learning. Stanford Economics Working Paper, 2010. Ross Levine. International ï¬?nancial liberalization and economic growth. Re- view of International Economics, 9(4):688–702, November 2001. Guido Lorenzoni. Inefficient credit booms. Review of Economic Studies, 75 (3):809–833, 2008. 39 Matteo Maggiori. Financial intermediation, international risk sharing, and reserve currencies. EFA 2008 Athens Meetings Paper. Available at SSRN: http://ssrn.com/abstract=1093137, 2008. Kiminori Matsuyama, Nobuhiro Kiyotaki, and Akihiko Matsui. Toward a theory of international currency. Review of Economic Studies, 60(2):283– 307, 1993. Enrique G. Mendoza, Vincenzo Quadrini, and Jose-Victor Rios-Rull. On the welfare implications of ï¬?nancial globalization without ï¬?nancial develop- ment. NBER International Seminar on Macroeconomics, 2007. Atif R. Mian and Amir Suï¬?. What explains high unemployment? the aggre- gate demand channel. SSRN working paper, 2012. Virgiliu Midrigan and Thomas Philippon. Household leverage and the reces- sion. NYU Working Paper No. FIN-11-038, 2011. Pablo A. Neumeyer and Fabrizio Perri. Business cycles in emerging economies: the role of interest rates. Journal of Monetary Economics, 52(2):345–380, 2005. A Appendix A.1 Proof of Lemma 1 Let λt be the Lagrange multiplier on the aggregate budget constraint of time t (equation 16). The FOC of the Lagrangian with respect to kd,t+1 is: ∂F (kd,t+1 , l) λt − λt+1 ( + 1 − δ) = 0 (42) ∂k 40 Replacing kd,t+1 with kem,t+1 (and multiplying by Ï?) yields the ï¬?rst order condition with respect to kem,t+1 . Thus, ∂F (kd,t+1 , l) ∂F (kem,t+1 , l) = ⇒ kd,t+1 = kem,t+1 (43) ∂k ∂k The FOC with respect to cd,t and cem,t yields: β t u (cd,t ) = λt (44) Ψβ t u (cd,t ) = λt (45) It follows that β t u (cd,t ) = Ψβ t u (cd,t ), and by equation 42 the Euler equation follows. By standard arguments, this system of equations converges kss ,l) to a steady state in which β 1 = ∂F (∂k + 1 − δ , and the budget constraint is satisï¬?ed with equality. A.2 Proof of Lemma 2 Denote the Lagrange multipliers on equations 9, 6, 4 and 5 by λ1 2 3 t , λt , λt and λ4 t respectively (it is easy to see that the constraint in equation 10 is never binding). Note that λ3 4 t and λt are the constraints relevant at time t, when the ï¬?rm is choosing Bi,t+1 and B Ëœi,t+1 . The FOC of the Lagrangian are as follows: • With respect to ct : u (ct ) = λ1 t (46) • With respect to li,t : ∂F (ki,t , lt ) λ1 t( − wt ) − λ2 t wt = 0 (47) ∂l 41 • With respect to ki,t+1 : ∂F (kt+1 , lt+1 ) − λ1 1 t + βE (λt+1 ( + 1 − δ )) + γλ4 t = 0 (48) ∂k • With respect to bi,t+1 : λ1 t − + βE (λ2 1 t+1 + λt+1 ) = 0 (49) 1 + rt • With respect to Bi,t+1 : λ1 t − βE (λ1 3 t+1 ) − λt = 0 (50) 1 + rt • With respect to Ëœ bi,t+1 : λ1 t − + βE (xt+1 (λ2 1 t+1 + λt+1 )) = 0 (51) 1+r Ëœt Ëœi,t+1 : • With respect to B λ1 t − βE (xt+1 λ1 4 t+1 ) − λt = 0 (52) 1+r Ëœt The autarkic equilibrium in the developed economy. To show that, for the developed economy, the equilibrium satisï¬?es λ3 4 2 t = λt = λt = 0 for every S t+1 , I solve for the equilibrium under this assumption and verify that the constraints are satisï¬?ed. First, note that the assumption λ2 t = 0 (for every realization of xt ) implies that consumption is deterministic; to see this, note that xt enters only in the budget constraint (equation 9) and the liquidity constraint (equation 6). Since the liquidity constraint is not binding, the problem is equivalent to one in which xt appears only in the budget constraint; however, by symmetry and market clearing, it must be 42 the case that Ëœ Ëœi,t ; it follows that the term xt (Ëœ bi,t = B Ëœi,t ) = 0, thus there bi,t − B is no consumption risk in equilibrium. The equilibrium can be described by equation 46 and the following system of equations: ∂F (kt , l) = wt (53) ∂l ∂F (kt+1 , l) λ1 1 t = βλt+1 ( + 1 − δ) (54) ∂k λ1 1 t = βλt+1 (1 + rt ) (55) λ1 1 t = βλt+1 (1 + r Ëœt )E (xt ) (56) In equilibrium, the wage bill is given by ∂F (k t+1 ,l) ∂l l = wt+1 l; using the Cobb- Douglas speciï¬?cation, the equilibrium wage bill is (1 − α)F (kt+1 , l). Let bi,t+1 = Bi,t+1 ≥ (1 − α)F (kt+1 , l), such that Bi,t+1 ≤ mt+1 (the set of such B ’s is non-empty by the assumption θd ≥ (1 − α). Let Ëœ bi,t+1 = BËœi,t+1 ≤ γki,t+1 . Note that the solutions in this set satisfy the constraints in equations 6, 4 and 5. The standard neoclassical growth model that we are left with converges to a steady state, that can be computing by replacing time t and t + 1 variables in the equilibrium equations with steady state values. The autarkic equilibrium in the emerging economy. First, note that the emerging economy is deterministic, as it lacks any ability to issue collat- eral backed claims (γ em = 0). Note that the liquidity constraint is binding: recall that to ï¬?nance the unconstrained wage bill, the liquidity supply must be at least a fraction 1 − α of total output. In the emerging economy, there are only publicly backed claims, and publicly backed claims as a fraction of output are assumed to be less than 1 − α (θem < 1 − α). Thus, in equilibrium the liquidity constraint is binding for all ï¬?rms, and 43 λ2 t+1 > 0: wt li,t = bi,t (57) Labor market clearing requires that li,t = l for all t, and thus wt l = bt . Using the FOC with respect to li,t : ∂F (kt ,l) λ1 t( ∂l − 1) = λ2 t (58) wt Substituting into the FOC with respect to bi,t+1 : ∂F (kt+1 ,l) λ1 t λ1 t+1 ( ∂l − 1) = − λ1 t+1 (59) wt+1 β (1 + rt ) ∂F (kt+1 ,l) λ1 t ⇒ λ1 t+1 ∂l = (60) wt+1 β (1 + rt ) ∂F (kt+1 ,l) ⇒ λ1 t+1 ∂l β (1 + rt ) = λ1 t (61) wt+1 Using the FOC with respect to Bi,t+1 , note that: ∂F (k ,l) ∂F (kt+1 ,l) λ1 t t+1 λ3 t = 1 1 − βλt+1 = βλt+1 ∂l − βλ1 t+1 = βλ1 t+1 ( ∂l − 1) > 0 1 + rt wt+1 wt+1 (62) It follows that λ3 t em > 0 and thus bt = Bt = mt = θ F (kt , l) for all t. Since γ em = 0, the FOC of the household with respect to ki,t+1 can be rewritten as the standard Euler equation: ∂F (kt+1 , l) λ1 1 t = βλt+1 ( + 1 − δ) (63) ∂k Market clearing with respect to bt and bt+1 implies the aggregate budget constraint. Furthermore, since there is no supply of collateral backed claims, Ëœt = −1 (an inï¬?nite price for collateral backed claims in terms of current r goods) clears the market. 44 The rest of the proof follows trivially. The economy converges to a steady state, as the evolution of kt and ct can be described by a standard neoclassical growth model. A.3 Proof of Proposition 1 Recall that by Lemma 1, any Pareto efficient allocation converges to a steady kss ,l) state in which kem = kd = k ss , and β 1 = ∂F (∂k + 1 − δ. I show that the steady state is not an equilibrium outcome of the inte- grated economy. Using the household’s FOC with respect to ki,t+1 (equation 48), and equating λ1 1 d,t+1 = λd,t , the autarkic steady state capital level im- plies that λ4 d = 0 at the steady state. In tern, using the developed economy household’s FOC with respect to B Ëœi,t+1 , this implies that 1 + r Ëœdss = βE1 . (xt ) Inserting this into the developed economy’s household’s FOC with respect to Ëœbi,t+1 yields λ2 d = 0. Using the FOC with respect to bi,t+1 , this yields ss 1 1 + r = β , and thus (using the same condition for the emerging economy), λ2em = 0. Thus, for the Pareto efficient steady state to be an equilibrium outcome it must be the case that λ2 2 em = λd = 0; the liquidity constraint cannot bind in equilibrium, and wages must be equal to the marginal product of labor (using equation 47). Thus, the sum of wage bills are (1−α)F (k ss , l)(1+Ï?) (regardless of xt+1 ). By assumption, this violates the aggregate liquidity constraint when xt+1 = 1, as aggregate liquidity is given by F (k ss , l)(θd + Ï?θem ) + γk ss . It follows that λ4 d > 0 at the steady state, and the steady state capital level in the developed economy is higher than in any Pareto efficient allocation. A.4 Proof of Proposition 2 First, I solve for the integrated steady state in the riskless economy (p = 0). Using equations 49 and 47, and imposing steady state values for λ1 , it follows that the wedge between the marginal product of labor and the wage 45 is equated across regions: ∂F (ki , l) wi = β (1 + r) (64) ∂l If β (1 + r) = 1, the marginal product of labor is equated with the wage in both countries. In this case, λ2 = 0 in both countries. Using equations 51 and 52, it follows that λ4 d = 0. Using equation 48, it then follows that the steady state capital level in the developed economy is equal to its autarkic steady state level. Note that, as γ em = 0, by equation 48, the steady state capital level in the emerging economy is the same as in the autarkic steady state. Thus, (1 + r)β = 1 implies that both in emerging and in developed economies the steady state capital levels are the same as under autarky, and the liquidity constraint is not binding in either country. But this violates As- sumption 1, according to which the aggregate liquidity issued in the autarkic steady state is insufficient to ï¬?nance the unconstrained wage bill. Thus, wi < ∂F ( ki ,l) ∂l in both countries, and β (1 + r) < 1. ∂F (ki ,l) Since wd < ∂l , it follows that the developed economy sells publicly backed liquid claims in equilibrium: otherwise, since θd > (1−α), there would be enough domestically held publicly backed liquid claims to ï¬?nance the unconstrained wage bill, and the liquidity constraint would not be binding. It follows that in equilibrium, the emerging economy lends to the devel- oped economy in every period (bss ss em − Bem > 0). To show that when initial conditions are sufficiently similar, the emerging market is better off under autarky, I use the following reasoning: when initial conditions are the same, autarky is Pareto efficient. I show that (regardless of initial conditions) the developed economy is made strictly better off by ï¬?nancial integration; it follows that emerging economies are made worse off by ï¬?nancial integration. By continuity, this comparison holds true for initial conditions that are not identical but sufficiently close. To show that the developed economy is made better off by ï¬?nancial inte- 46 gration, it is sufficient to show that, given equilibrium prices, the autarkic al- location is feasible. To see this, note that an agent in the developed economy can replicate his autarkic consumption sequence by excluding himself from ï¬?nancial markets, and ï¬?nancing his wage bill with self-issued publicly backed claims. Formally, consider the choice bi,t+1 = Bi,t+1 = (1 − α)F (kd,t+1 , l) (for an agent i in country d). Note that this choice is feasible as θd > (1 − α) (and mt is the same for all ï¬?rms, regardless of their individual capital levels). Since wt l ≤ (1 − α)F (kd,t , l), the agent always has sufficient liquidity to choose to hire l units of labor (li,t = l). The agent receives the market wage, so his labor income is wt+1 l. The agent’s budget constraint (under the assumptions bi,t = Bi,t and li,t = l) is therefore reduced to: ci,t + ki,t+1 = F (ki,t , l) + (1 − δ )ki,t − wt l + wt l = F (ki,t , l) + (1 − δ )ki,t (65) For t > 0. For t = 0, by assumption the wage is set (at time -1) such that all agents have enough liquidity to hire l units of labor; the only difference is some “initial wealthâ€?, bi,0 − Bi,0 . This sequence of budget constraints replicates the autarkic sequence of budget constraints. It follows that agents in developed economies can repli- cate the autarkic consumption sequence; the fact that they choose not to implies that they are made strictly better off by ï¬?nancial integration. As the autarkic equilibrium is efficient when initial conditions are identical, it follows that emerging economies are made strictly worse off. 47