Current Account and the Planner’s Pecuniary Tradeoff Salim B. Furth∗ Department of Economics, University of Rochester, Rochester, NY 14627

June 20, 2011

Abstract Large, sustained changes in current accounts are among the most significant global macroeconomic trends of the last quarter century. Since relative parity during 1950-1980, the U.S. current account deficit (along with the closely correlated trade deficit) has rapidly ballooned to over 6% of GDP. In the meantime, the current account surpluses of Asian economies have grown correspondingly – Japan’s in the 1980’s, China’s and India’s more recently, along with a host of smaller developing countries. In this paper, I extend and qualify the now-familiar argument that current account imbalance may be optimal. This contribution consists of a two-country heterogeneous agent model in which a constrained social planner in the better-insured country will maximize welfare by running a current account deficit. The constrained social planner in my model is similar to that used by Davila, Hong, Krussell, and RiosRull (2005). He can determine the level of savings of every agent in the home country, but not in the foreign country. World interest rates, however, are determined in equilibrium. Thus, the planner cannot fully control interest rates, but he can take into account his impact on them. I find that the planner opts for less indebtedness than would result from an unplanned, competitive steady state. Thus, although current account deficits are optimal, the ones realized by a competitive equilibrium may be too large. Thanks to Mark Aguiar, Jay Hong, Alan Stockman, and seminar participants at the University of Rochester. All errors are my own. ∗

1

Introduction

The magnitude and persistence of recent current account imbalances have occasioned much discussion within the discipline of economics and in the broader world. Large, sustained changes in current accounts are among the most significant global macroeconomic trends of the last quarter century. Since relative parity during 1950-1980, the U.S. current account deficit (along with the closely correlated trade deficit) has rapidly ballooned to over 6% of GDP, with a return to parity only during the recession of 1990 (Fed San Francisco). In the meantime, the current account surpluses of Asian economies have grown correspondingly – Japan’s in the 1980’s and China’s and India’s more recently (Caballero, Farhi, and Gourinchas, 2007). From 2003 to 2007, I found that 50 of 51 developing countries ran current account surpluses (Furth, 2010). In this paper, I extend and qualify the now-familiar argument that current account imbalance may be optimal. Several papers have explored mechanisms for permanent shocks or heterogeneity among optimizing agents to induce optimal current account imbalance. This contribution consists of a two-country heterogeneous agent model in which a constrained social planner in the better-insured country will maximize welfare by running a current account deficit. The constrained social planner in my model is similar to that used by Davila, Hong, Krussell, and Rios-Rull (2005). He can determine the level of savings of every agent in the home country, but not in the foreign country. World interest rates, however, are determined in equilibrium. Thus, the planner cannot fully control interest rates, but he can take into account his impact on them. I find that the planner opts for less indebtedness than would result from an unplanned, competitive steady state. Thus, although current account deficits are optimal, the ones realized by a competitive equilibrium may be too large. This result raises a clear policy question: if the current account deficits experienced by the United States presently are too large, should fiscal and monetary authorities seek to slow the growth of the current account deficit?

2

Literature

In a basic neoclassical setting, Sachs (1982) showed that current account balance may not be optimal for countries when they face both transitory and 2

permanent productivity shocks. Recent literature has proliferated explanations for optimal current account deficits and surpluses, even in the absence of aggregate shocks. The current work explores the notion of constrained optimality through a model that is able to match the large, consistent U.S. current account deficits in the data. Mendoza et al. (2007a, 2007b) propose to investigate the results of differing degrees of financial deepness across countries, which they model as a limited liability constraint differing across countries. Effectively, residents of one country can insure against a greater span of shocks than the other. They find that the country with better insurance is willing to go into debt to the less insured country. They argue that the effects of globalizing credit markets include welfare losses among the poorest agents outside the U.S. and net welfare losses by the non-U.S. world. Meanwhile, globalization of credit is a net benefit to the U.S., though it causes losses for the richest agents in the U.S. Likewise, Willen (1997 and 2004) studies a situation where one country has more complete markets for risk, and consequentially its citizens can better insure against volatile income shocks. That country will run a trade deficit with a country that has less developed risk markets, as the former seeks less precautionary savings than the latter. He employs data from the financially deep United States and relatively shallow Japan to argue that the trade balance between the two countries is, at least in part, a product of their financial markets. In a setting similar to those of Mendoza et al. and Willen, I contribute the solution of a national social planner in a large country with perfect insurance markets. I find that the social planner improves outcomes in the home country by borrowing less than agents would on their own, and keeping interest rates virtually unchanged from the competitive case. The secular trend of falling interest rates has proven elusive to researchers in this literature. Caballero et al. (2006), as well as Fogli and Perri (2006) and Mendoza et al. employ models that predict rising or mixed interest rates in the most straightforward cases. Caballero et al. obtain a falling interest rate trend by assuming that a fixed share of national income in each region is “not capitalizable”. Thus, when the regions with the least capitalizable national incomes grow, world savings increases and interest rates drop. The deeper question at issue between Caballero et al.’s approach and others is whether lower interest rates worldwide are in fact caused by higher total saving, or structural factors such as better insurance, less income variability, 3

or lower returns. An adjacent literature seeks to explain the phenomena through monetary rather than real frictions. Hunt and Rebucci (2005) look only at the 1990’s, and cite irrational exuberance and slow learning as the causes of large exchange rate and current account movements. Gourinchas and Rey (2005) argue that exchange rate movements could reconcile current account movements to final wealth results, which have not been explained elsewhere in the literature. However they note the limitations of a non-rational expectations approach in concluding,“A natural question arises as to why the rest of the world would finance the U.S. current account deficit and hold U.S. assets, knowing that these assets will underperform.” While short-run aspects of current account movements are no doubt related to the exchange-rate and equity premium puzzles, this paper seeks to address macroeconomic trends in the broadest terms.

3

Model

In this section, I propose a parsimonious two-country model of international capital movements and interest rate determination. This setup allows us to investigate the effects of free trade in goods and capital between countries with heterogeneous risk markets. In the first country, styled after the U.S. and referred to as “Home”, there are complete markets and a social planner who achieves a constrained efficient outcome. In the second country, “Foreign”, agents are subject to uninsurable idiosyncratic income shocks.

3.1

Key assumptions

As discussed in Section 2, researchers have made a variety of modeling choices in representing diverse asset markets. Mendoza et al. and Caballero et al. limit their modeling of lack of credit markets to a borrowing constraint. Willen allows agents access to asset markets that span more of the uncertainty of one country than another. More similar in approach to Willen, my model assumes perfect asset markets – and hence perfect risk sharing – in the U.S. This obviously counterfactual assumption allows clear exposition and maintains the key difference between the countries. The assumption of a constrained social planner in the U.S. allows this 4

model to achieve results comparable in spirit to the constrained optimum of Davila et al. (2005). Using the Aiyagari (1994) framework, they achieve normative results with potential policy implications for a central bank. However, the assumption can also be interpreted positively: since the social planner only controls savings rates, a central government taking prices into account could construct non-linear taxation schemes to achieve the same equilibrium. In Davila et al., taxes would have to be state-dependent; in this model, the previous assumption of perfect risk sharing obviates the need for state-dependency. The simplified asset structure – only physical capital is analyzed – precludes this model from adding to the discussion of current account composition. However, since capital accumulation is fully endogenous, its inclusion frees the model from exogenously imposed supply restrictions on tradable assets. Perhaps the strongest assumption, since this model is primarily concerned with transition dynamics, is that asset markets are static. This is a clear weakness of my approach, which like others assumes active agents in an impassive world. Even as the model predicts that the U.S. will become indebted to the rest of the world in the long run, foreign agents’ inability to insure their incomes remains.

3.2

Home autarky

Consider an economy inhabited by µ workers maximizing expected lifetime utility and a large number of competitive firms. The firms produce a single good using mobile capital k, and inelastic, immobile labor µn and a technology F (k, n) which is characterized by the Inada conditions. The good can be freely consumed or invested, but not stored for future consumption. Agents have full insurance against all shocks and face a borrowing constraint B. Workers share a discount rate β; u (ci ) is the strictly concave, twice differentiable von Neumen-Morgenstern period utility function; ci is individual consumption; n is effective labor endowment per worker; r is the interest rate; w is the wage. An exogenous budget constraint B ≤ 0 limits individual debt, and is at least as tight as the natural borrowing limit. A representative worker i takes prices as given and solves:

5



max u cit + βV ait+1 , n


V ait , n = cit

ait+1 ,cit

s.t. + ait+1 ≤ (1 + rt ) ait + wt n ait+1 ≥ B

(1)

(2)

For our purposes, additionally assume that Home agents are ex ante identical in wealth and preferences. In autarky, then, a Home representative agent’s solution is a deterministic capital accumulation problem. First order conditions give the deterministic Euler equation, where λit is the multiplier on the borrowing constraint 2.


i uc cit = β 1 + rt+1 uc cit+1 + λit

(3)

The solution to the representative firm’s problem equates the marginal products of capital and labor to their rental rates: wt = Fn (kt , µn) rt = Fk (kt , µn)

(4) (5)

Definition 1. (Home autarky equilibrium) Given initially identical agents, a ∞ general equilibrium is characterized by prices {rt , wt }∞ t=0 and policies {at+1 }t=0 for all i ∈ [0, 1] that solve a representative agent’s problem and prices that satisfy a representative firm’s competitive profit conditions. This familiar solution yields β (1 + r) = 1 when ct+1 = ct . This steady state will arise from any initial level of assets, as mentioned by Aiyagari (1994) and others.

3.3

Foreign autarky

A similar economy to Home, Foreign is inhabited by 1 − µ workers. Unlike Home workers, Foreigners experience individual effective labor endowment shocks, ni∗ t , that are idiosyncratic, persistent and stationary. The shock is drawn from the finite set N and evolves according to stochastic process Π. The shocks are not fully insurable, since the only asset is physical capital. 6

There are no aggregate shocks. A single Foreign worker, therefore, takes prices as given and solves: i∗ V i ai∗ t , nt

ci∗ t




=



 i∗ i∗ i∗ u c + βE V a , n max t t+1 t+1 i∗ i∗

(6)

at+1 ,ct

s.t. ∗ i∗ ∗ i∗ + ai∗ t+1 ≤ (1 + rt ) at + wt nt ai∗ t+1 ≥ B

(7)

This is identical to the economy solved by Aiyagari (1994), and yields an Euler Equation where λi∗ t denotes the multiplier on the borrowing constraint 7:


 ∗ uc ci∗ = β 1 + rt+1 E uc ci∗ + λi∗ t t+1 t

(8)

This differs from Equation 3 due to the uncertainty of next-period consumption. Definition 2. (Foreign autarky equilibrium) Given an initial asset and labor i∗ distribution {ai∗ 0 , n0 }i∈[µ,1] , general equilibrium is characterized by policies n o ∞ i∗ ∞ that solve Equation 6, distributions {ai∗ ai∗ t , nt }t=0,i∗∈[µ,1] int+1 i∈[µ,1] t=0

duced thereby and prices {rt∗ , wt∗ }∞ t=0 that satisfy a representative firm’s competitive profit conditions. The following lemmas restate Aiyagari’s key results, which arise due to precautionary savings. I omit the proofs.

Lemma 1. A steady state of the the general equilibrium described in Definition 2 exists, with r ∗ > 0 when the borrowing limit B is at least as tight as the natural borrowing limit. Lemma 2. In an autarkic steady state, this equilibrium yields β (1 + r ∗ ) < 1. For a lower r ∗ , total foreign assets will fall; for a higher r ∗ , total foreign assets will rise. For discussion below, I denote the autarkic foreign steady-state interest ∗ rate rss .

7

3.4

Competitive integration

Now I consider equilibrium where Home and Foreign trade goods freely and capital is fully mobile across countries. Home residents (only) continue to have access to complete insurance; no asset besides physical capital is traded. Capital-worker ratios will be equalized across countries. The notation for assets quickly becomes unwieldy in the ensuing discussion. Thus, let total assets in the Home economy be at = µait (recalling that home agents are assumed ex ante identical) while total foreign assets are R1 ∗ a∗t = µ ai∗ t di∗. Thus, world capital is kt = at + at . Firms have an identical CRS production function F (k, n) with Fk > 0, Fkk < 0, Fnk > 0, F (0, n) = 0, F (ǫ, n) > 0 for ǫ, n > 0. Firms are competitive and set wages and interest rates accordingly. Since capital is mobile, it must yield the same return anywhere employed. In addition, firms will arbitrage any wage differences by adjusting the capital-labor ratios throughout the world to equality. That is: wt = Fn (k, 1) rt = Fk (k, 1)

(9) (10)

Definition 3. (Competitive integrated equilibrium) Given an initial asset and  i∗ labor distribution a0 , {a0 , ni∗ 0 }i∈[µ,1] , general equilibrium is characterized n o∞  by policies ait+1 , ai∗ that solve Equations 1 and 6, distributions t+1 i∈[µ,1] t=0   ∗ ∗ ∞ i∗ ∞ ait , {ai∗ t , nt }t=0,i∈[µ,1] induced thereby and prices {rt = rt , wt = wt }t=0 that satisfy competitive profit conditions of representative firms in each country. The only steady state that can arise in a competitive integrated world economy involves binding indebtedness of Home residents. The asymmetric valuation of savings leads to capital flows from Home to Foreign. This is formalized in the following lemma. Lemma 3. If any steady state exists, it will be characterized by Home residents having assets equal to the borrowing limit B. Proof. Suppose in the steady state, a Home worker maintains constant asset level A > B. Then his borrowing constraint does not bind, and the nonbinding Euler Equation, 3, holds. Thence it follows that β (1 + r) = 1. If this is 8

true, then the proof of Lemma 2 implies that consumption must grow perpetually for all competitive agents, which violates the definition of a steady state. Thus, an utter immiseration result may obtain for Home residents under competitive integration. They will take advantage of low interest rates to tilt consumption forward, and continue to borrow until the exogenous constraint prevents them going further into debt. If the borrowing constraint is equal to the natural borrowing limit, then Home agents consume nothing in the steady state.

3.5

Constrained efficient integration

In this section, I assume a benevolent national planner can determine savings among Home inhabitants. He cannot, however, limit capital mobility or investment. The planner can achieve an allocation comparable to the “constrained efficiency” of Davila et al. (2005). The Home planner seeks to maximize the utility of Home citizens, taking into account pecuniary externalities on wages and interest rates and the optimal responses of the rest of the world to those new prices. He solves: Ht (at ) =

max {u (ct ) + βE [Ht+1 (at+1 )]}

at+1 ,ct

(11)

s.t. ct + at+1 ≤ (1 + rt ) at + wt at+1 ≥ B Unlike a purely competitive agent, the planner cannot act without influencing aggregates; unlike a pure command economy, he cannot ignore prices. In order to use the Benveniste-Scheinkman Theorem, the evolution of foreign assets and the world interest rate must also be characterized. I abuse notation in Equation 12 to emphasize the endogenous response of a∗t+1 to rt+1 . rt+1 = Fk at+1 + a∗t+1 (rt+1 )




(12)

An equilibrium in which the Home planner determines Home residents’ savings and small-country workers act independently is characterized below. 9

Definition 4. (Constrained efficient An equilibrium achieving  equilibrium) ∞ i∗ 1 constrained efficiency is a sequence {at }i=µ , at , rt , wt t=0 that solves Problem 11 and, for all Foreign workers, Problem 6 under rational expectations, with prices arising from Equations 9 and 10. Home’s first order condition, when the borrowing constraint is nonbinding, contains derivatives of the pricing functions. uc (ct ) = (13)     ∗  dat+1 βE uc (ct+1 ) 1 + 1 + [Fk (kt+1 ) + Fkk (kt+1 )at+1 − Fnk (kt+1 )n] dat+1 Since aggregate Foreign steady state assets is a function of the interest rate, expectations, and the full distribution of assets, and the interest rate is itself a known function of world capital, the planner can fully determine the world asset distribution and equilibrium by choosing the Home asset level. There is not, however, a closed-form solution for this. In computation, I find that the interest rate as a function of Home’s asset level is strictly decreasing and small-country assets as a function of the interest rate are strictly increasing. These conditions, along with Inada conditions, yield a one-to-one correspondence between Home’s asset choice and the interest rate in equilibrium. This does not, however, hold generally.

3.6

Capital in a steady state

Using numerical methods, it is possible to find a unique steady state for the world for a given interest rate. Assuming sufficient differentiability, the Home planner’s Euler equation for capital in a non-binding steady state then reduces to:     da∗ss 1 =β 1 + 1 + [Fk (kss ) + Fkk (kss )ass − Fnk (kss )n] dass

(14)

By Inada conditions, Fn k is always positive and Fk k is always negative. From the representative firm’s problem and Foreign’s solution, we can con∗ ss is negative. That is, for positive asset values, the Planner has clude that da dass three terms which tend to make the right side of 14 smaller, so a steady state 10

with positive Home assets would have to have β(1 + r) > 1, which would not be a steady state for Foreign. However, when Home assets become negative, the sign of the Fk k terms changes, and the importance of that term grows with the absolute value of Home debt. Intuitively, this occurs because the Planner internalizes a secondary attenuation of the value of more savings when assets are positive, since it lowers the interest rate he receives on the rest of Home assets, but he internalizes a secondary aggravation of more debt when assets are negative, since it increases the interest rate he must pay on the rest of Home debt. Although we cannot draw further conclusions about the size of any of the terms in 14, it is possible that an interior steady state solution exists for the Home planner with β(1 + r) < 1 satisfying the Foreign steady state conditions. In computation, I find that this is the case for the functional forms and parameters I choose below.

3.7

Identifying trade variables

Since the production function is CRS, we can identify the location of production and some trade variables. Labor in Home in any given period equals µ, so firms will allocate capital (the mobile factor) optimally so that kt = µ ((1 − µ) a∗t + µat ) as well. Home national debt is then dt = kt − at . Trade balance and current account are easy to identify. T Bt = F (kt , µ) − ct CAt = T Bt − rt dt = dt+1 − dt

4

Calibration

I specified the model using familiar functional forms and parameters, following Aiyagari (1994) and modifying as necessary. The model is specified annually, with a common discount factor of 0.95. Production is Cobb-Douglas with capital’s share of income set at 0.36 and unit total factor productivity. Capital depreciates at 8% per year. Utility is of constant relative risk aversion form with a risk aversion coefficient of 3. A symmetric Markov process approximating a first-order autoregression a la Tauchen (1986) determines effective labor shocks. In contrast to Aiyagari, I use only two states, and I 11

set the underlying serial correlation coefficient to 0.9 and the coefficient of variation to 0.15 in order to match a steady state world capital-income ratio of approximately 3. The effective labor values and transition matrix are as follows. nihigh = 1.2214 nilow = 0.8187 0.9805 0.0195 M = 0.0195 0.9805 Like Mendoza et al., I fix the U.S. proportion of world effective labor, µ; this is simpler than the alternative of employing varying TFP across the two countries. I set µ = 0.25 for computation, roughly matching the U.S. share of world output. I chose to compute the model in the case where Foreign agents cannot have negative savings; this is not a necessary constraint for the qualitative results, but eases computation. This individual borrowing constraint rarely binds, since the uninsured agents have a precautionary savings motive. The Home planner exhibits full commitment, and may borrow up to his natural borrowing constraint, which is negative. In a steady state under reasonable parameter values, Home will have negative savings but will not reach the natural borrowing constraint. That is, not only will Home use solely borrowed foreign capital in production, Home will borrow in order to consume. The model proves robust to various alterations in its calibration, and to a stochastic process featuring more Markov states.

5

Results

The computational results in this basic model are attractive and intuitive, confirming the analysis above and matching trends in the data. The competitive agents employ precautionary savings to insure against idiosyncratic shocks, while the Home planner takes advantage of low interest rates to tilt Home’s consumption profile forward. In order to investigate the numerical properties of the model, I compute the steady state of the model. The Home planner’s policy function implies that he will dis-save until reaching a steady state somewhere above the natural borrowing constraint. 12

Table 1: Steady States

With Social Planner Home

Foreign World

Without Social Planner Home

Foreign

World

Y

0.45

1.35

1.80

0.46

1.36

1.82

A/Y

-6.56

5.89

2.78

-12.38

7.73

2.83

C/Y

0.31

0.93

0.78

0

1.01

0.76

r

5%

5%

w

1.13

1.13

B/Y

-12.64

-12.38

The availability of excess foreign savings - from the precautionary motive allows investment of foreign assets in Home. A key result is that the presence of the social planner sharply distinguishes the steady state results. The Home planner, for any given interest rate, faces a natural borrowing constraint, where Home’s labor income will be entirely consumed by paying interest on debt. However, in the computed steady state, I find that the Home planner does not approach this limit. Instead, Home dissaving will approach a level of debt that allows positive consumption. In contrast, the same model without a Home social planner, but with complete markets in Home, would result in Home dissaving asymptotically to a natural borrowing constraint. The only steady state with no Home social planner is one in which Home citizens consume nothing. This type of immiseration result is familiar, but has not been addressed in much of the literature on global capital mobility. In Table 1, I compare the first moments of the steady states that arise with and without a Home planner. As can be seen, the principle difference in the results is distributional: the Home planner avoids utter immiseration for his citizens. These results extend the findings of Davila et al. (2005), who showed that a social planner with constrained powers would maximize social welfare by having greater capital accumulation than either a free market or an omnipotent social planner. In this framework, a social planner with the same powers also chooses greater capital accumulation (that is, less debt) - but only domestically. Total world capital accumulation is virtually unchanged across the environments. 13

6

Conclusion

This stylized model of savings, investment, and international capital movements provides a tractable and accessible tool to analyze the ability of a large country to use its power over prices to its advantage. This setup provides an application of the constrained efficiency of Davila et al. (2005). In a setting where the social planner of a single large, perfectly insured country faces an otherwise competitive, uninsured world, the large country will take advantage of excess worldwide savings to tilt consumption toward the present. This buttresses the analysis of Stockman (2005), who noted that data show growing U.S. current account deficits are a product of increased foreign saving. Computation of the model confirms others’ findings and matches the U.S. stylized facts of the past 40 years. The model confirms that large U.S. borrowing is a windfall for world lenders but drives up the cost of borrowing throughout the world. However, interest rate changes predicted by this model are of second order importance over the long-run. The principal change is that U.S. consumption is tilted forward, and the rest of the world will see its consumption rise permanently as U.S. debts come due. However, this model predicts that the social planner will take into account the impact of home dis-saving on interest rates, and thus dis-save less than competitive agents would on their own. This suggests that while current account deficits in the U.S. are optimal, they may also be too large. Future work on this problem should include a full computation of the transition path under both the competitive and socially planned equilibria.

14

References Aiyagari, S. R. (1994, August). Uninsured idiosyncratic risk and aggregate saving. The Quarterly Journal of Economics 109 (3), 659–84. Caballero, R. J., E. Farhi, and P.-O. Gourinchas (2006, February). An equilibrium model of ‘global imbalances’ and low interest rates. Working Paper 11996, National Bureau of Economic Research. Davila, J., J. H. Hong, P. Krusell, and J.-V. Rios-Rull (2005). Constrained efficiency in the neoclassical growth model with uninsurable idiosyncratic shocks. Working Paper 05-023, Penn Institute for Economic Research. Fogli, A. and F. Perri (2006, November). The ‘great moderation’ and the US external imbalance. Working Paper 12708, National Bureau of Economic Research. Gourinchas, P.-O. and H. Rey (2005, February). International financial adjustment. Working Paper 11155, National Bureau of Economic Research. Hunt, B. and A. Rebucci (2005). The US dollar and the trade deficit: What accounts for the late 1990s? International Finance 8 (3), 399–434. Mendoza, E. G., V. Quadrini, and J.-V. Ros-Rull (2007, September). On the welfare implications of financial globalization without financial development. Working Paper 13412, National Bureau of Economic Research. Sachs, J. (1982). The current account in the macroeconomic adjustment process. Scandinavian Journal of Economics 84 (2), 147–59. Stockman, A. C. (2005, April). How i learned to stop worrying and love the current account deficit. Working paper, Shadow Open Market Committee. Tauchen, G. (1986, March). Finite state markov chain approximations to univariate and vector autoregressions. Economic Letters 20 (2), 177–181. Willen, P. (2004). Incomplete markets and trade. Working Papers 04-8, Federal Reserve Bank of Boston.

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A

Computational Procedures

The computational procedures for this model build on Aiyagari (1994), using value function iteration to find optimal policies for agents. Throughout, I employ the functions, stochastic process, and parameters discussed in the paper.

A.1

Steady state procedure

In order to identify steady states in the economy, I employ the following algorithm. 1. Take an interest rate value, and use a grid of asset values 2. Iterate on competitive value function to find a partial-equilibrium “steady state” (zero net savings) (a) Use previous value function as initial guess (b) Identify the crossing segment of marginal utility and expected future value (c) Use linear interpolation to find the precise policy at this point (d) Update value function (e) Check for convergence (f) Export policy function and value function. 3. Iterate on competitive CDF (a) Invert the policy function (b) Guess an initial CDF (c) Using the transition matrix and the policy inverse, update the CDF (d) Check for convergence (e) Export the CDF 4. Compute the PDF, and aggregate across states using the invariant distribution. 16

5. Compute aggregate Foreign assets. 6. Return to step 1 with the next interest rate. 7. Find equilibrium interest rate for all asset values in grid using linear interpolation. 8. Iterate on Home value function according to similar procedure, to find Home policy function, taking Foreign steady-state savings for each interest rate as given. 9. Find total capital and equilibrium interest rate and wage level for each Home asset value. Home asset levels that induce a policy of zero net saving represent general equilibrium steady states, and induce a unique interest rate, wage, and Foreign policy rule. I find a continuum of such asset levels in computation, for many specifications.

17