Capital Flows, Growth and the Financial System Matias Fontenla University of New Mexico September 29, 2008

Abstract This paper studies the e¤ects that capital ‡ows have on the …nancial system and growth. In our model, short-term capital ‡ows increase longterm growth, by changing the term structure of interest rates. However, they also reduce the welfare of domestic agents by altering the banking contract. Thus, a welfare trade-o¤ occurs, where short-term foreign in‡ows reduce welfare of the current generation, but increase welfare of future generations via increased economic growth. A social planner may prefer a deposit contract that o¤ers less risk sharing within each generation, but one which generates higher growth rates of the economy. JEL classi…cation: D92, E44, F32, G21. Keywords: Financial Intermediation, Capital Flows, Liquidity Provision, Growth.

1

Introduction

The past decade has seen many developing economies move towards opening their …nancial systems to unrestricted ‡ows of capital, particularly in Latin America. In general, short-term ‡ows have been viewed as potentially detrimental, while long-term foreign investments are considered good for emerging economies. For example, Rodrik and Velasco (1999), and Fontenla and Gonzalez (2007) …nd that the short-term debt is a robust predictor of …nancial crises. More generally, sudden stops of capital in‡ows are an empirical regularity in …nancial crises (Calvo et al.,2006). In contrast, the bene…ts of capital ‡ows have mainly been associated with long-term ‡ows. As an example, Reisen and Soto (2001) …nd foreign direct investments to have a signi…cant impact on growth. Preliminary …rst draft. Comments and suggestions are greatly appreciated. [email protected]

1

Contact:

More generally, Galindo et al. (2002, 2007) …nd evidence that …nancial liberalization positively a¤ects growth, both by increasing the size of markets and by improving the e¢ ciency with which funds are allocated. These empirical …ndings are in agreement with the results of our theoretical paper. This paper constructs an endogenous growth model embedded in an overlapping generations framework with banks, similar to Ennis and Keister (2003), where we introduce two types of agents. Agents are either domestic or foreign depositors. Domestic agents don’t know, at the moment they deposit in banks, at which time they will want to withdraw their funds. In contrast, foreigners know before depositing whether they will want to consume in the short- or long-term. By this we mean to represent short- and long-term capital in‡ows. Agents also di¤er in that the income of domestic agents stems from their supply of labor, while the endowments of foreigners come from abroad. This asymmetry represents the idea that capital is mobile while labor is not, which has implications for growth in our model. Banks arise endogenously in this environment as coalitions of domestic agents to provide two services. They invest optimally on behalf of agents, and they provide liquidity to ex-ante identical agents who need to consume at di¤erent times. However, when banks are not able to distinguish domestic from foreign deposits, an adverse-selection problem arises. That is, short-term capital ‡ows have the incentive to enter the …nancial system while bene…cial long-term capital does not. Further, as short-term capital ‡ows in, the term structure of interest rates shifts, where short-term rates of return continuously fall with the number of short-term capital ‡ows. This reduces welfare of domestic agents. However, long-term rates of return increase, and banks portfolio allocation shifts toward long-term investments. In this sense, short-term capital ‡ows indirectly increase long-term growth when we implicitly model the banking contract. A welfare trade-o¤ occurs, where short-term foreign in‡ows reduce welfare of the current generation, but increase welfare of future generations via increased economic growth. Thus, a social planner may prefer a deposit contract that o¤ers less risk sharing within each generation, and allocates more resources to long-term investments, which in turn generates higher average growth rates of the economy. The remainder of the paper proceeds as follows. Section 2 describes the model. Section 3 depicts the problem of the bank with capital ‡ows, and how short-term capital ‡ows reduce welfare of the current generation. In section 4 we describe the equilibrium of the economy and use numerical methods to illustrate. Section 5 brie‡y discusses the problem of a social planner and its implications on the economy’s long-term growth. Section 6 o¤ers concluding remarks.

2

2

The model

2.1

Environment

The economy consists of an in…nite sequence of two-period lived, overlapping generations. There is a single consumption good in each period, which is produced using capital and labor. Agents preferences have the CRRA form u(c) = c(1 ) =(1 ), with the coe¢ cient of relative risk aversion > 1. There are two types of agents, which we will call domestic and foreigners. Domestic agents learn their need of liquidity after the portfolio decision is made, and thus are the classic DiamondDybvig agent. They are endowed with one unit of labor when young, for which they receive income wt ; and nothing when old. Let d1 and d2 be the total population of domestic impatient and patient agents, respectively, with d d 1 + 2 = 1. In contrast, foreigners know at the time they are born whether they will prefer to consume in their …rst or second periods of life. The second distinction between types of agents is that foreigners do not work in our economy, but bring their endowments from abroad. We label f1 ; f2 as the total population of impatient and patient foreigners, respectively.1 Agents’ type, domestic or foreigner, is observable. Further, there is no aggregate uncertainty about the total population or the share of impatient and patient agents. However, the liquidity preference shock is private information for both types of agents.

2.2

Production and investment

There is a large number of competitive …rms who produce output using capital and domestic labor as inputs according to the production function Yt = kt1

Kt L1t

(1)

where kt is the average capital-labor ratio in the economy at time t, which is taken as given by each individual …rm. The capital externality generates endogenous growth, and the economy will always be on a balanced growth path, with no transitional dynamics. Also, one unit of consumption placed into investment in period t yields R > 1 units of capital in period t+1. If investment is liquidated at the end of period t, it yields x < 1 units of consumption per unit invested. In addition, there is another saving technology called storage. One unit of consumption placed into storage at time t yields one unit of consumption regardless of whether it is liquidated in period t or held until period t + 1. In this sense, storage dominates investment in the short-term, while investment dominates the liquid asset in the long-term. we can think of the f1 foreigners as Diamond-Dybvig agents with a larger share of impatient agents relative to domestic agents, where here we look at the limiting special case where all are impatient. Likewise, the f2 foreigners have a lower probability relative to locals of becoming impatient, set here at zero. 1 Alternatively,

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2.3

Timing of events

At the beginning of period t; production takes place, and young domestic agents receive the wage wt : Since they do not know their preferences until after the opportunity to invest has passed, they will form coalitions that we call banks. Banks announce contracts which specify returns to depositors that depend on their liquidity preference (early vs late-withdrawers) reported by agents. Once banks announce contracts, foreign agents decide whether they want to bring their endowments into the local economy and deposit them in a bank. Next deposits are made, and banks place a fraction of deposits in storage and the rest in investment. Only after the portfolio decision is made is it that domestic agents learn whether they will want to consume in t or t + 1. Following this, impatient agents report to the bank and consume. At t + 1, banks rent out their capital investment to …rms, which produce using this capital and labor from the new generation of young agents. After production takes place banks sell the undepreciated capital. They receive (rt+1 + (1 )qt+1 ), where rt+1 ; and qt+1 denote the rental rate, depreciation and the price of capital, respectively. The return from investing a unit of consumption in capital is therefore t+1

R(rt+1 + (1

)qt+1 ):

(2)

Following this, patient old agents withdraw their deposits and consume.

3

Bank Behavior

Banks arise endogenously in our environment as a coalition of domestic agents. This is because domestic agents bene…t from pooling their resources in order to overcome idiosyncratic uncertainty, and they gain from insuring themselves against their liquidity preference shock. In contrast, foreign agents face no uncertainty at the time the investment decision is made, and thus have no need to pool their resources nor require insurance. In this sense, banks arise naturally as domestic banks that care about domestic agents. Given this, domestic banks will o¤er a contract that maximizes the expected utility of local agents. We assume that banks o¤er simple demand deposit contracts, and we do not impose a sequential service constraint. This, coupled with no aggregate uncertainty rules out banking crises in our environment.2 Foreign agents are able to achieve their optimal outcome without the need for banks. Young foreigners that know that they will want to withdraw in the …rst period, can simply acquire the liquid asset, while foreign late-withdrawers can invest all of their endowment in the illiquid technology in order to realize higher returns. We assume that endowments per foreign agent equal to the domestic wage, to simplify the exposition. 2 It is fairly straightforward in these type of models to generate banking crises, but here we rule them out for simplicity. See Fontenla (2006, 2007) on related environments with crises.

4

Once we introduce a banking contract, the possibility that foreigners disguise themselves as domestic agents may arise. Let mt denote liquid storage reserves. Then, banks will face the constraint mt + kt+1 = wt :

(3)

Denote cd1 and cd2 as consumption for domestic early and late-withdrawers, respectively. Then the problem of a domestic bank becomes vt

d 1 u(c1;t )

max

c1;t ;c2;t

d 1 )u(c2;t )

+ (1

(4)

subject to c1;t = mt (1 f 1

f 2

)c2;t = 0

=

if c2;t if c2;t >

f 2

c1;t ; c2;t

0;

t+1 kt+1

(6)

if c1;t wt if c1;t > wt

f 1

0

=

(5)

c2;t

c1;t

t+1 wt t+1 wt

(7) (8)

V >Va

where(5) and (6) are the bank’s resource constraints, with the share of total impatient depositors given by =

d 1

+

d 1 d 2

+ +

f 1 f 1

+

f 2

:

(9)

While banks maximize the expected utility of domestic agents using probabilities d i ; the participation of foreigners may change the actual shares of patient and impatient withdrawers, given by : is endogenous, since domestic banks decide whether to allow foreign agents to enter by way of choice of the consumption schedule. This is described by the constraints (7) and (8), which are the incentive compatibility or participation constraints of foreign agents, where f1 and f2 are the number of impatient and patient foreigners that choose to enter, respectively.3 We begin the process of solving this problem by showing that an adverse selection problem arises, where long-term foreign investors entering the economy would increase welfare of domestic agents, but choose not to deposit in banks given relatively high levels of risk aversion. Proposition 1 vt 0 (

f 2)

> 0, and

f 2

= 0 for

> 1:

f f 3 Truly, when c = w ; ) t 1 1 2 [0; 1 ], where foreigners are indi¤erent between entering or not. In this case we assume that they choose not enter.

5

In our problem, > 1 entails that early returns will be greater or equal to the wage. In other words, short-term rates of return are positive. This is the service of liquidity provision, or risk-sharing, achieved through banks. Then by feasibility, long-term returns will be less than or equal to t+1 . Since the return for patient foreigners in autarky equals t+1 , they will not enter the banking contract.4 In contrast, short-term foreign agents may have the incentive to enter, depending on the value of c1;t chosen by banks, as described by the constraint (7). Having ruled out the participation of long-term foreign investors, we turn our attention to the bank’s problem where only short-term foreign agents may want to deposit in a bank. Consider initially the pooling case where banks opt to let them enter, that is f1 = f1 . In this case, the solution to (4) sets the optimal storage reserves, which we label mpt ; as " # 1 1= 1 1= d (1 ) (1 ) (1 )= 1 mpt = 1 + wt (10) t+1 d 1

Proposition 2 c01;t (

f 1)

< 0, and mp0 t (

f 1)

> 0 for the pooling case.

In words, optimal short-term rates of return continuously fall with the number of short-term foreign deposits entering the economy. However, the actual portfolio share that banks allocate to liquid reserves does increase, partially o¤setting the previous e¤ect. Consider now the separating case where f1 = 0. Domestic agents may prefer a contract that gives foreigners the incentive not to deposit in banks. This implies from the participation constraint (7) that period t consumption needs to be set to c1 wt . It follows that from resource constraint (5), the solution sets mst = d1 wt (11) where the superscript s stands for separating. Proposition 3 The solution to the bank’s problem is the contract (c1 ; c2 ) given by ) c1;t = 1 mpt for f1 bf1 c2;t = (1 t+1) (wt mpt ) c1;t = wt c2;t = t+1 wt

for

where the threshold is de…ned as the point where 4 We

bf1 =

vtp

=

1 d 1 ( t+1

1)

f 1

>

bf1

(12)

(13)

vts :

could still have foreign long-term capital enter the economy for > 1; if we assumed domestic long-term returns being greater than foreign returns, that is dt+1 > ft+1 ; which is the usual rationale for long-term foreign direct investment. In this case patient foreigners would enter as long as c2;t > ft+1 wt :

6

The solution portrays the trade-o¤ between the bank’s contract providing insurance and the loss of resources to foreign agents who exploit this service. When domestic agents implement a risk-sharing contract, they redistribute resources from late to early-withdrawers. Therefore, when foreign earlywithdrawers enter this contract, they are receiving transfers from domestic latewithdrawers. This unintended transfer of goods reduces the welfare of domestic agents. For a small enough share of short-term in‡ows, domestic agents will prefer the loss of transferring some resources rather than give up the insurance service. Conversely, for shares of foreign agents greater than bf1 , agents will prefer the self-selection outcome. Here the costs exceed the bene…ts of insurance, so separation is chosen. In this case, both short- and long-term domestic rates of return are equalized with the return for foreigners, and thus foreign ‡ows are indi¤erent between entering or not. Notice that the threshold bf1 given by (13) is increasing in d1 , and t+1 . That is, when d1 is large, then a bigger share of agents bene…t from insurance and thus the threshold at which they want to give it up is larger.5 Also, the higher the degree of risk aversion, the more agents value insurance, and thus are less willing to sacri…ce this function of banks. In the limit we have that as ! 1; bf1 ! 1. Finally, the higher the return on the production technology, the higher intertemporal transfers, and thus the threshold at which domestic agents are willing to give up insurance is raised. Lastly notice that while insurance is reduced in the pooling case, or is completely lost for the separating case, domestic agents still prefer to deposit in banks. This is so since the other service banks provide, e¢ cient intertemporal investment, is still achieved. However, as x ! 1, V s ! V aut for f1 > bf1 . That is, as the potential cost of holding the production technology disappears, banks lose their reason to exist when they do not provide insurance.

4

Equilibrium

We now turn to the analysis of the equilibrium behavior of the economy. We …rst derive the market-clearing conditions and the equilibrium law of motion for the capital stock as a function of the contract o¤ered by banks. We then use numerical methods to illustrate the equilibrium behavior of the economy.

4.1

Market clearing and aggregate investment

In equilibrium all …rms will choose the same capital-labor ratio, and hence kt = kt holds. Firms are competitive and therefore factors are paid their marginal products. The equilibrium wage and rental rate therefore reduce to wt = (1

)kt ;

rt = : 5 However, as d increases, the amount of insurance they obtain is smaller, which works in 1 the opposite direction.

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The marginal product of capital is constant, which is why the economy is always on a balanced growth path. The return to using a unit of consumption to purchase existing capital is rt + (1

)qt+1 qt

The return from investing a unit of consumption in new capital formation is given by (2) : Then the market clearing price of existing capital which will make banks be indi¤erent between purchasing existing capital or investing in new capital is 1 qt = ; R and thus t+1 = R + (1 ) in equilibrium. Since rt and qt are constant over time, the bank’s problem is exactly the same in every period and thus the solution will be independent of time. In other words,banks will o¤er the same deposit contract in every period. Combining our previous results with the equilibrium conditions above, we have Proposition 4 The law of motion for the capital stock per domestic agent is (1 (1

kt+1 = where

= 1+

(1

)

1 1=

f 1 )(1

)(1 + d 1 )(1

)kt

)kt d 1)

(1

1=

[R + (1

d 1

f 1 f 1

for for (1

)]

bf1 > bf1 )=

(14) 1

.

The law of motion is divided into two segments. For relatively low quantities of foreign impatient agents ( f1 bf1 ); short-term ‡ows enter the economy. As f 1 increases, banks respond by reducing short-term rates of return (prop. 2), long-term rates increase, and resources are shifted toward capital accumulation and production. That is, @kt+1 =@ f1 > 0 in the …rst segment of (14) : In this sense, short-term capital ‡ows increase long-term growth. In the second segment of the law of motion ( f1 > bf1 ); the banking contract creates the incentives such that short-term ‡ows do not enter the economy ( f1 = 0). In this case, there are two distinct positive e¤ects on growth. First, this contract completely eliminates liquidity provision, and thus no resources are redistributed from late to early-withdrawers. Second, since foreigners do not enter the economy, there is no unintended transfer of goods between domestic and foreign agents. Consider a numerical example to illustrate capital accumulation as a function of short-term ‡ows.6 Speci…cally, consider the following parameters: the coe¢ cient of relative risk aversion is = 3, the share of domestic young consumers is d1 = 0:5; initial capital is set to kt = 10; depreciation is set to = 0:1; the share of production that belongs to capital is = 0:4; and the return to investments are R = 3 and x = 0:5. Figure 1 depicts the bank’s optimal choice of long-term investments in capital as a function of short-term ‡ows. 6 All

computations are performed in Mathematica. Code available upon request.

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[Figure 1 here] As can be seen in our numerical example, kt+1 is an increasing function of f1 up to the threshold bf1 ; after which it becomes constant. Capital per domestic depositor increases as liquidity provision is lowered due to the increase in foreigners. Beyond the threshold bf1 , there is no liquidity provision, foreigners do not enter, and all the resources of patient agents are invested in the long-term production technology.

5

Implications for welfare

Our model so far provided the optimal banking contract that maximizes the expected utility of a single generation of agents. We have shown how shortterm foreign in‡ows reduce welfare of the current generation. However, the above analysis implies, through its e¤ect on growth, that the deposit contract used at time t a¤ects all future generations. Larger capital stocks increase welfare of future generations via higher wages. Consider a social planner that places equal weight on all members of a given generation, and discounts the expected utility of generation t agents by t , for some 2 [0; 1). We restrict the planner to choose a simple deposit contract in each period, which implies that the set of feasible allocations for the planner is the same as the set of feasible allocations in the competitive economy. For a given deposit contract, let vt be the value of the objective function given by (4) : Then we can write the social welfare maximization problem as max

1 X

t

vt

t=1

subject to the law of motion (14) : The solution to this problem portrays the trade-o¤ in welfare between current and future generations. Short-term foreign in‡ows reduce welfare of the current generation, but increase welfare of future generations via increased economic growth. When there are many generations, the intertemporal impact of the bank’s investment decision at time t can be very large. A social planner who places su¢ cient weight on future generations may therefore prefer a deposit contract that o¤ers less risk sharing within each generation, but that generates higher average growth rate by placing more resources into investment.

6

Conclusion

This paper studies the e¤ects that capital ‡ows have on the …nancial system in the context of a demand deposit banking model with growth. In our model, short-term capital ‡ows enter the …nancial system while bene…cial long-term capital does not. Further, as short-term capital ‡ows in, short-term rates of return fall, which reduces the welfare of domestic agents. However, long-term 9

rates of return increase, and banks portfolio allocation shifts toward long-term investments. In this sense, short-term capital ‡ows indirectly increase long-term growth when we implicitly model the banking contract. A welfare trade-o¤ occurs, where short-term foreign in‡ows reduce welfare of the current generation, but increase welfare of future generations via increased economic growth. Thus, a social planner may prefer a deposit contract that o¤ers less risk sharing within each generation, but that generates higher growth rates of the economy.

References [1] Calvo, Guillermo A., A. Izquierdo and E. Talvi (2006). “The Economics of Sudden Stops in Emerging Economies.” American Economic Review, V.96-2, May, pp. 405-410. [2] Diamond, Douglas and Philip Dybvig (1983). "Bank Runs, Deposit Insurance and Liquidity." Journal of Political Economy, 85,191-206. [3] Ennis, Huberto and Todd Keister (2003). "Economic Growth, Liquidity and Bank Runs." Journal of Economic Theory, 109, 220-245. [4] Fontenla, Matias and Fidel Gonzalez, (2007). "Self-ful…lling and Fundamental Banking Crises: A Multinomial Logit Approach." Economics Bulletin, Vol. 6, No. 17 pp. 1-11. [5] Fontenla, Matias (2006). "Corridas bancarias sunspot y de tipo fundamental." El Trimestre Económico, 289, pp. 67-86. [6] Fontenla, Matias (2007). "Liquidity provision and banking crises with heterogeneous agents." UNM working paper. [7] Galindo, A., Micco, A., Ordoñez, G., (2002). "Financial liberalization: does it pay to join the party?" Economia 3 (1), pp.231-261. [8] Galindo, Arturo, Fabio Schiantarelli and Andrew Weiss (2007). "Does …nancial liberalization improve the allocation of investment? Micro-evidence from developing countries." Journal of Development Economics, 83, pp. 562–587. [9] Reisen, H. and M. Soto, (2001). "Which types of capital in‡ows foster developing-country growth?" International Finance, 4:1, pp. 1-14. [10] Rodrik, Dani and Andrés Velasco (1999). "Short-Term Capital Flows." in Annual World Bank Conference on Development Economics, edited by Boris Pleskovic and Joseph Stiglitz, pp. 59-90. [11] Smith, Bruce D. (2003). "Taking Intermediation Seriously" Journal of Money, Credit and Banking, Vol. 35, No. 6,Dec., pp. 1319-1357.

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