Financial Development and the Instability of Open Economies

This paper introduces a framework for analyzing the role of financial factors as a source of instability in small open economies. Our basic model is a dynamic open economy model with a tradeable good produced with capital and a country-specific factor. We also assume that firms face credit constraints, with the constraint being tighter at a lower level of financial development. A basic implication of this model is that economies at an intermediate level of financial development are more unstable than either very developed or very underdeveloped economies. This is true both in the sense that temporary shocks have large and persistent effects and also in the sense that these economies can exhibit cycles. Thus, countries that are going through a phase of financial development may become more unstable in the short run. Similarly, full capital account liberalization may destabilize the economy in economies at an intermediate level of financial development: phases of growth with capital inflows are followed by collapse with capital outflows. On the other hand, foreign direct investment does not destabilize.


Introduction
This paper introduces a framework for analyzing the role of …nancial factors as a source of instability in small open economies. Our basic model is a dynamic open economy model with a tradeable good produced with internationally mobile capital and a country-speci…c factor. Moreover, …rms face …nancial constraints: the amount they can borrow is limited to times the amount of their current level of investible funds. 1 A high then represents an e¤ective and developed …nancial sector while a low represents an underdeveloped one.
Our model can provide some answers to a number of important and rather basic questions. First, we show that it is economies at an intermediate level of …nancial development -rather than the very developed or underdeveloped -that are the most unstable. This is true both in the sense that temporary shocks will have large and persistent e¤ects and also in the sense that these economies can exhibit stable limit cycles. Thus, countries going through a phase of …nancial development may become more unstable in the short run. Second, the model allows us to examine the e¤ects of …nancial liberalization on the stability of the macroeconomy. Once again it turns out that the interesting economies are the ones at an intermediate level of …nancial development. In these economies, full …nancial liberalization (i.e., opening the domestic market to foreign capital ‡ows) may actually destabilize, inducing chronic phases of growth with capital in ‡ows followed by collapse with capital ‡ight. On the other hand, foreign direct investment never destabilizes since foreign direct investors come in with their own credit-their ability to invest is unrelated to the state of the domestic economy. Overall, this suggests that economies at an intermediate stage of …nancial development should consider carefully how they liberalize their capital account. Allowing foreign direct investment while initially restricting portfolio investment may sometimes be a reasonable approach. Third, our model allows us to assess the macroeconomic e¤ects of speci…c shocks to the …nancial sector such as overlending by banks (leading to a phase of bank failures) or overreaction by investors to a change in fundamentals. 2 Once again, our model predicts these shocks to have their most persistent e¤ects when …nancial markets are at an intermediate stage of development.
The basic mechanism underlying our model is a combination of two forces: on one side, greater investment leads to greater output and ceteris paribus, higher pro…ts.
Higher pro…ts improve creditworthiness and fuel borrowing that leads to greater investment. Capital ‡ows into the country to …nance this boom. At the same time, the boom in investment increases the demand for the country-speci…c factor and raises its price relative to the output good (unless the supply of that factor is extremely elastic).
This rise in input prices leads to lower pro…ts and therefore, reduced creditworthiness, less borrowing and less investment, and a fall in aggregate output. Of course, once investment falls all these forces get reversed and eventually initiate another boom. It is this endogenous instability which causes shocks to have persistent e¤ects and in more extreme cases leads to limit cycles.

The reason why an intermediate level of …nancial development is important for this
result is easy to comprehend: at very high levels of …nancial development, most …rms' investment is not constrained by cash ‡ow so shocks to cash ‡ow are irrelevant. On the other hand, at very low levels of …nancial development, …rms cannot borrow very much in any case and therefore their response to cash- ‡ow shocks will be rather muted 2 Perhaps as a consequence of herd behavior.
-extra cash means more investment but only a little more. Therefore shocks will die out without causing any great turmoil. It is then at intermediate levels of …nancial development that shocks to cash ‡ow will have an e¤ect intense enough to be a source of instability.
This last argument also helps us understand why opening the economy to foreign capital may destabilize: essentially, the response of an economy with a closed capital market to a cash ‡ow shock is limited since only so much capital is available to entrepreneurs. Additional funding sources in an open economy potentially increases the response to a shock and therefore the scope for volatility.
The basic mechanics of instability described here -an increase in input price leading to a pro…t squeeze and eventual output collapse -have been documented in a number of countries. For example, in the years leading up to the crisis of the early 1980's in the Southern Cone countries, there is evidence that pro…ts in the tradeable sector sharply deteriorated due to a rise in domestic input prices (see Galvez and Tybout, 1985, Petrei and Tybout, 1985, or De Melo, Pascale and Tybout, 1985. Moreover, ample anecdotal evidence supports the impact of 'competitiveness'(e.g., a real appreciation) on the …nancial conditions of …rms.
The dynamic impact of a liberalization predicted by the model is also consistent with the experience of several emerging market countries that have liberalized, in particular in Southeast Asia and Latin America, but also in some European countries. In the years prior to their respective crises, these economies had been going through a process of rapid …nancial sector liberalization, which facilitated borrowing by domestic …rms. Partly as a result of this liberalization, capital ‡owed into these economies in large quantities, allowing rapid growth in lending and a boom in investment. However, episodes of large capital in ‡ows have often been associated with growing imbalances, such as a real currency appreciation 3 , an increase in real estate prices (e.g., see Guerra de Luna, 1997), or an increase in non-performing loans (see World Bank, 1997, p. 255). When the crisis came, most of these forces got reversed -capital ‡owed out, the currency collapsed, real estate prices dropped, lending stopped, and investment collapsed. 4 It is however important to emphasize that the goal of this paper is not to explain exactly what happened in some particular country, but rather to propose a uni…ed macroeconomic framework that gives a central role to …nancial constraints and …nancial development. There are certainly a number of strands of the existing literature anticipating a signi…cant part of what we have done here. Gertler and Rogo¤ (1990) study an open economy model with credit-market imperfections. However, they do not consider business cycle ‡uctuations. 5 The idea that …nancial constraints on …rms can play a role in the propagation of the business cycle was modeled in Bernanke and Gertler (1989).
Subsequent work by Kiyotaki and Moore (1997), Aghion, Banerjee, and Piketty (1999) and Azariadis and Smith (1998) have shown that these constraints can lead to oscillations, though only in the context of a closed economy. However, none of these papers study the e¤ects of opening up the domestic …nancial sector to foreign capital ‡ows and none of them, except Aghion, Banerjee, and Piketty (1999), focus on the level of …nancial development as a factor determining the extent of instability. While the model's struc- 3 See, for example, Calvo et al. (1996). The degree of real appreciation varies across countries; for example, it has been more pronounced in Latin America than in Asia. 4 See World Bank (1997) and Milesi-Ferretti and Razin (1998) for systematic descriptions of the link between and capital ‡ow reversals and currency crises. Gourinchas, Valdés, and Landerretche (2001) provide a systematic analysis of lending booms which coincide with movements in output, capital in ‡ows, the current account and the real exchange rate that are fully consistent with our results. See also Honkapohja and Koskela (1999) for an illuminating description of the Finnish crisis of the 1990's, which …ts well our analysis: …rst, an economic environment characterized by a large proportion of credit-constrained enterprises, for which investments are highly elastic w.r.t. current pro…ts; second, a …nancial market deregulation in the 1980's that leads to a huge expansion of bank lending, to major in ‡ows of foreign capital and to a sharp increase in real asset prices (in particular real estate prices) during the boom; and subsequently in the 1990's, a sharp fall in real asset prices, investments, and real GDP, and the occurrence of a banking crisis that eventually led to a tightening of banking regulations and to a devaluation of the Finnish currency after hopeless e¤orts to maintain a …xed exchange rate. 5 Caballero and Krishnamurthy (2001) distinguish between credit constraints from foreign investors and constraints from domestic investors to explain the ampli…cation of shocks in an open economy. They also abstract from business ‡uctuations issues. ture is in a spirit similar to Aghion, Banerjee, and Piketty (1999), this paper di¤ers in key respects. First, the economic mechanisms at work are of a di¤erent nature. Second, the economic questions and the types of policy shocks we focus on are entirely di¤erent. Finally, at a methodological level, unlike Aghion, Banerjee, and Piketty (1999) we show that our results are robust to the introduction of forward-looking entrepreneurs.
A separate literature focuses on the case for free capital mobility. Policy interest in the debate has been aroused by the recent, rather mixed, experience of a number of countries that have liberalized their capital account. 6 However, a number of important aspects, including the implications of liberalization on volatility, have not been widely studied. 7 More importantly, none of these papers attempt to relate the e¤ect of liberalization to the functioning of the domestic …nancial sector.
Finally a number of recent papers stress that speci…c shocks to the …nancial sector, such as those brought on by policy mistakes, herd behavior, panics, or corruption in the …nancial sector, may lead to crises in the real economy. While accepting the validity of these arguments, we feel these models su¤er from ignoring some of the interactions between the …nancial sector and the rest of the economy. As our model makes clear, volatile behavior may arise even in the absence of such shocks; while on the other hand, the presence of such shocks does not automatically imply they will have large and persistent real e¤ects.
The paper is organized as follows. Section 2 represents the core of the paper, with a description of a basic version of the open-economy model and a characterization of the conditions under which macroeconomic volatility arises. Section 3 presents the model under more general assumptions and provides numerical simulations to assess the plausibility for volatility. Section 4 analyzes the impact of a capital account liberalization 6 See, for example, Johnston et al. (1997) or Eichengreen et al. (1998). 7 Obstfeld (1986), McKinnon (1993), Bacchetta (1992), Bartolini and Drazen (1997) analyze capital account liberalizations. McKinnon and Pill (1997) and Bacchetta and van Wincoop (2000) are among the …rst examining the issue of volatility. and contrasts the stabilizing e¤ect of unrestricted FDI with the potentially destabilizing e¤ects of either foreign indirect investments or restricted foreign direct investments. Section 5 describes various extensions and draws some tentative policy conclusions.

The Basic Mechanism
For pedagogical purposes we consider …rst a simple model with constant saving rates and a Leontief technology involving a inelastic supply of the country-speci…c factor.
In Section 3, we consider a more general model with three main extensions: …rst the supply of domestic input is elastic; second, the production technology is more general ; and third, saving decisions result from intertemporal utility maximization.

A Simple Framework
We consider a small open economy with a single tradeable good produced with capital and a country-speci…c factor. One should typically think of this factor as input services such as (skilled) labor or real estate. We take the output good as the numeraire and denote by p the price of the country-speci…c factor when expressed in units of the output good. The relative price p can also be interpreted as the real exchange rate. In this basic framework we assume that the supply of the country-speci…c factor is inelastic and equal to Z.
For the sake of presentation, in this subsection we also assume that all agents save a …xed fraction (1 ) of their total end-of-period wealth and thus consume a …xed fraction : The intertemporal decisions of lenders are of no consequence for output in such an open economy since investors can borrow in international capital markets. They will, however, a¤ect net capital ‡ows. 8 8 Notice that the separation between the decisions of lenders and entrepreneurs does not imply separation between total national savings and investment. Gertler and Rogo¤ (1990) show that a framework with credit constraints can explain the high correlation between total savings and investment (Feldstein and Horioka, 1980). We obtain a similar result in our framework. However, in general this result also depends on lenders'savings behavior.
There are two distinct categories of individuals in the economy. First, the lenders, who cannot directly invest in production, but can lend their initial wealth endowments at the international market-clearing interest rate r. Second, the entrepreneurs (or borrowers) who have the opportunity to invest in production. There is a continuum of lenders and borrowers and their number is normalized to one for both categories.
Output y is given by the following production function: where 1=a > r, i.e., we assume that productivity is larger than the world interest rate. where the interest rate is endogenously determined by domestic investment demand and domestic savings supply. Yet, for convenience, we shall maintain the assumption of a that does not depend on the interest rate in that section as well. As shown in Aghion-Banerjee-Piketty (1999), this corresponds to a particular parametrization of the more general model of the credit market presented in that paper. Our results would only be stronger if we allowed the usual negative relation between the interest rate and . 9 Production decision: Denote by L the amount borrowed. The funds available to an entrepreneur with total initial wealth W B are I = W B + L. When the credit constraint is binding, I = (1 + )W B . Entrepreneurs will choose the level of the country-speci…c factor z, with corresponding investment K = I p z, to maximize current pro…ts. Given the above Leontief technology, the optimum involves z = K a ; so that: Depending on the level of entrepreneurs'wealth, there are three cases: i) Binding credit constraint and p = 0. W B is low so that the credit constraint is binding (L = W B ) and K a < Z. In this case, there is an excess supply of the country-speci…c input. This immediately gives us p = 0: Output at date t is then given by: ii) Binding credit constraint and p > 0. W B is low so that L = W B , but K a Z.
Thus, there is excess demand for the immobile factor. Therefore p > 0 and output is determined in equilibrium by the supply of the country-speci…c input: y t = Z: From (2) and the de…nition of I, the equilibrium price of the country-speci…c input is given by: 9 >From Aghion-Banerjee-Picketty, we …nd = 1=(1 =ac), where is the cost of cheating for the borrower and c is proportional to the debt collection cost in case of default for the lender. With a higher level of …nancial development, is larger and c smaller. This implies that is larger.
Notice that in this case the entrepreneur's entire wealth is invested in the domestic technology since it has returns higher than the world interest rate, i.e., y rL > rW B . 10 iii) Unconstrained entrepreneurs. W B is large enough so that L < W B . As in ii), p > 0 and y t = Z, but p is not a¤ected by the level of investment. When W B is large, entrepreneurs borrow until pro…ts equal the international interest rate: y rL = rW B , i.e., until y = rI. This determines the maximum price level. Hence, I = Z=r so that the price is given by: The equilibrium price p t , i.e., the real exchange rate, which is a positive function of W B ; is the key variable whose movements over time will produce volatility.
The Timing of Events: The timing of events within each period t is the following.
Investment, borrowing and lending, and the payment of the country-speci…c factor services p Z by entrepreneurs to the owners of that factor, take place at the beginning of the period (which we denote by t ). Everything else occurs at the end of the period (which we denote by t + ): the returns to investments are realized; borrowers repay their debt, rL, to lenders; and …nally, agents make their consumption and savings decisions determining in turn the initial wealth of borrowers at the beginning of the next period (i.e., at (t + 1) ): where e is an exogenous income in terms of output goods, y t = min I a ; Z is output in period t (also equal to the gross revenues of entrepreneurs during that period). The expression in brackets is the net end-of-period t revenue of entrepreneurs. The net disposable wealth of entrepreneurs at the beginning of period t + 1 is what remains of this net end-of-period return after consumption, hence the multiplying factor (1 ) on the right-hand-side of equation (4).
Entrepreneurs invest and borrow only if their pro…ts are larger than or equal to the international return. When or W B are large, entrepreneurs invest only up the point where y rL = rW B : Any remaining wealth is invested at the international market rate.
In this case, no pure pro…ts are earned from production and the evolution of wealth is simply given by: Thus, the dynamics are fully described either by di¤erence equation (4) or by di¤erence equation (5).

Volatility
When the dynamic evolution of domestic entrepreneurs'wealth is described by equation (4), an increase in entrepreneurs'wealth W B t at the beginning of period t has an ambiguous e¤ect on next period's wealth W B t+1 . This is due to the fact that the amount of invested wealth itself depends negatively on the input price p, whilst p depends positively on current wealth. Using the fact that: we have: Then, from (4), the impact of last period wealth on current end of period wealth can be decomposed into two e¤ects: On the one hand, there is a positive wealth e¤ect of current wealth on future wealth: for a given price of the country-speci…c factor p t ; a higher inherited wealth W B t from period (t 1) means a higher level of investment (1 + )W B t in period t which, all else equal, should produce higher revenues and thus higher wealth W B t+1 at the beginning of period t + 1: On the other hand, there is a negative price e¤ect of current wealth on future wealth: more investment in period t also implies a greater demand for the country-speci…c factor to thus raise its price p t during that period. This, in turn, has a detrimental e¤ect on period t revenues and therefore on the wealth W B t+1 at the beginning of period t + 1: With the above Leontief speci…cation, the price e¤ect is eliminated whenever the current wealth W B t is so small that current investment cannot absorb the total supply of the country-speci…c factor. In this case p t 0 and: On the other hand, the price e¤ect dominates when the current wealth W B t is suf-…ciently large that current investment exhausts the total supply of the country-speci…c factor. In this case, we simply have: so that dW B t+1 =dW B t < 0.
[ Figure 1 about here] Figure 1 shows the relationship between W B t+1 and W B t in this basic Leontief setup.
This relationship is represented by three segments corresponding to the three cases described in 2.1. The …rst one is the upward sloping curve described by (6) for W < W = aZ 1+ ; this is the case where the wealth e¤ect dominates as p = 0: The second segment, for W < W < W = Z (1+ )r ; is described by (7); in this case, the price e¤ect always dominates. Finally, the third segment (W > W ) represents equation (5) where entrepreneurs are not credit-constrained. As drawn in the …gure, the 45 line intersects curve at the point c W which lies in the second segment. This intersection can also be in either of the other two segments. It will be in the …rst segment when r g , the …xed point of equation (6); is less than W : Since r g is increasing in while W is decreasing, it is clear that this can only happen when is very small. On the other hand, the intersection will be in the third segment when the …xed point of equation (5) If these conditions hold, one can easily derive additional su¢ cient conditions under which long-run volatility actually occurs. For example, a two-cycle (W 1 ; W 2 ) will satisfy: 11 with W 1 < W < W 2 < W . This two-cycle will be stable whenever (1 ) 2 r ( 1+ a r ) < 1: Conditions for the existence of longer (and more plausible) cycles can be derived using standard techniques. The dynamic simulations will show that the ‡uctuations can be complex since wealth can ‡uctuate between the constrained (the …rst two segments in Figure 1) and the unconstrained (the third segment) regions.
Intuitively, the basic mechanism underlying this cyclicality can be described as follows: during a boom the demand for the domestic country-speci…c factor goes up as (high yield) investments increase, thus raising its price. This higher price will eventually squeeze investors'borrowing capacity and therefore the demand for country-speci…c factors. At this point, the economy experiences a slump and two things occur: the relative price of the domestic factor collapses, while a fraction of the factor available remains unused since there is not enough investment. The collapse in the factor price thus corresponds to a contraction of real output. Of course, the low factor price will eventually lead to higher pro…ts and therefore to more investment. A new boom then begins.
The reason why the level of …nancial development matters is also quite intuitive: economies at a low level of …nancial development have low levels of investment and do not generate enough demand to push up the price of the country speci…c factor while economies at a very high level of development have su¢ cient demand for that factor to keep its price positive. 11 This follows immediately from the equations:

Discussion
Although the above framework is extremely simple, it generates a number of predictions for empirical analysis on emerging markets. In particular, our model predicts: (i) that the investment to GDP and private credit to GDP ratios should increase during a "lending boom"; 12 (ii) that lending booms are times of net capital in ‡ows; (iii) that the real exchange rate (p t in our model) should increase during a lending boom; (iv) that the fraction of defaulting loans should increase towards the end of a lending boom (in a straightforward extension of our model with uncertainty and defaults, which we develop in section 5.1 below). Recent work by Gourinchas, Valdés, and Landerretche (2001) provides an interesting cross-country study of lending booms and examine the pattern of a set a macroeconomic indicators around these booms. 13 The behavior of these indicators is shown to be fully consistent with the above predictions. In particular, by comparing with "tranquil periods", Gourinchas et al. show that during lending booms the output gap is higher, the investment/GDP ratio increases, the proportion of short term debt increases, the current account worsens, the real exchange rate appreciates, especially at the end of the boom period. When lending declines, all these movements are reversed. In particular, the fact that investment follows a credit expansion and is sharply procyclical is fully consistent with our approach.
The above model is very simple, but simplicity and tractability always come at a cost. In particular, the analysis has been drastically simpli…ed by assuming a Leontief technology, a constant savings rate, and an inelastic supply of the non-tradeable input.
In the next section we relax these three assumptions. Moreover, in the concluding section 12 In the context of the above model, we have: which indeed increases during a lending boom as a result of the price e¤ect. 13 See also Tornell and Westermann (2002).
we discuss mechanisms that lead to a procyclical and therefore amplify the underlying volatility.
An important question is whether the basic mechanism leading to volatility depends on the assumption of discrete time. It is well known that volatility occurs more easily

Generalizing our framework
We modify our previous model by assuming: 1. Elastic Supply of the Country-Speci…c Factor: we relax the assumption of a …xed supply of the country-speci…c factor and assume that Z is instead produced by (domestic) lenders using the tradeable good at a cost c(Z) = 'Z , where > 1.
Maximization of a domestic lender's pro…t pZ 'Z , yields the optimal supply of the country-speci…c factor: 2. CES Technology: we replace the Leontief technology by a CES production function, with f (K; z) = A(K + z ) 1= , with A > r and > 0. 16 The parameter determines the elasticity of substitution between K and z (we assume < 1 for concavity). This CES speci…cation includes as special cases, both the Cobb-Douglas technology when = 0; and a Leontief technology when ! 1.
The …rst order conditions for this problem give us: where M t = t =W B t . It is clear from equation (9) that the ratio as increases. This implies that an increase in (a reduction in the elasticity of intertemporal substitution) reduces consumption changes and gives correspondingly larger intertemporal savings changes, i.e., savings become more pro-cyclical over time. This, in turn, will tend to amplify the cycle as the price of the country-speci…c input increases more sharply during a boom. True, to the extent that the returns to savings are higher when the economy is in a slump (slumps are typically followed by periods with high investment pro…tability), there should be a greater tendency to save more in a slump, thereby attenuating the cyclical variations. However, this latter e¤ect is weaker, the higher the cost of intertemporal substitution (i.e., with a larger ). 17 Entrepreneurs'wealth available for next period is now a weighted average of past pro…ts and expected future wealth. While this second order (highly non-linear) di¤erence equation does not lend itself to analytical solutions, it can be resolved numerically as we show in the next subsection.

Simulations
We present our simulation results by successively varying three parameters: i) the elasticity of substitution between capital and the other factor in the production function, In each case, we consider the dynamic impact on output of a negative shock that makes wealth fall by 1% below the steady-state wealth. We normalize output so that it is initially equal to 100 and we look at the dynamic evolution of output over 30 periods after the shock. Figures 2 and 3c and 3d display the simulations in the log utility case where = 1. It can easily be shown (see the working paper version) that this case is equivalent to the constant savings rate economy analyzed in the previous section. 18 Figure 2 presents the log utility case with a …xed supply of the country speci…c factor. 18 Note that the simulation technique di¤ers between the constant savings rate case and the log-utility case with in…nitely lived and forward-looking entrepreneurs. In the former case, we simply need to run a …rst order di¤erence equation with given initial wealth level. In the latter case, as shown in footnote 17, the dynamic system is described by a forward-looking second order di¤erence equation which requires that we compute the initial consumption level for given initial wealth (e.g., using a shooting algorithm). When = 1, however, the two methods generate exactly the same dynamics.

The diagrams show four cases corresponding to di¤erent values of input substitutability
, each leading to a di¤erent dynamic path. In Figure 2a, where = 0:5, there is no instability and output converges smoothly to its initial level. When decreases to 1:5 ( Figure 2b), output still converges but includes oscillations. Figure 2c shows a two-cycle, which arises when = 2. Finally, when = 4 ( Figure 2d), more complex dynamics arise due to 'regime switching': large increases in wealth lead the system to the unconstrained region (the third segment in Figure 1), but the system returns to the constrained region since r < 1. Notice that the ‡uctuations in 2c and 2d are larger than the initial shock, so that small shocks are ampli…ed (actually in…nitesimal shocks would lead to similar ‡uctuations).
In Figures 3a and 3b, we assume that = 4 with an inelastic supply of the country-speci…c factor, while we depart from log utility by varying the intertemporal elasticity parameter . With a lower elasticity of intertemporal substitution, = 10, the system tends to be even more unstable and switches more easily across regimes. When entrepreneurs are more ready to substitute intertemporally, which in this …gure corresponds to the case where = 0:5, regime switches are less frequent. The most important conclusion from Figure 3, however, is that the long-run instability results established under constant savings rates (or with optimal intertemporal savings in the log utility case), carry over to a wide range of elasticities of intertemporal substitution.
Finally, in Figures 3c and 3d we show simulations with an elastic supply of the country-speci…c factor, assuming = 4 and log utility. Obviously, with an elastic supply there is less scope for ‡uctuations. For example, Figure 3d shows that with a supply elasticity of 30 percent ‡uctuations die out rapidly. However, with an elasticity of 15 percent, which appears reasonable in the short run, we still have ‡uctuations with a two-cycle.
Thus, even though our model is highly stylized, long-run output volatility and/or large ampli…cation of shocks occur for empirically reasonable parameter values and are not con…ned to one particular functional form.

Financial Liberalization and Instability
The previous analysis shows that a fully open economy with imperfect credit markets can exhibit volatility or a cycle. We show in this section that the same economy can be stable if it is closed to capital ‡ows or if only foreign investment (FDI) is allowed. Thus, a full liberalization to capital movements may destabilize an economy: while it stabilizes the real interest rate, it also ampli…es the ‡uctuations in the price of the country-speci…c factor. This in turn, increases the volatility in …rms'cash- ‡ows and therefore aggregate output. We …rst consider the case of an economy that opens up to foreign lending.
Then, we examine the case of FDI, where foreign investors are equity holders and are fully informed about domestic …rms. Even though the results are valid with general production functions, we present the Leontief case for pedagogical reasons.

Liberalizing Foreign Lending
We consider an economy with low domestic savings, with the Leontief technology spec-i…ed in Section 2.1, and we …rst assume that this economy is not open to foreign borrowing and lending (this closed economy is described in details in Appendix A). In that case, at each date, the current wealth of domestic lenders W L matters since domestic investment is constrained by domestic savings W B + W L . Now suppose that the initial levels of wealth held by entrepreneurs and domestic lenders, W B and W L respectively, are su¢ ciently small so that initially p 0 = 0 This corresponds to a situation where domestic entrepreneurs cannot exhaust the supply of country-speci…c inputs. Let us also assume that at date 0 domestic savings W B 0 + W L 0 are less than the investment capacity (1 + )W B 0 . 19 If > 1 there will then be excess investment capacity in following periods as long as p t remains equal to zero. To see this, note that the domestic interest rate r t , determined in a closed economy by the comparison between W L t and W B t ; is such that entrepreneurs are indi¤erent between borrowing and lending, that is: r t = 1 a in the Leontief case. Therefore, if p t = 0 and W L t < W B t ; we have: and so that W L t < W B t implies that: W L t+1 < W B t+1 and therefore r t+1 = 1 a : In Appendix A we provide su¢ cient conditions under which p t = 0 and r t = 1 a for all t: Under these conditions, entrepreneurs'wealth will grow as the (low) rate 1 a , since it is constrained by the (low) level of domestic savings, and the W B t+1 (W B t ) schedule will intersect the 45 0 line on its …rst branch along which p t = 0: This, in turn, implies that there will be no persistent ‡uctuations in this closed economy.
What happens if this economy is fully opened up to foreign borrowing and lending?
The interest rate will be …xed at the international level r: By itself, this could only help stabilize any closed economy that otherwise might (temporarily) ‡uctuate in reaction to interest rate movements. However, the opening up of the economy to foreign lending also brings net capital in ‡ows as investors satisfy their excess funds demand in international capital markets. The corresponding rise in borrowing in turn increases the scope for bidding up the price of the country-speci…c factor, thereby inducing permanent ‡uctuations in p, W B and aggregate output. = 0, …nancial opening will not help investment and no capital in ‡ow will occur, so there will be no upward pressure on the price of the country-speci…c input. 21 The above example therefore suggests that it might be desirable for a country to increase its , i.e., to develop its domestic …nancial sector before fully opening up to foreign lending.  20 When several developed countries did liberalize their capital movements in the 1970s and 1980s periods of high instability could not be observed. 21 This may be the case in some of the poorer African and Asian countries. 22 Typically, measured FDI implies participations of more than 10% in a …rm's capital so this appears to be a reasonable assumption. Razin et al (1998) make a similar distinction about FDI. benchmark case where the supply of FDI is in…nitely elastic at some …xed price greater than the world interest rate, say equal to r + . 23 Starting from a situation in which domestic cash ‡ows are small so that domestic investment cannot fully absorb the supply of country-speci…c factors, foreign direct investors are likely to enter in order to pro…t from the low price of the country-speci…c factors. This price will eventually increase and may even ‡uctuate as a result of FDI.

Foreign Direct Investment
But these price ‡uctuations will only a¤ect the distribution of pro…ts between domestic and foreign investors, not aggregate output. For example, in the Leontief case with FDI, aggregate output will stabilize at a level equal to the supply of factor resources Z, whereas the same economy may end up being destabilized if fully open to foreign portfolio investment (i.e., to foreign lending).

Consider a closed Leontief economy open to foreign direct investment only. Assume
also that W L is large enough so that …rms can still borrow their desired amount domestically (otherwise investment is still constrained by savings and the scope for ‡uctuations is much smaller). Then FDI will ‡ow into the economy as long as the rate of return on that investment remains greater than or equal to r + . Thus, if F denotes the net in ‡ow of direct investment, in equilibrium we obtain the free-entry condition: where R = y e rL W B +F is the net rate of return on foreign direct investment and e r is the domestic interest rate. If domestic savings are less than the investment capacity of domestic entrepreneurs (i.e., W L < W B ), we would have e r = 1 a : However, as domestic savings exceed the investment capacity of domestic entrepreneurs, e r = , where is the return of an alternative, ine¢ cient, storing technology (as in Aghion, Banerjee, and Piketty (1999)). In a closed economy, lenders will invest their excess savings in this technology.
Assume that R > r + as long as p = 0 (this implies r + < 1 a (1 + ) ), so that there will be a positive ‡ow of FDI as long as p = 0. Using the fact that L = (W B + F ) and that y = Z when p > 0, we can rewrite the above free-entry condition as: This, together with the price equation (3), implies that: which in turn gives a stable value for p. Thus, even though FDI leads to a price increase it does not generate price and output volatility.
Consider now an economy which has already been opened up to foreign borrowing and lending at rate r, that is to foreign portfolio ‡ows only, and which, as a result has become volatile as in the example depicted in Figure 4. What will happen if this economy is now also opening up to FDI? By the same reasoning as before, opening up to FDI will stabilize the price of the country-speci…c factor at level p such that: This again will eliminate investment and output volatility in this economy (assuming that initially the country is attracting FDI). In other words, if there are no limitations on FDI in ‡ows and out ‡ows (and FDI involves complete information on domestic …rms), the price of the country-speci…c factor and therefore aggregate domestic GDP or GNP will remain constant in equilibrium.
The reason why FDI acts as a stabilizing force is again that, unlike foreign lending, it does not depend on the creditworthiness of the domestic …rms, and furthermore it is precisely during slumps that foreign direct investors may prefer to come in so as to bene…t from the low price of the country-speci…c factor.
What happens if foreign direct investment is complementary to domestic direct investment, that is, to W B ? Such complementarity may be due to legal restrictions whereby the total amount of FDI cannot be greater than a …xed fraction x of domestic investors' wealth W B , or it may stem from the need for local investors to enforce dividend payments or to help exert control. Appendix A shows that foreign direct investments subject to complementarity requirements of the form F xW B may sometimes de-stabilize an emerging market economy. Indeed, in contrast to the unrestricted FDI case analyzed above, such direct investments ultimately will fall during slumps, that is, when investors' wealth W B t+1 is experiencing a downturn. Downturns will also typically be deeper than in absence of FDI since, by amplifying the increase in p t during booms, FDI increases production costs and thus accentuates the credit-crunch induced on …rms. Thus, whilst unrestricted FDI has a stabilizing e¤ect on an open emerging market economy, opening such an economy to restricted FDI may actually have the opposite e¤ect.

Extensions and Policy Conclusions
The previous sections have analyzed a stylized model that illustrates how the interaction between credit market imperfections and real exchange rate ‡uctuations can cause instability in some open economies. We have purposely abstracted from numerous factors making the analysis more realistic which could further a¤ect the dynamics. In this section we examine several directions in which our simple framework can be extended and discuss policy implications.

Uncertainty and Defaults
The model presented above can easily be extended to incorporate random project returns and defaults. We consider the case of a CES production function. With a risk of default from borrowers, lenders will charge a risk premium on their loans. If we denote the interest rate on a risky loan by R, we have R > r where r is the international interest rate (the interest rate in the absence of default risk); the risk premium is thus R r.
Suppose that the tradeable output technology is random, equal to e f (K; z N ) where the …rm-speci…c productivity shock e is uniformly distributed on the interval [ ; ] and is realized at the end of the period. The same will be true for the equilibrium gross return generated by investors, namely: But now additional uncertainty about the productivity parameter e introduces the possibility of ex post liquidity defaults, namely whenever e < where is de…ned by the zero pro…t-condition: where R is the repayment obligation speci…ed in the loan contracts between lenders and borrowers (borrowers are protected by limited liability, and therefore cannot be asked to repay more than min( (p)(W B + L); RL)): Competition among lenders will set the equilibrium repayment schedule R so as to make any lender indi¤erent between making a (risky) loan on the domestic market and making a safe loan at rate r on the international credit market (R = r in the absence of uncertainty). More formally: rL = Z min(RL; e (p)(W B + L)) d (11) Appendix B shows that the number of defaulting …rms, equal to ( )=( ), can be easily derived from (10) and (11). It is shown that this number is increasing in p (and thus in W B ) when entrepreneurs are credit constrained. Thus, the number of defaults increases during periods of real appreciations, which in turn happen towards the end of booms. This prediction appears to be consistent with available anecdotal evidence on the dynamics of default rates in emerging market economies. 24 Once a …rm defaults, it is often declared bankrupt. If we assume that bankruptcy is declared one period after the default, then our model predicts a counter-cyclical number of bankruptcies in equilibrium, with the highest number of bankrupted …rms being observed in slumps. If we further assume that bankruptcies involve a substantial liquidation or restructuring cost, borne by the entrepreneurial class in the following periods either directly (disruption of supply chains, etc.) or indirectly (because the government needs resources for the clean-up and taxes the entrepreneurs for them), then the slumps may ultimately be signi…cantly deeper and longer-lasting than what our benchmark model predicts. Notice, however, that bankruptcy costs will signi…cantly deepen the slumps only in those economies facing credit constraints.

Amplifying Factors
Additional destabilizing factors of the kinds discussed in the recent literature on …nancial crises, which in economies with highly developed …nancial systems would have little or no impact on the dynamics of real economic activity, are likely to exacerbate output volatility in economies with intermediate levels of …nancial development. In the model, 24 See Mishkin (1996) for the case of Mexico, and World Bank (1997) for capital in ‡ows episodes.
this implies that can be pro-cyclical. The following discussion is largely informal and suggestive, as a more elaborated analysis would certainly require another paper.

Moral hazard on the lenders'side
Suppose that the bulk of lending activities is performed by banks, which in turn are  25 Competition may increase because of an increase in the volume of lending -loan o¢ cers who fail to make lots of loans at time when everybody else is increasing lending, may fear that they will look inept. 26 When is su¢ ciently high the 45 line intersects the wealth schedule W B t+1 (W B t ) on its rightward upward sloping part, so that the dynamics of wealth is actually independent of .

Investors'overreactions to changes in fundamentals
Consider further a straightforward extension of our model with defaults in which foreign investors have imperfect information about the e¢ ciency of creditors'monitoring (and therefore about the actual value of the credit-multiplier ). 27 Then, suppose that the economy experiences a negative but temporary productivity shock (i.e., a negative but temporary shock to ) which will naturally have the e¤ect of increasing the equilibrium amount of defaults in the short-run. Now, given that the lenders are uncertain about ; if they do not observe the shock to ; they will not know whether to ascribe these extra defaults to a change in or to lower value of -in other words, they will be unsure of whether most of these are strategic defaults (suggesting incompetence of the …nancial sector) or rather liquidity defaults (associated with a shock to pro…ts). As a result they will respond in part by adjusting their assessment of downwards. Once again, the model tells us that overreactions by investors, as captured for example in models which stress herd behavior, can only be source of substantial instability in economies at a certain stage of …nancial development.

Some Policy Conclusions
Our model provides a simple and tractable framework for analyzing …nancially-based crises in economies which are at an intermediate level of …nancial development. The story we tell is based on some very basic features of these economies, in contrast with other more institutionally-based theories which invoke moral hazard among lenders, herd behavior among investors, etc. This is not to say that our model is inconsistent with this class of theories-as shown in the previous subsections. However, our model does suggest a somewhat di¤erent policy response: slumps should be seen as part of a normal process in economies like these which are both at an intermediate level of …nancial development and in the process of liberalizing their …nancial sectors. We should therefore not overreact to the occurrence of …nancial crises, especially in the case of emerging market economies. In particular, hasty and radical overhauling of their economic system may do more harm than good. 29 Second, policies allowing …rms to rebuild their credit worthiness quickly will at the same time contribute to a prompt recovery of the overall economy. In this context it is worth considering the role for monetary policy and, more generally, for policies a¤ecting the credit market. Whilst our model in its present form cannot be directly used for this purpose since money is neutral (and in any case the interest rate is …xed by the world interest rate), it can be extended to allow for both monetary non-neutrality and a less in…nitely elastic supply of foreign loans (see Aghion-Bacchetta-Banerjee (2000, 2001a, 2004). Once we take our framework in this direction it quickly becomes clear that a 29 Indeed, if our model is right, the slump sets in motion forces which, even with little interference, should eventually bring growth back to these economies. The risk is that by trying to overhaul the system in a panic, one may actually undermine those forces of recovery instead of stimulating them. This is not to deny that there is a lot that needs changing in these economies, especially on the institutional side with the establishment and enforcement of disciplinary rules in credit and banking activities. For example, in the context of our model, banks may typically engage in preemptive lending to speculators in domestic inputs and/or to producers during booms. This in turn will further increase output volatility whenever inadequate monitoring and expertise acquisition by banks increases aggregate risk and therefore the interest rate imposed upon domestic producers. low interest rate policy is not necessarily the right answer even in a slump induced by a credit crunch. The problem is that while such an interest rate reduction may help restore the …rms'…nancial health (and therefore their investment capacity), the net obligations of those who have borrowed in foreign currency will also rise if it leads to a devaluation of the domestic currency. Therefore, the optimal interest rate policy ex post during a …nancial crisis cannot be determined without knowing more about the details of the currency composition of the existing debt obligations of domestic enterprises.
This emphasis on creditworthiness as the key element in the recovery from a slump, also suggests that a policy of allowing insolvent banks to fail may in fact prolong the slump if it restricts …rms' ability to borrow (because of the comparative advantage of banks in monitoring …rms'activities 30 ). If banks must be shut down, there should be an e¤ort to preserve their monitoring expertise on the relevant industries. Moreover, to the extent that the government has to spend resources on restructuring and cleaning-up after a spate of bankruptcies, it should avoid raising taxes during a slump since doing so would further limit the borrowing capacity of domestic entrepreneurs and therefore delay the subsequent recovery. Third, our model also delivers ex ante policy implications for emerging market economies not currently under a …nancial crisis. In particular: (i) an unrestricted …nancial liberalization may actually destabilize the economy and engender a slump that would otherwise not have happened. If a major slump is likely to be costly even in the long-run (because, for example, it sets in process destabilizing political forces), fully liberalizing foreign capital ‡ows and fully opening the economy to foreign lending may not be a good idea at least until the domestic …nancial sector is su¢ ciently well-developed (that is, until the credit-multiplier becomes su¢ ciently large); (ii) foreign direct investment does not destabilize. Indeed, as we have argued above, FDI is most likely 30 See Diamond (1984).
to come in during slumps when the relative price of the country-speci…c factor is low; furthermore, even if this price ends up ‡uctuating when the economy is open to FDI, these ‡uctuations will only a¤ect the distribution of pro…ts between domestic and foreign investors but not aggregate output. Therefore there is no cost a priori to allowing FDI even at low levels of …nancial development; 31 (iii) what brings about …nancial crises is precisely the rise in the price of country speci…c factors. If one of these factors (say, real estate) is identi…ed to play a key role in sparking a …nancial crisis, it would be sensible to control its price, either directly or though controlling its speculative demand using suitable …scal deterrents. This, and other important aspects in the design of stabilization policies for emerging market economies, await future elaborations of the framework developed in this paper. 31 This strategy of allowing only FDI at early stages of …nancial development is in fact what most developed countries have done, in particular in Europe where restrictions on cross-country capital movements have only been fully removed in the late 1980's whereas FDI to -and between -European countries had been allowed since the late 1950's.
We now show that a closed economy which satis…es assumptions (a), (b), (c), (d), is stable, with constant price p t 0 and constant interest rate r t 1 a , and wealth levels W B t and W L t which both converge monotonically to c W as t ! 1.
First, assumption (c) implies that r 0 = 1 a , and it also implies that I 0 = W L 0 + W B 0 ; assumptions (d)-(iii) and (d)-(iv) then imply that I 0 < aZ , so that p 0 = 0. Next, one can show that at any date s, r s = 1 a and p s = 0. To see this, suppose that for all s t, r s = 1 a and p s = 0, and let us show that r t+1 = 1 a and p t+1 = 0. If r s = 1 a and p s = 0 for all s t, then for all s t the wealth levels W L s+1 and W B s+1 satisfy the equations: It then follows from assumption (d)-(i), i.e., from > 1, and from assuming that r t = 1 a (which implies that W B t > W L t ), that W B t+1 > W L t+1 and therefore r t+1 = 1 a . Furthermore, it follows from assumption (d)-(iii) and equations (1) s and (2) s for s t, that W L s < c W and W B s < c W for all s t + 1; this in turn implies that: so that I t+1 < aZ by assumption (d)-(iv) and therefore p t+1 = 0. We have thus shown that if r s = 1 a and p s = 0 for all s t, then r t+1 = 1 a and p t+1 = 0. Together with the fact that r 0 = 1 a and p 0 = 0, this proves by induction that r s = 1 a and p s = 0 for all s, so for the existence of two-cycles. And one can easily verify that the two sets of conditions are consistent, in the sense that there exists a non-empty set of parameters which satisfy both sets of conditions simultaneously.

B) Restricted FDI
Let F denote the current amount of FDI, and let us impose the constraint: F xW B , with the fraction x being initially small. We assume that foreign investors receive their proportional share of output and that this is always larger than their reservation return r + (given the constraint x, the supply is no longer fully elastic as in the preceding case). The equilibrium price for the country-speci…c factor is now equal to: p t = max(0; (1 + )(W B t + F t ) aZ Z ): Let L t = (W B t + F t ): Then the dynamics of investors' wealth is described by the equations: when W B t is small and therefore p t 0 (part 1 of the W B t+1 (W B t ) curve), and: when there is excess demand for the country-speci…c factor and therefore p t becomes positive (part 2 of the W B t+1 (W B t ) curve).
(In (I) and (II) the variable e r denotes the domestic interest rate, which is equal to if (W B + F ) < W L and to the pro…t rate otherwise.
For x su¢ ciently small, we have F s = xW B s so that the above equation (II) implies a total level of direct investment (domestic and foreign) equal to: which for e small is decreasing in x. In particular, starting from an economy without any FDI, introducing highly constrained FDI may end up deepening the slump which it was meant to eliminate.

Appendix B: Uncertainty and Defaults
Here we derive the number of defaulting …rms when there is …rm-speci…c uncertainty.
Deriving RL from (10) and substituting into (11) gives: The number of defaulting …rms, ( )=( ), can be derived from (12). When …rms are credit constrained, we can use the fact that L=(W B + L) = =r and get: where I is determined by the world interest rate r.