Francisco Vazquez The Lending Channel in a Small Open Economy Under Predetermined Exchange Rates
The lending channel in a small open economy under predetermined exchange rates Francisco Vázquez* University of Maryland, College Park
Preliminary Draft Comments welcome
This paper studies the role of banks in the propagation of nominal shocks in a small open economy. It builds on the framework developed in Edwards and Végh (1997), by relaxing the assumption of perfect asset substitutability between foreign and local bonds. The main results are as follows. Financial liberalization induces a decrease in loan spreads, an expansion in the volume of bank credit, and a decrease in the local bond's risk premium. An increase in foreign interest rates, in required reserves, or in exchange rate depreciation, generate exactly the opposite. JEL No E-44, E-52, G-21
1. Introduction This paper develops a simple optimizing model to illustrate the role of banks in the transmission of nominal shocks in a small open economy. It is aimed at providing some structure to a companion empirical paper. In the lending channel literature,1 it is argued that the banking system may play a non-trivial role in the transmission of monetary policy. In particular, if capital market imperfections prevent banks from completely offsetting a policy-induced contraction in deposits with alternative forms of finance (for example commercial paper), they may cut back the supply of credit, affecting the
* 1
[email protected]
For a review and a discussion on the main issues addressed in this literature see Kashyap and Stein (1994), Bernanke and Gertler (1995).
liquidity position of bank-dependent firms. To date, there is a large amount of literature trying to assess the validity and importance of this mechanism. Paradoxically, almost all this research effort focuses on the US case, ignoring the reliance of the mechanism on capital market imperfections. Almost by definition, capital market failures are expected to be higher in developing countries. Thus, one may conjecture that the mechanism, if it exists, should be stronger in these countries. Moreover, as different countries have different degrees of capital market development, using cross-country data may be useful to provide a source of variation not exploited in previous studies. From the theoretical point of view, studying the lending channel in developing countries has some particularities. For example, under perfect capital mobility, as is arguably the situation in most cases, the monetary authority has low capacity to set local interest rates and shocks to banks deposits may come from international interest rates via the foreign exchange market. Moreover, negative shocks to deposits may arise as a result of currency risk, so they will coincide with a lower capacity of banks to issue their own debt, especially if this debt is denominated in local currency. In other worlds, the restrictions on arm-length finance will tend to be higher exactly precisely when banks are in more need of external financing, and when firms are more dependent on bank credit. This suggests that the lending channel may be stronger in developing countries, and that the models should account for issues related to the foreign exchange market. This paper develops a model to study the functioning of the lending channel in a small open economy. In particular, it shows the effects of financial liberalization, exchange rate depreciation, monetary policy, and exogenous shocks to international interest rates, on the volume of bank credit, the risk premium attached to the local bond, and the lending and deposit spreads. The model described here uses the framework developed in Edwards and Végh (1997). As will become clear below, it adds to the original formulation just in one dimension. It relaxes the assumption of perfect substitutability between foreign and local bonds. In other words, it considers the possibility of imperfections in the local capital market. The contribution is to show explicitly what is the response of the risk premium attached to the local bond to different nominal shocks (like exchange rate depreciation, foreign interest rates, and required reserves), as well as to institutional development (for example, liberalization of the local 2
capital market). In addition, it shows explicitly what is the optimal financing structure of banks balance sheets, and how this structure changes in response to the aforementioned shocks. In Edwards and Végh model, both the size of banks, and their balance sheet structure are undetermined. This indeterminacy comes from the assumption of perfect substitutability between banks' non-insured debt and an international bond. As both instruments have the same return, a bank can grow to infinity by buying the foreign bond with its own debt (so that the bank's net asset holdings do not change). By relaxing this assumption, this paper shows how the model behaves under more general conditions. The structure of this paper is as follows. Section 2 describes the model. Section 3 presents the equilibrium in the benchmark case of perfect capital markets. Section 4 deals with the case of capital markets imperfections, studying the effects of monetary and exchange rate policy on the behavior of banks, and on the credit market. Section 5 concludes with a summary of the main testable implications of the model. 2. The model Consider a small open economy made up of four sectors: households, firms, banks, and the government. Households are the owners of firms and banks, and are endowed with a unit of time to allocate between work and leisure. In addition to their wage income, households receive dividends from firms and banks, and the return on their financial assets. Three assets are available to households: a risk-free foreign bond, a bond issued by local banks, which is viewed by the market as an imperfect substitute of the foreign bond, and deposits in the banking system. In addition to render interests, deposits are required to carry out transactions (more formally, households are subject to a depositin-advance constraint). Production takes place in perfectly competitive firms, which use labor as the only input to production. Firms are bank-dependent, in the sense that they need bank credit to finance their operations. To provide this credit, banks take deposits from the households, and issue bonds. Deposits and bonds share the same characteristics, except by the fact that the former are insured against bank failure by a government agency, while bonds are non-protected.
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The economy is freely integrated with the rest of the world in good and capital markets. Accordingly, the price of the good expressed in local currency, which is used as the numeraire, is given by Pt = Et Pt* , where Et stands for the exchange rate and Pt* is the price of the good in foreign currency. As usual, nominal return on the foreign bond expressed in foreign currency is given by it* = r * − π t* , where it* stands for the nominal interest rate, r* for the (constant) real rate, and πt* for the foreign inflation rate. Under the assumption of imperfect substitutability between the foreign asset and the local bond, the nominal rate of return of the local bond equals it = it* + ε t + at φ , where the term atφ≥0 is a risk-premium to be characterized more precisely in the following section. The role of the government is to set a predetermined rate of devaluation εt, and to exchange local currency for international reserves (or vice versa) at the corresponding exchange rate. In addition, the government performs monetary policy by setting the ratio of required reserves to deposits. Given this brief description, let's now turn to consider each sector in more detail. Banks There are infinitely many price-taker banks located on the interval [0,1]. The components of the banks' balance sheets are the following. On the asset-side, banks hold reserves ht and loans zt. Reserves render no interest and are subject to the requirement ht ≥δ d t , where δ is the proportion of required reserves to deposits, chosen by the Central Bank. Loans are priced at a nominal rate of itl. On the liabilities-side, banks issue demand deposits dt that pay a nominal rate itd, and bonds bt, whose interest is denoted by it. Demand deposits and bonds share the same characteristics, expect by the assumption that deposits are insured against bank failure, while bonds are not protected. In a world of imperfect information, depositors and bondholders are not able to exert perfect monitoring over bank-lending activities, and a risk premium is added to the cost of noninsured debt. Accordingly, the nominal rate on the local bond is equal to the international rate it*, plus the exchange depreciation rate εt, plus a risk premium. The easiest way to
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model this is to assume that banks face an increasing marginal cost of non-insured debt financing. That is, the nominal rate of bonds is given by:
it = i * + ε t + at φ (bt ) ,
with φ ' > 0, φ ' ' ≥ 0, φ (0) = 0
(1)
This assumption is similar to that in Kashyap and Stein (1994) and has been derived from first principles by Stein (1994).2 For analytical convenience, it is also assumed that φ(.) if homogeneous of degree n. The shift parameter at is introduced to study differences in the slope of the marginal cost curve. Although not explicitly modeled here, this parameter may vary from bank to bank. For example, as suggested by Kashyap and Stein (1994), smaller banks may face higher external finance premiums than their larger counterparts. Studies for the United States have found empirical evidence to support this (see for example Ashcraft (2000), Kishan and Opiela (2000), Kashyap and Stein (2000)). Also, and more in line with the objective of this paper, the slope of the marginal cost curve may differ systematically across countries, depending on the degree of capital market development. Almost by definition, capital market imperfections are expected to be higher in countries with less developed capital markets. Therefore, one could hypothesize that the cost of raising external debt will be steeper in those cases. In other words, that banks will tend to be more liquidity constrained in developing countries. Going back to equation (1), the particular case at=0 corresponds to a perfect capital market. This is the case studied in Edwards and Végh (1997), in which the international asset and the bank's bond become perfect substitutes. Lately it will be seen that, as in Romer and Romer (1990), this is sufficient to shut down the credit channel, and the credit market will be completely isolated from shocks to banks reserves. For reasons that will become clear below, it is assumed that in the steady state, capital markets are perfect, that is: lim at = 0 . t→ ∞
2
In the credit channel literature, it has been argued extensively that the external finance premium is an increasing function of the amount of debt. For example, if there is asymmetric information between the bank and investors, moral hazard and adverse selection problems may arise. These sorts of problems will tend to make the risk premium an increasing function of the amount of outstanding debt.
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Given the absence of frictions, banks maximize profits on a period-by-period basis. They take itl and itd as given and choose the optimal mix of liabilities b l d max Ω t = it z t − it d t − it bt ,
(2)
d t ,bt
subject to the marginal cost curve (1), to the balance sheet constraint ht + zt = d t + bt , and to the reserve requirements.3 In equilibrium, the interest rate charged to loans will be higher than the opportunity cost of money. Therefore, excess reserves will be always zero ( ht = δ t d t ). Plugging this into the balance sheet constraint gives: z t = (1 − δ t )d t + bt
(3)
Substituting into the objective function gives the following first-order conditions:
itl − it = at φ ' bt
(4)
itl − itd = δ t itl
(5)
Equation (4) is the credit supply. It states that, in equilibrium, the marginal benefit of financing a loan through debt issuing (i.e. the lending spread) has to be equal to the marginal cost of debt issuing. In the case of perfect capital markets (a=0), equation (4) specializes to the familiar itl = it and the equilibrium loan rate equates the international interest rate expressed in local currency (it*+εt). On the other hand, under capital market imperfections (a>0) the interest on loans will exceed the interest on banks debt and the lending spread will be positive. Equation (5) states that the marginal benefit of loans has to be equal to the marginal cost of deposits (after taking into account the opportunity cost of associated reserves). Combining (4) and (5), the demand of deposits by banks is given by:
3
Banks may be allowed to acquire the foreign bond. Nevertheless, as long as the return of local loans is higher than the risk-free international asset, banks will optimally set their holdings of the foreign asset to zero.
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it − itd = δ t it − (1 − δ t )atφ ' bt
(6)
Equation (6) is the typical equality between the marginal rate of substitution and the isoquant slope that must hold in equilibrium 4. In perfect capital markets, the difference between the bond's rate and the deposit rate (i.e. the deposit spread) will be always positive, the difference being the opportunity cost of required reserves. On the other hand, under imperfect capital market the increasing cost of bond financing will tend to reduce the deposit spread. For a high enough risk premium the market for the local bond will disappear and banks will finance exclusively through deposits. In what follows this paper will restrict the attention to equilibriums where the deposit spread is positive. It can be checked that this implies that the level of bonds will satisfy 5 δ (i * + ε ) t t t bt < φ −1 at [n − δ t (n + 1)]
(6')
Notice that the range of bond financing considered here increases arbitrarily as at goes to zero. Firms There is a continuum of firms in the interval [0,1]. Production uses only labor with constant returns: yt=lt, and it is assumed that firms must use bank credit to pay salaries. In particular, credit demand is given by the credit-in-advance constraint: z t = γwt lt
(7)
Equation (7) can be viewed as a shortcut to a well-known condition for the existence of the lending channel. (At least some) firms must be bank-dependent in the sense that they must not be able to freely substitute bank credit for direct financing. In other words, there has to be some sort of capital market imperfection that prevents firms to issue their
The "production function" of loans is given by the balance sheet constraint z t = (1 − δ )d t + bt . Rearranging (6) to get it + atφ ' bt = 1 , the left-hand side is the marginal rate of substitution between deposits 1−δ itd and bond, while the right-hand side gives the slope of the isoquant. 4
5
Given the assumption of homogeneity of φ(.), Euler's theorem implies bφ'=nφ.
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own debt at the risk-free international interest rate. One way to integrate this into the analysis would be to assume that firms are able to issue their own debt only at an increasing marginal cost, as in the case of banks. Again, this result will naturally arise from an asymmetric information problem between firms and their bondholders. This paper pursues a different strategy. In order to focus on the bank lending channel mechanism, it makes the extreme assumption that firms are not able to issue their own debt. Shutting down this channel keeps the model simpler without affecting the qualitative results. Under this assumption, firms' financial assets vtf are given by international bonds bt* plus local bonds bt, minus credit from banks zt. Let's now consider the opportunity costs. The real return of the local bond is given by rt ≡r*+atφ(bt); therefore, the opportunity cost of holding the risk-free international bond can be expressed as r*≡rt-atφ(bt). Similarly, the real cost of bank loans can be written as itl-π*-ε ≡(it- itl)-aφ(bt). Using these, the evolution equation of firms' assets is given by:
v&tf = rt vtf − atφ (bt )bt* f + yt − wt lt − (itl − it ) z t − Ωtf
(8)
Integrating forward and imposing the no-Ponzi game condition, the present discounted value of dividends can be written as: ∞
∫
f Ωt Rt dt
0
∞
=∫
{lt − wt lt [1 + γ (itl
0
− it )]Rt }dt ,
t with Rt ≡exp− ∫rs ds 0
(9)
Where the discount factor is the real rate of the local bond rs= r*+asφ(bs). Product and labor markets are perfectly competitive. Firms take the path of the real wage wt, and interest rates as given and maximize the left-hand side of (9) by choosing labor. The first-order condition implies that the marginal cost of labor (real wage plus the financial costs of salaries has to be equal to the marginal productivity of labor (=1):
wt [1 + γ (itl − it )] = 1
(10)
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Households There is a representative agent who chooses consumption, ct, and leisure, xt, to maximize lifetime utility. ∞
∫[log(ct ) + log( xt )] exp( βt )dt
(11)
0
where β is the subjective discount factor equal to the risk-free international interest rate (β=r*).6 The assumption of logarithmic utility is not necessary for what follows, but convenient in terms of the functional forms of the solution.7 Households are endowed with 1 unit of time to allocate between labor and leisure. They cannot lend money directly to firms (as discussed in the previous section) their financial assets are given by the international bond bt*h, the domestic bond bth, and bank deposits dth. Accordingly, households' financial wealth vh is given by:
vth = bt*h + bth + d t
(12)
The real return on the consumers' portfolio is as follows. The foreign bond pays a real return of r* (≡rt-atφ(bt)), the real return on banks' debt is rt, and the return on deposits is given by itl-π*-ε (≡ rt+(itd-it)). Using these, households' financial assets evolve according to:
v&th = rt vt + wt (1 − xt ) + τ t + Ωbt + Ωtf − atφ (bt )bt*h − (it − itd )d t − ct
(13)
Where τt represent government lump sum transfers from the government, Ωf and Ωb dividends received from firms and banks, respectively. Again, following Edwards and Végh, it is assumed that households must hold demand deposits to carry out transactions. That is, they are subject to a deposit-in-advance constraint: d t = αct
6
(14)
As usual, this assumption is made to rule-out unimportant dynamics.
7
Following Edwards and Végh, it is also assumed that the utility function is separable. Non-separable preferences will introduce effects that are non-interesting to the issues at hand.
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Plugging (14) into (13), integrating forward, and imposing the no-Ponzi game condition, gives the household's lifetime budget constraint: v0h
∞
+ ∫{wt (1 − xt ) − [1 + α (it − itd )]ct + Ωt + Ωbt + τ t − atφ (bt )bt*h }Rt dt = 0 f
(15)
0
Households choose consumption and leisure to maximize (11), subject to (15) taking wages and interest as given. The optimality conditions of this problem are: 1 λ[1 + α (it − itd )] = ~ ct Rt
t
~ Where Rt = exp( ∫(rs − β )ds )
(16)
0
1 λwt = ~ xt Rt
(17)
Where λ is the time-invariant Lagrange multiplier associated with the lifetime budget constraint (15). Equation (19) indicates that, at the optimum, the discounted marginal utility of consumption has to be equal to the marginal utility of wealth times the present value of the price of the consumption good (which includes the opportunity costs of holding deposits to carry out the transactions). Notice that, under perfect capital markets, the real discount rate is constant and equal to the international risk-free interest rate. In ~ this case Rt collapses to unity, and consumption depends only on the deposit spread, which, in turn, depends only on required reserves. By increasing required reserves, the policymaker is able to increase the deposit spread and induce a reduction in consumption. On the other hand, under imperfect capital markets, the real rate of return on banks' bonds is higher than the international rate (rs>β). In this case the path of consumption is affected not only by required reserves, but also by the risk premium (and therefore by the time path of the banks' debt). Thus, the decision of individual banks regarding the level of debt financing produces an externality that distorts households' decisions. Plugging (6) into (16) and taking the partial derivative with respect to δ it is easy to see that the effect of a contractionary monetary policy on consumption will still be negative but larger than the perfect capital markets case. The reason is that, under imperfect capital markets, the deposit spread is more sensitive to fluctuations in required reserves. 10
Equation (17) states that the marginal utility of leisure (left-hand side) has to be equal to the marginal utility of wealth, times the present value of the real wage. As before, under imperfect capital markets, the time path of bonds influences the time path of leisure. Higher risk premiums will induce a higher level of leisure. Given this brief discussion, it is apparent that the first best equilibrium under imperfect capital markets is to have a zero level of debt. This completely isolates consumption and leisure from the various shocks that may hit the economy. Nevertheless, the decentralized economy is unable to attain a zero-debt equilibrium level, as banks fail to internalize the effects of higher indebtedness on the time paths of consumption and leisure. On the other hand, if capital markets are perfect, the level of debt is irrelevant and the decentralized economy attains the first-best equilibrium. Government The government's monetary authority sets the devaluation of the exchange rate, εt, and the reserve requirement ratio, δt. The government cannot lend to the domestic banking system. It receives income from its net holdings of foreign assets, collects revenues from money creation, and gives lump-sum transfers to households. Accordingly, the government's flow constraint is given by:
v&tg = r *bt*g + h&t + (ε t + π t* )ht − τ t
(18)
Let's now turn to the equilibrium in this economy. General equilibrium Imperfect asset substitution between the risk-free foreign bond and the domestic bond implies that equation (1) holds. In turn, equilibrium in the labor market requires: lt=1-xt
(19)
The aggregate flow constraint for the economy comes from adding (8), (13), and (18), after taking into account the balance sheet constraint (3). Noticing that both national and foreign households can hold bank's bonds, the economy's net financial assets kt, are given by:
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kt ≡bt*h + bt*g + bt* f − (bt − bth ) Using this, the economy's aggregate flow constrain (the current account) is given by:
k&t ≡rt*kt − (bt − bth )atφ (bt ) + (1 − xt − ct )
(20)
This is the usual flow constraint augmented by the excess real return paid to foreign holders of the local bond. The following section studies the equilibrium in the perfect capital markets' case. 3. Benchmark case: equilibrium under perfect capital markets Plugging (16) into (14) gives the deposit supply, a decreasing function of the deposit spread. Under perfect capital markets (at=0), it collapses to: dt =
α λ[1 + α (it − itd )]
(21)
This, together with equation (6) gives the equilibrium in the deposit market. Given the simple functional form, it is easy to see that the equilibrium level of deposits is a decreasing function of the international risk-free interest rate, and the required reserves. Accordingly, the monetary authority can control directly the level of banks' deposit financing by changing the reserve requirements. Using the equilibrium in the labor market (19) after plugging (10) into (7) gives the demand for credit: zt =
γ 1 + γ (itl
− it )
−
γ λ
(22)
In the case of perfect capital markets, the credit supply (4) collapses to itl-it=0. Plugging this into (22) gives a constant equilibrium level of loans z=γ(λ-1)/λ. By (7), this implies that the wage bill is constant, and by (10) that the output level is also constant. Therefore, even if the monetary authority is able to control the amount of deposits in the banking sector, monetary policy does not have any effect on the level of output. This result is identical to the costless-banking case in Edwards and Végh (1997) and illustrates a point made in Romer and Romer (1990). That is, if banks are able to freely substitute 12
deposits for other forms of debt (say large denomination CD's) without facing an upwardsloping cost of raising external finance, then the loan supply will be completely isolated from shocks to deposits. Therefore, by setting higher reserve requirements, the monetary authority is able to raise the deposit spread and reduce the level of deposits, but banks simply resort to debt finance and the equilibrium in the loan market is not affected. Other nominal shocks like an increase in the risk-free international interest rate, or an increase in the rate of depreciation will have the same outcome. In other words, nominal shocks will have no effects on the level of real activity. Consumption, on the other hand, will be affected by unexpected changes in the riskfree international interests or in the rate of depreciation of the exchange rate. An unexpected increase in either will cause a drop in consumption. However, by using monetary policy, the government can attain a welfare-improving outcome. Setting δt to offset unexpected variations on the risk-free international interest rate or on the depreciation rate, (such that δ tit remains unchanged), the government can completely isolate the economy from external shocks. Trivially, this is a welfare improving situation since it smoothes consumption. Let's now study the effects of an unexpected increase in the rate of devaluation on the liability structure of banks' balance sheet. From equations (21) and (22), it is immediate that, all else equal, an increase in ε will cause an increase in the proportion of debt to deposits, a decrease in deposit to loans, and an increase in debt to loans. 4. Equilibrium under capital market imperfections By doing the same substitutions as in the previous section, equations (21) and (22) counterparts are now given by:
dt =
~ αRt λ[1 + α (it − itd )]
~ γRt zt = − 1 + γ (itl − it ) λ γ
(21')
(22')
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Equation (21) states that, for a given level of debt, deposit supply is a decreasing function of the deposit spread. This simply relates with the opportunity cost of holding deposits instead of bonds. More interesting, under capital market imperfections the deposit supply is also a function of the risk premium. In particular, an increase in the volume of bond financing increases the risk of non-insured bank liabilities, and households decide to shift to insured forms of bank financing (i.e. deposits). Let's now turn to equation (22). According to it, the demand for loans now also depends on the risk premium. For a given loan spread, higher level of bond financing by banks increases the risk premium, inducing a fall in loan demand. But this is not the complete story. Higher level of bond financing also decreases the loan supply (equation (4)), so the equilibrium level of loans goes down due to a contraction in both the demand and the supply of loans. This illustrates the difficulties involved in trying to isolate supply and demand side effects in the credit market. Interestingly, as argued by Kashyap (1994), the fact that the loan spread increases at the same time as the total volume of credit goes down indicates a contraction in the loan supply. Nevertheless, demand-side effects may also be at work.8 Also, notice that from equation (4), countries with less developed capital markets (higher a) have larger lending spreads and experience larger contractions in the credit market in response to a substitution of deposit by bond financing. From the previous discussion, the equilibrium levels of credit and deposits depend on the risk premium, which itself depends on the amount of bond financing. Given the absence of frictions, the equilibrium at a given point in time involves solving a system of seven equations. The deposit market is given by equations (6) and (21'); the credit market is given by equations (4) and (22'); the bond market is given by equation (1) and the balance sheet constraint (3). The seventh equation is given by the definition of the ~ discount factor Rt (in equation (19)). The solution gives the time paths of banks' bonds, deposits, loans, consumption, real wages, hours, and the real rate of the local bond. As stated before, this paper restricts the attention to parameter configurations that generate a positive deposit spread in equilibrium. The following result can be stated.
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Proposition 1: Consider an economy described by equations (6), (21'), (4), (22'), (1), (3), (19) and the evolution equation (20). There exist a unique equilibrium satisfying (ititd)>0. At that equilibrium, the level of bank bonds is strictly positive as long as the loan demand in equation (22') evaluated at (it-itl)=0 exceeds
α (1 − δ ) 1 + αδ (it* + ε t )
.
Proof. See Appendix. The first part of this result states that this economy exhibits a locally unique equilibrium with a positive deposit spread. It can be checked that, for a low enough at, the economy will attain an equilibrium involving a positive deposit spread. Intuitively, if the risk premium is positive but low, banks will find optimal to finance the portion of credit demand not covered by deposit finance though bond issuing. The second part simply states that the demand for bank credit will be partly financed by bonds only if deposits are not large enough. In other words, if deposits exceed the demand for bank credit, banks will optimally finance credit exclusively with deposits, using any remaining difference to buy foreign bonds. In this case the loan spread will be zero. On the other hand, if deposits are insufficient to cover the demand for bank credit (at a zero loan spread), then banks will optimally liquidate their holdings of foreign bonds and issue their own bonds to finance the residual demand for credit. In this case, the loan spread will be positive. Clearly, the first case is uninteresting to the purposes of this study. In what follows, all the results refer to the second case (i.e. an equilibrium with positive levels of bank's bonds). Let's now turn to some comparative static exercises. The following summarizes the effects of exchange rate depreciation (which by construction is analogous to a shock to the international risk-free interest rate). Proposition 2. Consider a perfect-foresight equilibrium path along which δt=δ, and at =a for all t∈ [0,∞). Suppose that there is a t=T such that εt increases (falls). Then, ~ it, Rt , (it-itd), and bt will also increase (fall).
8
Trying to assess the relative importance of supply- versus demand-driven effects has been subject of
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Proof. See Appendix. This result states that an increase in the rate of devaluation increases the interest rate of local bonds for two reasons. First, the interest rate of local bonds increases through the nominal effect implied by the interest parity condition (this is also present in the case of perfect capital markets (i.e. it=it*+εt)). Second, the interest rate of local bonds also increases due to an increase in the risk premium via an increase in bond financing. With this result in mind, it is possible to keep track of the effects of devaluation on the rest of the variables. Consider first the lending spread. By equation (4) it increases due to the increase in bond financing. Using this in equation (10) it is apparent that the real wage goes down. This, combined with the increase in the discount factor, implies that leisure goes up (see equation (20)). Accordingly, the wage bill goes down unambiguously, as both hours and the real wage decrease. As a result, the credit market collapses. This conclusion can also be readily obtained by looking at equation 21'. The increase in the lending spread is a contraction in credit supply (again the bank lending channel in action), which arises from the upward-sloping marginal curve of bond financing. In addition, credit demand itself also contracts due to the increase in the risk premium. The model then predicts contractionary devaluations for economies with less developed capital markets (the contraction in output is higher for higher values of the parameter a). To complete the picture, the proposition also states that the deposit spread also goes up following an increase in the depreciation rate. In the new equilibrium, total credit goes down, bonds increase and therefore, deposit finance decrease. By equation (21') this implies that the deposit spread must be going up. The intuition is as follows. Holding constant the stock of local bonds, an increase in the rate of depreciation increases the deposit spread (equation (6)). This, in turn, implies that deposits go down (equation (16)), so banks have to resort to bond financing which tends to increase in the risk premium and decrease the deposit spread. These two effects tend to increase deposits, counteracting the initial effect. Accordingly, the substitution of deposit financing by bond financing is lower for less developed capital markets.
extensive research using US data (for two recent studies see Kashyap and Stein (2000), Ashcraft (2000)).
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In summary, following an increase in the rate of devaluation, the model predicts: (i) a contraction in loans, which is higher for economies with less developed capital markets; (ii) an increase in bond to assets ratios higher for economies with more developed capital markets; (iii) an increase in bond to deposit ratios, which is higher for more developed capital markets; (iv) increases in the lending spread, which are higher for less developed capital markets; (v) increases in the deposit spread, which are higher in countries with more developed capital markets. The implications of monetary policy for the equilibrium of the economy are summarized in the following result. Proposition 3. Consider a perfect-foresight equilibrium path along which at=a, and εt =ε for all t∈ [0,∞). Suppose that there is a t=T such that δt increases (falls). Then, it, ~ Rt , (it-itd), and bt will also increase (fall). Proof. See Appendix. This result states that a contractionary monetary policy induces an increase in bond financing, which under imperfect capital markets increases the interest rate of bonds via an increase in the risk premium. By inspection, it is possible to track the effect of the policy on the rest of the variables. From equation (4), the lending spread increases. This is the bank "lending channel" in action. In this simple model, the increase in the lending spread is a contraction in the credit supply by banks. Notice that this channel only exists in the case of imperfect capital markets, and is more powerful the less developed the capital markets are (because the lending spread is an increasing function of the parameter at). Going back to the results, equation (10) implies that the increase in the lending spread reduces the real wage. In addition, by equation (20), the increase in the real discount factor together with the decrease in the real wage implies that leisure goes up, so the wage bill decreases both by the reduction in hours and in the real wage. By equation (7), total credit goes down. The same conclusion can be readily obtained by inspecting equation (22'). With a higher lending spread, the equilibrium credit goes down. This is reinforced by the increase in the real discount rate, which induces a fall in credit demand. Finally, with
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credit going down and bonds going up, equilibrium deposits must be falling, so the increase in the deposit spread stated in the proposition must be higher than the increase in the discount factor. The intuition behind this result is the following. Higher required reserves increase the price of deposits from the bank's perspective. Banks then substitute deposit by bond financing, which increases both the lending spread and the risk premium, and induce a collapse in the credit markets. Notice that this collapse is higher for less developed capital markets, as the effect of risk premium on credit demand increases on the parameter a. Therefore, the model suggest that, in response to a contractionary monetary policy, (i) a contraction in loans, which is larger for less developed capital markets; (ii) an increase in bond to asset ratios, which is higher for economies with more developed capital markets; (iii) an increase in bond to deposit ratios, which is larger in economies with more developed capital markets; (iv) increases in the lending spread, larger for less developed capital markets; (v) increases in the deposit spread, larger in economies with more developed capital markets. Let's now turn to the final analysis, an improvement in conditions in the capital market. The following states the main result. Proposition 4. Consider a perfect-foresight equilibrium path along which δt=δ, and εt =ε for all t∈ [0,∞). Suppose that there is a t=T such that at falls (increases). Then, it ~ and Rt will also fall (increase), and bt and (it-itd) will increase. Proof. See Appendix. This exercise can be interpreted as the effect of capital account liberalization or any other institutional policy that improves the functioning of the local capital markets. For a given level of bond finance, the reduction in at leads to a decrease in the interest rate on bank bonds. Thus, banks increase the amount of bond finance. Interestingly, the risk premium (given by atφ(bt)) falls in the new equilibrium despite the increase in the volume of bond financing. Using this, it is possible to characterize the response of other variables. From equation (4) it follows that the loan spread falls, which in turn increases the equilibrium level of loans. Notice that this effect is reinforced by the response of the
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loan demand, which expands as the risk premium goes down. From equation (10), the real wage goes up which in turn implies, by equation (20) that total hours also increase. Keeping track of the effects on the deposit spread is less direct. Nevertheless, it can be shown that under reasonable reserve requirements (i.e. δt
