## Abstract

This paper interprets contagion effects as an increase in the volatility of shocks impinging on the economy. The implications of this approach are analyzed in a model in which domestic banks borrow at a premium on world capital markets, and domestic producers borrow at a premium from domestic banks. Financial spreads depend on a markup that compensates lenders, in particular for the expected cost of contract enforcement. Higher volatility increases financial spreads and the producers’ cost of capital, resulting in lower employment and higher incidence of default. Welfare effects are nonlinearly related to the degree of international financial integration.

THE MEXICAN peso crisis of December 1994 brought turmoil to financial and foreign exchange markets worldwide, but nowhere more dramatically than in Argentina. Between December 1994 and March 1995, prices of Argentine bonds and stocks traded on domestic and international markets fell abruptly. The central bank lost about one-third of its liquid international reserves, and the interest rate spread between U.S. dollar-denominated bonds issued by Argentina and U.S. treasury bills increased sharply. to more than 700 basis points during 1995 (Figure 1), whereas the spread between domestic and U.S. interest rates widened to about 900 basis points during the same period. Turbulences in financial markets escalated very quickly into a full-blown economic crisis: bank deposits and bank credit dropped dramatically, and domestic interest rates (on both peso- and dollar-denominated loans) increased sharply—from about 10 percent to more than 40 percent and 30 percent per annum, respectively, between December 1994 and March 1995. Real GDP fell by almost 5 percent for 1995 as a whole (Figure 2), and unemployment increased sharply. Bank closures and restructuring operations led to a consolidation of the banking system.

Several observers have argued that the collapse of the Mexican peso in December 1994 and the ensuing sharp swing in investors’ sentiment toward emerging markets (the so-called Tequila effect) triggered Argentina’s economic crisis.^{1}

**Argentina and Mexico; Industrial Output**

(December 1994= 100)

Citation: IMF Staff Papers 1998, 003; 10.5089/9781451974164.024.A001

**Argentina and Mexico; Industrial Output**

(December 1994= 100)

Citation: IMF Staff Papers 1998, 003; 10.5089/9781451974164.024.A001

**Argentina and Mexico; Industrial Output**

(December 1994= 100)

Citation: IMF Staff Papers 1998, 003; 10.5089/9781451974164.024.A001

Various papers have recently attempted to model contagious shocks of this type. Uribe (1996), for instance, formalizes the Tequila effect as a situation in which domestic agents learn at a given moment in time that, at some point in the future, foreign investors will liquidate their holdings of domestic assets—in effect imposing a binding constraint on domestic borrowing. Goldfajn and Valdes (1997) highlight the role of liquidity factors in the spread of exchange market pressures across countries, and show how currency crises can have contagious effects of the type observed in the aftermath of the Mexican peso crisis. Agenor (1997) formalizes a contagious shock as a temporary increase in the autonomous component of the risk premium (reflecting “country risk” factors or exogenous elements in market perceptions) that domestic borrowers face on world capital markets. The real effects of such a shock in Agenor’s model are captured by linking the financial sector and the supply side via firms’ working capital needs, namely, the need to finance labor costs prior to the sale of output. The model’s predictions, under the assumption that the shock was perceived to be of a sufficiently long duration, replicate some of the main features of Argentina’s economic downturn.^{2}

The analysis.presented in the present paper departs from existing studies in two important ways. First, we model not only distortions on world capital markets but also *domestic* credit market imperfections. We do so by considering a two-level financial intermediation process: domestic banks borrow at a premium on world capital markets, and domestic agents (which consist only of producers) borrow at a premium from domestic banks. The reason why modeling domestic credit market imperfections is important is well illustrated by Figure 3: not only did the “foreign” financial intermediation spread increase sharply in the immediate aftermath of the peso crisis in Argentina (as well as Mexico), but so did the spread between domestic bank lending and deposit rates. As it turns out, the model is capable of accounting for this fact by showing how financial intermediation spreads are related to default probabilities and underlying shocks. Second, and in contrast with the existing literature, contagion is assumed to take the form of an increase in the volatility of aggregate shocks impinging on the domestic economy—or, more precisely, a mean-preserving increase in the range of values that such shocks may take. To the extent that such increases translate into a rise in the probability of default of domestic producers on their loan commitments, domestic and foreign interest rate spreads will tend to rise, leading to a drop in expected output. Our analysis therefore helps to identify factors that may propagate and magnify an initial exogenous shock. It also helps to clarify the effects of changes in the expected cost of enforcement of loan contracts, both at the domestic and international levels.^{3}

**Argentina and Mexico: Domestic Interest Rate Spread**

Citation: IMF Staff Papers 1998, 003; 10.5089/9781451974164.024.A001

Sources: IMF, International Financial Statistics.^{1}Lending rate minus deposit rate.

^{2}Average cost of funds minus the deposit rate.

**Argentina and Mexico: Domestic Interest Rate Spread**

Citation: IMF Staff Papers 1998, 003; 10.5089/9781451974164.024.A001

Sources: IMF, International Financial Statistics.^{1}Lending rate minus deposit rate.

^{2}Average cost of funds minus the deposit rate.

**Argentina and Mexico: Domestic Interest Rate Spread**

Citation: IMF Staff Papers 1998, 003; 10.5089/9781451974164.024.A001

Sources: IMF, International Financial Statistics.^{1}Lending rate minus deposit rate.

^{2}Average cost of funds minus the deposit rate.

The predictions of our framework are consistent not only with the observed increase in financial intermediation spreads and a contraction in activity in Argentina and Mexico (as discussed earlier) but also with higher volatility of output. Our calculations, as discussed below, support this prediction. Our framework is also useful in understanding some of the real and financial aspects of the crisis that developed in Asia following the collapse of the pegged exchange rate regime in Thatland on July 2, 1997—and the role played by banking sector inefficiencies in compounding spillover effects, particularly in those cases where economic fundamentals (as was the case in Malaysia, Korea, and the Philippines) appeared stronger than in Thatland.

### I. Output and the Credit Market

We consider an economy in which two categories of domestic agents operate: producers and commercial banks. Both categories of agents are risk neutral—an assumption that allows us to use expected income as a measure of welfare—and behave identically. The representative bank borrows on world capital markets, facing a gross expected cost of funds equal to 1 +ř^{f}_{b} and lends to domestic agents at the contractual gross interest rate 1 + r_{r} Domestic banks have comparative advantage in enforcing repayment of their loans to domestic producers and are therefore not subject to direct competition from foreign lenders. Thus, producers borrow only from domestic banks, and not directly from foreign lenders. To simplify exposition, we do not model domestic saving. Specifically, we assume that domestic saving is zero at the international interest rate that the country faces.^{4}

Output of producer *h* is a function of labor employed and a composite productivity shock:

In the above equation,*n _{h}* is employment, and δ is an aggregate shock with zero mean and a density function g(δ) defined over the interval (-δ

_{m}, δ

_{m}), with δ

_{m}> 0

^{5}. ε

_{h}is a producer-specific, idiosyncratic shock with zero mean and a density function f(ε

_{h}) defined over the interval (-ε

_{m}ε

_{m}), where ε

_{m}> 0. Because δ and ε

_{h}have zero mean, expected productivity is 1 + ε

_{0}). The aggregate shock will be viewed as capturing random shifts in external factors.

The process of domestic financial intermediation can be characterized as follows. Producers must finance their entire working capital needs (which are assumed to consist only of labor costs, for simplicity) prior to the sale of output. They cannot issue claims on their capital stock to finance those needs, and therefore borrow from domestic banks. Total production costs faced by producer *h* are thus equal to the wage bill plus interest payments made on bank loans needed to pay labor in advance, (1 + r_{L})*Wn* _{h} where *W* is the going wage (assumed constant). If producer *h* chooses to default on part or all of his repayment obligations (after ail shocks are realized), domestic banks have the capacity to force him (through appropriate legal actions) to pay a fraction 0 ≤ K ≤ 1 of his realized output. Enforcing repayment involves a cost C (measured in units of output) to the bank.^{6}

In line with the willingness-to-pay approach to debt contracts, producer *h* will choose to default if the following constraint is satisfied:^{7}

If the probability of default is zero, the contractual lending rate is equal to the bank’s expected cost of borrowing on world capital markets r_{L} = ř^{f}_{b} and producer *h’s* expected profits are given by

From the first-order condition for profit maximization, optimal employment n_{a} is thus given by

Given that employment is set optimally, equation (2) implies that for the probability of default to be zero over the whole range of realizations of є_{h} and δ requires that, setting є_{h}= є_{m} and δ=-δ_{m}:

or equivaiently, using the first-order condition given above:

which can be rearranged to give

To make the problem nontrivial, we assume that δ_{m} + ε_{m} is sufficiently large to ensure that inequality (4) is reversed.^{8} Thus, ex ante, some producers are always expected to default on their loan obligations. At the same time, we assume for expositional simplicity that no producer will default if the economy is in the “best” (aggregate) state of nature (that is, if δ = δ_{m} all producers would opt to repay fully their loan obligations).

The contractual interest rate charged by the representative bank to any given domestic producer r_{L} is determined by the condition that expected gross repayment from borrower *h* (evaluated over the whole range of variation of ε_{h} and δ, and thus taking into account partial repayment and enforcement costs in adverse states of nature) be equal to the gross expected value of the loan contracted on world capital markets by the bank. In turn, this value equals the size of the loan to producer *h* times the expected cost of funds faced by domestic banks abroad, 1 +ř^{f}_{b}

where ^{9}

and δ^{*} defined as

and ε^{*} defined as

In the above expressions, δ^{*} is the threshold value of the aggregate productivity shock below which realizations of δ (satisfying therefore the condition δ ≤ δ may induce some producers to default. ε_{*} is the threshold value of the idiosyncratic shock to productivity associated with partial default, for a given realization of δ. The term Φ(δ) measures the expected repayment per producer, conditional on a given realization of the aggregate shock δ it can be verified that ∂Φ(δ)/∂ > 0. The second term of equation (5) captures the fact that, even for realized values of δ satisfying the necessary condition δ ≤ δ^{*}, values of ε_{h} that are greater than ε^{*} ensure that the cost of default exceeds contractual repayment obligations.

We assume in what follows that each bank deals with a large number of small independent producers, and as a result the law of large numbers applies.^{10}

Equation (5) can be rearranged to give^{11}

where

Equation (8) shows that the contractual lending rate charged by the representative bank on loans to domestic producers exceeds the bank’s expected borrowing cost by a margin that compensates for the expected loss in revenue incurred in states of nature in which partial default occurs, as given by the expression

adjusted for the expected enforcement cost

Figure 4 defines the region in which default will occur. The figure is cast in terms of ε_{h} and 1 + δ_{0} + δ for convenience. Although 1 + δ_{0}+ δ can take realized values over the range given by the segment *AC* (with mean value of 1 + δ_{0}), default can occur only for values on the segment *BC*—with point *B* corresponding to the lowest possible realization of ε_{h} -ε_{m} For any realized value of 1 + δ_{0}+ δ in that range, the threshold value of the idiosyncratic shock (as defined by equation (7)) is given by the negatively sloped segment *BD*. The dotted triangle *V*, defined by *BCD*, defines the set of realizations of 1 +δ_{0}+δ and ε_{h} for which producers will choose to default on their repayment obligations.

**Determination of the Default Region**

Citation: IMF Staff Papers 1998, 003; 10.5089/9781451974164.024.A001

**Determination of the Default Region**

Citation: IMF Staff Papers 1998, 003; 10.5089/9781451974164.024.A001

**Determination of the Default Region**

Citation: IMF Staff Papers 1998, 003; 10.5089/9781451974164.024.A001

Equation (8) can be rewritten as

Let 1 + ř_{P} denote the expected gross cost of funds for producer *h*. This cost is determined from the condition that

which differs from the right-hand side expression in equation (5) essentially because producers, in forming their expectations, do not internalize the enforcement cost incurred by lenders in case of default. Using equations (5) and (8), it follows that

where

is the probability that any given producer will default. Thus

Equation (12) shows that, in the absence of enforcement costs (C = 0), or with a zero probability of default *(Pr(d/p) -* 0), the producers’ expected cost of borrowing is simply equal to the representative bank’s expected cost of funds.

Producer *h*’s decision problem is to choose employment n_{h} that maximizes expected profits, which are given by an expression similar to equation (3) with the contractual lending rate—which can be shown from equation (9) to be equal to the bank’s expected cost of funds, ř_{p} in the absence of default risk—replaced by the expected cost of borrowing from domestic bank ř_{p}:

Substituting equation (10) in the above expression implies that expected profits can be written as

or more compactly, using equation (11):

Deriving the above expression with respect to n_{h} and setting the result to zero gives

which determines the optimal demand for labor.^{12}

We will assume that the shocks ε_{h} and δ follow a uniform distribution, so that.(ε_{h}) = l/2ε_{m}, g(ε) = l/2ε_{m}, and Pr(z > x) = (z_{m} - x)/2z_{m} with z = ε_{h}, δ From equations (8) and (13). we can thus establish the following proposition:^{13}

**Proposition 1**.*Higher volatility and lower expected productivity reduce employment and increase the bank’s contractual lending rate*:.

Figure 5 illustrates these results graphically. The downward-sloping curve *NN* represents the combinations of employment and the contractual lending rate implied by the first-order condition (13). whereas the convex curve *BB* represents the combinations of n_{h} and r_{L} associated with zero expected profits by the representative bank, as implied by equation (5). The intersection of these two curves gives the pair (r_{L}, n_{h}) consistent with (expected) profit maximization by producer *h* and zero expected profits by the representative bank on its loan to producer *h*. Simulation I is the benchmark case. Simulation 2 (respectively, 3) corresponds to an increase in the standard deviation of the idiosyncratic (respectively, aggregate) shock by 50 percent relative to the benchmark case. Simulation 4 corresponds to a drop in expected productivity by 10 percent relative to the benchmark case. Note that a similar adjustment occurs in all these cases—a significant increase in the financial intermediation spread (an increase in r_{L} relative to ř^{f}_{p}) drop in employment. Simulation 5 traces the adjustment to a combination of the above three shocks, showing a profound drop in employment and a sharp increase in the financial intermediation spread. Finally, Simulation 6 shows the adjustment to a rise in the bank’s expected real cost of funds, from 0 to 10 percent. Again, the results are an increase in r_{L} and a fall in employment.

**Optimal Employment and Domestic Borrowers’ Interest Rate**

(Simulated for C = 0.15, γ = 0.5, Ŗfl= 0, K = 0.6)

Citation: IMF Staff Papers 1998, 003; 10.5089/9781451974164.024.A001

**Optimal Employment and Domestic Borrowers’ Interest Rate**

(Simulated for C = 0.15, γ = 0.5, Ŗfl= 0, K = 0.6)

Citation: IMF Staff Papers 1998, 003; 10.5089/9781451974164.024.A001

**Optimal Employment and Domestic Borrowers’ Interest Rate**

(Simulated for C = 0.15, γ = 0.5, Ŗfl= 0, K = 0.6)

Citation: IMF Staff Papers 1998, 003; 10.5089/9781451974164.024.A001

### II. The World Capital Market

Domestic banks have access to world capital markets and borrow, at the contractual interest rate r*_{b}, wn_{h} per domestic producer. If domestic banks default partially, repaying less than wn_{h}(1+r*_{b}), foreign lenders have the ability to force domestic banks to pay a fraction K_{b} of realized revenue, Φ(δ). Enforcing that repayment involves real costs C_{h} to the foreign lender.

In this setting, a domestic hank tending to producer *h* will default if and only if

where Φ(δ) is as given in equation (5).

Let δ denote the threshold value of the aggregate shock below which domestic banks will choose to default. It is defined implicitly by the condition K_{b}Φ (δ) = *wn _{h}(1 + r*_{h})*..

Let r_{0}^{f}.be the foreign lender’s cost of funds, which is equal to the risk-free interest rate in the absence of transactions costs. Under risk neutrality, the interest rate r*_{h} charged by foreign lenders to domestic banks is again determined by the condition that expected gross repayment be equal to the gross value of the loan, measured at the risk-free rate. Expected repayment accounts for the possibility that, in adverse states of nature, the lender may be able to appropriate only a fraction of realized output, subject to enforcement costs:

where

From the point of view of the domestic bank, the expected cost of funds rfis determined by the condition

which shows that the domestic bank’s expected cost of funds is the sum of the expected interest repayment in relatively good states of nature (the first term on the right-hand side of the equation) plus the expected repayment in adverse states of nature, when partial default occurs (the second term on the right-hand side). Again, the expression on the right-hand side of equation (16) differs from the expression on the right-hand side of equation (14) because domestic banks do not internalize the enforcement costs that foreign lenders must incur in case of partial default. Combining equations (14) and (16) yields

where

is the probability that the representative domestic bank will default. Alternatively, using equation (16):

From the above result, we have Where

which, together with equation (12), can be summarized in the following propositions.

**Proposition 2**.*The expected cost of funds for domestic honks on world capital markets, and for producers on the domestic capital market, can be written as a markup over the world risk-free interest rate*:.

*The markup adjusts the lender’s cost of capital by the expected cost of contract enforcement and state verification*..

**Proposition**3. *The domestic and foreign financial intermediation spreads, defined as the difference between the relevant contractual interest rate and the relevant expected cost of funds, are equal to the sum of the expected contract enforcement costs plus the expected revenue lost in adverse states of nature, when partial default takes place*:.

*where Γ and Γ _{h} are defined in equations (8) and (15)*..

### III. VOLATILITY AND CONTAGION

Having established the mechanism through which financial spreads, employment and output are determined, we are now in a position to study the adjustment process to a rise in the volatility of macroeconomie shocks. A key feature of a debt contract in our framework is the nonlinear dependency of the capacity to repay on the aggregate shock δ. To illustrate this point, recall that domestic banks will default on their foreign debt if K_{b},Φ(δ) < (1 + r*_{b})wn_{h}. This condition is plotted in Figure 6, where curve *RR* draws the debt repayment schedule if banks default, K_{b},Φ(δ), whereas curve *DD* plots the repayment due, (1 + r*_{b})wn_{h}The bold kinked curve depicts actual repayment. All things being equal, higher volatility does not affect repayment in good states of nature, but increases the incidence and severity of partial default in adverse states of nature. In terms of Figure 6, higher volatility adds segment Δ to the range of default. The partial equilibrium effect is to increase the probability of default by (approximately) Δ/2δ_{m} thereby reducing expected repayment and raising the expected cost of funds. There is also a general equilibrium effect, which results from the fact that foreign lenders increase the interest rate charged to domestic banks to compensate for lower expected repayment and for the higher expected cost of contract enforcement. This adjustment leads to an upward shift in curve *DD* (as shown in the figure), further increasing the incidence of default. The general equilibrium effect therefore magnifies the increase in the probability of default, because it leads also to a rise in the expected cost of funds and a rise in financial intermediation spreads.

**Effect of an Increase in Volatility**

Citation: IMF Staff Papers 1998, 003; 10.5089/9781451974164.024.A001

**Effect of an Increase in Volatility**

Citation: IMF Staff Papers 1998, 003; 10.5089/9781451974164.024.A001

**Effect of an Increase in Volatility**

Citation: IMF Staff Papers 1998, 003; 10.5089/9781451974164.024.A001

A similar analysis applies for the impact of higher volatility on domestic financial intermediation. Thus, by showing how interest rate spreads are related to default probabilities and changes in volatility of underlying shocks, our analysis is capable of explaining not only the increase in “foreign” financial intermediation spreads recorded by Argentina in the immediate aftermath of the Mexican peso crisis, but also the sharp increase in the spread between the country’s bank lending and deposit rates (see Figure 3).

A key empirical prediction of our analysis is an inverse relationship between volatility and economic activity. Figure 7 illustrates a simple way of testing this proposition, using data for a group of Asian and Latin American countries for which monthly data on output (measured by either the industrial output index or the manufacturing production index) were readily available. The variable measured on the horizontal axis is the ratio of the standard deviations of post- and pre-Mexican peso crisis of the cyclical component of output, calculated in each case by taking the difference between actual output and its trend level, computed with the Hodrick-Prescott filter. The variable measured on the vertical axis is the ratio of post-and pre-Mexican peso crisis of the average rate of growth of the trend component of output. The figure shows indeed that higher volatility tends to be associated with a slowdown in economic activity. Of course, we do not view the evidence presented in Figure 7 as compelling or definitive; more sophisticated econometric tests would be needed to assert in a rigorous manner the links between volatility and economic activity. The fact remains, however, that simple calculations are not at variance with one of the main predictions of our analytical framework.

**Changes in Output Volatility and Trend Output Growth Before and After the Mexican Peso Crisis**

Citation: IMF Staff Papers 1998, 003; 10.5089/9781451974164.024.A001

**Changes in Output Volatility and Trend Output Growth Before and After the Mexican Peso Crisis**

Citation: IMF Staff Papers 1998, 003; 10.5089/9781451974164.024.A001

**Changes in Output Volatility and Trend Output Growth Before and After the Mexican Peso Crisis**

Citation: IMF Staff Papers 1998, 003; 10.5089/9781451974164.024.A001

### IV. Welfare Effects

We turn now to an evaluation of the impact of a contagious shock (or, more precisely here, an increase in volatility) on welfare, as approximated by the expected producers’ surplus, S^{e}_{p.} ^{14}Suppose that there are *N* identical producers in the economy. Based on our discussion in the previous section, we can infer that the expected producers’ surplus (at the optimal level of employment) is, taking into account the expected cost of borrowing by producers, as given in equation (12):

Our welfare criterion is the sum of expected surpluses of all the domestic agents in the economy. Having competitive banks implies that banks’ rents are dissipated; hence, banks’ expected surplus is zero. The limited liability and costly enforcement of debt contracts implies, however, that the producers’ rent does not dissipate. Therefore, our welfare criterion is the expected producers’ surplus. Note that capital market imperfections may imply that producers would not be able to finance their project even if their expected profits are positive and high enough to cover all costs. This will be the case if ineffective contract enforcement does not allow the bank to recover its costs of intermediation—time-inconsistency considerations imply that producers’ promise to service their debt is not credible. Our welfare function quantifies the welfare effects of time inconsistency, as reflected by the need to spend resources on information verification and contract enforcement.^{15}

Consequently, the effect of higher volatility on the expected producers’ surplus is given by

By virtue of the envelope theorem, the first term on the right-hand side of the above expression is zero (recall that each producer *h* sets employment so as to maximize S^{e}_{p} Applying Proposition 2 to substitute for ∂ř^{f}_{b}/∂ δ it follows that

The above equation can be reduced to a simple form for the case where the repayment associated with partial default is approximated by a linear function (see the Appendix for details). In the range of partial default, in which *Pr(d/p)* and *Pr{dlb)* are both positive, it can be shown that

where *B* is a constant term measuring the partial effect of 8 in the linear approximation to Ω(.), and *‖*. is defined by

In the Appendix we establish that all the denominators appearing on the left-hand side of equation (21) are positive if the economy operates on the efficient portion of the borrower’s interest rate-bank cost of credit schedule. Henceforth we assume that competition among banks induces this condition to hold, and thus all the terms in equation (21) are positive for *Pr(d/p)* and *Pr(dlb)*..

Let Pr refer to the probability of default of either domestic producers or domestic banks and suppose that (everything else equal) a highly integrated capital market is characterized by a low incidence of default. The term 1 - Pr, the probability of repayment, may thus be viewed as a measure of the country’s integration with the global financial market. It can be verified that 1-Pr depends positively on the creditor’s bargaining power (coefficients K and K_{b}), and negatively on the cost of state verification and contract enforcement, *C* and C_{f ,} , (see the Appendix for further discussion). Applying equation (21), it follows that the impact of volatility is large for countries that are on the verge of full integration with global financial markets, because for these countries the expression 1 - Pr is maximized. These countries are in a precarious state—for low volatility the marginal effect of more turbulent markets is zero, but for volatility above a threshold, this effect can be profound. This may explain why countries like Argentina are now the most exposed to volatility. The above equation also implies that higher volatility matters very little for highly risky countries where the probability of full repayment is low. Such countries operate, to begin with, on the relatively inelastic portion of the supply of funds, hence higher volatility has little effect on welfare at the margin.

This, in turn, implies a nonlinear association between volatility and the expected producers’ surplus, as illustrated in ^{Figure 8} (which is based on equation (18)). For small enough volatility (assuming a high enough expected productivity), the probability of default is zero. In these circumstances higher volatility does not have any impact on welfare. Once a threshold is reached (point *A)*, higher volatility increases the probability of default, leading to a welfare loss proportional to the cost of intermediation times ΔPr. This nonlinearity may explain why contagious shocks may have highly heterogeneous effects across countries. Suppose that a crisis like the Mexican peso collapse increases financial markets’ perception of volatility in Latin America in general. The adverse domestic effects of this perception will differ across countries, even if the perceived increase in volatility is identical across them. For countries that are viewed as relatively safe. Pr=0, there will be no effect on welfare. For countries that were viewed, to begin with, as mildly risky ventures (Pr > 0 but close to point *A)*, the welfare loss will be large. For countries whose degree of financial openness is relatively small, the welfare loss tends to be smaller because for these countries the probability of default is large.

**Volatility and the Expected Producers’ Surplus**

Citation: IMF Staff Papers 1998, 003; 10.5089/9781451974164.024.A001

**Volatility and the Expected Producers’ Surplus**

Citation: IMF Staff Papers 1998, 003; 10.5089/9781451974164.024.A001

**Volatility and the Expected Producers’ Surplus**

Citation: IMF Staff Papers 1998, 003; 10.5089/9781451974164.024.A001

For a given probability of default, the adverse effect of higher volatility tends to be magnified for countries where the cost of contract enforcement is large. In terms of ^{Figure 8}, a larger cost of financial intermediation *(C* or C_{h)}) is associated with an inward shift of the downward-sloping portion of the curve from the soiid line that starts at point *A*, to the broken line that starts at point *A* ^{16} If the cost of financial intermediation is large enough, the welfare effect of higher volatility would be traced by the dotted curve that starts at point *A”*. In these circumstances, volatility may lead to a situation akin to credit rationing, where producers are not able to obtain bank financing for their working capital.

### V. Summary and Conclusions

The purpose of this paper has been to analyze the aggregate effects and transmission process of contagious shocks. In contrast to the existing literature, our model does so by capturing imperfections on both world capital markets and domestic credit markets. Specifically, we assumed a two-level financial intermediation process with risk-neutral lenders: domestic banks borrow at a premium on world capital markets, and domestic producers borrow, also at a premium, from domestic banks. In addition, we offered a different interpretation of contagion effects: in our analysis contagion takes the form of a rise in volatility of aggregate shocks impinging on the domestic economy—more specifically, a mean-preserving increase in the range of values that such shocks may take.

Our analysis showed that both foreign and domestic interest rate spreads are determined by a markup that compensates for the expected cost of contract enforcement and state verification, and for the expected revenue lost in adverse states of nature. Higher volatility raises financial intermediation spreads as well as the producers’ cost of funds, resulting in lower employment and higher incidence of default. In addition, our analysis showed that the welfare effects of an increase in volatility are highly nonlinear. Higher volatility does not impose any welfare cost on countries characterized by relatively low volatility and efficient financial intermediation to begin with. By contrast, adverse welfare effects may be large (small) for countries that are at the threshold of full integration with international capital markets (close to financial autarky), that is, countries characterized by relatively low (high) probability of default. A general implication of our analysis is thus that increased integration with world financial markets may be accompanied by a potential cost resulting from greater exposure to volatility—an implication also emphasized by Calvo (1997), in a different setting. Simple empirical calculations, based on data relative to the pre- and post-Mexican peso crisis periods for a small group of Asian and Latin American countries, suggest that (as predicted by our analysis) increased volatility tends to be associated with reductions in economic activity.

Our model can be extended in various directions. For instance, if lenders on both domestic and world financial markets are risk averse, the greater perceived volatility will induce a further increase in interest rate spreads to account for a higher risk premium, magnifying therefore the effect of an increase in the probability of default and the welfare cost of volatility. The pricing of risk by foreign lenders could be formulated so as to capture the existence of implicit insurance from the domestic country’s central bank. The existence of bail-out options would naturally affect the foreign intermediation spread, particularly in the presence of uncertainty regarding the extent and timing of domestic public assistance.

We also refrained from modeling the precise mechanism leading to an increase in the volatility of shocks. The reason for this is our contention that any external event that leads to an increase in the volatility of shocks will trigger the type of adjustment modeled in this paper, This does not preclude. of course, the existence of alternative channels that may complement or alter the transmission mechanism discussed here. For instance, it is sensible to assume that information asymmetries may lead foreign lenders to increase the real interest rate (that is, the risk premium) that they would demand from a country like Argentina. This, in turn, will lead to higher incidence of default in that country. Our model can be used to account for this sequence. Specifically, it can be shown that the ultimate welfare cost of asymmetric information will depend positively on the cost of financial intermediation.

An extended version of our model would show that even if the “trigger mechanism” is the existence of asymmetric information, as discussed above, it would lead to a higher variance of domestic shocks, inducing the adjustment mechanism described in ilie present paper. This will hethe case if there are complementarities among producers, on either the supply or the demand side.^{17} While we did not explicitly model these channels of transmission, one may view our framework as a reduced form of a more complex economy, characterized by the above complementarities. In such an environment, the higher cost of credit would lead both to a drop in the expected productivity as well as to a higher volatility of the productivity shocks, magnifying the ultimate adverse output effects. Finally, our model can also be extended to account for several mitigating factors that reduce the adverse effects of volatility and interest rate shocks, like the use of collateral and the “rolling over” (or partial refinance) of debt obligations. It is worth noting, however, that the effectiveness of these factors would be ultimately determined by the efficiency of the financial intermediation process. For instance, if the legal system is such that contract enforcement is both time consuming and costly, liquidating a collateral would also be costly—thereby reducing its potential benefits. Furthermore, if the market value of the collateral falls in “bad” times (or if the collateral is more valuable to the producer than to the lender), it would help little *m* alleviate the costs of volatility.

Notwithstanding these extensions, the present framework (despite being static and partial equilibrium in nature) offers a particularly useful setting for interpreting some of the events that occurred in Argentina and Mexico in early 1995. In particular, it helps to understand how changes in the volatility of aggregate shocks may have played a role in the transmission and magnification of an initial adverse shock on world capital markets.^{18} It also highlights the role of domestic factors (such as the cost of contract enforcement) in this process. This prediction is consistent with the econometric results of Powell, Broda, and Burdisso (1997), which emphasize the role of default risk and the lack of legal security for debt contracts in the determination of bank lending rates in Argentina. It is also broadly consistent with the analysis of contagion effects by Sachs. Tornell. and Velasco (1996), whose study focuses on the evolution of 20 emerging market economies in the aftermath of the Mexican peso crisis. They emphasized the role of domestic imbalances in countries that suffered the most from speculative attacks, and identified as important factors not only overvalued exchange rates and low foreign exchange reserves, but also banking system fragility. As noted in the introduction, banking sector weaknesses have also played a crucial role in compounding the spillover effects associated with the currency turmoil that followed Thatland’s decision to abandon its exchange rate peg in July 1997.

### APPENDIX

This Appendix derives the probability of default for the case in which the partial repayment function can be approximated by a linear curve. For simplicity of exposition we do it for the case in which employment *n _{h}* is constant, and focuses on intermediation between foreign lenders and domestic banks.

^{19}

Suppose that in the relevant region domestic banks’ revenue is given by the linear approximation

with *A, B >* 0. The threshold value δ of the aggregate shock δ that makes banks indifferent between partial default and repayment is thus’

or equivalently

and the probability of bank default is

Using equation (14), we infer that, with g(δ)=l/2δ

that is.

Solving equation (A3) yields

that is, using equation (A2):

Using equations (A1) and (A3), we can infer that the slope of the borrower’s interest rate-bank cost of fund curve is

In general, raising the borrower’s interest rate has two opposing effects on the bank’s expected profits. First, the revenue goes up in states of nature where no default takes place, increasing expected profits. Second, the higher borrower’s interest rate increases the probability of default, thereby increasing the expected cost of financial intermedialion. In terms of equation (A5), the first effect is 1 - Pr*(d/h)* (per unit of loan), and the second is given by C_{h}/2K_{h} *Bδ _{m}*. Hence, in general, the borrower’s inieresi rale-bank cosi of credit curve is backward bending, with the backward-bending portion depicting an inefficient region. The analysis in the paper assumes that competition among banks implies that, if Pr

*(dlb)*>0, the country operates on the upward-sloping portion of the curve. The denominator of equation (A5) is hence positive.

Using equations (A1) and (A2), we can also solve for the contractual interest rale facing domestic banks, r*_{h}. in terms of Pr*(d/b)*. Substituting the result in equation (A4) yields a quadratic equation for the probability of default:

Applying the implicit function theorem to this equation yields

which can be combined w’itb equation (20) to give equation (21).

Note also that, for δ_{m} given:

If creditors’ capacity to enforce partial repayment is small (that is, if K or K_{h} is small), or if the cost of financial intermediation is large enough, there is no internal solution—that is, the value of Pr that solves the quadratic equation given above is outside the [(),1] interval. Furthermore, for certain parameter values we may observe multiple equilibria, as is the case where there are two values of Pr. satisfying 0< Pr < 1. corresponding to low or high interest rate rates. Henceforth we assume that the model’s parameters are such that an internal equilibrium exists. Specifically, we assume that creditors’ bargaining power is large enough, and that the cost of financial intermediation is small enough to ensure that the probability of default is zero in the absence of aggregate volatility (δ = 0). and the probability of default is positive for large enough volatility. We also assume that, in the presence of multiple equilibria, the markcl chooses the equilibrium associated with the lower interest rate. This is also the equilibrium associated with the lower probability of defauli and the higher welfare level. It can be shown that these assumptions imply dial, in an internal equilibrium satisfying (0 < Pr < 1) equation (A6) is positive.

A similar analysis applies for the impact of higher volatility on the producer’s probability of default. The main difference between analyzing the partial effects ∂Pr*(d/b)* /∂δ_{m} and ∂Pr*(d/b)* /∂δ_{m} is that, as can be inferred from Proposition 2. higher volatility increases the cost of funds for domestic banks by

whereas higher volatility dues not affect the domestic banks’ expected cost oi’ funds on world capital markets (which is equal to the safe interest rale ř_{b}^{f}). Adjusting for this effect, and assuming that the default repay mein Φ(.) is linear, it follows that

implying that

which can be rearranged to give

where Ω is defined by

Using equation (A6), this expression becomes

which can be substituted in equation (20) to give equation (21).

## REFERENCES

Agenor, Pierre-Richard, 1997, “Borrowing Risk and the Tequila Effect,”

*IMP Working Paper 97/86*(Washington: International Monetary Fund. July).Agenor, Pierre-Richard, and Joshua Aizenman, 1998,

*“Volatility and the Welfare Costs of Financial Market Integration”*(unpublished: Washington: Economic Development Institute. World Bank. March).Aizenman, Joshua Michael Gavin, and Ricardo Hausmann. 1996, “Optimal Tax and Debt Policy with Endogenously Imperfect Credit worthiness,”

*NBER Working Paper No. 5558 (Cambridge, Massachusetts: National Bureau of Economic Research. May*).Bemanke, Ben S. and Mark Gertler 1989, “Agency Costs, Net Worth, and Business Fluctuations.”

. Vol. 79 (March) pp. 14–31.*American Economic Review*Boot, Arnoud W. Anjan V. Thakor, and Gregory F. Udell, 1991, “Credible Commitments, Contract Enforcement Problems and Banks: Intermediation as Credibility Assurance,”

. Vol, 15 (June), pp. 605–32.*Journal of Bunking and Finance*Calvo, Guillermo A., 1997, “Credibility Crises and State-Contingent Markets: Emerging Markets and Financial Engineering” (unpublished: College Park. Maryland: University of“Maryland, February).

Calvo, Guillermo A., and Gracicla L. Kaminsky, 1991, “Debt Relief and Debt Rescheduling: The Optimal Contract Approach,”

. Vol. 36 (July), pp. 5–36.*Journal of Development Economics*Catao, Luis, 1997, “Bank Credit in Argentina in the Aftermalh of (he Mexican Crisis: Supply or Demand Constrained?” IMF Working Paper 97/32 (Washington: International Monetary Fund, March).

Eaton, Jonalhan. 1986, “Lending with Costly Enforcement of Repayment and Potential Fraud.”

. Vol. 10 (June), pp. 281–93.*Journal of Banking and Finance*Goldfajn Han, and Rodrigo O. Valdes, 1997, “Capital Flows and the Twin Crises: The Role of Liquidity,” IMF Working Paper 97/87 (Washington: International Monetary Fund, July).

International Monetary Fund, 1996,

(Washingion: International Monetary Eund).*International Capital Markets: Developments. Prospects, and Key Policy Issues*, World Economic and Financial SurveysJaffee Dwighl, and Joseph Stiglitz 1990, “Credit Rationing.”

*Chapter 16 in*. Vol. 2. ed. by Benjamin M. Friedman and Frank H. Halm (Amsterdam: North-Holland), pp. 837–88.*Handbook of Monetary’ Economics*Kaufman. Martin D., 1996, “An Incursion into the Confidence Crisis-Credii Rationing-Real Activity Channel: Evidence from the Argentine Tequila’ Crisis” (unpublished; Buenos Aires: Central Bank of Argentina. February),

Powell, Andrew, A. Broda, and T. Burdisso, 1997, “An Analysis of Lending Interest Rates in Argentina: A Panel Interpretation of a Search Model with Bargaining” (unpublished: Buenos Aires; Central Bank of Argentina. April).

Sachs, Jeffrey, Aaron Tornell, and Andres Velasco, 1996,

*”Financial Crises in Emerging Markets: The Lessons from 1995,”*: l, Brookings Institution (June), pp. 147–98,*Brookings Papers on Economic Activity*Townsend, Robert M, 1979, “Oplimal Contracts and Competitive Markets with Costly Slate Verification.”

*Journal of Economic Theory*. Vol, 21 (October), pp. 265–93.Uribe, Martm, 1996, “The Tequila Effect: Theory and Evidence from Argentina.”

*International Finance Discussion Paper No. 552 (Washingion: Board of Governors of the Federal Reserve System, June*).

^{}*

Pierre-Richard Agenor is a Senior Economist in the Research Department of the IMF. Joshua Aizenman is Champion Professor of International Economics at Dartmouth College. The authors would like to thank, without implication, Guillermo Calvo, Luis Catao, Robert Flood, Joseph Haimowitz, Martin Kaufman, Paulo Neuhaus, Maurice Obstfeld, Andrew Powell, Evan Tanner. Carlos Vegh, an anonymous referee, and participants at seminars at Dartmouth College, the University of Washington, and the WEA Conference held in Seattle (July 9-14) for helpful discussions and comments on an earlier version. Brooks Calvo provided excellent research assistance.

^{}1

There appears to be some agreement that this shift in market sentiment was not entirely warranted by fundamentals. On the one hand, the real exchange rate had indeed appreciated substantially since the introduction of the Convertibility Plan in April 1991. and the current account deficit (as a share of output) was increasing. On the other hand, inflation was low and falling, output and exports were growing at a relatively high rate (with real GDP growing by more than 7 percent a year between 1991 and 1994), and ample liquid reserves appeared to be available to defend the fixed parity between the U.S. dollar and the peso.

^{}2

In addition to these studies, Kaufman (1996) uses the Stiglitz-Weiss model of credit rationing (see Jaffee and Stiglitz, 1990) to argue ihai the credit crunch in Argentina resulted from an increase in the share of illiquid borrowers induced by the rise in interest rates, and increased incidence of adverse selection problems. Essentially, banks faced greater difficulties screening out between “safe” and “risky” borrowers because those borrowers mosi willing to pay a higher interest rate on loans were precisely those for which the potential risk of default had increased. Catao (1997, p. 6) estimates that problem loans had already exceeded 10 percent of the loan portfolio of all financial institutions by end-1994.

^{}3

In contrast to some of the existing studies, our model is static and partial equilibrium in nature. In particular, we do not explicitly model consumption decisions or central bank regulations. Some of these features could be added at the cost of greater complexity, but without adding much insight.

^{}4

Modeling domestic saving would be relevant under financial autarky, in which case all lending is supported by domestic saving. Adding a domestic saving schedule would not change the key results of this paper. In countries where the real interest rate that prevails in autarky is high relative to the international rate, the marginal source of funds is foreign saving. Henceforth we assume that funds are relatively scarce in the country under consideration, and that as a result the interest rate that prevails in autarky exceeds the world rate. See Agenor and Aizenman (1998) for a discussion of more general cases,

^{}5

Although we use, throughout the paper, the expression “aggregate productivity shock” to refer to 5, a more general interpretation is to think of 8 as a composite (or reduced-form) shock to output. See the discussion in the concluding section.

^{}6

The enforcement cost can be related, in particular, to the idea of costly state verification (see Townsend, 1979). That is, it costs *C* to verify the realization of e_{;}, and to force the producer to repay accordingly. Although C is modeled as a fixed monitoring and enforcement cost per loan, the analysis can be extended to allow for a variable cost, proportional to the size of the loan, without changing the key results derived below. K could also be made endogenous. For earlier models of impeded creditworthiness with costly state verification in a related context, see Aizenman, Gavin, and Hausmann (1996), Bemanke and Gertler (1989), Boot, Thakor, and Udell (1991), Calvo and Kaminsky (1991), and Eaton (1986).

^{}7

As is usual in the literature, repayment obligations are assumed not to be contingent on the state of nature. Loan agreements in practice typically specify a single contractual rate, which lenders are allowed to adjust only it’the borrower violates some specific terms of the contract.

^{}8

Note that if the bargaining power of creditors is too low, so that β/K > 1, the probability of default is always positive and condition (4) is always violated.

^{}9

Note that Φ(.) is a function of δ through the effect of that variable on y_{h}as shown in equation (1).

^{}11

_{h}and q=f, g

^{}12

Note that r_{L} is taken as given by each producer in determining optimal employment. The reason is that we assume the existence of a large group of ex ante homogeneous producers; all of them are charged the same interest rate by lenders. As shown earlier, r_{t} is determined in equilibrium by a break-even condition that internalizes all the information about the distribution of shocks—including idiosyncratic shocks.

^{}13

An Appendix providing formal derivations of these results is available upon request. This proposition assumes that volatility is sufficiently small to warrant an internal solution, which is such that the country operates on the upward-sloping portion of the borrower’s interest rate-bank cost of funding curve. See the discussion in the Appendix, following equation (A5), for a formal statement of this condition.

^{}14

A similar analysts would apply to labor, where the ultimate welfare effect associated with the fall in employment is given by the reduction in employment times the difference between the producers’ real wage and the supply price of labor.

^{}15

Our discussion focuses on the welfare effects of volatility, comparing the welfare to the benchmark of integrated capital markets in the absence of volatility. To compare welfare with financial autarky, one should model the naiure of financial intermediation and domestic saving in autarky. See Agenor and Aizenman (1998) for such a comparison in a related framework.

^{}16

The case of high values of C and C_{h} may be particularly relevant for Argentina. As discussed by Caiao (1997) and Powell, Broda, and Burdisso (1997), severe limitations to the seizure of collateral property still prevail in that country. Judicial aclions take lime, have uncertain outcomes, and are relatively costly—thereby affecting lending rates by raising the potential cost of default.

^{}17

An example of supply complementarity is the case where producers use non-traded inputs provided by other producers. Default by some producers due to higher cost of credit will trigger default by other producers due to the increase in the price of needed inputs, implying that the increase in the cost of credit may trigger higher volatility of domestic productivity shocks of domestic producers. Similar examples of demand complementarities will arise if producers have some market power—as is the case in a world of monopolistic competition.

^{}18

In Argentina, various other factors have also played a role in this process An increase in the perceived risk of confiscation of bank deposits—as occurred in December 1989, when the government, in an effort to reduce inflation, forced the conversion of time deposits and public sector debt into U.S. dollar-denominated government (BONEX) securities—and the fact that bank deposits were not insured certainly played a role in the bank run and the credit crunch that look place in earl) 1995 (see Catao, 1997). There may also have been increased doubts about the sus-lainability of full convertibility of current and capital account transactions, as well as perceived constraints on the lender-of-last-resort function of the central bank, under the currency board in place since the Convertibilitv Plan was introduced in early 1991.