FINANCIAL SECTOR INEFFICIENCIES AND THE DEBT LAFFER CURVE

Transcription

1 INTERNATIONAL JOURNAL OF FINANCE AND ECONOMICS Int. J. Fin. Econ. 10: 1 13 (2005) Publised online in Wiley InterScience ( DOI: /ijfe.251 FINANCIAL SECTOR INEFFICIENCIES AND THE DEBT LAFFER CURVE PIERRE-RICHARD AGÉNOR a, *,y and JOSHUA AIZENMAN b a Scool of Economic Studies and Centre for Growt and Business Cycle Researc, University of Mancester, UK b Department of Economics, University of California, USA, and National Bureau of Economic Researc, USA ABSTRACT Tis paper analyses te implications of inefficient financial intermediation for debt management in a model were firms rely on bank credit to finance teir working capital needs and lenders face state verification and contract enforcement costs. We sow tat lower expected productivity, iger enforcement and verification costs, or iger volatility of productivity socks, may sift a country to te wrong side of its debt Laffer curve, wit potentially sizable output and welfare losses. We also sow tat debt relief may bring few welfare benefits unless it is accompanied by reforms aimed at reducing financial sector inefficiencies. Copyrigt # 2005 Jon Wiley & Sons, Ltd. JEL CODE: E44; F36; I31 KEY WORDS: Credit market imperfections; contract enforcement costs; debt Laffer curve NON-TECHNICAL SUMMARY Tis paper examines te implications of inefficient financial intermediation (taking te form of ig costs of contract enforcement and state verification) for an economy in wic firms are faced wit a ig level of initial debt and contract new borrowing from domestic banks to finance labour costs. After presenting te producer s decision problem, we analyse te determination of te contractual lending rate on te new debt, wic is sown to be a mark-up over te cost of borrowing, wit te size of te mark-up related positively to te probability of default. We also sow tat optimal employment depends negatively on te cost of state verification and contract enforcement, as well as te initial stock of debt obligations eld by firms. We ten derive a debt Laffer curve wit regard to te initial debt, and determine te optimal level of debt consistent wit te absence of a debt overang. We analyse te effect of an increase in contract enforcement and verification costs, as well as an expected negative sock to output and an increase in te volatility of productivity socks, on te optimal level of debt. We sow tat, as a result of eiter one of tese socks, te economy may move on te wrong side of te debt Laffer curve. Moreover, our analysis sows tat tis sift may be accompanied by (possibly large) employment and output losses in te sort term (in addition to te possible adverse longer-run effects associated wit lower investment and growt rates). Tus, in countries were financial intermediation is igly inefficient (in te sense tat enforcement costs of loan contracts are relatively ig), or in a country experiencing large adverse output socks and iger volatility, te likeliood of an inefficient equilibrium is also ig. We also argue tat, because of well-known moral azard problems, debt relief as a policy response to an economy tat as sifted on te wrong side of te Laffer curve (as a result of iger state verification costs) may not be feasible or desirable. On te contrary, wat our analysis suggests is tat financial sector reform (in te sense of measures aimed at reducing te cost of financial intermediation, including contract *Correspondence to: Pierre-Ricard Ag!enor, University of Mancester, Oxford Road, Mancester, M13 9PL, UK. y pagenor@worldbank.org Copyrigt # 2005 Jon Wiley & Sons, Ltd.

2 2 P.-R. AGÉNOR AND J. AIZENMAN enforcement costs) may be essential}indeed, not only to reduce te adverse incentive effects of a debt overang, but more generally to increase economic efficiency. 1. INTRODUCTION Tere is substantial agreement among economists tat inefficiencies in financial intermediation and weaknesses in te banking sector ave exacerbated some of te recent economic and financial crises tat ave devastated so many countries in te developing world and transition economies. 1 Hig costs of operation, inadequate lending practices, large volumes of nonperforming loans, excessive exposure to some sectors, large unedged sort-term liabilities in foreign currency, and lax supervision were all pervasive features of te financial system in many crisis-stricken countries. An important source of inefficiency in te financial system in many developing and transition economies relates to te ig costs associated wit te enforcement of loan contracts, wic are due in part to te weaknesses of te legal infrastructure (te inability of lenders to seize collateral in case of default, for instance) and a ig degree of asymmetry in information between lenders and borrowers. Te present paper examines te implications of tis type of inefficiency for debt relief in an economy in wic tere exists a direct link between bank credit and te supply side, troug firms working capital needs. Section 2 describes te analytical framework, wic combines te costly state verification approac pioneered by Townsend (1979) and te model of limited enforceability of contracts used in te external debt literature, as in Eaton et al. (1986) and Helpman (1989a). 2 In addition to te new debt contracted to finance labour costs during te production period, firms also old a large initial stock of debt tat tey must repay out of current revenue. Section 3 derives a debt Laffer curve and determines te optimal level of debt. Section 4 analyses te effect of a reduction in te efficiency of te financial intermediation process (caracterized by an increase in contract enforcement and verification costs), an adverse expected sock to productivity, and iger volatility of productivity socks, on te optimal level of debt. It is sown tat all of tese socks may sift te economy to te wrong side of te debt Laffer curve. Section 5 draws some of te policy implications of te analysis. In particular, altoug reducing te face value of debt could make bot lenders and borrowers better off}as empasized by Krugman (1988) and Sacs (1989) in teir analysis of te debt overang in a more general context}a iger degree of financial sector inefficiency may prevent any welfare gain. 2. THE ANALYTICAL FRAMEWORK We consider an economy producing one composite tradable good, wose price is normalized to unity. 3 Risk-neutral banks provide intermediation services to producers, wic demand credit to finance teir working capital needs, consisting only of labour costs. Output is subject to random, idiosyncratic productivity socks. Following Townsend (1979), te realized productivity sock is revealed to banks ex post only at a cost. In te event of default by any given producer on its bank loans, te creditor seizes a fraction of te realized value of output. Seizing involves two types of costs: first, te cost involved in verifying te actual value of output, as mentioned earlier; second, te cost of enforcing repayment, because enforcement of te terms of loan contracts requires costly recourse to te legal system Producers We assume tat te representative domestic producer starts te period wit an initial level of debt, denoted D. Tis initial debt could be interpreted in various ways. Te interpretation tat comes te closest to wat we ave in mind is an economy tat as borrowed significantly on world capital markets during a number of periods prior to te current one and suddenly finds itself cut off (or rationed out) from tese markets}as a result for instance of contagion effects, tat is, a crisis elsewere tat leads foreign lenders to Copyrigt # 2005 Jon Wiley & Sons, Ltd. Int. J. Fin. Econ. 10: 1 13 (2005)

3 THE DEBT LAFFER CURVE 3 suddenly ration credit to a class of borrowers assumed to sare similar risk caracteristics or weaknesses in fundamentals. Tis interpretation is, of course, also quite relevant for countries tat are temselves undergoing a financial crisis; te country risk premium tat suc countries face on world financial markets may climb to proibitive levels as a result of te uncertainties created by te crisis (suc as an increase in te perceived risk of default of domestic borrowers due to a sarp slowdown in economic activity), effectively rationing tem out of te market. In eiter case, we assume tat te initial level of debt must be serviced in te current period, and tat te inability to borrow on world capital markets does not lead to an outrigt default; rater, domestic producers borrow from domestic banks to finance teir working capital needs and, depending on te state of nature, coose or not to repay te initial debt and te new borrowing from local intermediaries. We take te interest rate on te initial debt as predetermined at te beginning of te current period, and for simplicity set it to zero. We also assume tat te debt matures at te end of te current period, an assumption tat can easily be relaxed. Tus, D represents also total repayment obligations on te initial debt. Te production function relating output, y, of producer to employment, n, is given by y ¼ n b ð1 þ d þ e Þ; ¼ 1;...; N ð1þ were d40 is a constant term and e an idiosyncratic sock assumed to be distributed symmetrically over te interval (,e m ). 4 Producer repays te initial debt in good states of nature, and cooses to default in bad states. In case of default on te initial debt, creditors are able to confiscate a fraction w of te realized value of output. Tus, default occurs wen, ex post: wn b ð1 þ d þ e Þ5D; 05w41 ð2þ Te left-and side of equation (2) is te producer s repayment following a default, wereas te rigtand side is te contractual repayment. Equivalently, te producer will service te initial debt according to 5 min½d; wn b ð1 þ d þ e ÞŠ ð3þ Let *e denote te tresold value of te productivity sock below wic default occurs on te initial level of debt, tat is D ¼ wn b ð1 þ d þ *e Þ Solving tis equation for *e yields D=wn b 1 d. Clearly, tis value of *e can be less tan te lower support of te distribution,. In tat case, we impose *e ¼. Wen *e ¼, default never occurs because any realization of te sock will always induce full repayment. We can tus write " # *e ¼ max D wn b 1 d; ð4þ Eac firm finances its labour costs wit bank credit. Let k denote te representative bank s bargaining power on te new debt. Tere may be a difference between te ability to enforce te initial ( old ) debt and te new debt contracted at te current period}tat is, k may differ from w. Tis difference may reflect te possibility tat te new debt is financed mostly by domestic banks, wereas te initial debt is mostly foreign debt. 6 Let e be te tresold value of te productivity sock tat induces default on te new debt. We assume tat, in bad states of nature, te producer would coose to default on te old debt, before defaulting on te new one; tat is, e 5*e. Tis assumption implies tat wenever te producer defaults on te new debt (tat is, wen te realization e 5e ), default necessarily occurs also on te initial debt}in wic case creditors seize a fraction wy of te realized value of output, leaving a fraction (1 w)y of output from wic creditors of te new debt can seize k. 7 Given tese assumptions, debt service on te new debt is determined by min½ð1 þ r L Þwn ; kð1 wþn b ð1 þ d þ e ÞŠ ð5þ Copyrigt # 2005 Jon Wiley & Sons, Ltd. Int. J. Fin. Econ. 10: 1 13 (2005)

4 4 P.-R. AGÉNOR AND J. AIZENMAN were r L denotes te contractual interest rate on te new debt and (1 þ r L )wn contractual repayment obligations (wit w te exogenous wage rate). Tis condition implies tat e is given by ð1 þ r L Þwn ¼ kð1 wþn b ð1 þ d þ e Þ or, rearranging terms, 8 e ¼ ð1 þ r LÞwn kð1 wþn b 1 d ð6þ Using equations (4) and (6), te assumption tat e 5*e is tus equivalent to Dð1 wþ k 4ð1 þ r L Þwn ð7þ w Condition (7) is likely to be met for a large enoug level of te initial debt D, or for a relatively large k relative to w. Let f(e ) denote te density function of e. Assuming tat condition (7) olds, and tat te price of output is constant and normalized to unity, expected profits of te representative producer are given by Z *e P ¼ *e ½nb ð1 þ d þ e Þ DŠ f ðe Þde þð1 wþ n b ð1 þ d þ e Þf ðe Þde ð1 þ r L Þwn e f ðe Þde kð1 wþ n b ð1 þ d þ e Þf ðe Þde ð8þ Te first two terms in tis equation represent expected revenue, net of repayment on old debt, wereas te last two terms account for expected repayment on te new debt. Te first term on te rigt-and side of tis equation measures net revenue in good states of nature (in wic case te borrower repays te old debt D in full), wereas te second measures net revenue after confiscation in bad states (in wic case te producer s repayment is only a fraction w of te realized value of output). Te tird term measures repayment on te new debt in good states of nature, wereas te last term measures te amount confiscated by creditors wen tere is default on te new debt Te contractual lending rate Te representative bank as information about te coice of labour input by producer, and determines te interest rate suc tat te expected net repayment on te new debt is equal to te cost of credit. Eac bank is assumed to deal wit a large number of independent producers, allowing te bank to diversify te idiosyncratic risk, e. In te absence of default, te representative bank s net profit, P b, is given by te difference between contractual repayment and te gross cost of funds: P b ¼ð1 þ r L Þwn ð1 þ r C Þwn were r C denotes te cost of funds for te bank, assumed exogenous. In case of default, te representative bank s net profit is equal to te representative producer s repayment (tat is, te value of realized output seized by te bank) minus te (gross) cost of funds and minus te cost of state verification and contract enforcement, denoted C, wic is assumed to be independent from te cost (and amount) of funds borrowed by producer : 9 ð9þ P b ¼ kð1 wþn b ð1 þ d þ e Þ ð1 þ r C Þwn C ð10þ Te first term in tis expression accounts for te fact tat te producer first repays a fraction w on te initial debt, before servicing te new debt. Copyrigt # 2005 Jon Wiley & Sons, Ltd. Int. J. Fin. Econ. 10: 1 13 (2005)

5 Assuming risk-neutrality and competitive banks, te rent dissipation condition implies tat te interest rate on te new debt, r L, is set according to, using equations (9) and (10): ð1 þ r C Þwn ¼ð1 þ r L Þwn e f ðe Þde þ ½yn b ð1 þ d þ e Þ CŠ f ðe Þde ð11þ were y ¼ kð1 wþ: Tis expression can be rewritten in te form ( r L r C ¼ 1 ) y n b wn ðe e Þf ðe Þde þ C f ðe Þde ð12þ Equation (12) sows tat te spread between te contractual lending rate and te bank s funding cost is te sum of two terms: te first measures te expected revenue lost due to default in bad states of nature, and te second te expected state verification and contract enforcement costs wen default occurs Expected profits and optimal employment Applying equation (11) to equation (8), we can rewrite te expression for te representative producer s expected profits as P ¼ *e ½nb ð1 þ d þ e Þ DŠ f ðe Þde þð1 wþ Z *e n b ð1 þ d þ e Þf ðe Þde ð1 þ r C Þwn C f ðe Þde ð13þ were e, te tresold level of productivity associated wit default on te new debt, is determined by rewriting equation (6), using equation (11), as yn b ð1 þ d þ e Þ¼ð1 þ r C Þwn þ ½yn b ðe e ÞþCŠ f ðe Þde tat is ( e ¼ ð1 þ r ) CÞw yn b 1 þ yn b ½yn b ðe e ÞþCŠ f ðe Þde 1 d ð14þ Te optimal level of employment is determined by maximizing expected profits, equation (13), subject to equation (14). 10 Te corresponding first-order condition is obtained by setting P n ¼ 0; tat is ( Z ) *e bn b 1 *e ð1 þ d þ e Þf ðe Þde þð1 wþ ð1 þ d þ e Þf ðe Þde were, from equation (14): de ¼ ybnb 1 ð1 þ d þ e Þ wð1 þ r C Þ ybn b 1 R e ðe e Þf ðe Þde dn yn b R em e f ðe Þde Cf ðe Þ Substituting equation (14) into te rigt-and side of de =dn yields de ð1 bþð1 þ rc Þwn bc R e e ¼ m f ðe Þde dn 1 n yn b R em e f ðe Þde Cf ðe Þ THE DEBT LAFFER CURVE 5 ð1 þ r C Þw Cf ðe Þ de dn ¼ 0 wic implies tat, as long as C is not too large, de /dn We can state te following proposition. Copyrigt # 2005 Jon Wiley & Sons, Ltd. Int. J. Fin. Econ. 10: 1 13 (2005) ð15þ

6 6 P.-R. AGÉNOR AND J. AIZENMAN Proposition 1. Te optimal level of employment, *n ; can be written as *n ¼ *n ðw; r C ; C; DÞ ð16þ and it depends negatively on te four arguments in (16). To establis for instance tat d *n =dc50; note first tat sg d *n ¼ sg P n C dc P n n Applying te second-order condition for maximization yields sg½p n CŠ¼ f ðe de Þ 50 dn wic implies in turn tat d *n =dc50: 12 Suppose now tat te idiosyncratic productivity sock, e, follows a continuous uniform distribution, so tat f ðe Þ¼1=2e m ; Prðe 4xÞ ¼ðe m xþ=2e m ; wit zero mean and variance 4e 2 m =12 ¼ e2 m =3: Ten, in addition to te results summarized in Proposition 1, te following result can also be establised. Proposition 2. An increase in e m, wic can be interpreted as a (mean-preserving) increase in volatility, reduces optimal employment. To sow tat indeed d *n /de m 50ife follows a uniform distribution, note first tat sg d *n ¼ sg½p n e de m Š m From equation ( (15), P n ¼ 0 now yields Z bn b 1 y ) *e y *e de þð1 wþ f ðe Þde ð1 þ r C Þw C de ¼ 0 2e m 2e m 2e m dn From equation (6), de /dn ¼ (1 b)(1 þ r L )wn b /k(1 w), wic does not depend on e m. Tus, te above expression implies tat P n e m ¼ ð1 þ r CÞw 50 e m 3. THE DEBT LAFFER CURVE Assuming, to simplify notations, a zero subjective discount rate, te expected value of te initial debt from te point of view of te lenders is given by 8 >< D if *e ¼ V ¼ D R e m *e f ðe Þde þ R *e >: g f ðe Þde if *e 4 e m were g ¼ wn b ð1 þ d þ e Þ C Tis expression assumes, for simplicity, tat verification and enforcement costs associated wit servicing te new and te initial debt are te same. It sows tat wen default never occurs ð*e ¼ Þ, te expected value of te debt is simply its face value. By contrast, wen te possibility of default exists ð*e 4 e m Þ, te expected value of te debt depends also on contract enforcement and state verification costs, as discussed earlier. In addition, wen tere is te possibility of default, it can also be establised from te above Copyrigt # 2005 Jon Wiley & Sons, Ltd. Int. J. Fin. Econ. 10: 1 13 (2005)

7 expressions tat a iger initial debt as an ambiguous effect on te expected value of te debt: dv dd ¼ *e f ðe Þde Cf ð*e Þ wn b ( Z ) *e þ bwn b 1 ð1 þ d þ e Þf ðe Þde þ Cf ð*e Þ bd wn bþ1 dn dd ð17þ Equation (17) defines a debt Laffer curve, wic is depicted in te upper panel of Figure 1 as LL. It is linear (as depicted by te segment OB) up to a tresold level of debt *D, given by *D ¼ wn b ð1 þ d e mþ wic corresponds to equation (4) wit *e ¼. Equivalently, expected repayment increases one-for-one wit te initial value of debt (dv/dd ¼ 1); te segment OB is tus a 458 line. For levels of initial debt (marginally) above *D, equation (17) boils down to 13 dv dd ¼ 1 Cf ð*e Þ wn b 1 bd dn n dd THE DEBT LAFFER CURVE 7 ð18þ V dv/dd = 0 H A L A'' A' B L' L 0 D ~ E'' H' E' D* D ~ n E H H' n Figure 1. Te debt Laffer curve and financial intermediation. Copyrigt # 2005 Jon Wiley & Sons, Ltd. Int. J. Fin. Econ. 10: 1 13 (2005)

8 8 P.-R. AGÉNOR AND J. AIZENMAN Assuming tat enforcement costs C are small enoug, tat is, tat C is suc tat 14 Cf ð*e Þ wn b 1 bd dn ð19þ n dd ten, for relatively small levels of initial debt above *D, te curve LL is upward sloping. Note also tat a larger level of initial debt increases *e, tereby reducing te first term on te rigt-and side of equation (17); tis term approaces zero for a large enoug level of initial debt. Similarly, iger initial levels of debt raise te absolute value of te second, negative term in te above expression, because dn =dd50: a iger level of initial debt lowers employment and tus output, making default more probable and lowering te value of claims tat creditors can seize in case of default. Hence, for a large enoug level of initial debt, te rigt-and side of equation (17) is negative. Te optimal level of initial debt, denoted by D, corresponds to te value of te stock of debt for wic dv=dd ¼ 0 and is obtained at point A. Beyond point B, te probability of repayment falls below unity; and beyond point A, levels of debt are so ig tat additional amounts of debt actually lower expected repayments. Consequently, te association between te contractual value of te initial debt and its expected value as te typical inverted U sape tat caracterizes te debt Laffer curve (see Krugman, 1988, 1989; Sacs, 1989). Te difference between te (present) value of te country s contractual debt obligations and te expected resource transfers tat must be made to service tat debt, V, measures te debt overang. Tus, as long as *e 4 e m (tat is, as long as te possibility of default is allowed for in some states of nature) and as long as D4D, te country will suffer from a debt overang. Creditors would ten benefit from a lower contractual value of te initial stock of debt, because it would increase te expected value of teir debt claims. Te lower panel of Figure 1 depicts te relation between optimal employment and te initial level of debt, as given by (16). Te first segment of te curve, HH 0, is flat, because optimal employment, in te absence of default risk ð*e ¼ Þ; and given te assumption tat e 5*e ; does not depend on initial debt. Te reason is tat te cost of credit depends on expected verification and enforcement costs, wic in turn depend on te probability of default; for D less tan *D tat probability is zero and tus te level of initial debt as no effect on te cost of credit, as can be inferred from equation (12). Beyond point H 0 te curve is convex to te origin. At te optimal level of initial debt D, employment is given by *n (point E). Te following proposition can easily be establised. Proposition 3. Less efficient financial intermediation, as measured by iger state verification and contract enforcement costs (a rise in C), or lower expected productivity (a lower value of d), reduces te optimal value of te initial debt. In bot cases te debt Laffer curve sifts downwards and to te left. To establis tat dd =dc50, for instance, note tat by te implicit function teorem, we ave dd =dc ¼ V DC =V DD Applying te second-order condition for maximization yields sg dd ¼ sg½v DC Š¼ f ð*e Þ dc wn b 1 bd dn 50 n dd A diagrammatic illustration of tis proposition is also provided in Figure 1. Except for te linear segment OB, te sape of te debt Laffer curve depends on bot te cost of financial intermediation and te expected productivity sock. 14 An increase in enforcement costs (a rise in C) sifts te BL segment of te curve in te upper panel leftwards and inwards, to BL 0. Te optimal value of te initial debt is now determined at point A 00, wic is lower tan te initial value at A. In te lower panel, te relation between optimal employment and initial debt also becomes steeper beyond te tresold value *D; te new optimal value of employment is determined at point E 00, and is lower tan *n ; as establised in Proposition 1. Te figure also illustrates an important implication of te analysis: if, at te initial level of C, D is te optimal value of initial debt (tat is, te value for wic dv=dd ¼ 0), at te new value of C te initial D will be too ig because it will be located on te wrong side of te debt Laffer curve (point A 0 ). Copyrigt # 2005 Jon Wiley & Sons, Ltd. Int. J. Fin. Econ. 10: 1 13 (2005)

9 THE DEBT LAFFER CURVE 9 Employment, at E 0 will also be lower tan te new optimal value E 00. Tus, less efficient financial intermediation not only increases te likeliood tat te economy may be stuck in an inefficient equilibrium (on te wrong portion of te debt Laffer curve), but is also associated wit (potentially large) employment and output losses. Under te assumption tat te idiosyncratic sock e is uniformly distributed, te following proposition can also be establised. Proposition 4. An increase in e m, wic is equivalent to a (mean-preserving) increase in volatility, as qualitatively similar effects on te sape of te debt Laffer curve as tose associated wit an increase in intermediation costs or lower expected output. Finally, it can readily be establised tat an increase in te volatility of aggregate productivity socks}wic can be captured in te present setting by treating d as a uniformly distributed random disturbance}leads to a proposition similar to te one above, as can be inferred from te results in Ag!enor and Aizenman (1998). 4. POLICY IMPLICATIONS Despite te stylized nature of our analysis, te foregoing results are useful to understand some aspects of te crisis in East Asia and te policy responses tat it could ave led to. To many observers, one of te surprises tat surfaced in te immediate aftermat of te crisis was tat te outstanding stock of private external debt, particularly in Korea and Tailand, was muc larger tan previously assumed (see Aizenman and Marion, 200 l). Tis is consistent wit te assumption in our model of an initial level of debt tat must be serviced out of current resources. Furtermore, simple calculations sow tat tere was a significant increase in output volatility in te aftermat of te crisis. Te coefficient of variation of te industrial production index increased between te period January 1991 June 1997 and July 1997 December 1998 (tat is, in te immediate aftermat of te crisis) from 3.6% to 6.8% in Korea, from 4.3% to 5.2% in Malaysia, and from 6.3% to 6.6% in Tailand. Tis is captured in our framework by examining te impact of iger volatility on te sape of te debt Laffer curve. Finally, te crisis revealed also te state of te private banking system, and te relatively ig cost of bankruptcy procedures. Altoug we do not ave firm evidence tat verification and enforcement costs of loan contracts increased in te region in te aftermat of te crisis, it is plausible indeed tat suc costs rose significantly. Asymmetric information problems tend to be exacerbated in a more volatile economic environment, tereby forcing banks to expend more resources to assess and verify claims made by borrowers regarding teir situation and teir ability to service teir debt. Tese developments may ave led some of te crisis-stricken countries}suc as Korea, were domestic firms were igly indebted}to move on te wrong side of teir debt Laffer curve. As sown earlier, lower productivity, iger volatility of output, and iger financial intermediation and enforcement costs sift te debt Laffer curve leftwards and inwards, wereas a larger outstanding stock of debt sifts te economy s position to te rigt}possibly to an extent tat is large enoug to create a debt overang problem. Wat does te model imply, terefore, in terms of policy response? One approac is to argue tat debtors and creditors sould act collectively to reduce te face value of debt, because it is beneficial to bot parties. A large debt overang entails indeed well-known economic costs, induced by bot illiquidity and disincentive effects (see Krugman, 1989; Sacs, 1989). 15 In te context of our analysis, te sort-term employment and output costs associated wit a debt overang can also be substantial. In practice, owever, tere are also well-known difficulties associated wit a coordinated debt reduction among a (large) group of creditors, te moral azard problems tat suc operations entail: eac creditor as an incentive to refrain from offering debt relief on its own claims and wait for oters to do so, tereby raising te expected value of its own claims. 16 Tis type of free-rider problem may make it impossible, in practice, to consider debt relief as a viable policy response. Copyrigt # 2005 Jon Wiley & Sons, Ltd. Int. J. Fin. Econ. 10: 1 13 (2005)

10 10 P.-R. AGÉNOR AND J. AIZENMAN To te extent tat asymmetric information problems tend to be exacerbated by crises (as noted earlier), and as a result financial intermediaries in post-crisis countries may experience an increase in te cost of verifying and enforcing loan contracts, our model suggests an alternative response to a debt overang}namely, financial sector reform. Te ability of lenders to ave recourse to an efficient legal system to seize collateral in case of default, for instance, is an important determinant of contractual relations (in a crisis context or not) and as a significant impact on te determination of lending rates}and tus eventually te levels of output and employment. In terms of our Figure 1, te reduction in C could lead, for instance, to a sift in te Laffer curve from an initial segment BL 0 to BL. Moreover, as can be inferred from our analysis, it is possible tat debt relief may not be sufficient to sift te economy to te rigt side of te debt Laffer curve if at te same time enforcement or verification costs increase. In terms of Figure 1, tis would be te case, for instance, if debt reduction, starting from a level of debt equal to or greater tan D, moves te economy from a point to te rigt of A to a point to te left, suc as H; if tere is at te same time a rise in C (because of an increase in verification costs, as discussed earlier), te economy may settle to a point suc as H 0 on te new BL 0 segment and to te left of A 0, implying tat te economy would still be on te wrong side of te Laffer curve. In suc conditions, debt relief is not sufficient and would need to be accompanied by deeper reforms in te financial intermediation process. 5. SUMMARY AND CONCLUDING REMARKS Te purpose of tis paper as been to examine te implications of inefficient financial intermediation (taking te form of ig costs of contract enforcement and state verification) for an economy in wic firms are faced wit a ig level of initial debt and contract new borrowing from domestic banks to finance labour costs. After presenting te producer s decision problem, we analysed te determination of te contractual lending rate on te new debt, wic was sown to be a mark-up over te cost of borrowing, wit te size of te mark-up related positively to te probability of default. We also sowed tat optimal employment depends negatively on te cost of state verification and contract enforcement, as well as te initial stock of debt obligations eld by firms. We ten derived a debt Laffer curve wit regard to te initial debt, and determined te optimal level of debt consistent wit te absence of a debt overang. We analysed te effect of an increase in contract enforcement and verification costs, as well as an expected negative sock to output and an increase in te volatility of productivity socks, on te optimal level of debt. We sowed tat, as a result of eiter one of tese socks, te economy may move on te wrong side of te debt Laffer curve. Moreover, our analysis sowed tat tis sift may be accompanied by (possibly large) employment and output losses in te sort term (in addition to te possible adverse longer-run effects associated wit lower investment and growt rates). Tus, in countries were financial intermediation is igly inefficient (in te sense tat enforcement costs of loan contracts are relatively ig), or in a country experiencing large adverse output socks and iger volatility, te likeliood of an inefficient equilibrium is also ig. We also argued tat, because of well-known moral azard problems, debt relief as a policy response to an economy tat as sifted on te wrong side of te Laffer curve (as a result of iger state verification costs) may not be feasible or desirable. On te contrary, wat our analysis suggests is tat financial sector reform (in te sense of measures aimed at reducing te cost of financial intermediation, including contract enforcement costs) may be essential}indeed, not only to reduce te adverse incentive effects of a debt overang, but more generally to increase economic efficiency. ACKNOWLEDGEMENTS We would like to tank, witout implication, seminar participants at various universities and te World Bank for elpful comments on an earlier draft. Te views expressed ere do not necessarily represent tose of te Bank. Copyrigt # 2005 Jon Wiley & Sons, Ltd. Int. J. Fin. Econ. 10: 1 13 (2005)

11 THE DEBT LAFFER CURVE 11 APPENDIX Tis Appendix considers te case in wic te initial debt, D, is senior to te new debt. New lending is done by foreign banks. For simplicity, tese banks ave identical enforcement costs to te senior banks. Tis cost is paid by te relevant bank in a lump-sum fasion eac time tat te country defaults on its obligations to tat bank. In states of default, new (junior) banks get only te residual of te debt service after repaying te initial debt to te senior banks. In tis set-up, te country will default first on te junior debt at a low enoug value of te productive sock, e. Te country will default on bot types of debt at a lower value of te productivity sock, *e 5e. Te repayment rule for producer is given by min½ð1 þ r L Þwn þ D; wy Š ða1þ were y is given in equation (1), tat is, n b ð1 þ d þ e Þ. Te tresold value e is now determined by te equality wn b ð1 þ d þ e Þ¼ð1 þ r L Þwn þ D so tat " # e ¼ max ð1 þ r LÞwn þ D wn b 1 d; *e is now given by wn b ð1 þ d þ *e Þ¼D and expected profits of producer by P ¼ e ½y D ð1 þ r L Þwn Šf ðe Þde w y f ðe Þde Te net junior debt service from te point of view of te junior banks is given by ( maxfwy D; 0g C if e 5e ð1 þ r L Þwn if e 4e ða2þ ða3þ Expected repayment to te representative bank, wic determines te contractual interest rate on te new debt, r L, is tus determined by ð1 þ r C Þwn ¼ð1 þ r L Þwn e f ðe Þde þ *e ðwy DÞf ðe Þde C f ðe Þde ða4þ Using equations (A2) and (A4) yields P ¼ e ðy DÞf ðe Þde w y f ðe Þde ð1 þ r C Þwn þ *e ðwy DÞf ðe Þde C f ðe Þde Copyrigt # 2005 Jon Wiley & Sons, Ltd. Int. J. Fin. Econ. 10: 1 13 (2005)

12 12 P.-R. AGÉNOR AND J. AIZENMAN wic can be rewritten as P ¼ e y f ðe Þde D *e f ðe Þde Z *e ð1 þ r C Þwn w y f ðe Þde C f ðe Þde ða5þ Finally, te expected market value of te initial debt is given by, for *e 4 e m : Z *e V ¼ D *e f ðe Þde þ ðwy CÞf ðe Þde ða6þ From equations (A5) and (A6), it can be readily establised tat all te results summarized in Propositions 1 and 2 given in te text continue to old. In addition, assuming tat e is distributed uniformly, Propositions 3 and 4 can be sown to old as well. NOTES 1. See, for instance, te discussion of te causes and propagation of te Asian crisis in Alba et al. (1999) and Radelet and Sacs (1998). 2. See Freixas and Rocet (1997) for a useful description of te costly state verification approac to credit markets. Attar and Campioni (2003) provide a more critical review. 3. Te model presented in tis paper is based on te framework developed by Ag!enor and Aizenman (1998, 1999). It as been used to examine a variety of oter issues, including te real and financial effects of contagious socks (as in Ag!enor et al., 1998), and te welfare costs of financial openness. Te present setting differs from tese oter papers in tat we assume tat tere exists an initial level of debt, wic must be fully serviced in good states of nature. 4. To ensure tat output is positive in all states of nature, we impose 1 þ d2e m 40. Note also tat, in contrast to te original model in Ag!enor and Aizenman (1998), we do not account for aggregate socks. Tis could be done by treating d as a random, economywide disturbance. 5. In wat follows indifference on te borrower s part is resolved in favour of te lender. 6. Te qualitative features of our analysis are basically uncanged if k ¼ l. 7. As sown in te Appendix, results qualitatively similar to tose derived below continue to old in te case were te old debt as seniority. 8. Again, if default never occurs, we assume tat e is set at te lower end of te support of te distribution (e ¼ ). 9. Te analysis can easily be extended to consider te case were C is proportional to repayment; see Ag!enor et al. (1998). It would be more involved, owever, if some costs were assumed to accrue after te information about te idiosyncratic sock is obtained. In suc circumstances, banks would refrain from forcing debt repayment wen realized productivity is below a tresold of enforcement. For simplicity of exposition, and because tey would not modify te key results discussed below, we abstract from tese considerations. We also ignore all oter real costs associated wit financial intermediation. 10. Following our earlier paper (Ag!enor and Aizenman, 1998) we assume in wat follows tat eac individual producer takes te contractual lending rate as given wen determining te optimal level of employment. 11. Te condition tat C is not too large is needed to ensure tat we operate on te upward-sloping portion of te supply of credit facing te economy, leading to te results stated. Operating on te backward-bending portion of te supply of credit can be sown to be sub-optimal, and to affect te comparative statics results. 12. A more detailed appendix providing exact expressions for all te derivatives sown in Proposition 1 is available upon request. 13. In principle, te relationsip between te level of debt and its expected value given in equation (18) is only valid for marginal increases in D, starting from an initial level in wic tere is no possibility of default. Equation (17), by contrast, would provide te value of dv/dd more globally, and te condition on C sown in te inequality (19) would also be more general. However, te general case is quite intractable. 14. Te reason is tat, from equation (4), *e is equal to along OB, and depends on bot te optimal level of employment beyond point B. 15. In particular, a ig level of debt creates uncertainty about te country s capacity to service its debt and discourages private (domestic and foreign) investment, tereby reducing te rate of economic growt. Furtermore, ig debt service may be perceived by investors as a form of tax on te future income of te country, tus dissuading new investment. 16. See Sacs (1989). As sown by Helpman (1989b). If lenders interact noncooperatively, eac of tem taken individually may in fact be willing to provide some debt relief}altoug not as muc as tey would if tey were to act collectively. REFERENCES Ag!enor P-R, Aizenman J Contagion and volatility wit imperfect credit markets. IMF Staff Papers 45: Copyrigt # 2005 Jon Wiley & Sons, Ltd. Int. J. Fin. Econ. 10: 1 13 (2005)

13 THE DEBT LAFFER CURVE 13 Ag!enor P-R, Aizenman J Volatility and te welfare costs financial market integration. In Financial Crises: Contagion and Market Volatility, Ag!enor P-R, Miller M, Vines D, Weber A (eds). Cambridge University Press: Cambridge. Ag!enor P-R, Aizenman J, Hoffmaister A Contagion, bank lending spreads, and output fluctuations. Working Paper No. 6850, National Bureau of Economic Researc. Aizenman J, Marion NP Uncertainty and te disappearance of international credit. In Financial Crises in Emerging Markets, Glick R, Moreno R, Spiegel M (eds). Cambridge University Press: Cambridge. Alba P, Battacarya A, Claessens S, Gos S, Hernandez L Te role of macroeconomic and financial sector linkages in East Asia s financial crisis. In Financial Crises: Contagion and Market Volatility, Ag!enor P-R, Miller M, Vines D, Weber A (eds). Cambridge University Press: Cambridge. Attar A, Campioni E Costly state verification and debt contracts: a critical resume. Researc in Economics 57: Eaton J, Gersovitz M, Stiglitz J Te pure teory of country risk. European Economic Review 30: Freixas X, Rocet J-C Microeconomics of Banking. MIT Press: Cambridge, MA. Helpman E. 1989a. Te simple analytics of debt equity swaps. American Economic Review 79: Helpman E. 1989b. Voluntary debt reduction: incentives and welfare. IMF Staff Papers 36: Krugman P Financing versus forgiving a debt overang: some analytical notes. Journal of Development Economics 29: Krugman P Market-based debt reduction scemes. In Analytical Issues in Debt, Frenkel J, Dooley M, Wickam P (eds). International Monetary Fund: Wasington, DC. Radelet S, Sacs JD Te East Asian crisis: diagnosis, remedies, prospects. Brookings Papers on Economic Activity 1: Sacs J Te debt overang of developing countries. In Debt, Stabilization and Development, Findlay R, Calvo G, Kouri PJ, Braga de Macedo J (eds). Basil Blackwell: Oxford. Townsend RM Optimal contracts and competitive markets wit costly state verification. Journal of Economic Teory 21: Copyrigt # 2005 Jon Wiley & Sons, Ltd. Int. J. Fin. Econ. 10: 1 13 (2005)