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Lenders' reputation and the soft budget constraint
Economics Letters 84 (2004) 69 – 73 www.elsevier.com/locate/econbase
Lenders’ reputation and the soft budget constraint Michael Alexeev a,*, Sunghwan Kim b a
Department of Economics, Indiana University, Bloomington, IN 47405-5301, USA Management Research Laboratory, KT Corporation, Sungnam City, South Korea
b
Received 20 December 2003; accepted 8 January 2004 Available online 2 April 2004
Abstract Suppose at t = 0 lenders can choose whether to be ‘‘tough’’ or ‘‘soft,’’ and some borrowers learn the lenders’ type (reputation). In a decentralized lending market, being tough is optimal for a wider range of parameters than under centralization, because a soft lender who refinances poor projects is hurt by the tough lenders’ presence, as the quality of the lenders’ project pool is affected by the other lenders’ reputation. D 2004 Elsevier B.V. All rights reserved. Keywords: Soft budget constraint; Reputation; Centralization; Decentralization JEL classification: L14; P51
1. Introduction The presence of a soft budget constraint (SBC) is a major incentive problem that affects markets in various economic systems.1 In a seminal paper, Dewatripont and Maskin (1995) demonstrated that SBC can result from the inability of a lender to commit to not bailing out poor projects that require refinancing.2 They showed that this commitment problem can be solved by limiting the funds available to lenders, so that they would not be able to refinance poor projects even if, given adequate funds, it would have been a subgame perfect strategy. A major implication of Dewatripont and Maskin’s approach is that a decentralized lending market is better at hardening budget constraints than centralization, because each lender in a decentralized market * Corresponding author. Tel.: +1-812-855-7103; fax: +1-812-855-3736. E-mail addresses: [email protected] (M. Alexeev), [email protected] (S. Kim). 1 See Kornai (1980) and surveys by Maskin and Xu (2001); Kornai et al. (2003). 2 Schaffer (1989) provides an earlier but somewhat incomplete analysis of this problem. 0165-1765/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.econlet.2004.01.003
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has only a small amount of capital. Casual observation suggests, however, that large banks in market economies have vast amounts of capital, making it difficult to argue that they can precommit to no refinancing of poor projects because of limited funds. At the same time, the existing literature does not rigorously analyze the effect of lenders’ reputation on the SBC problem. We argue that reputation can be crucial in hardening budget constraints, and decentralized lending has an advantage over centralization in this respect. If a lender has reputation for toughness among some of the borrowers under centralization, the pool of submitted projects improves because those who are aware of the lenders’ type do not submit poor projects. Thus, there is a tradeoff between short-term losses from liquidating a poor project and long-term gains due to a reputation for toughness. This tradeoff is more likely to favor tough lender behavior in a decentralized market than under centralization. When both tough and soft lenders are present in a market, the pool of projects submitted to known soft lenders worsens more than it would under centralization, because soft lenders receive poor projects that would have otherwise been submitted to tough lenders. Therefore, reputational effects make being tough more attractive to lenders in a decentralized lending market. We are not modeling the acquisition of reputation. This is a subject of future research. Here, we simply argue that reputation is more valuable under decentralization. The next section formalizes this argument.
2. The model Consider an economy with the number of entrepreneurs normalized to 1. At the beginning of each period, each entrepreneur draws a project from a population with aa(0, 1) share of good projects and (1 a) poor projects (a is common knowledge). An investment of 1 unit of capital in a good project yields a net monetary return of Rg > 0 (gross return of 1 + Rg>1) and a non-monetary return of Eg>0. Returns to investment in a poor project depend on whether the project is liquidated or refinanced with another unit of capital. Liquidation results net monetary and non-monetary returns of, respectively, La( 1, 0) and El < 0, while the respective returns to refinancing are Rpa( 1, 0) and Ep>0. We assume that Rp>L. All returns occur by the end of the period. There are two types of entrepreneurs. Inexperienced entrepreneurs do not know the type of their projects, while experienced entrepreneurs know their project types. (At t = 0, all entrepreneurs are inexperienced.) Each entrepreneur lives for two periods. During the first period, the entrepreneur is inexperienced. In the second period, he becomes experienced. There is attrition of entrepreneurs that takes place at the exogenous rate ba[0, 1]. In a steady-state, there are 1/(1 + b) of inexperienced entrepreneurs and c = b/(1 + b) of experienced ones.3 Entrepreneurs have to borrow capital for projects from a lender who does not observe the project type but learns about it and its monetary return after investing the first unit of capital. The lender extracts the entire monetary return of the project. The nonmonetary return accrues only to the entrepreneur. There is an infinite number of periods and the lenders decide at t = 0 whether to be ‘‘tough’’ or ‘‘soft’’. Tough lenders always liquidate poor projects, while soft lenders always refinance them. The experienced entrepreneurs know the type of each lender.
3
Extending the range of c beyond 1/2 would not change the qualitative results.
M. Alexeev, S. Kim / Economics Letters 84 (2004) 69–73
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The lenders have sufficient capital to finance only the first K projects submitted each period, 0 < Kb1. The returns from the good projects can be used to refinance the poor projects and these returns are assumed sufficient for that purpose. That is, lenders never refrain from refinancing simply due to the lack of capital. Moreover, the proportion of good projects is sufficiently large to assure positive net returns in each period for all lenders. At the end of each period, the lenders distribute their net returns to the shareholders. The entrepreneurs have zero reservation payoffs and are randomly drawn from their population. The experienced entrepreneurs with poor projects always choose a soft lender if he exists. If there are no soft lenders, experienced entrepreneurs do not submit their projects for funding. All other entrepreneurs choose lenders randomly.
3. Centralization Under centralization, if the lender decides to be tough, experienced entrepreneurs would not submit poor projects. Therefore, the lenders’ payoffs from being soft (RC,S) and tough ( PC,T), are PC;S ¼ K½aRg þ ð1 aÞRp
1 1d
ð1Þ
PC;T ¼ K½aRg þ ð1 aÞL þ K½aRg =d þ ð1 cÞð1 aÞL=d
d 1d
ð2Þ
where d = a+(1 c)(1 a) and da(0, 1) is time discount rate. (The division by d in Eq. (2) takes place because experienced entrepreneurs do not submit poor projects.) The first subscript stands for centralization. The second subscript denotes the lenders’ type. The first term in Eq. (2) represents the tough lenders’ initial period payoff. Proposition 1. Under centralization, the lender chooses to play tough if dzdCðcÞ u
ð1 ð1 aÞcÞðRp LÞ : acðRg LÞ
Also, dC(c) < 1 implies a>aC u payoffs Eqs. (1) and (2).)
ð1cÞðRp LÞ cðRg Rp Þ or
ð3Þ R L
c>cC u ð1aÞRpp þaRg L. (The proof follows from comparing
4. Decentralization Consider now the economy with two lenders, with each funding up to K/2 projects. (We briefly discuss the case of more lenders in the concluding section.) When both lenders choose the same type, their payoffs are equal to 1/2 of the corresponding payoffs under centralization. When the lenders choose opposite types, the payoffs become more complicated. Suppose lender 1 is tough, while lender 2 is soft. Then, all experienced entrepreneurs with poor projects would submit them only to the soft lender. This changes the distribution of projects among the lenders. For t>0, the quality of the projects submitted to
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the tough lender improves relative to centralization, while the soft lender attracts worse project pool than he would under centralization. Specifically, out of K funded projects, the soft lender receives F=(1 a)(1 + c)(K/2) poor projects and (K/2) F good projects, while the tough lender attracts the remaining aK (K/2 F)=(2a 1)(K/2) + F good projects and (1 a)K F=(1 a)(1 c)(K/2) poor projects. This is because now the soft lender attracts (1 a)/2 share of poor projects from inexperienced entrepreneurs and all poor projects from cK experienced entrepreneurs. The tough lender attracts poor projects only from inexperienced entrepreneurs. The payoffs of lenders of opposite types are: PD;TS
K ¼ ½aRg þ ð1 aÞL þ 2
PD;ST ¼
K K d ð2a 1Þ þ F Rg þ ð1 aÞð1 cÞ L 2 2 1d
K K d ½aRg þ ð1 aÞRp þ Rg F þ Rp F 2 2 1d
ð4Þ
ð5Þ
Here, PD,IJ denotes the payoff to type I lender when the other lender is type J. The following main result holds: Proposition 2. Under decentralization, both lenders choosing to be tough constitutes a unique Nash R L ð1cÞðRp LÞ . equilibrium if d z dD(c) = cðRpg LÞ and a>aD = Rg cRp ð1cÞL Moreover, dD(c) < dC(c) and aD < aC for all c such that dD(c) < 1, which includes c>cC. (Proof is available upon request.) Therefore, both lenders would choose to be tough under decentralization for a wider range of parameters than the single lender would under centralization.
5. Conclusion The effect of reputation on the lenders’ behavior crucially depends on the value of time discounting rate, d. If d = 0, being soft is optimal for all lenders. The attractiveness of this choice under either market structure declines in d. At what value of d does being tough become optimal and how does this threshold value depend on the market structure? We showed that each lender being tough constitutes an equilibrium under a broader range of values of d under decentralization than under centralization. That is, the reputation for toughness is more likely to be valuable under decentralization and to the extent reputational considerations can induce lenders to be tough, their impact is more likely to result in a hard budget constraint under decentralization. The direction of the effect of reputation does not depend on the number of lenders in a decentralized market. However, the worsening of the pool of projects submitted to soft lenders caused by the presence of tough lenders would not be as pronounced if the tough lenders’ market share is relatively small. Also, if the number of lenders is sufficiently high, it may become costly to acquire knowledge about their reputation. Nonetheless, if it is worthwhile for a borrower to engage in a search of the market to find soft lenders, the adverse selection effect described above would be present. Furthermore, the greater is the
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number of lenders, the more likely the lenders’ budget constraints would play a role as they do in Dewatripont and Maskin (1995) model. We conclude that reputation can be a powerful mechanism for alleviating a SBC and the value of reputation is greater in a decentralized lending market than under centralization. Acknowledgements We are grateful to Richard Ericson, Jim Leitzel, William Pyle, and Richard Rosen for helpful comments and discussion. All remaining errors and omissions are our own.
References Dewatripont, M., Maskin, E., 1995. Credit and efficiency in centralized and decentralized economies. Review of Economic Studies 62, 541 – 556. Kornai, J., 1980. Economics of Shortage North-Holland, Amsterdam. Kornai, J., Maskin, E., Roland, G., 2003. Understanding the soft budget constraint. Journal of Economic Literature 41, 1095 – 1136. Maskin, E., Xu, C., 2001. Soft budget constraint theories: from centralization to the market. Economics of Transition 9, 1 – 27. Schaffer, M., 1989. The credible commitment problems in center – enterprise relationship. Journal of Comparative Economics 13, 359 – 382.
Lenders’ reputation and the soft budget constraint Michael Alexeev a,*, Sunghwan Kim b a
Department of Economics, Indiana University, Bloomington, IN 47405-5301, USA Management Research Laboratory, KT Corporation, Sungnam City, South Korea
b
Received 20 December 2003; accepted 8 January 2004 Available online 2 April 2004
Abstract Suppose at t = 0 lenders can choose whether to be ‘‘tough’’ or ‘‘soft,’’ and some borrowers learn the lenders’ type (reputation). In a decentralized lending market, being tough is optimal for a wider range of parameters than under centralization, because a soft lender who refinances poor projects is hurt by the tough lenders’ presence, as the quality of the lenders’ project pool is affected by the other lenders’ reputation. D 2004 Elsevier B.V. All rights reserved. Keywords: Soft budget constraint; Reputation; Centralization; Decentralization JEL classification: L14; P51
1. Introduction The presence of a soft budget constraint (SBC) is a major incentive problem that affects markets in various economic systems.1 In a seminal paper, Dewatripont and Maskin (1995) demonstrated that SBC can result from the inability of a lender to commit to not bailing out poor projects that require refinancing.2 They showed that this commitment problem can be solved by limiting the funds available to lenders, so that they would not be able to refinance poor projects even if, given adequate funds, it would have been a subgame perfect strategy. A major implication of Dewatripont and Maskin’s approach is that a decentralized lending market is better at hardening budget constraints than centralization, because each lender in a decentralized market * Corresponding author. Tel.: +1-812-855-7103; fax: +1-812-855-3736. E-mail addresses: [email protected] (M. Alexeev), [email protected] (S. Kim). 1 See Kornai (1980) and surveys by Maskin and Xu (2001); Kornai et al. (2003). 2 Schaffer (1989) provides an earlier but somewhat incomplete analysis of this problem. 0165-1765/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.econlet.2004.01.003
70
M. Alexeev, S. Kim / Economics Letters 84 (2004) 69–73
has only a small amount of capital. Casual observation suggests, however, that large banks in market economies have vast amounts of capital, making it difficult to argue that they can precommit to no refinancing of poor projects because of limited funds. At the same time, the existing literature does not rigorously analyze the effect of lenders’ reputation on the SBC problem. We argue that reputation can be crucial in hardening budget constraints, and decentralized lending has an advantage over centralization in this respect. If a lender has reputation for toughness among some of the borrowers under centralization, the pool of submitted projects improves because those who are aware of the lenders’ type do not submit poor projects. Thus, there is a tradeoff between short-term losses from liquidating a poor project and long-term gains due to a reputation for toughness. This tradeoff is more likely to favor tough lender behavior in a decentralized market than under centralization. When both tough and soft lenders are present in a market, the pool of projects submitted to known soft lenders worsens more than it would under centralization, because soft lenders receive poor projects that would have otherwise been submitted to tough lenders. Therefore, reputational effects make being tough more attractive to lenders in a decentralized lending market. We are not modeling the acquisition of reputation. This is a subject of future research. Here, we simply argue that reputation is more valuable under decentralization. The next section formalizes this argument.
2. The model Consider an economy with the number of entrepreneurs normalized to 1. At the beginning of each period, each entrepreneur draws a project from a population with aa(0, 1) share of good projects and (1 a) poor projects (a is common knowledge). An investment of 1 unit of capital in a good project yields a net monetary return of Rg > 0 (gross return of 1 + Rg>1) and a non-monetary return of Eg>0. Returns to investment in a poor project depend on whether the project is liquidated or refinanced with another unit of capital. Liquidation results net monetary and non-monetary returns of, respectively, La( 1, 0) and El < 0, while the respective returns to refinancing are Rpa( 1, 0) and Ep>0. We assume that Rp>L. All returns occur by the end of the period. There are two types of entrepreneurs. Inexperienced entrepreneurs do not know the type of their projects, while experienced entrepreneurs know their project types. (At t = 0, all entrepreneurs are inexperienced.) Each entrepreneur lives for two periods. During the first period, the entrepreneur is inexperienced. In the second period, he becomes experienced. There is attrition of entrepreneurs that takes place at the exogenous rate ba[0, 1]. In a steady-state, there are 1/(1 + b) of inexperienced entrepreneurs and c = b/(1 + b) of experienced ones.3 Entrepreneurs have to borrow capital for projects from a lender who does not observe the project type but learns about it and its monetary return after investing the first unit of capital. The lender extracts the entire monetary return of the project. The nonmonetary return accrues only to the entrepreneur. There is an infinite number of periods and the lenders decide at t = 0 whether to be ‘‘tough’’ or ‘‘soft’’. Tough lenders always liquidate poor projects, while soft lenders always refinance them. The experienced entrepreneurs know the type of each lender.
3
Extending the range of c beyond 1/2 would not change the qualitative results.
M. Alexeev, S. Kim / Economics Letters 84 (2004) 69–73
71
The lenders have sufficient capital to finance only the first K projects submitted each period, 0 < Kb1. The returns from the good projects can be used to refinance the poor projects and these returns are assumed sufficient for that purpose. That is, lenders never refrain from refinancing simply due to the lack of capital. Moreover, the proportion of good projects is sufficiently large to assure positive net returns in each period for all lenders. At the end of each period, the lenders distribute their net returns to the shareholders. The entrepreneurs have zero reservation payoffs and are randomly drawn from their population. The experienced entrepreneurs with poor projects always choose a soft lender if he exists. If there are no soft lenders, experienced entrepreneurs do not submit their projects for funding. All other entrepreneurs choose lenders randomly.
3. Centralization Under centralization, if the lender decides to be tough, experienced entrepreneurs would not submit poor projects. Therefore, the lenders’ payoffs from being soft (RC,S) and tough ( PC,T), are PC;S ¼ K½aRg þ ð1 aÞRp
1 1d
ð1Þ
PC;T ¼ K½aRg þ ð1 aÞL þ K½aRg =d þ ð1 cÞð1 aÞL=d
d 1d
ð2Þ
where d = a+(1 c)(1 a) and da(0, 1) is time discount rate. (The division by d in Eq. (2) takes place because experienced entrepreneurs do not submit poor projects.) The first subscript stands for centralization. The second subscript denotes the lenders’ type. The first term in Eq. (2) represents the tough lenders’ initial period payoff. Proposition 1. Under centralization, the lender chooses to play tough if dzdCðcÞ u
ð1 ð1 aÞcÞðRp LÞ : acðRg LÞ
Also, dC(c) < 1 implies a>aC u payoffs Eqs. (1) and (2).)
ð1cÞðRp LÞ cðRg Rp Þ or
ð3Þ R L
c>cC u ð1aÞRpp þaRg L. (The proof follows from comparing
4. Decentralization Consider now the economy with two lenders, with each funding up to K/2 projects. (We briefly discuss the case of more lenders in the concluding section.) When both lenders choose the same type, their payoffs are equal to 1/2 of the corresponding payoffs under centralization. When the lenders choose opposite types, the payoffs become more complicated. Suppose lender 1 is tough, while lender 2 is soft. Then, all experienced entrepreneurs with poor projects would submit them only to the soft lender. This changes the distribution of projects among the lenders. For t>0, the quality of the projects submitted to
72
M. Alexeev, S. Kim / Economics Letters 84 (2004) 69–73
the tough lender improves relative to centralization, while the soft lender attracts worse project pool than he would under centralization. Specifically, out of K funded projects, the soft lender receives F=(1 a)(1 + c)(K/2) poor projects and (K/2) F good projects, while the tough lender attracts the remaining aK (K/2 F)=(2a 1)(K/2) + F good projects and (1 a)K F=(1 a)(1 c)(K/2) poor projects. This is because now the soft lender attracts (1 a)/2 share of poor projects from inexperienced entrepreneurs and all poor projects from cK experienced entrepreneurs. The tough lender attracts poor projects only from inexperienced entrepreneurs. The payoffs of lenders of opposite types are: PD;TS
K ¼ ½aRg þ ð1 aÞL þ 2
PD;ST ¼
K K d ð2a 1Þ þ F Rg þ ð1 aÞð1 cÞ L 2 2 1d
K K d ½aRg þ ð1 aÞRp þ Rg F þ Rp F 2 2 1d
ð4Þ
ð5Þ
Here, PD,IJ denotes the payoff to type I lender when the other lender is type J. The following main result holds: Proposition 2. Under decentralization, both lenders choosing to be tough constitutes a unique Nash R L ð1cÞðRp LÞ . equilibrium if d z dD(c) = cðRpg LÞ and a>aD = Rg cRp ð1cÞL Moreover, dD(c) < dC(c) and aD < aC for all c such that dD(c) < 1, which includes c>cC. (Proof is available upon request.) Therefore, both lenders would choose to be tough under decentralization for a wider range of parameters than the single lender would under centralization.
5. Conclusion The effect of reputation on the lenders’ behavior crucially depends on the value of time discounting rate, d. If d = 0, being soft is optimal for all lenders. The attractiveness of this choice under either market structure declines in d. At what value of d does being tough become optimal and how does this threshold value depend on the market structure? We showed that each lender being tough constitutes an equilibrium under a broader range of values of d under decentralization than under centralization. That is, the reputation for toughness is more likely to be valuable under decentralization and to the extent reputational considerations can induce lenders to be tough, their impact is more likely to result in a hard budget constraint under decentralization. The direction of the effect of reputation does not depend on the number of lenders in a decentralized market. However, the worsening of the pool of projects submitted to soft lenders caused by the presence of tough lenders would not be as pronounced if the tough lenders’ market share is relatively small. Also, if the number of lenders is sufficiently high, it may become costly to acquire knowledge about their reputation. Nonetheless, if it is worthwhile for a borrower to engage in a search of the market to find soft lenders, the adverse selection effect described above would be present. Furthermore, the greater is the
M. Alexeev, S. Kim / Economics Letters 84 (2004) 69–73
73
number of lenders, the more likely the lenders’ budget constraints would play a role as they do in Dewatripont and Maskin (1995) model. We conclude that reputation can be a powerful mechanism for alleviating a SBC and the value of reputation is greater in a decentralized lending market than under centralization. Acknowledgements We are grateful to Richard Ericson, Jim Leitzel, William Pyle, and Richard Rosen for helpful comments and discussion. All remaining errors and omissions are our own.
References Dewatripont, M., Maskin, E., 1995. Credit and efficiency in centralized and decentralized economies. Review of Economic Studies 62, 541 – 556. Kornai, J., 1980. Economics of Shortage North-Holland, Amsterdam. Kornai, J., Maskin, E., Roland, G., 2003. Understanding the soft budget constraint. Journal of Economic Literature 41, 1095 – 1136. Maskin, E., Xu, C., 2001. Soft budget constraint theories: from centralization to the market. Economics of Transition 9, 1 – 27. Schaffer, M., 1989. The credible commitment problems in center – enterprise relationship. Journal of Comparative Economics 13, 359 – 382.