Debt Overhang and Lack of Lender's Commitment

• Published date: 01 December 2023
• Author: KEIICHIRO KOBAYASHI,TOMOYUKI NAKAJIMA,SHUHEI TAKAHASHI
• Date: 01 December 2023
• DOI: http://doi.org/10.1111/jmcb.12969

DOI: 10.1111/jmcb.12969

KEIICHIRO KOBAYASHI

TOMOYUKI NAKAJIMA

SHUHEI TAKAHASHI

Debt Overhang and Lack of Lender’s Commitment

The debt overhang of sovereigns or rms is modeled in the recent literature

as a constrained efcient outcome of dynamic debt contracts under the lack

of the borrower’s commitment, where debt relief is not Pareto-improving.

The early literature observes another type of debt overhang where the bor-

rower is discouraged from expending effort, anticipating the lender to take

all output ex post. We show that this inefciency is due to the lack of the

lender’scommitment and debt relief is Pareto-improving. Nevertheless, debt

overhang may persist, as frictional bargaining over debt relief can take a

long time.

JEL codes:E30, G01, G30

Keywords:backloading, debt Laffer curve, two-sidedlack of commitment

I  ,   the relationship between the

amount of debt and the borrower’s economic activity in a model for a long-term debt

contract between a sovereign or private borrowerand lenders. We assume that debt is

not state contingent and evolves at a xed interest rate; thus, debt can grow too large.

Debt can accumulate beyond the repayable amount as a result of repeated and/or large

negativeshocks.However, debt relief, though possible, takes time, as it involves time-

consuming bargaining, such as a war of attrition among lenders. It is demonstrated

We would like to thank Sanjay K. Chugh (editor) and the anonymous referee for insightful com-

ments and suggestions. We also thank Tamon Asonuma, Toni Braun, YiLi Chien, Nobuhiro Kiyotaki,

Alex Monge-Naranjo, Jose Scheinkman, Hajime Tomura, and Vivian Yue for valuable discussions, and

the seminar participants at the IMF-OAP PRI Conference in Tokyo; SAET 2018 in Taipei; GRIPS-UT

Macroeconomics and Policy Workshop 2018; CIGS Conference on Macroeconomic Theory and Policy

2016; FRB Atlanta, FRB St. Louis, National University of Singapore, and Tsinghua University for their

useful comments. Nakajima is grateful for the nancial support from the JSPS Grant-in-Aid for Scientic

Research (16H02026, 18H03638, 21K01385, 22H00058).

K K is a Professor at Faculty of Economics, Keio University, and Canon Institute

for Global Studies (CIGS) (E-mail: keiichirokbys@gmail.com).T N is a Professor at

Graduate School of Economics, University of Tokyo,and CIGS (E-mail: tomoyuki.nakajima@gmail.com).

S T is an Associate Professor at Institute of Economic Research, Kyoto University, and

CIGS (E-mail: takahashi@kier.kyoto-u.ac.jp).

Received August 19, 2021; and accepted in revised form July 18, 2022.

Journal of Money, Credit and Banking, Vol. 55, No. 8 (December 2023)

© 2022 The Authors. Journal of Money, Credit and Banking published by Wiley Periodicals

LLC on behalf of Ohio State University.

This is an open access article under the terms of the Creative Commons Attribution License,

which permits use, distribution and reproduction in any medium, provided the original work

is properly cited.

2154 :MONEY,CREDIT AND BANKING

that large debt can hinder the borrower’seconomic activity in two respects. One is the

standard debt overhang, which we call the rst type of debt overhang, and the other

is the second type of debt overhang that we highlight in this study.

The rst type of debt overhang is caused by a lack of commitment on the borrower

side, which is well known in the literature on optimal debt contracts. The borrower

can default on the debt at any time; in the constrained optimal debt contract, the bor-

rower’s economic activity measured by output is smaller when debt is larger. This

is because a larger output tempts the borrower to default when the output is the bor-

rower’s payoff of defaulting (Albuquerque and Hopenhayn 2004, Kovrijnykh and

Szentes 2007, Aguiar, Amador, and Gopinath 2009).

We show that as debt increases and exceeds a certain threshold, the economy that

was originally in the rst type of debt overhang enters the second type. It is the debt

overhang that Sachs (1988) observes: The borrowerhesitates to invest in a new project

because the debt is so large that the borrower expects all return on the investment to

be taken by the lenders ex post (see pp. 29–31 of Sachs 1988). This line of thinking

emerges because lenders cannot credibly commit to making the repayment smaller

than the face value of debt. This inability of lenders to commit causes inefciency,

which we call the second type of debt overhang. The rst type of debt overhang in, for

example, Albuquerque and Hopenhayn (2004) is a situation wherein the lender can-

not lend the rst-best amount because the borrower would abscond with the borrowed

money.In the second type of debt overhang, the borrower cannot expend the rst-best

amount of effort because the lender would take all output, as the existing debt is too

large. Suppose that lenders keep the contractual amount of debt unchanged, and, nev-

ertheless, promise that they will give a sufcientamount to the borrower. The lenders’

promise is not trustworthy when the debt is larger than the borrower’soutput, because

lenders have the legitimate right to take all as repayment. The contractual amount of

debt works as a commitment device when it is small, as it gives the upper bound for

the amount that lenders can demand. The upper bound no longer works as a commit-

ment device for the lenders when it is so large that it exceeds the maximum repayable

amount. Note that the lack of commitment on the borrower side always exists regard-

less of how large the debt is, whereas the lender loses credibility when debt becomes

large. Therefore, debt relief can be effective in restoring the commitment of lenders

and reducing the inefciency caused by the lack of lenders’ commitment.

Sachs (1988) claries the idea of (the second type of) debt overhang with a sim-

ple numerical example. The differences between our study and Sachs (1988) can be

summarized in the following three points: (i) we clarify that the problem is the lack of

lender’s commitment and formally construct its model in the framework of dynamic

contract; (ii) we prove that the second type of debt overhang occurs when debt is

large; and (iii) we solve the dynamic model numerically to conrm our main theoret-

ical ndings.

Simple Example.Let us explain how the lack of lenders’ commitment emerges in

the following intuitive example. Suppose that borrowers owe lenders Ddollars, and

the borrowers can earn USD 1,000 if they work hard, but earn USD 100 if they do

KEIICHIRO KOBAYASHI, TOMOYUKI NAKAJIMA,AND SHUHEI TAKAHASHI:2155

not. They will work hard if their payoff is no less than USD 200, but will not work

if their payoff is less than USD 200. Obviously, the maximum repayable amount is

USD 800 (=1,000−200).

• Now, suppose that Dis smaller than USD 800, say, D=500. In this case, the

lenders’ promise to the borrowers, that is, “You pay Ddollars and you get the

remaining,” is trustworthy because the lenders have no legitimate right to take

more than Ddollars. Therefore, the lenders’ commitment to the repayment plan is

credible, and the contractual amount of debt, D, is a payoff-relevant state variable

on which the repayment plan depends. Given this promise, as the borrowers can

take 1,000 −D(>200) if they work hard, they actually choose to work hard

and repay D.

•Next, suppose that Dis larger than USD 800, say, D=10,000. Here, we assume

that the debt relief that reduces Dfrom 10,000 to 800 is impossible to implement,

because bargaining frictions make it prohibitivelycostly to reach an agreement on

debt relief.1In this case, the lenders will offer the following plan if theycan: “You

pay USD 800 and you take the remaining USD 200.” However, this repayment

plan is not credible, because Dis larger than USD 800, and lenders have the

legitimate right to demand that the borrowers repay D. Suppose that the lenders

make the above promise: “You pay USD 800, and you get the remaining USD

200,” and the borrowers trust this promise and work hard. Subsequently,they earn

USD 1,000 and, ex post, the lenders will demand the borrowers to pay the full

USD 1,000, as they have the legitimate right to demand full repayment. Thus, the

ex-ante promise that lenders will not demand more than USD 800 is not credible.

Therefore, if D=10,000, any offer made by the lenders is not trustworthy, the

borrowers will not work hard, and they earn only 100. Ultimately,lenders obtain

USD 100 as repayment and borrowers obtain zero. Note also that when Dis

larger than the maximum repayable amount, it is no longer a payoff-relevantstate

variable.

In short, when the contractual amount of debt is very large, the lenders’ offer of the

repayment plan is not credible ex ante, because they can and will demand the bor-

rowers to pay more ex post. This lack of a lender’s commitment makes the borrower

reluctant to work hard and reduces output. This is the second type of debt overhang,

which Sachs (1988) observes.

Theoretically, we can explain that the inefciencyof the secondtype of debt over-

hang emerges because the contractual amount of debt, D, is no longer a payoff-

relevant state variable, if it exceeds a certain threshold. As we see in the simple ex-

ample in Section 2 or in the model of Section 3, when Dis small, the lenders and

borrower agree on a constrained optimal repayment plan contingent on Dthat back-

loads the borrower’s payoff. That is, they agree that the borrower pays as much as

1.An episode relating to and the literature on frictional bargaining on debt restructuring are dis-

cussed later.