Household Debt Overhang and Unemployment

• Author: GIORGIA PIACENTINO,ANJAN THAKOR,JASON RODERICK DONALDSON
• Published date: 01 June 2019
• DOI: http://doi.org/10.1111/jofi.12760
• Date: 01 June 2019

THE JOURNAL OF FINANCE •VOL. LXXIV, NO. 3 •JUNE 2019

Household Debt Overhang and Unemployment

JASON RODERICK DONALDSON, GIORGIA PIACENTINO, and ANJAN THAKOR∗

ABSTRACT

Weuse a labor-search model to explain why the worst employment slumps often follow

expansions of household debt. We find that households protected by limited liability

suffer from a household-debt-overhang problem that leads them to require high wages

to work. Firms respond by posting high wages but few vacancies. This vacancy posting

effect implies that high household debt leads to high unemployment. Even though

households borrow from banks via bilaterally optimal contracts, the equilibrium level

of household debt is inefficiently high due to a household-debt externality. We analyze

the role that a financial regulator can play in mitigating this externality.

PERSONAL BANKRUPTCY IS PERVASIVEIN THE United States—about one in 10 Amer-

icans will declare bankruptcy in his lifetime.1Under the U.S. bankruptcy code,

households are protected by limited liability. That is, they can discharge their

debt and still keep a substantial amount of their assets. Such limited-liability

protection distorts the incentives of indebted households, just as it distorts

the incentives of indebted firms in corporate finance. In this paper, we investi-

gate how this distortion can affect the labor market. In particular, we ask the

following questions.

How does limited-liability debt distort household labor supply, and how does

this affect aggregate employment in equilibrium? Further, do households take

∗Jason Roderick Donaldson is with Washington University in St. Louis and CEPR. Giorgia Pia-

centino is with Columbia and CEPR. Anjan Thakor is with WashingtonUniversity in St. Louis and

ECGI. We gratefully acknowledge helpful comments from two anonymous referees and especially

the Editor (Bruno Biais) as well as Steven Ambler; Ulf Axelson; Juliane Begenau; Nittai Bergman;

Jonathan Berk; Asaf Bernstein; V.V. Chari; Alex Edmans; Vincent Glode; Radha Gopalan; Kyle

Herkenhoff; Anastasia Kartasheva; Amir Kermani; Deborah Lucas; Fred Malherbe; Asaf Manela;

Holger Mueller; Christian Opp; Alessandro Previtero; Adriano Rampini; Felipe Severino; Kelly

Shue; Ngoc-Khanh Tran; Randy Wright; and seminar participants at Berkeley Haas, the Bank of

England, BI Oslo (Norway), the 2016 Cambridge Corporate Finance Theory Symposium, the 2015

Canadian Economic Association, the 2015 CFF Conference on Bank Stability and Regulation in

Gothenburg (Sweden), the 2015 European Summer Symposium in Financial Markets at Gerzensee,

the Federal Reserve Bank of Cleveland, the Federal Reserve Bank of Philadelphia, the Federal

Reserve Bank of St. Louis, the 2015 IDC Summer Finance Conference, the IMF, the 2015 Labor

and Finance Group conference at Vanderbilt, the 2015 LBS Summer Symposium, the 2015 Mid-

west Macro conference, the 2015 SED Meetings, the 2016 SFS Cavalcade, the Sixth Duke–UNC

Corporate Finance Conference, the ToulouseSchool of Economics, and the University of Lancaster,

Washington University in St. Louis. We alone are responsible for any remaining errors. We have

read the Journal of Finance’s disclosure policy and have no conflict of interest to disclose.

1See Stavins (2000).

DOI: 10.1111/jofi.12760

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1474 The Journal of Finance R

on too much limited-liability debt, and should a regulator intervene to mitigate

the resulting distortions?

Model preview. To address these questions, we develop a two-date general

equilibrium model of household borrowing and the labor market. At the first

date, households borrow from banks. At the second date, firms post vacancies,

and households and firms are randomly matched in a decentralized labor mar-

ket `

a la Diamond–Mortensen–Pissarides. Once matched, firms and households

negotiate wages bilaterally. Households then work or do not. If households

work, firms produce output and pay wages. Households use these wages to

repay banks. If households do not work, firms do not produce output and do

not pay wages. In this case, households cannot repay banks, so they default.

Results preview. Our first main result is that limited-liability debt on house-

holds’ balance sheets leads to a debt overhang problem that makes indebted

households reluctant to work. They act like indebted firms in corporate fi-

nance, whose equityholders are reluctant to pay the cost of new investments

because they must use their cash flows to make repayments to existing credi-

tors. Indebted households in our model are reluctant to bear the cost of working

because they must use their wages to make repayments to the banks they bor-

rowed from. Hence, firms must pay high wages to induce households to work.

Our second main result is that high levels of household debt lead firms to

post relatively few vacancies, which leads, in turn, to low employment. This

is a result of the household debt overhang problem. Because firms must pay

indebted workers high wages, they cannot afford to hire as many of them, and

thus they post fewer vacancies. This vacancy posting effect implies that high

household debt leads to high unemployment.

Our third main result is that households take on excessive debt in equilib-

rium, even though they borrow from banks via bilaterally optimal contracts.

This is due to a household debt externality that works through the vacancy

posting effect. Specifically, when a household takes debt onto its balance sheet,

this decreases the likelihood that households are employed, as implied by the

vacancy posting effect. Since unemployed households are likely to default on

their debt, this increases the default rate on all loans, including other banks’

loans to other households. In other words, when households take on debt, they

do not take into account the negative effect that their borrowing has on other

agents in the economy through the labor market. Thus, there is scope for a

financial regulator to intervene to mitigate this externality.

Our fourth main result is that banks’ beliefs about future employment are

self-fulfilling, which generates multiple equilibria. If banks believe that the

rate of employment will be low, so household default risk is high, banks re-

quire high face values of debt to offset this risk. Households thus have high

debt, so employment is indeed low due to the vacancy posting effect. In con-

trast, if banks believe that employment will be high, so household default

risk is low, banks require low face values of debt, and employment is indeed

high. Thus, there is another reason for regulatory intervention: to prevent

the economy from ending up in the “bad” equilibrium with high debt and low

employment.